Using the distance formula, find the length of CD when; C(-3 , -4) D(1 , -2)
Answers
Answer:
Please see the answer in the picture:
Related Questions
Find each angle measure to the nearest degree
sin x = 0.7547
Answers
The each angle measure of the trigonometric ratios are obtained.
Define the term trigonometric ratios?A mathematical discipline called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.The given values is:
sin x = 0.7547,
Using trigonometric properties,
cos x = √(1 - sin²x)
= √(1 - 0.7547²)
cos x = 0.6560
Cosec x = 1 / sin x
= 1 / 0.7547
Cosec x = 1.3250
Now,
1 + cot²x = cosec²x
cot x = √(cosec²x - 1)
= √(1.3250² - 1)
cot x = 0.8692
tan x = 1 / cot x
= 1 / 0.8692
tan x = 1.1544
Thus, the each angle measure of the trigonometric ratios are obtained.
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Analia is a school district manager. Here are some details about two schools in her district for the last school year: School A School B Number of students 3000 30003000 4000 40004000 Number of teachers 190 190190 380 380380 Graduation rate 86 % 86%86, percent 90 % 90%90, percent Budget per student $ 10 , 500 $10,500dollar sign, 10, comma, 500 $ 10 , 000 $10,000dollar sign, 10, comma, 000 % of students in sports club 62 % 62%62, percent 68 % 68%68, percent Number of sports medals won 9 99 7 77 SAT average 1200 12001200 1050 10501050 SAT range (max-min) 900 900900 700 700700 Analia wants to know which school has higher academic achievements relative to the number of teachers per student. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Answers
The two different quantities to measure which school has higher academic performance are :
• Graduation rate / Budget per student
• SAT average / Budget per student
How to calculate the performance?To specify a number that represents academic achievement. We compare the budget per pupil for each school to a related metric or parameter that measures the academic performance of the students in each school.
The following variables could be used to gauge academic achievement:
• Each school's graduation rate.
• Each school's average SAT score.
Therefore, Graduation rate / Budget per student and SAT average / Budget per student are appropriate in this case.
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Last year, Chris opened an investment account with 5200 . At the end of the year, the amount in the account had increased by 7%
Answers
Answer:
Step-by-step explanation:
By the way you've worded this, I'm guessing that you're looking for how much money Chris made at the end of the year.
When we're dealing with annual income, we must always consider how much was already present in savings before actually performing any operation, because that will give us the final answer.
Since Chris started with $5200, we do [tex](0.07)($5200) = $364[/tex] to find that Chris made $364 by the end of the year.
Lastly, to find his total income at the end of the year, we add [tex]5200 + 364 =[/tex] $5,564 at the end of the year.
Draw the graph of 5-3x-2x^2=0
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This is a answer of graph format. (1 - x) • (2x + 5) = 0
what is graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.A network with paths connecting any two of its vertices. Any two vertices or nodes in a disconnected graph are those that are separated by a path.Graph that completes a cycle is called a cycle graph. Complete Graph is a graph is said to be complete when every pair of vertices is connected by an edge.A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. Any two nodes, often referred to as vertices, in a network are connected by edges.Pull out like factors : [tex]-2x^{2} - 3x + 5 = -1 • (2x^{2} + 3x - 5)[/tex]
Factoring [tex]2x^{2}[/tex] + 3x - 5
The first term is, [tex]2x^{2}[/tex] its coefficient is 2 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -5
Multiply the coefficient of the first term by the constant 2 • -5 = -10
Find two factors of -10 whose sum equals the coefficient of the middle term, which is 3 .
-10 + 1 = -9
-5 + 2 = -3
-2 + 5 = 3 That's it
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 5
[tex]2x^{2} - 2x + 5x - 5[/tex]
Add up the first 2 terms, pulling out like factors :
2x • (x-1)
Add up the last 2 terms, pulling out common factors :
5 • (x-1)
Add up the four terms of step 4 :
(2x+5) • (x-1)
Which is the desired factorization.
Equation :
(1 - x) • (2x + 5) = 0
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The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 25 B, and 35 C responses. Show the frequency and relative frequency distributions (use 0 decimals for the frequency column and 2 decimal for the relative frequency column).
Answers
The relative frequency of A, B and C BE 0.5, 0.20 and 0.29.
What is meant by relative frequency?The proportion between a given event's frequency and all events' frequencies in a statistical experiment.
The ratio of the total number of occurrences occurring in a particular scenario to the frequency of an event can be used to determine relative frequency. Relative frequency is defined as Subgroup frequency divided by Total frequency.
Due to the possibility of interpreting the heights of relative frequency histograms as probabilities, they are significant. These probability histograms offer a graphical representation of a probability distribution that may be used to estimate the probability that specific outcomes will materialize within a given population.
The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.
The total samples be 60 + 25 + 35 = 10
Also, the frequency corresponding to A is: 60
Corresponding to B is: 25
and corresponding to C is: 35
Hence, the Frequency table is as follows:
Data Frequency
A 60
B 25
C 35
The relative frequency table is given by:
Data Relative Frequency
A 60/120 = 0.5
B 25/120 = 0.20
C 35/120 = 0.29
Therefore, the relative frequency of A, B and C BE 0.5, 0.20 and 0.29.
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The television show Found has been successful for many years. That show recently had a share of 31, meaning that among the TV sets in use, 31% were tuned to Found. Assume that an advertiser wants to verify that 31% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a Found broadcast.
Find the probability that none of the households are tuned to Found.P(none) =
Find the probability that at least one household is tuned to Found.P(at least one) =
Find the probability that at most one household is tuned to Found.P(at most one) =
if at most one household is tuned to Found, does it appear that the 31% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Found unusual?)
yes, it is wrong?
no, it is not wrong?
Answers
The probabilities are given as follows:
None: 0.0116 = 1.16%.At least one: 0.9884 = 98.84%.At most one: 0.0744 = 7.44%.The 31% share value is not wrong, as at most one household is not an unlikely outcome, as the probability is higher than 5%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 12, p = 0.31.
The probability of none is given as follows:
P(X = 0) = (0.69)^12 = 0.0116.
The probability of at least one is given as follows:
P(X >= 1) = 1 - 0.0116 = 0.9884.
The probability of at most one is given as follows:
P(X <= 1) = P(X = 0) + P(X = 1)
In which:
P(X = 1) = 12 x 0.31 x 0.69^11
P(X = 1) = 0.0628.
Hence:
P(X <= 1) = P(X = 0) + P(X = 1)
P(X <= 1) = 0.0116 + 0.0628
P(X <= 1) = 0.0744.
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Need Help ASAP
I still don't understand this
Read carefully and do as it says
Answers
By using divisibility rule, the possible factors of number are-
495 : 3, 5 and 9924 : 3 and 4210 : 2, 5 and 10Explain the term divisibility rule?A simple technique to determine if a given number may be divided by such a fixed divisor before carrying out the division operation is to run a divisibility test. When a number is fully divided by yet another number, the remainder should equal zero and the quotient ought to be a whole number. A factor is really a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, or else the numbers we are adding are factors of both the product since the product is divisible by them.For the stated number:
495 : 3, 5 and 9 as 495 is completely divisible by 3, 5 and 9.924 : 3 and 4, as 924 is completely divisible by them.210 : 2, 5 and 10 as 210 is completely divisible by 2 and 5.To know more about the divisibility rule, here
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Urgently!! You are kindly requested to describe in DETAILS the solution of the problem. Certainly, thanks.
The growth rate of the number of bacteria is given by the formula V = 10000 - 100*m*t, where t is the time expressed in hours, m = 11. Write the equation for the growth of the number of bacteria x(t) if x(0) = 10000*m.
Answers
The equation for the growth of the number of bacteria is x(t) = 10000t - 550t² + 110000
How to determine the equation for the growth function?The growth rate of the number of bacteria is given as:
V = 10000 - 100mt,
Such that
t = time in hours,
m = 11.
To find the equation for the growth of the number of bacteria x(t), we can integrate this formula with respect to t.
Using the initial condition x(0) = 10000*m, we have
x(t) = ∫V dt + C
Substitute the known values in the above equation, so, we have the following representation
x(t) = ∫(10000 - 100mt) dt + C
Integrate
x(t) = 10000t - 50mt² + C
Recall that x(0) = 10000*m.
So, we have
10000m = 10000 * 0 - 50 * m * 0² + c
Evaluate
c = 10000m
c = 10000 * 11
c = 110000
So, the equation is
x(t) = 10000t - 50mt² + 110000
Since m = 11, we have
x(t) = 10000t - 550t² + 110000
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FILL IN THE BLANK when a study uses the__________method of data collection, participants complete a questionnaire about their thoughts, feelings, and behavior at the end of each day.
Answers
The correct answer is Diary.
We acquire a different understanding of participants' experiences than we might from other techniques when participants immediately record their observations or perceptions. Participants may feel more comfortable expressing themselves in a diary than in an interview since sometimes personal reflections are more open. The participant's commitment to following through is, of course, a requirement of diary systems. It can be difficult to anticipate someone's availability to write within the time range set by the researcher. To get over these challenges, contemporary diary researchers employ a range of strategies, including as utilizing apps and technology or combining textual and artistic techniques
Hence, The correct answer is Diary Method.
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ap stats the random variable x has mean 12 and standard deviation 3 the random variable w is defined as w
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The mean of the random variable w is 15, and the standard deviation is 3.46.
The formula for the mean of a random variable is μ = E(x), and the formula for the standard deviation of a random variable is σ = sqrt(Var(x)). In this case, the mean of the random variable x is 12, and the standard deviation is 3. We can calculate the mean and standard deviation of the random variable w as follows:
E(w) = E(x) + 3 = 12 + 3 = 15
Var(w) = Var(x) + 9 = 9 + 9 = 18
SD(w) = sqrt(Var(w)) = sqrt(18) = 3.46
Therefore, the mean of the random variable w is 15, and the standard deviation is 3.46.
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Two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from other end of the park. What is the length of the park? Their speeds are constant, but not identical.
Answers
The length of the park will be 598 meters.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from another end of the park.
The length of the park will be calculated as,
H² = P ² + B²
B² = (720)² - ( 400 )²
B = √ ( 358400 )
B = 598 meters
The length of the park would be 598 meters.
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What is the result of isolating y^2 in the equation below? 4x^2 + 25y^2= 100
Answers
Answer:
In factored form: [tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]
In standard form: [tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]
Step-by-step explanation:
Generally for these type of equations we want to get the term with "y" by it self (ignoring coefficients and any operations such as square root, etc...) so we want to get rid of the [tex]4x^2[/tex] from the left side which we can do by subtracting this from both sides to maintain equality and get rid of it on the left side.
[tex]25y^2=-4x^2+100[/tex]
One thing I want to note here is we can actually factor the right side which we generally want to do, we can rewrite it as: [tex]-(4x^2-100)[/tex] and from here we have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex] so we can rewrite this as: [tex]-(2x-10)(2x+10)[/tex]
[tex]25y^2=-(2x-10)(2x+10)[/tex]
From here we divide both sides by 25:
[tex]y^2=-\frac{1}{25}(2x-10)(2x+10)[/tex]
Now from here to get rid of that square we do the inverse which is taking the square root:
[tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]
The reason factoring is useful in this case is we can now easily determine the domain of the function since inside the square root we have a quadratic which is opening down meaning it's only not negative between the zeroes (including the zeroes since they're... zero not negative) and this would be the domain of the graph. But if we wanted it to not be in factored form we would just put back what we had so we would have:
[tex]y=\sqrt{-\frac{1}{25}(4x^2-100)}[/tex]
then distribute the -1/25 to get:
[tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]
Susan bought three video games at one price
and 2 videos priced $2 below the others. The
total cost was $91.50. Find the prices of the
video games.
Answers
The price of first 3 video games is $57.3 and the other 2 videos games is $34.2 in the given arithmetic problem.
What is arithmetic problem?The study and use of numbers, mathematical relationships between numbers, and mathematical observations are all covered by the branch of mathematics known as arithmetic.
The core ideas in number theory, measurement, and computation are typically referred to as "arithmetic" (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). It hasn't always meant the same thing, though, in the mathematical community.
Susan bought total 5 games
Lets the higher price be x
and lower be y
3x + 2y = $91.50
and
x - y = $2
x = 2 + y
Putting the value of x in first formula
3(2 + y) + 2y = 91.50
6 + 3y + 2y = 91.50
3y + 2y = 91.50 - 6
5y = 85.5
y = 85.5/5
y = 17.1
2y = 34.2
Putting the value of y in x
x = 2 + (17.1)
x = 19.1
3x = 57.3
Thus, the price of first 3 video games is $57.3 and the other 2 videos games is $34.2.
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in a company 70% of the workers are men is 1380 women work for the company how many workers are there in all?
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An investor bought a share of a stock at the beginning of 2015. At the beginning of 2017, the share was worth $1050From the beginning of 2015 to the beginning of 2017 the value of the share halved each year, but from the beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each yearThe investor sold the share at the beginning of 2019 Find and interpret the difference between what the investor paid for the share and what the investor sold the share for
Answers
$656.25 is the difference between the investor paying for the share and the investor selling the share.
What is Equation?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that At the beginning of 2017, the share was worth $1050.
From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.
In 2017 it is 1050.
In 2016, it is 2100
In 2015, it is 4200
Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.
In 2017, 1050×1.5=1575
In 2018, 1575×1.5=2362.5
In 2019, 2362.5×1.5=3543.75
The investor paid for the share 4200 and the investor sold 3543.75.
Difference =4200-3543.75
=656.25
Hence, $656.25 is the difference between the investor who paid for the share and the investor who sold the share.
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HELP PLSSS URGENT
IMAGE ATTACHED
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c From the graph, it appears that around 50% of seniors had used alcohol in 2015.
d.This gives us: A=-0.8(25)+63=50%. So, both the line graph and the formula estimate that around 50% of seniors had used alcohol in 2015.
What is line graph and determine it?A line graph is a type of chart that displays data as a series of points connected by linesIt is used to visualize trends over time or changes in valueLine graphs can have multiple data series represented by different colors or styles of linesThey are useful for comparing data and identifying patterns or fluctuations.Line graph is good for showing the trend of a continuous variable over time. A=-0.8n+63 can be changed to A=25 (because 2015 is 25 years after 1990) to get the proportion of seniors who had ever drank alcohol in 2015 using the formula. A=-0.8n+63 can be changed to A=25 (because 2015 is 25 years after 1990) to get the proportion of seniors who had ever drank alcohol in 2015 using the formula.To learn more about line graph refer:
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Round your answer to the nearest thousandth.
Answers
The correlation coefficient for the data in the table is given as follows:
r = 0.724.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The input and output variables are given as follows:
Input: initial approval rating.Output: final approval rating.Hence the points that compose the data-set are given as follows:
(48, 34), (70, 46), (81, 38), (81,49), (86,49).
Inserting these points into a calculator, the correlation coefficient for the data is given as follows:
r = 0.724.
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the slope field for the given differential equation is provided. sketch both branches of particular solution curve that passes through the point
Answers
The solution curve for the differential equation dy/dx = (y - y²) / x is plotted in the slope field.
What is a slope field?
The solutions to a scalar function's first-order differential equation are shown graphically by slope fields, also known as direction fields. Functions depicted as solid curves are solutions to a slope field. In order to determine the estimated tangent slope at a point on a curve, where the curve is some solution to the differential equation, one can use a slope field, which displays the slope of a differential equation at specific vertical and horizontal intervals on the x-y plane.
The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, we can find a solution to the differential equation.
The differential equation is dy/dx = (y - y²) / x.
The solution curve is drawn using the solution points (1,2) for the differential equation.
Therefore, the solution curve is obtained.
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Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning
Answers
The pair of figures are similar because:• Both figures are parallelograms
• All sides are congruents and • Scale factor 1: 2.5
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruents
• Angles W and Y are congruent with angles P and R
• Angles X and Z are congruent with angles S and Q
• Scale factor 1: 2.5
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A bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients. draw a tape diagram to show how many flavors have chocolate and how many dont
Answers
The flavors that have chocolate as one of the ingredients will be 10 and the flavors that don't have chocolate as one of the ingredients will be 30.
How to calculate the number of chocolate?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, the bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients
The flavors that have chocolate as one of the ingredients will be:
= 25% × 40
= 10
The flavors that don't have chocolate as one of the ingredients will be:
= 40 - 10
= 30
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Briley answered 85% of the 60 quiz questions correctly. How many questions did she answer correctly?
Answers
Answer:
51 questions she answered correctly.
Step-by-step explanation: 85/100 x 60
= 510/10
= 51
Answer:
51 questions
Step-by-step explanation:
To do this we need to realize that 85% is equal to 85/100. This can be simplified in fraction form to .85.
Looking at the question, we see that it says "Briley answered 85% of the 60 quiz..." A key word here is of. Of always means multiply. So we can see if we were going to form an equation, we would be multiplying.
Briley answered correctly = (85%) times (60 questions)
Mathematically, ?=(.85)x(60)=51
So we know she answered 51 correctly, and that 51 is 85% of 60.
I hope this helps you!
Find the x-intercept of the function `y=3x+6`
Find the y-intercept of the function `y=3x+6`
Answers
Question 1 : find x intercept
y=0
0=3x+6
subtract 6 from both sides, after doing that, the equation would be : -6=3x
Then divide by -3 on both sides, the answer would be : x=3
Therefore the x intercept as a coordinate is (3,0)
Question 2 : find the y intercept
x=0
y=3(0)+6
y=6
Therefore the y intercept as a coordinate would be (0,6)
Hope this helped =)
-YinAhara
if a coin is tossed five times: find the probability of getting at least one tail. give answer as simplified fraction.
Answers
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.
3/8
The probability of obtaining at least one tail is equal to 1 minus the probability of obtaining all heads. The probability of obtaining all heads is 1/2^5 = 1/32. Therefore, the probability of obtaining at least one tail is 1 - 1/32 = 31/32. This simplifies to 3/8.
The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times. The probability of obtaining all heads is one out of two to the power of five, which is equal to one out of thirty-two. Therefore, the probability of obtaining at least one tail is one minus one out of thirty-two, which is equal to thirty-one out of thirty-two. This simplifies to three out of eight.
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Can you work out at what height the ladders cross?
Are you surprised that we don't need to know the distance between the
two walls?
Suppose now the first ladder is 10m above the
base of the second wall, with the second ladder
remaining as before.
Can you work out at what height the ladders
cross now?
5m
Suppose the first ladder meets the wall at a
height of a metres, as in the diagram.
At what height do the ladders cross now?
Suppose the second ladder meets the wall at a
height of b metres, as in the diagram.
At what height do the ladders cross now?
5m
nrich.maths.org/510
© University of Cambridge
10m
a
Answers
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them.
What is the height of ladder ?Five equations link these eight variables together. There are two equations given by the Pythagorean Theorem.
[tex]a^ 2=x^ 2+w^2 \ b^2=y^2+w^{\} 2[/tex]\
Two more are provided by the side ratios of similar triangles.
[tex]x/w=c/v[/tex]
[tex]y/w=c/u[/tex]
The two triangles are connected by the fifth equation, which is a straightforward linear relationship.
[tex]w=u+v[/tex]
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them. But it might or might not be simple. What comes next will involve two distinct circumstances.
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Given g (x)=5x − 3, find g( −2)
Answers
f(x)=5x−3f(x)=5x-3 g(x)=x2−3g(x)=x2-3
Set up the composite result function. g(f(x))g(f(x))Evaluate g(5x−3)g(5x-3) by substituting in the value of f(5x−3)=(5x−3)2−3g(5x-3)=(5x-3)2-3
Simplify each term: g(5x−3)=25x2−30x+9−3g(5x-3)=25x2-30x+9-3 Subtract 33 from g(5x−3)=25x2−30x+6
To find the value of the function g(x) = 5x - 3 at x = -2, substitute -2 for x. This gives g(-2) = -13.
Explanation:The function given is g(x) = 5x - 3. To find the value of this function when x = -2, you substitute -2 for x in the equation. This yields:
g(-2) = 5(-2) - 3
Which simplifies to:
g(-2) = -10 - 3
So, g(-2) = -13.
In summary, you substituted -2 for x in the function g(x)=5x−3 and then performed the arithmetic operations to find that g(−2) equals -13.
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Round 38.297 to the nearest hundredth
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Hope this helps
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Boden has 45 CDs in his collection, and Camden has 61. If Boden buys 4 new CDs each month and Camden buys 2
new CDs each month, after how many months will Boden and Camden have the same number of CDs? Write an
equation and solve.
Answers
After 8 months both Boden and Camden will have the same number of CDs.
Define the term equation with one variable?Equations with a maximum from one variable of order 1 are referred to as linear equations in one variable equations. It has the formula axe + b = 0, with x serving as the variable. There is just one answer to this equation.The given data:
Current CD's of Boden : 45.Current CD's of Camden : 61.Let 'n; be the total number of months, when both have the same amount of CDs.
Thus,
For 4 new CDs each month bought by Boden: 45 + 4n.
For 2 new CDs each month bought by Camden : 61 + 2n.
Then, the equation becomes:
45+ 4n = 61 + 2n
45 + 2n = 61
2n = 16
n = 8
Thus, after 8 months both Boden and Camden will have the same number of CDs.
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One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
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The number of pounds of the chemical container can hold with given dimension is, 3600 pounds
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
Given that,
1 ft³ = 60 pounds
A container which has dimensions,
length = 6 ft
height = 4 ft
width = 5/2 ft
Volume of container = length × height × width
= 6 × 4 × 5/2
= 60 ft³
1 ft³ = 60 pounds
60 ft³ = 60 × 60 pounds
= 3600 pounds
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Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.(1 point)
Answers
The cost of the guitar string is given by the equation b = $ 1.30
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the cost of one guitar pick be = c
Let the cost of one guitar string be = b
And , Patrick bought 25 guitar picks and 25 guitar strings for = $ 40
Substituting the values in the equation , we get
25c + 25b = 40 be equation (1)
Now , cost of one guitar string = 1 + c
b = 1 + c be equation (2)
Substituting the value of b in equation (1) , we get
25c + 25 ( 1 + c ) = 40
On simplifying the equation , we get
25c + 25 + 25c = 40
Subtracting 25 on both sides of the equation , we get
50c = 15
Divide by 50 on both sides of the equation , we get
c = $ 0.30
So , the cost of one guitar string = $ 1 + $ 0.30 = $ 1.30
Hence , the cost of one guitar string is $ 1.30
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the 16-cm diameter disk in (figure 1) can rotate on an axle through its center. what is the net torque about the axle?
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The net torque about the axle is zero, as no external forces are acting on the disk. Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.
The net torque about the axle is calculated by summing up all the torques about the axle due to external forces. Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.
The net torque about the axle of the 16-cm diameter disk in is zero, since there are no external forces acting on the disk. To calculate the net torque about the axle, we need to take the sum of all the torques about the axle due to external forces. Since there are no external forces, this sum must be zero. This means that the net torque about the axle is zero. This is because there is no force causing the disk to rotate and therefore, the net torque about the axle must also be zero. This result is consistent with the law of conservation of angular momentum, which states that when no external forces are acting on an object, the total angular momentum of the system must remain constant. Thus, the net torque about the axle of the 16-cm diameter disk in is zero.
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