Answers
The equation of the line parallel to y = (-3/4)x + 1 and passing through (8, 6) is y = (-3/4)x
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The slope intercept form of a straight line is:
y = mx + b
Where m is the slope and b is the y intercept.
Two lines are parallel if they have the same slope.
Given the line y = (-3/4)x + 1, the slope is -3/4. The line parallel to y = (-3/4)x + 1 would have same slope of -3/4.
The parallel line passes through (8, -6), hence:
y - y₁ = m(x - x₁)
y - (-6) = (-3/4)(x - 8)
y + 6 = (-3/4)x + 6
y = (-3/4)x
The equation of the line is y = (-3/4)x
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Related Questions
3x−3≥9 Responses x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3 x = 4 x, = 4
Answers
The value of x in the given inequality is x ≥ 4
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality, 3x−3 ≥ 9
Solving for x,
3x−3 ≥ 9
Adding 3 both the side,
3x -3 + 3 ≥ 9 + 3
3x ≥ 12
Diving both sides by 3,
3x / 3 ≥ 12 / 3
x ≥ 4
Hence, the value of x in the given inequality is x ≥ 4
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Jane and some friends entered a snowman building contest I don't winter carnival before getting started they predicted the height of a snowman what build when they finish the snowman with 80 inches taller prediction was 10% lower than that how tall are the group predicted the snowman will
Answers
The answer is the tall are the group predicted the snowman will 800/9 or alternative form was 88.8.
What is meant by predicted?
Predict is often used interchangeably with the words forecast, foretell, prognosticate, and prophecy. All of these phrases refer to "telling in advance," but predict typically connotes drawing conclusions from known facts or natural principles.A predicted grade is the level of proficiency that an applicant's school or college predicts they will achieve under ideal conditions.Universities and colleges utilize these predicted grades to understand the potential of applicants as part of the admissions process.When a model is expected to produce a prediction in relation to what it is predicting is known as the prediction time. For systems that change dynamically throughout time, it is crucial to comprehend prediction time, when events have occurred, and when predictions are being produced.Based on the given conditions, formulate :: 80 ÷ (1 - 10%)
Calculate the sum or difference:
= 80 / 1 - 0.1
= 80 / 0.9
Multiply both the numerator and denominator with the same integer : 800 / 9 or alternative form was 88.8
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Simplify
this
expression:
(48/2) -4^2 +2 x 2
Answers
Answer:
12
Step-by-step explanation:
Divide the numbers
(48/2)-1x4^2+2x2
(24)-1x4^2+2x2
*Evaluate the exponent
24-1x4^2+2x2
24-1x16+2x2
*multiply the numbers*
24-1x16+2x2
24-16+2x2
*Again*
24-16+2x2
24-16+4
*add the numbers*
24-16+4=12
Answer:
-4
Step-by-step explanation:
Since this equation uses order of operations, you should solve what's in the parenthesis first.
48 ÷ 2 = 24
Now you have 24 - 4²2 + 2 × 2. The next thing to solve in order of operations is exponents, so square 4.
4² = 16
Now you should have 24 - 16 (2) +2 × 2. Next is multiplication, so multiply 16(2) and 2 × 2.
16 × 2 = 32, and 2 × 2 = 4
Now you have 24 - 32 + 4. This should look a lot more simple now. Simply do the math from here; doesn't matter how.
24 - 32 = -8
-8 + 4 = -4
I hope this helped you! :)
An investor has asked his stockbroker to rate three stocks (A, B, and C) and list them in the order in which she would recommend them. Consider the following events: i. iii. iv. V. ● · · L: Stock A doesn't receive the lowest rating M: Stock B doesn't receive the lowest rating N: Stock C receives the highest rating Define the random experiment and list the simple events in the sample space List the simple events in each of the events L, M, and N List the simple events belonging to each of the following events: (L or N), (L and M), and M Is there a pair of mutually exclusive events among L, M, and N? Is there a pair of exhaustive events among L, M, and N?
Answers
Intuitively speaking two events are independents when the occurrence of one event (A) does not exert influence over the event (B)
How do you know if two events are exhaustive?Symbolic speaking in terms of sets
P(A∩B)= P(A) * P(B)
Examining each alternative
A. Flipping two coins and having one show a head and the other show a head
Independent. Each flipping coin does not exert any influence on the other
B. Being sneezed on and catching a cold
Dependent. This sequence of events expresses cause consequences effects.
C. When rolling a pair of dice, getting a total of 6 and having one die show a 3
Dependent
Under these conditions, the second event is dependent since all we need is a sum of six, having the first dice showing three. The second one has to show three. So it does exert influence under the result.
D. Rolling a 4 on one die and rolling a 2 on another die
Independent. To get a 4 does not exert any influence on getting a 2 on another dice.
E. Seeing clouds and winning the lottery
Independent.
There is no influence seeing clouds and winning the lottery.
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this is the question I need help with
Answers
The Sun's rays hit the Earth most directly close to the equator, whereas near the poles they hit at a sharp angle.
This indicates that the tropics are warmer than the poles and that higher latitudes absorb less solar radiation per square centimeter (or inch) of surface area than lower latitudes do.
The incoming solar energy is more direct (almost perpendicular or closer to a 90° angle) when the sun's rays hit the surface of the Earth close to the equator. Warmer temperatures result from the solar radiation being concentrated over a smaller surface area.
Near the equator, the incoming solar radiation impacts the Earth's surface more directly (nearly perpendicular or closer to a 90° angle). Because the sun radiation is concentrated over a smaller surface area, it leads to warmer temperatures.
Why do areas close to the equator get hotter than those close to the poles?Since less surface area receives sunlight at the equator than at the poles, it warms up more quickly. Less atmosphere needs to be traveled through at the equator than at the poles.
As a result, the Earth's surface receives more solar heat. The variance in solar energy received at various latitudes affects atmospheric circulation.
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Complete Question -
How is the heat energy per area received from sunlight different at the equator than at the poles?
Choose the system of inequalities that best matches the graph below.
Answers
The set of inequality that most closely resembles the graph below is called y<4 , [tex]$y \geq 4 x-4$[/tex].
What is the system of inequality ?Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.
At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.
Therefore the correct answer is option A ) y<4 , [tex]$y \geq 4 x-4$[/tex]
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the best combination of belts and coats for this economy to produce is responses 95 belts and 1 coat 95 belts and 1 coat 85 belts and 2 coats 85 belts and 2 coats 70 belts and 3 coats 70 belts and 3 coats 40 belts and 4 coats 40 belts and 4 coats indeterminate with the available information
Answers
The best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
The best combination of belts and coats for this economy to produce can be determined using the economic order quantity (EOQ) formula. The EOQ formula helps businesses determine the most cost-effective order quantity when ordering goods. The EOQ formula is expressed as:
EOQ = √2AS/C
Where A is the annual demand for the product, S is the setup cost, and C is the cost per unit.
Using the EOQ formula, the best combination of belts and coats for this economy to produce is determined by calculating the EOQ for each product. For example, if the annual demand for belts is 95, the setup cost for belts is $1 and the cost per unit for belts is $2, then the EOQ for belts is:
EOQ = √2(95)(1)/(2)
EOQ = 95 belts
Similarly, if the annual demand for coats is 1, the setup cost for coats is $2, and the cost per unit for coats is $3, then the EOQ for coats is:
EOQ = √2(1)(2)/(3)
EOQ = 1 coat
Therefore, the best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
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(X2-4x-1)-2/3 quiero que me ayuden a resolver este problema
Answers
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
What is Differentiation ?A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.
Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.
The function is [tex](x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex]
After differentiating
[tex]\frac{d}{dx}(x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex] = [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }\frac{d}{dx}(x^{2} - 4x - 1)[/tex]
= [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
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In each case, indicate whether the distribution of the random variable X is best described as binomial, geometric, negative binomial, Poisson, uniform, exponential, or normal. (a) X is the sum of the numbers obtained by rolling a die 500 times. (b) X is the number, out of the next 15 customers at a clothing store, who are women. (c) X is the number of murders committed in a city during a week. (d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth. (e) X is the amount of time that it will take until a call center receives a phone call. (f) X is the number of times we drive through an intersection before getting one red light. (g) X is the average GPA of 60 randomly chosen UC San Diego students.
Answers
for the given scenario the distribution is applicable, (a) negative binomial (b) binomial (c) normal (d) exponential (e) Poisson (f) uniform, (g) geometric.
The waiting process is frequently a part of geometric, negative binomial, and exponential random variables; in these cases, the waiting process is continuous until something occurs, rather than a count of trials. (Exponential). Large numbers of independent quantities that are averaged and summed typically have distributions that are close to normal. For observed counts, there are two models: Poisson and binomial. For binomial, there is a predetermined number of trials, leading to a clearly defined maximum count; for Poisson, there is no clearly defined maximum potential count. When there is no evident preference for one interval of distance or time over another such equal-length interval, the distribution is continuous.
We have to identify the best described as binomial, geometric, negative binomial, Poisson, uniform distribution and so on.
(a) X is the sum of the numbers obtained by rolling a die 500 times.
in that case negative binomial distribution suitable choice.
(b) X is the number, out of the next 15 customers at a clothing store, who are women. the binomial is the best distribution for this condition.
(c) X is the number of murders committed in a city during a week.
normal distribution.
(d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth.
exponential distribution.
(e) X is the amount of time that it will take until a call center receives a phone call
Poission distribution.
(f) X is the number of times we drive through an intersection before getting one red light. uniform distribution.
(g)X is the average GPA of 60 randomly chosen UC San Diego students.
geometric distribution.
learn more about binomial distribution.
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draw lines to match the expressions on List A with their equivalent expressions in list B.
Answers
Answer:were are the lists ? Pls include the lists.
Step-by-step explanation:
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 180 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Answers
The probability that the entire batch will be accepted, 0.981
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Given that,
A sample of items is randomly selected without replacement
Entire batch is accepted if every item in the sample is okay
The ABC Electronics Company has just manufactured 2100 write-rewrite CDs
Defective CDs = 180
Probability of entire batch selected = ?
Probability of selecting a first non-defective item = 2087/2100
Probability of selecting a second non-defective item = 2086/2099
Probability of selecting a third non-defective item = 2085/2098
Probability of entire batch selected = 2087/2100×2086/2099×2085/2098
Probability of entire batch selected = 0.981
Hence, the probability will be 0.981
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a raffle is being held to raise money for wildlife conservation efforts. ten different gift cards are being awarded. if 3,125 people each bought a single raffle ticket, which of the following expressions represents the number of ways the gift cards can be awarded? assume that each person can win only once. A. (3,125-10)!/3,125! B. (3,125-10)! 10!/3,125! C. (3,125)!/(3,125-10)!10! D. 3. 125!/(3,125-10)!
Answers
option D 3,125!/(3,125-10)! is the correct expression, because it represents the number of ways to choose 10 people from a group of 3,125 people (without regard to order) and accounts for the fact that each person can win only once.
A. (3,125-10)!/3,125! is not the correct expression, because this would represent the number of ways that 10 people can be chosen from a group of 3,115 people (without regard to order) and doesn't account for the fact that each person can win only once.
B. (3,125-10)! 10!/3,125! is also not the correct expression, because this is the number of ways to choose 10 people out of 3,115 and then arrange them in a specific order of 10 gift cards, and this doesn't account that each person can win only once.
C. (3,125)!/(3,125-10)!10! is also not the correct expression, because this represents the number of ways to arrange 3,125 people, regardless of the fact that only 10 can win, and this doesn't account for the fact that each person can win only once.
Therefore, the correct expression is D. 3,125!/(3,125-10)!
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203,199,195 find the 35th term
Answers
Answer:
67
Step-by-step explanation:
The given arithmetic sequence is,
203, 199, 195,......
In the sequence, the first time a = 203,
And common difference of the sequence d = -4
Formula for nth term of the sequence,
aₙ = a + (n-1) . d
To find 35th term of the sequence, substitute n= 35,
a₃₅ = 203 + (35-1).(-4)
= 203 + 34x-4
= 203 - 136
= 67
©Thank You
Answered By Solution 49
The table Shows Daily low temperatures for a winter week in coolerville find the average low temperature for the week round to the nearest tenth of a degree the average of a set of data values is found by adding the values and dividing by the number of values
Answers
Note that given the temperature values, the average low temperature for the week is 1° (Option A).
How do you compute an Average?It is important to remember that the average of a set of data values is calculated by adding the values and dividing by the number of values.
Thus, the Average Low temperature is given as:
Average (A) = sum of data values / no of data values
⇒ Average (A) = [8+7+(-3)+(-8)+(-5)+3+5]/7
A = 7/7
A = 1
Thus, the Average Low temperature is given as 1° (Option A)
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Full Question:
See the attached table
Mrs. Menswar is selling chocolate bars and yogurt cups. The cost of the chocolate bar is $3.00
and the yogurt cups are $5.00. She sold 11 more chocolate bars than yogurt cups and earned $233.
Write and solve a system of equations to represent this situation. Then describe what the solution
means.
Answers
Answer:
36 chocolate bars and 25 yogurt cups were sold
Step-by-step explanation:
c= # of choc. bars sold = y + 11
y = # of yogurt cups sold
3(y + 11) + 5y = $233
3y + 33 + 5y = 233
8y = 200
y = 200/8 = 26
c = y + 11 = 25 + 11 = 36
Given the function: x(t) = 6T3 - 7+2
- 6t + 50. What is the
value of x
at t = 7?
Answers
the value of the function at t = 7 is 1723.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given the function: x(t) = 6T³ - 7t²- 6t + 50.
the value of x at t = 7
Substitute the value of t in the given function
x(7) = 6 * 7³ - 7*7² - 6 * 7 +50
x(7) = 1723
Therefore, the value of the function at t = 7 is 1723.
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Stainless steel contains at least 10.5% chromium. If a steel container that weighs 40 grams contains 5 grams of chromium, does it meet the standard for stainless steel?
Answers
The steel container meet the standard for stainless steel because it contains 12.5% of chromium.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Stainless steel contains at least 10.5% chromium.
We need to determine if a steel container that weighs 40 grams contains 5 grams of chromium is stainless steel.
Therefore:
Percentage of chromium in the steel container = (5 grams / 40 grams) * 100% = 12.5%
12.5% > 10.5%, hence the steel container meet the standard for stainless steel
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Remove all perfect squares from inside the square root. Assume yyy is positive.
\sqrt{39y^9}=
39y
9
Answers
The final expression is
sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.
Rewrite
39 y ^9 as ((y^2)^2)^2 . 39 y
Factor out y^8.
√39(y^8 . y).
Rewrite [tex]y^8 as (y^4)^2[/tex]
√39(y^4)^2 . y).
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
sqrt(x8)=x4
sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
sqrt(x5)=x2•sqrt(x)
sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(y9) = y4 • SQRT(y)
Therefore, sqrt (39y9) = y4 • sqrt(39y)
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if a doctor prescribes 200 mg of a medication every 4 hours, how many grams of the medication would a patient receive in one day?
the patient should receive how many grams in one day?
PLEASE HELP ASAP
Answers
Answer:
1.2 grams (or) 1200 mg per day
Step-by-step explanation:
The amount needed for 1 hour,
→ 200 mg ÷ 4 hour
→ 200 ÷ 4
→ 50 mg
Patient will receive in one day is,
→ 1 day = 24 hours
→ 50mg × 1 day
→ 50 × 24
→ 1200 mg
Converting mg into grams,
→ 1 g = 1000 mg
→ 1200 mg
→ 1200 ÷ 1000
→ 1.2 grams
Hence, the answer is 1.2 grams.
Answer:
1.2 grams
Step-by-step explanation:
There are 24 hours in one day.
Therefore, if the medication is to be taken every 4 hours, the patient receives:
24 ÷ 4 = 6 doses in one dayGiven that the doctor prescribes 200 mg of medication every 4 hours, the amount in milligrams that the patient will receive in one day is:
200 mg × 6 doses = 1200 mgThere are 1000 milligrams in one gram.
Therefore, to convert milligrams to grams, divide by 1000:
1200 mg ÷ 1000 = 1.2 gTherefore, the patient should receive 1.2 grams of medication in one day.
Schools, churches, and corporations are examples of __________ groups.a. secondaryb. actingc. primaryd. informal
Answers
Schools, churches, and corporations are examples of Secondary Groups.
What does a secondary formal group mean?
A secondary group is a comparatively larger group made up of impersonal, purpose-driven, and frequently transient interactions.
These groups typically involve significantly less emotional engagement and are built around reaching a goal that is unrelated to the relationship itself.
What do main and secondary social institutions entail?
Small and distinguished by long-lasting, close-knit ties, primary groups are common. Non-personal, ad hoc, and goal-driven interactions are examples of secondary groupings.
An exchange of implicit goods, such as love, care, concern, support, etc., is what constitutes a primary group. Family units, romantic partnerships, crisis support networks, and religious organizations are a few examples of these.
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The ratio of 1.5 to 29 is the same as the ratio of 4.5 to
Answers
Answer:
4.5:87
Step-by-step explanation:
First, we can set up an equation because 1.5:29 is equal to 4.5:x
[tex]\frac{1.5}{29} = \frac{4.5}{x}[/tex]
Now, we can solve for x by:
1.5x = 4.5 * 29
1.5x = 130.5
x = 87
The ratio will be 4.5:87
This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs? The answer is Segments A and C only. Explain.
Answers
The correct option for the given question is an option (C) which is Segments A and C only.
The goal of image segmentation techniques is to separate the image's various components according to the region of interest. Videos are collections of images, therefore motion segmentation separates them into moving foreground and background by separating the elements that exhibit various motion patterns.
We can extract visual information by classifying visual elements from the scenes into different groups and analyzing these spatial and temporal changes that take place in the image sequence. Each group represents an object's motion in the dynamic sequence.
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The complete question is:
This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs?
A) None of the segments could represent work being done by springs.
B) Any of the segments could represent work being done by springs.
C) Segments A and C only.
D) Segments B and D only.
E) Segment A only.
f(x) = x-1 /5
g(x) = 2x + 7
For what value of x is g(x) = ƒ−¹(x) true?
-1
Answers
According to the given statement, The value of x = -5 / 36.
What is a variable (x) ?The x variable is ubiquitous in math and stands for an unknown. It doesn't always have to be an x - any letter of our alphabet can represent an unknown. To work with variables, the first step is to identify the unknown and label it. Next is writing an equation you can solve to find the unknown.
Given: f(x) = x-1 /5
g(x) = 2x + 7
Solving for g(x) = ƒ(x),
2x + 7 = x-1 /5
10x + 35 = 5x - 1
5x = -36
x = -36 / 5
Hence, the value of x for g(x) = ƒ−¹(x) is x = -5 / 36.
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An equilateral triangle has a perimeter of 159 centimeters. Find the length of each side of this triangle.
The length of each side of the equilateral triangle is ____ cm
Answers
If the topic is an equilateral triangle that has a perimeter of 159 cm, and you need to find the length of each of this triangle’s side, I think that since the triangle has equal sides then you would take 159 and divide it by three to get the answer of 53. The answer would be 53 cm.
Answer: 53
Step-by-step explanation: We know that the a triangle has three sides.
We also know that all of the sides are equal. And all the sides equal 159. So do 159/3 which equals 53.
Ollowing: f(x) = x² - 8x +4; g(x) = 4x − 3; and h(x) = x + 2.
Complete the following: (hg)(x)
Answers
The value of (hg)(x) would be 4x.
What is the function?
A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided. The outputs are usually represented by expressions, such as 'x² - 8x + 4' in the example f(x) = x² - 8x + 4.
(hg)(x) is the composition of two functions h(x) and g(x). In this case, it would be equivalent to h(g(x)), which means to first apply the function g(x) to the input x, then apply the function h(x) to the output of g(x).
(hg)(x) = h(g(x)) = h(4x - 3) = (4x - 3) + 2 = 4x.
Hence, the value of (hg)(x) would be 4x.
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Answer question below
Answers
Answer:
x =1,69 or x= -0,44
step by step explanation[tex] \frac{3}{4x - 5 } = \frac{x}{1 \\ } [/tex]you cross multiply [tex]4x ^{2} - 5x - 3 = 0[/tex]you use quadratic formula [tex]x = \frac{ - b + - \sqrt{ b ^{2} - 4ac } }{2a} [/tex]you substitutea = 4 ; b=-5 and c =-3Ashley has a rectangular poster. The poster is 1.5 meters long and 1.2 meters wide. What is the area of the poster in square centimeters?
Answers
Answer: 18000 cm^2
Step-by-step explanation:
1.5 meters = 150 cm
1.2 meters = 120 cm
Area = length * width
= 150 cm * 120 cm
= 18000 cm^2
The square of the sum of a number and 24
Answers
the following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. the mean of the population is
Answers
The mean of the population can be calculated by finding the sum of all the heights and dividing it by the total number of observations.
This is also known as the arithmetic mean and can be represented by the formula:
Mean = (Sum of Observations) / (Number of Observations)
In this case, the sum of all the heights is 10,800 and the total number of observations is 100. Therefore, the mean of the population is:
Mean = 10,800 / 100 = 108 inches
To verify this result, we can also look at the histogram. Since the heights are grouped into intervals of 10 inches, the mean should be around the midpoint of the tallest bar, which is 108 inches. This confirms our calculation of the mean.
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A concert promoter must sell 1820 tickets for an upcoming concert. They can sell discount tickets for $40 each, and premium tickets for $45 each, but the total sales must equal $76,300. Let x be the number of discount tickets sold, and y be the number of premium tickets sold. Set up, and solve, the system of equations to find the number of tickets of each type sold.
Give your answer in the form (x, y)
Answers
Answer:
(x, y) = (1120, 700)
Step-by-step explanation:
You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.
EquationsThe equations reflect the relationships stated in the problem:
x + y = 1820 . . . . . . the total number of tickets sold is 1820
40x +45y = 76,300 . . . . . total sales must be $76,300
SolutionIt usually works well to substitute for the variable representing the lower-price tickets:
40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation
5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify
y = 700 . . . . . . . . . . . . divide by 5
x = 1820 -700 = 1120
The numbers of tickets of each type sold are (x, y) = (1120, 700).
