Most linear systems will have exactly one solution. Nevertheless, it is possible that there are no solutions or infinitely many. (but It is not possible that there are exactly two solutions of a linear system.)
Let's assume a system of two linear equations, then, there are three possibilities of solutions.
The possibilities are:
Two parallel lines
e.g. y = 3x + 1
y = 3x − 2 (with the same slope, different intercepts)
Two (distinct) intersecting lines
As we know two straight lines cannot meet at two points. Two points determine only one line (not two lines).
e.g. y = 3x + 1
y = 5x − 2 (different slopes)
These equations have the same line as their graphs
If two lines do have two points in common, then "the lines coincide" (which really means "there is only one line".) In this case, we say, "the two lines are the same".
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A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. The village plans to increase the length by 30%.
Answer:
A) 234 feet
B) Area of new parking lot = 28080 square feet
C) The new parking lot will be able to fit 20 more cars than the original parking lot.
Step-by-step explanation:
We are given the following information:
Length of parking lot = 180 feet
Width of parking lot = 120 feet
Number of cars that can be parked = 75
A) Increase in length = 30%
New length =
B) New area =
C) Space required by 1 car = 288 square feet
Number of cars we want to fit = 75 + 20 = 95
Area required =
Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.
please help, i dont understand!
10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the area of rectangle is 70y⁸+30y⁶
The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶
70y⁸+30y⁶
10y⁶(y²+3)
10y⁶ is the width of the rectangle.
y²+3 is the length of the rectangle.
Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
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Is 6(4b + 3d) and 24b + 3d equivalent or not
Answer:
No
Step-by-step explanation:
You must distribute 6 to BOTH numbers in the bracket
[tex]6(4b + 3d) = 24b + 18d[/tex]
Answer:
No, they are not equivalent !
Step-by-step explanation:
Simplify 6(4b + 3d)....
6(4b + 3d)
→ 6*4b+6*3d
→ 24b+18d
and we have....
→ 24b + 3d
So, no 6(4b + 3d) and 24b + 3d are not equivalent.
How many times more intense is an earthquake that measures 8 on the Richter scale than an earthquake that measures 4 on the Richter scale?.
A measures magnitude 8 on the Richter scale of an earthquake is 10,000 times stronger than a magnitude 4 measure on the Richter scale.
Earthquake Intensity: An earthquake is the release of energy from the movement of tectonic plates. Earthquakes can be measured on the Richter scale, which ranges from 2 to 10 and measures the magnitude of an earthquake.
Earthquake intensity is a qualitative estimate of the effects caused by an earthquake, so it has no numerical value. The Richter scale is a logarithmic scale. This means that as you move up each digit, the power increases by a factor of 10. So let's set the damage from 4 earthquakes to X. Then, 5 = 10X
=> 6 = 100X
=> 7 = 1,000X
=> 8 = 10,000X
Hence, the required intensity is 10,000.
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The Hall family and the Cox family each used their sprinklers last summer.
The water output rate for the Hall family's sprinkler was 25 L per hour.
The water output rate for the Cox family's sprinkler was 20 L per hour.
The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 875 L.
How long was each sprinkler used?
The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
How long was each sprinkler used?The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
Let h and n represent the amount of hours each household uses its sprinkler, the Halls and the Nguyens, respectively.
They use for a total of 50 hours, thus either h + n = 50 or h = 50 - n.
Additionally, their total water output is 1050 L, thus we may use the equation below.
35h + 15n = 1050
Replace h with h = 50 - n to get
35(50 - n) + 15n = 1050
1750 - 35n + 15n = 1050
35n - 15n = 1750 - 1050
20n = 700
34 hours, n
15 hours equal 50 h, 50 n, and 35 n.
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Compute Autin' total ocial ecurity and Medicare taxe for the fourth quarter, if he i elf-employed and earn $5,000. 00 on a emimonthly bai. (For elf-employed peron, ocial ecurity tax i 12. 4% of wage up to $128,400, and Medicare tax i 2. 9% of all wage. )
The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.
The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.
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Help me find x please!
Answer:
PSQ = x since PSQ + 3 x = 4 x
So the triangle PQS is an equilateral triangle
2 x + y = 180 (y = PQS the angle opposite 68)
y + 68 = 180 these must add to 180
x = 34 subtracting the previous two equations
When Gabriella moved into a new house, she planted two trees in her backyard. At
the time of planting, Tree A was 34 inches tall and Tree B was 14 inches tall. Each
year thereafter, Tree A grew by 2 inches per year and
Tree B grew by 6 inches per
Let A represent the height of Tree A t years after being planted and let B
present the height of Tree B t years after being planted. Write an equation for each
situation, in terms of t, and determine the height of both trees at the time when they
have an equal height.
PLEASE ANSWER ITS DUE TODAY!!!!!!
The equation for Tree A's height t years after being planted is:
[tex]A = 34 + 2t[/tex]
The equation for Tree B's height t years after being planted is:
[tex]B = 14 + 6t[/tex]
To determine the height of both trees at the time when they have an equal height, we can set the two equations equal to each other:
[tex]A = B[/tex]
[tex]34 + 2t = 14 + 6t[/tex]
And solving for t, we find that:
[tex]t = 10[/tex]
So, 10 years after being planted,
Tree A will be 54 inches tall [tex](34 + 2 * 10)[/tex] and Tree B will be 74 inches tall [tex](14 + 6 * 10)[/tex].
At this point, both trees will have an equal height.
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lution set.
-y-8<-3 ory+5>19
The solution set of the expression is y > -5
How to determine the solution set of the expression?From the question, we have the following parameters that can be used in our computation:
-y-8<-3 ory+5>19
Express the inequality properly
So, we have the following expression
-y - 8 < -3 or y + 5 > 19
Collect the like terms
This gives
-y < 8 - 3 or y > 19 - 5
Evaluate the like terms
This gives
-y < 5 or y > 14
Rewrite as
y > -5 or y > 14
When combined, we have:
y > -5
Hence, the solution set is y > -5
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Complete question
For the following inequality expression, determine the solution set
-y-8<-3 ory+5>19
A spherical toy needs a triangular sticker (with a base of 12cm and height of 15cm) on it. The sphere has a diameter of 50cm what is the surface area not covered by the sticker?
Answer: 65.65
Step-by-step explanation:
Carry over the decimals in each number.
2) Multiply. This will give you 6,565.
3) Carry the decimal place and count how many times you moved it over. (2=1+1) Therefore, it gives you 65.65
I really need help on this!
Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.
What is the product about?In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.
The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.
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PLEASE HELP ME I NEED TO TURN THIS IN BY TMMR!!
Answer:
[tex]\frac{4}{3}cm/s[/tex]
Step-by-step explanation:
By looking at the graph, we can use the slope formula.
[tex]slope=\frac{y^2-y^1}{x^2-x^1}[/tex]
We can substitute the point values into the equation.
[tex]\frac{16-0}{12-0}[/tex]
Then simplify.
[tex]\frac{16}{12}[/tex]
This fraction has the greatest common denominator of 4, so we will divide the numerator and the denominator.
[tex]\frac{16}{12}=\frac{4}{3}[/tex]
Therefore, the speed of the snail has a unit rate of [tex]\frac{4}{3} cm/s[/tex].
Per company charge $20 per day to rent a car and $. 10 for every mile driven. Addion want to rent a car knowing that he plan to drive 100 mile and he ha at mot $80 to pend right and olve an inequality which can be ued to determine X the number of day Addion can afford to rent or tay within her budget
Considering the definition of inequality, the inequality that can be used to determine x is 20x + 10 ≤ 80.
According to the question,
Addison wants to rent a car, we know that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x denotes the maximum number of days. Alyssa can afford to rent while staying within her budget.
Then, the inequality that can be used to solve x is:
20x + 0.1×100≤ 80
so,
20x + 10≤ 80
Hence, the inequality which can be used to determine x is 20x + 10≤ 80.
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A pair of shoes regularly cost $45. Today, they are marked down 25%. What is the sale price of the pair of shoes?
Answer:
$33.75
Step-by-step explanation:
25% of 45 is 11.25 meaning you would get that much off as a discount making the shoes be $33.75
What is the argument of 4 3i?.
The Argument of 4 + 3i is arg(z) = 36.97◦.
Now, According to the question:
Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The standard format of a complex number is:
[tex]a +bi[/tex]
In which:
a is the real part.b is the imaginary part.Given,
The complex number is:
z = 4 + 3i
We have to find the argument of the 4 + 3i.
The argument is given by:
θ = [tex]tan^-^1\frac{b}{a}[/tex]
tan θ = [tex]\frac{3}{4}[/tex]
θ = [tex]tan^-^1\frac{3}{4}[/tex]
θ = 36.97◦
The argument is θ = 36.97◦
We also have an abbreviation for argument: we write arg(z) = 36.97◦
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Express the lengths a and b in the figure in terms of theta. If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and pi/2, evaluate sin(x + y) Find all values of x such that sin 2x = sin x and 0 le x le 2pi. (List the answers in increasing) If you have had difficulty with these problems, you may wish to consult the Review of Trigonometry.
In the given figure, the length b is opposite the angle theta, and the length a is adjacent to the angle theta, so we can use the trigonometric ratios to express a and b in terms of theta:
What does trigonometry mean in plain English?
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
a = bsec(theta)
b = acosec(theta)
To evaluate sin(x+y), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
We can use the given information to substitute the values of sin(x) and cos(y)
sin(x) = 1/3, cos(y) = sqrt(1 - (5/4)^2) = sqrt(9/16)
sin(x+y) = (1/3) * sqrt(9/16) + sqrt(9/16) * (1/3) = (3sqrt(9) + 9) / 48
To find all values of x such that sin 2x = sin x and 0 le x le 2pi, we can set sin 2x = sin x and solve for x.
sin 2x = sin x
2sinxcosx = sinx
cosx = 1/2
x = pi/3,5*pi/3
So the values of x that satisfy the equation are x = pi/3 and 5*pi/3
Note that these values are in radians, if you need in degree, x=60°, 300°
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You have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2. Which of these statements is true?.
About 285 numbers lie between the values 10 and 14. (option C).
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.
There are 600 numbers and their mean is 10 where the standard deviation is 2.
47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.
By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]
Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.
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Which graph shows the solution to this inequality? 15≤−3x+6
Answer: Look below
Step-by-step explanation:
For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that used to find a solution for the equation. Be sure to include at least two terms from the word bank. 1/4 x < -3
The inequality equation is x ≤ ( -12 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( 1/4 )x ≤ -3 be equation (1)
On simplifying the equation , we get
x/4 ≤ -3
Multiply by 4 on both sides of the equation , we get
x ≤ ( -3 ) ( 4 )
x ≤ -12
Therefore , the value of x is less than or equal to -12
Hence , the inequality equation is x ≤ -12
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1.
(04.02 LC)
Which of the following is a common characteristic of a binomial distribution? (4 points)
There are more than two possible outcomes.
The probability of success is the same in all trials.
There are infinitely many observations.
You should perform x trials until you observe a success.
Each trial is dependent on the previous trial.
Answer: The probability of success is the same in all trials.
The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.
What is the independent probability?Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
You should perform x trials until you observe a success.
We have given that,
There are exactly two possible outcomes success and failure.
We have to determine the following is NOT a common characteristic of a binomial distribution.
By process of elimination:-
A binomial experiment is a statistical experiment that must meet certain requirements
All trials are independent.
There are a fixed number of n trials.
The probability of success, p, is the same for each trial.
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do you have 8 cups of flour a recipe calls for 2/3 cup of flour of the recipe calls are 1/4 cup of flour how much flour do you have left after making the recipes
Answer: Total cup of flour=8 cups
One recipe calls for cup of flour=2/3
Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour
Another recipe calls fro cup of flour=1/4
Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.
Amount of Floor left=7.08
Step-by-step explanation:
ΔRST is reflected across the line y = x to form ΔR’S’T’. Find the coordinates of the points R’, S’ and T’.
R(1,-2)
S(2,-8)
T(7,-4)
Answer:
R' ( -2,1)
S' (-8,2)
T' ( -4,7)
Step-by-step explanation:
15/20, 20/21 determine if the ratio are proportional
According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.
How to determine whether that two ratios are proportional
In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:
15 / 20
Second, multiply numerator and denominator by 4 / 3:
[15 · (4 / 3)] / [20 · (4 / 3)]
20 / 26.667
Ratio 15 / 20 is not proportional to ratio 20 / 21.
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Tristan has a points card for a movie theater.
He receives 25 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 110 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Tristan can make to earn his first free movie ticket.
The inequality that represents the number of visits Tristan can make to earn his first free movie ticket is 8.5x + 25 ≥ 110.
What is the inequality?In mathematics, an inequality is a relationship between two expressions or values that are not equal to each other.
In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
Here,
Let us refer to x as the number of visits.
He receives 8.5 points for each visit,
That is he receives 8.5x points for x visits. i
Then there are the 25 reward points for simply signing up.
So the total points expression would be 8.5x + 25.
He needs at least 110 points to get a freebie,
Therefore the inequality is 8.5x + 25 ≥ 110.
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The city of Los Angeles wants to build a suspension bridge over Lake Casitas. The suspension
cables that are connected between the towers must have a parabolic curve. Let the y-axis
represent the axis of symmetry. The road/deck represents the directrix and sits 15 meters
above the water surface (which represents the x-axis). The vertex or minimum point of the
cable is 12 meters above the directrix. Write an equation to represent the parabolic shape of the
cables on the suspension bridge.
anchor
tower
cable
deck
foundations
hanger
approaches
A suspension bridge: a parabola represents the profile of the cable of a suspended-deck suspension bridge.
What is graph ?A graph is a topic which gives us the numerical facts into visual form.
That is, a graph gives the visual representation of the data collected.
The towers supporting the cable of suspension bridge are 15m apart and 12m above the bridge it supports.
Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.
lets have the bridged centered at the origin
Three points are needed on the parabola
x = 0, y = 20
x = -7.5, y = 12
x = +7.5, y = 12
using the form ax^2 + bx + c = y, we know that c=20
x=-7.5, y = 12 and x =+7.5, y = 12; write two equations
-7.5^2a - 7.5b + 20 = 12
+7.5^2a + 7.5 + 20 = 12
use elimination
56.25a - 7.5b + 20 = 12
56.25a + 7.5b + 20 = 12
addition eliminates b
112.5a + 40 = 24
112.5=16
a = 16/112.5
a = 0.1422
Now we can write the equation
y = 0.1422x^2 + 2
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What is the value of a in the following image?
Check the picture below.
Solve the equation 6z2-7z-5=0
Answer:
-1/2, 5/3
Step-by-Step Explanation:
6z^2 - 7z - 5 = 0
=> 6z^2 - 10z + 3z - 5 = 0
=> 2z(3z - 5) + 1(3z - 5) = 0
=> (2z + 1)(3z - 5) = 0
=> z = -1/2, 5/3
Hope it helps.
If you have any query, feel free to ask.
How do you multiply 3-digit numbers by 2 digit numbers with regrouping?.
Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.
Follow along with example 343 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.
3 4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.
3 4 3
×3 2
_________
6 8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.
3 4 3
×3 2
__________
6 8 6
10 2 9×
__________
10 976
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How do you find the median of a cumulative frequency graph class 10?.
To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.
The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.
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What is the slope of the line that passes through the points (-9,-5) and (-1,-9)
Answer:
-1/2
Step-by-step explanation:
slope is rise over run so find the difference between the y values (-9-(-5)) and divide that by the difference between the x values (-1-(-9)).
