Mathematics College

In Triangle JKL. J(2,5), K(6,-7),L(-6,1) write the equation of the perpendicular bisector of LK

Answers

Answer 1

Answer:

The perpendicular bisector of LK is y = 1.5x - 3

--------------------------------------

Find the slope of LK:

m = (- 7 - 1) / (6 - (-6)) = - 8/12 = - 2/3

Find the midpoint of LK:

x - coordinate: x = (6 - 6)/2 = 0,y - coordinate: y = (- 7 + 1)/2 = - 3.

Perpendicular slope is:

-1/m = - 1/( - 2/3) = 3/2 = 1.5

The line is:

y - (-3) = 1.5(x - 0)y + 3 = 1.5xy = 1.5x - 3

Answer 2

Answer:

$y=\dfrac{3}{2}x-3$

Step-by-step explanation:

Given vertices of triangle JKL:

J = (2, 5)K = (6, -7)L = (-6, 1)

A perpendicular bisector is a line that intersects another line segment at 90°, dividing it into two equal parts.

To find the equation of the perpendicular bisector of LK, find the midpoint between the two points and the slope of the line LK.

$\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}$

Find the midpoint of LK:

$\implies \textsf{Midpoint}=\left(\dfrac{x_K+x_L}{2},\dfrac{y_K+y_L}{2}\right)$

$\implies \textsf{Midpoint}=\left(\dfrac{6+(-6)}{2},\dfrac{-7+1}{2}\right)$

$\implies \textsf{Midpoint}=\left(\dfrac{0}{2},\dfrac{-6}{2}\right)$

$\implies \textsf{Midpoint}=\left(0,-3\right)$

$\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}$

Find the slope of the line LK:

$\implies \textsf{Slope}\;(m)=\dfrac{y_K-y_L}{x_K-x_L}$

$\implies \textsf{Slope}\;(m)=\dfrac{-7-1}{6-(-6)}$

$\implies \textsf{Slope}\;(m)=\dfrac{-8}{12}$

$\implies \textsf{Slope}\;(m)=-\dfrac{2}{3}$

If two lines are perpendicular to each other, their slopes are negative reciprocals. Therefore, the slope of the perpendicular bisector is ³/₂.

$\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}$

Substitute the found midpoint and perpendicular slope into the point-slope formula to write the equation of the perpendicular bisector of LK:

$\implies y-(-3)=\dfrac{3}{2}(x-0)$

$\implies y+3=\dfrac{3}{2}x$

$\implies y=\dfrac{3}{2}x-3$

Related Questions

How to solve the problem of equivalent fractions

$How to solve the problem of equivalent fractions$

Answers

1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively

What is Equivalent Fraction?

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

1/2 = /6 = /8.

a. Multiply numerator and denominator by 3 for equivalenting the equation /6

Therefore,

3*3/6*3

=9/18

=1/2

therefore:1/2=1/2.

b. Multiply numerator by 4

Therefore,

4/8

=1/2.

Therefore:

1/2=1/2.

1/2=1/2=1/2.

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Problem 7: Use the known Laplace Transforms
$L({e}^{ λt}sinωt) = \frac{ ω}{(s - {λ)}^{2} + {ω}^{2} } $
and
$L({e}^{ λt}cosωt) = \frac{s - λ}{(s - {λ)}^{2} + {ω}^{2} } $
and the result of Exercise 6 to find
$L({te}^{ λt}cosωt)$
and
$L({te}^{ λt}sinωt) $

$Problem 7: Use the known Laplace Transforms[tex]L({e}^{ t}sint) = \frac{}{(s - {)}^{2} + {}^{2} } [/tex]and$

Answers

Let

$F(s) = L\left\{e^{\lambda t} \sin(\omega t)\right\} = \dfrac{\omega}{(s-\lambda)^2 + \omega^2}$

By the result of ex. 6,

$-F'(s) = L\left\{t e^{\lambda t} \sin(\omega t)\right\} = \boxed{\dfrac{2\omega (s-\lambda)}{\left((s-\lambda)^2 + \omega^2\right)^2}}$

In a similar way, you'll find that

$L\left\{t e^{\lambda t} \cos(\omega t)\right\} = \boxed{\dfrac{(s-\lambda)^2 - \omega^2}{\left((s-\lambda)^2 + \omega^2\right)^2}}$

A painting attributed to Vermeer (1632-1675), which should contain no more than 96.2% of its original carbon-14, contains 99.3% instead. Using the fact that Carbon-14 has half-life of 5730 years, determine the age of the forgery._____ years old.

Answers

The forgery is approximately 23,878 years old when A painting attributed to Vermeer (1632-1675), which should contain no more than 96.2% of its original carbon-14, contains 99.3% instead.

The half-life of a substance is the time it takes for half of the initial amount of the substance to decay or disintegrate.

The fact that the painting contains 99.3% of its original carbon-14 means that only 0.7% of the original carbon-14 has decayed. We can use the half-life formula to find how long it would take for 0.7% of the carbon-14 to decay:

$0.007 = (1/2)^{(t/5730)$

where t is the time in years. Solving for t, we get:

$t = 5730 * ln(0.007) / ln(0.5) \approx 23877.56$

Therefore, the forgery is approximately 23,878 years old.

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1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 QUESTION 1 [24] Gavin Pillay is employed at Maritzburg Engineering, a Steel manufacturing company in Pietermaritzburg. Below is a copy of his Payslip. 1. 3201 Company Maritzburg Engineering cc 21 Halsted Road Pietermaritzburg Employment No 105 Id Number Income Basic Salary Overtime M Gross Salary Maritzburg Engineering cc Employee Name Gavin Pillay Period 31/05/2023 Sex Male 790128514088 R8700 R1200 A Status Married Deductions PAYE UIF Total Deductions Net Pay 1200 87 B C Name the Employee? What does UIF stand for? Show by calculation that the UIF paid by Gavin is calculated correctly Which month is this Payslip for? Calculate the missing values A to C How old is Gavin this year? Give the address of Gavin's work place. Gavin would like to contribute towards a Pension fund (7,5% of his Basic Salary). H would this affect his net salary?

Answers

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Thirty-four percent of workers in the Unites States are college graduates. Suppose a random sample of 120 workers is obtained and 35 of them have a college degree.
a) What are the mean and standard deviation of the number of workers with a college degree respectively?
b) What is the probability that the number of workers with a college degree is at least 35?

Answers

The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

Given Sample size (n) is 120 workers

Proportion of workers who are college graduates (p): 34% or 0.34

a) Mean and Standard Deviation:

The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).

Substituting the values:

μ = 120 ×0.34 = 40.8

σ = √120 × 0.34 × (1 - 0.34)) = 5.37

To find the probability that the number of workers with a college degree is at least 35

we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.

Using a binomial probability calculator or a statistical software, we can find this probability.

Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:

P(X ≥ 35) = 1 - P(X < 35)

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

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A sociologist wishes to conduct a poll to estimate the percentage of Americans who favor affirmative action program for women and minorities for admission to colleges and universities. What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04, with 95% confidence, if she uses a 2003 estimate of 0.55 obtained from a Gallup Youth Survey

Answers

Answer:

A sample of 595 should be obtained.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence level of $1-\alpha$, we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

Estimate of 0.55

This means that $\pi = 0.55$

95% confidence level

So $\alpha = 0.05$, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$, so $Z = 1.96$.

What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04?

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.55*0.45}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.55*0.45}$

$\sqrt{n} = \frac{1.96\sqrt{0.55*0.45}}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.55*0.45}}{0.04})^2$

$n = 594.2$

Rounding up,

A sample of 595 should be obtained.

At a supermarket, there are 118 customers. If 45 have purchased shirts, 59 have
purchased pants, and 40 have purchased neither, how many purchased both shirts and
pants?

Answers

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

What is a Venn Diagram?

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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Find the perimeter of the rectangle

Answers

Answer:

22 in.

Step-by-step explanation:

Perimeter = Length + Length + Breadth + Breadth

Perimeter = 7 in. + 7 in. + 4 in. + 4 in.

Perimeter = 22 in.

Describe a function g(x) in terms of f(x) if the graph of g is obtained by vertically stretching f by a factor of 2, then shifting the graph of to the right 3 units and upward 3 units.

Answers

The function g(x) in terms of f(x) if the graph of g is obtained by vertically stretching f by a factor of 2, then shifting the graph of to the right 3 units and upward 3 units is g(z) = 2f(z + 3) + 3.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

If the graph of g is obtained by vertically stretching f by a factor of 2, then shifting the graph of f to the right 3 units and upward 3 units, then we have:

g(z) = A f(z - B) + C

where A is the vertical stretch factor, B is the horizontal shift, and C is the vertical shift.

Since the graph of f is being vertically stretched by a factor of 2, we have A = 2.

The graph of f is being shifted to the right 3 units and upward 3 units. This means that the point (0, 0) on the graph of f will be shifted to the point (3, 3) on the graph of g. Therefore, we have:

B = -3 (the opposite of the horizontal shift of f)

C = 3 (the vertical shift of f)

Putting it all together, we have:

g(z) = 2f(z + 3) + 3

Therefore, the function g(x) will be g(z) = 2f(z + 3) + 3.

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Am nevoie de raspuns la acest exercitiu.

Answers

This was handpicked for me and it’s in some foreign language like Spanish or something

PLEASE HELP

Divide.

(6.496×10^−6)÷(2.8×10^5)

Express your answer in scientific notation.

Answers

Answer:

=(6.496x10^-6)x10^-5/2.8

=6.496/2.8 x10^-6 x10^-5

= 2.32 x 10^(-6-5)

=2.32 x10^-11

=2.32/10^11

Philip wrote the following inequality on the board:
g> 15 Which value for g makes this statement true?
A. 17
B. 15
C. 13
D. 10

Answers

Answer:

A is the answer! (hope I wasn't too late)

What is the largest integer value of $m$ such that the equation $$3x^2 - mx + 21 = 0$$has no real solutions?.

Answers

The largest positive integer value of m such that the equation 3x^2 - mx + 7 = 0 has no real solutions is m = 9.

For the quadratic equation 3x^2 - mx + 7 = 0 to have no real solutions, the discriminant must be negative.

The discriminant of a quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac. In this case, a = 3, b = -m, and c = 7. So the discriminant is:

b^2 - 4ac = (-m)^2 - 4(3)(7) = m^2 - 84

For the equation to have no real solutions, the discriminant must be negative:

m^2 - 84 < 0

m^2 < 84

m < sqrt(84)

m < 9.165

The largest integer value of m that satisfies this inequality is 9.

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How many square feet of wallpaper are required to cover the wall surrounding the window?

Answers

Answer:

between C and D

im going to say C to be safe tho

Answer: 131 ft^2

Step-by-step explanation:

the window is 77 ft and the wallpaper is 208 ft

so you subtract 77 from 208 and your answer will be 131.

Find the output, y, when the input, x, is -9.
y =

Answers

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Solve for x:
5/8=X-1/9

Answers

Answer:

x=5/8+1/9

x=53/72

......

Answer:

53/72 you didn't give me the answer choices but this is the exact form of this equation

A student measures the mass of a sample is 2.7 grams. What is the percent error, given that the correct mass is 2.58 grams? Round to the nearest hundredth of a percent.

Answers

Answer:

the percent error in the student's measurement is 4.65%.

Step-by-step explanation:

The percent error can be calculated using the formula:

| (measured value - actual value) / actual value | * 100%

In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:

| (2.7 - 2.58) / 2.58 | * 100% = 4.65%

Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.

Therefore, the percent error in the student's measurement is 4.65%.

what is the sum of 2/3,1/2and1/4=

Answers

Answer:

17/12

Step-by-step explanation:

In order to add fractions, you have to have a common denominator. The denominators in these fractions are 3, 2, and 4 (the bottom numbers). To get a common denominator, figure out what number all three of them can go into. Their common factor would be 12 because all three numbers go into 12.

Multiply each numerator in the fraction (the top number) by how much it takes to get from our current denominators (3,2,4) to our final denominator (12).

For example, in 2/3 we know that 3 times 4 equals 12. Multiply the top number by 4 to get 8/12.

In 1/2 we know that 2 times 6 equals 12. Multiply by 6 to get 6/12.

In 1/4 we know that 4 times 3 equals 12. Multiply by 3 to get 3/12.

Add the fractions to get 17/12.

Find the mean, median, and mode of the set of data. 10, 11, 4, 7, 12, 11, 16, 6, 9, 15

Answers

Answer:

Step-by-step explanation:

Mean (Average):

10.1

Median (Middle):

(10+11)/2 = 10.5

Mode (Most Common):

Range & Totals Results

Range (Biggest - Smallest):

Total Numbers in Set:

Ascending Order:

4,6,7,9,10,11,11,12,15,16

Decending Order:

16,15,12,11,11,10,9,7,6,4

Even Numbers:

4,6,10,12,16

Odd Numbers:

7,9,11,11,15

Answer:

Mean = 10.1

Median = 10.5

Mode = 11

Step-by-step explanation:

We are given a set of data: 10,11,4,7,12,11,16,6,9,15

First we arrange into ascending order.

4, 6, 7, 9, 10, 11, 11, 12, 15, 16

Thus, The mean of given data is 10.1

Number of data is even.

Possible median: where, n=10

of the arranged data would be median.

Median: 10 and 11

Average of median

Thus, The median of given data is 10.5

Mode: It is maximum repeated number of data set.

In the given data set, 11 repeated two times.

Thus, The mode the given data is 11

Sorry My images didn't work

he diameter of the circle is 18 m. Eugene incorrectly says that the circumference of the circle is about 113.04 m. What is the circumference of the circle? What mistake did Eugene make? Use 3.14 for pi.

Answers

Answer:

The circumference of the circle is $C=56.55 \:m$.

Eugene confused the radius with the diameter to find the circumference of the circle.

Step-by-step explanation:

The circumference of a circle is the distance around the outside of the circle.

The circumference of a circle is found using this formula:

$\begin{matrix} C=\pi \cdot d\\or\\ \, C=2\pi \cdot r \end{matrix}$

From the information given the diameter of the circle is 18 m. Therefore, the circumference of the circle is

$C=\pi \cdot d\\\\C=3.14 \cdot 18 \approx 56.55 \:m$

Eugene used the wrong formula to find the circumference of a circle.

$C=2\cdot(3.14)\cdot 18=113.04 \:m$

He confused the radius with the diameter.

Answer:

Eugene used the wrong formula to find the circumference of a circle.

He confused the radius with the diameter.

Step-by-step explanation:

What is
(6.8) ( - 1.3)

Answers

Answer:

-8.84 = 0.

Step-by-step explanation:

PLS HELP

Determine the interval(s) on which you the given function is decreasing.

(Answer choices in picture)

Answers

Answer:

Step-by-step explanation:

What is the length of the missing leg of ️XZY if: |X2 = 10 and |XY = 26 X

Answers

The length of the missing leg is IXY=

Step-by-step explanation:

xz = 10

XY = 26

let ZY = x

xyz is a right angle triangle

XY^2 = xz^2 + zy^2

26^2 = 10^2 + x^2

676 = 100 +x^2

√576 = x^2

x = 24

hence ZY = 24

WILL GIVE BRAINLISES

The coordinate 1 has a weight of 4, and the coordinate 4 has a weight of 2. Find the weighted average.

Answers

Answer: 3

Step-by-step explanation: This is the average between your 2 numbers, 4 and 2.

Answer: its 2

Step-by-step explanation: i guessed and i got it right after this other dud said 3....ITS 2

Given f(x) = x² - 5x - 6 and g(x) =
x² - 6x, what are the domain restrictions
for (-)(x)?
A) x # +6
B) x = 0
C) x = 0,6
D) x = -2,6

Answers

The domain restrictions for (f/g)(x) are (c) x = 0, 6

How to determine the domain restrictions for (f/g)(x)?

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x = 6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

Answers

Step-by-step explanation:

This is an equation, where we need to find the value of x.

To solve this equation, we can first use the distributive property to expand 3.4(x + 7) which gives 3.4x + 3.4 * 7 = 3.4x + 23.8

Now we have the equation:

3.4x + 23.8 - 2.1 = 35.5

Next, we can add 2.1 to both sides of the equation:

3.4x + 23.8 = 37.6

Then, we can subtract 23.8 from both sides of the equation:

3.4x = 13.8

Finally, we can divide both sides of the equation by 3.4 to find the value of x:

x = 4

Therefore, the value of x that solves the equation is 4.

what is the property of 3x(5x7)=(3x5)7

Answers

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Terry is the school swimming champion and has won several races. If the ratio of the number of times he's won to the number of races he has swum in is 2 : 3, how many races has he won?

Answers

The given information tells us that Terry's wins-to-races ratio is 2:3, but we cannot determine the exact number of races he has won without additional information about the total number of races he has participated in.

If the ratio of the number of times Terry has won to the number of races he has swum in is 2:3, we can set up a proportion to determine the number of races he has won.

Let's denote the number of times Terry has won as x, and the total number of races he has swum in as y. According to the given ratio, we have:

x/y = 2/3

To find the value of x, we need to solve for x when y is known. Since y represents the total number of races, we don't have that information in the given problem. Therefore, we cannot determine the exact number of races Terry has won without knowing the total number of races he has participated in.

The ratio tells us the relationship between the number of wins and the total number of races, but without knowing the denominator (total races), we cannot find a specific value for the numerator (number of wins). We can only determine the ratio between the two quantities.

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lesson 6.1
Graph the image of the figure using the transformation given.
options are out of the last 3 images

Answers

The figure with the coordinates R'(-4, 2), S'(-4, 4), T'(1, 5) and U' (0, 0) are graph of the image of the figure.

Hence, Option B is the correct answer.

What is translation?

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other.

Given that,

The translation is 1 units left and 5 units up.

The coordinates of the given figure are R(-3, -3), S(-3, -1), T(2, 0) and

U(1, -5).

Now, If the translation is 1 units left and 5 units up, then the coordinates become (x - 1, y + 5).

Hence, Coordinates for the image of the graph are;

R' = (-4 - 1, 2 + 5) = (-5, 7)

S' = (-3 - 1, -1 + 5) = (-4, 4)

T' = (2 - 1, 0 + 5) = (1, 5)

U' = (1 - 1, -5 + 5) = (0, 0)

Hence, The coordinates are R'(-4, 2), S'(-4, 4), T'(1, 5) and U' (0, 0).

Therefore, The figure with the coordinates R'(-4, 2), S'(-4, 4), T'(1, 5) and

U' (0, 0) are graph of the image of the figure.

Hence, Option B is the correct answer.

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write and solve an inequality to find the possible values of x

Answers

The inequality that represents the value of x is (b) x > 80

Writing and solving the inequality for x

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80