The perimeter of a rectangle is 343434 units. Its width is 6.56.56, point, 5 units.
Write an equation to determine the length (l)(l)left parenthesis, l, right parenthesis of the rectangle.

Answers

Answer 1

The length of the rectangle is 10.5 units.

What is perimeter?

Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:

34 = 2l + 2(6.5)

Simplifying, we get:

34 = 2l + 13

Subtracting 13 from both sides, we get:

21 = 2l

Dividing both sides by 2, we get:

l = 10.5

So the equation to determine the length of the rectangle is:

2l + 2w = P

Substituting the known values, we get:

2l + 2(6.5) = 34

Simplifying and solving for l, we get:

2l + 13 = 34

2l = 21

l = 10.5

Therefore, the length of the rectangle is 10.5 units.

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Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.


Related Questions

Dylan claims that the coordinates of the center of dilation are (4.8, 3.2). He explains that to locate the center of dilation, he first joins P and P ’. Then, he marks a point X on line segment PP’ such that PX : XP’ = 1 : 4, since the scale factor of dilation is 4. Finally, he reads off point X from the coordinate plane, and concludes that point X has coordinates (4.8, 3.2).


Part A:


Explain how you know that Dylan’s claim is wrong in the space below. What is the location of the center of dilation (x,y)?

Part B:


What is the location of the center of dilation (x,y)?


I need help quick this is for a test

Answers

The correct coordinates of the center of dilation are (2.8, 3.8).

What is dilation?

In geometry, dilation is a transformation that changes the size of an object. When a figure is dilated, each point of the original figure is moved away from or toward the center of dilation.

Dylan's claim is incorrect because the center of dilation is not necessarily located on the line segment PP'.

To find the center of dilation, we need to locate the image point of a known point after dilation.

Let's consider a point Q on the same line as PP', but on the other side of P', such that PQ = 1 unit. After dilation with a scale factor of 4, the image of Q will be on the line passing through P and P'. Let's denote this image point by Q'.

Since PQ : P'Q' = 1 : 4, the distance from P to Q' is 4 units. Similarly, since PP' : PQ' = 1 : 5, the distance from P to Q' is 5 times the distance from P to P'. Thus, the distance from P to P' is 1 unit and the distance from P to Q' is 5 units.

Therefore, the center of dilation is located on the line passing through P and Q', and is 4 units away from P and 1 unit away from Q'.

Using the midpoint formula, we can find the coordinates of the center of dilation:

[tex]x &= \frac{1}{2}(4.8 + 0.8)[/tex]

[tex]&= 2.8[/tex]

[tex]y &= \frac{1}{2}(3.2 + 4.4)[/tex]

[tex]&= 3.8[/tex]

Thus, the correct coordinates of the center of dilation are (2.8, 3.8).

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The radius of a circle is 11 meters. What is the circle's circumference?
Use 3.14 for л.
r=11 m

Answers

Answer:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of r=11 m and using π = 3.14, we get:

C = 2πr

C = 2 x 3.14 x 11 m

C = 69.08 m

Therefore, the circumference of the circle is 69.08 meters

You are scheduled to receive annual payments of R15 000 for each of the next 13 years. The discount rate is 9%. What is the difference in the present value, if you receive these payments at the beginning rather than at the end of each year?

Answers

Answer:

Step-by-step explanation:

To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.

First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:

PV = PMT x [(1 - (1 / (1 + r)n)) / r]

where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06

Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:

PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)

where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97

So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:

R153,094.97 - R141,798.06 = R11,296.91

So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.

Write an equation to determine each unknown length. Then, solve the equation. Round your answer to the nearest tenth, if necessary.
X=___ Round to the nearest tenth (One number after the decimal)

Answers

Answer: 40

Step-by-step explanation:

a(2) + b(2) = c(2)

a(2) + 9(2) = 11(2)

121 - 81 = 40

4) It has been known that 18% of victims of financial fraud know the perpetrator of the fraud
personally. If a sample of 156 people were victims of fraud, what is the mean number of those
victims that know the perpetrator of the fraud personally?

Answers

Answer:

If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.

If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?

Answers

Answer: $194.79

Step-by-step explanation:

It is easiest to approach this question in two parts.

First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50

Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -

($12.50) | (60 min)  -    (x dollars) | (35 min)

then cross multiply and divide -  (12.5 * 35) / 60 = 7.291

This means you make $7.29 for 35 minutes of work.

$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.

(this is based on a per minute/hour scale)

What is the value of the angle?

Answers

The angle indicated by a green arc is 54 degrees.

What is the definition of a simple angle?

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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Explain the difference between a) comparing, b) non-standard units of measurement and c) standardised units of measurement.

Answers

Answer:

a) Comparing: Comparing means evaluating the similarity or difference between two or more objects, values, or variables. It is a process of identifying and highlighting the similarities and differences among objects, values, or variables based on specific criteria.

b) Non-standard units of measurement: Non-standard units of measurement are those that are not part of the International System of Units (SI) and are often created for specific purposes or contexts. These units may be used to measure variables such as time, distance, weight, or volume, but they are not universally recognized or standardized.

c) Standardized units of measurement: Standardized units of measurement are those that are part of the International System of Units (SI) and are universally recognized and accepted. These units provide a standard framework for measuring variables such as time, distance, weight, or volume, making it possible to compare and communicate measurements accurately across different contexts and languages. Some examples of standardized units of measurement include seconds, meters, kilograms, and liters.

FACTOR BY GROUPING


SEE ATTACHED IMAGE


SOLVE 4-6 BY STEPS 1-4

Answers

Answer:

see explanation

Step-by-step explanation:

(4)

5x³ - 10x² - 3x + 6

factor out 5x² from first 2 terms and - 3 from last 2 terms

= 5x²(x - 2) - 3(x - 2) ← factor out (x - 2) from each term

= (x - 2)(5x² - 3)

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

(5)

9a³ - 45a² - 7a + 35

factor out 9a² from first 2 terms and - 7 from last 2 terms

= 9a²(a - 5) - 7(a - 5) ← factor out (a - 5) from each term

= (a - 5)(9a² - 7)

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

(6)

5x²y - 15y - 2x² + 6

factor out 5y from the first 2 terms and - 2 from the last 2 terms

= 5y(x² - 3) - 2(x² - 3) ← factor out (x² - 3) from each term

= (x² - 3)(5y - 2)

Angles M, N, and P are supplementary.



What is the measure of angle P?

60°

34°

45°

36°

Answers

Step-by-step explanation:

The measure of angle p is 60°

2 eggs are needed to make 24 cookies. how many eggs are needed to make 60 cookies

Answers

Answer:

5 eggs.

Step-by-step explanation:

Since two eggs are needed for 24 cookies, we know by dividing both numbers by two that the rate is one egg for 12 cookies. 60/12 = 5. Multiply both numbers by 5 to get the answer. So, the answer is 5 eggs.

can someone please solve????!! thanks

Answers

Answer:

  (a)  Figure 3

  (b)  66.2 meters per second

Step-by-step explanation:

You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.

Best fit

The fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.

The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.

Estimated value

The speed is estimated by the equation of the curve of best fit as ...

  y = 0.6x² +2.1x +11

A slight rearrangement can make this easier to evaluate:

  y = (0.6x +2.1)x +11

For x=8, the value of y is ...

  y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2

The predicted speed at 8 seconds is 66.2 meters per second.

BONUS SECTION
This section is optional. Each correct answer will receive 2 points (12 points total)
which will be added to your test's raw score. Clearly indicate the necessary steps,
including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, correct numerical answers without work shown or an
explanation will not receive any credit.
1. Shanika has a dilemma. She has five choices for future employment but does not
know which job opportunity to take. Calculate the annual income for each option
and let her know which job would earn her the most money.

Option 1: Keeping her present job at $15,000 per
year plus a 20% year-end bonus.

Option 2: Taking a job that pays $1,250 per month

Answers

Answer:

A

Step-by-step explanation:

A college professor claims that students who major in engineering in college score higher on standardized test then students who major in ancient history. He randomly selected 50 students from each subject and gave them this assignment the results of which are shown here.

See chart and answer choices in photo!
Please answer quickly, tysm!

Answers

The option that describes the null and alternative hypothesis, test statistic and conclusion will be B. test statistic = -1.5625 and the conclusion is to reject the null hypothesis.

What is the hypothesis about?

In statistical hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference or relationship between two or more variables. It represents the default position that there is no effect or change, or that any observed effect is due to chance.

The alternative hypothesis (H1), on the other hand, represents the opposite of the null hypothesis. It states that there is a significant difference or relationship between the variables being tested. The alternative hypothesis is typically what the researcher is trying to prove or support with their study.

The test statistic will be:

= (116 - 121) / 16(✓1/50 + 1/50)

= -1.5625

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The circumference of the circle is 20 pi inches. What is the arc length of the shaded sector? Express the answer in terms of Pi. A circle. The shaded sector has an angle measure of 45 degrees. Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction. 2.5 pi inches 5 pi inches 7.9 pi inches 10 pi inches

Answers

The provided remark indicates that option (A) is accurate for 2.5 inches.

What length of time is an example?

The measurement or size of something to end to end is referred to as its length. To put it another way, it is the bigger of the upper two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.

Using the given equation:

Arc Length / 20π = 45/360

Cross multiply:

Arc length × 360 = 20π x 45

Arc length x 360 = 900π

Divide both sides by 360:

Arc length = 900π / 360

Arc Length = 2.5 π inches.

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The diagram below represents how rock is affected when water enters cracks in rock, freezes, and becomes ice.

Which geologic process is represented in the diagram?

Answers

Answer: Physical weathering, more specifically, ice wedging

Step-by-step explanation:

:D

Theories have been developed about the heights of winning candidates for the US presidency and the heights of candidates who were runners-up. Listed in the table are heights from recent presidential elections. Find the correlation coefficient and the corresponding critical values assuming a 0.05 level of significance. Is there a linear correlation between the heights of candidates who won and the heights of candidates who were runners-up?

Answers

There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.

Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:

Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.

Using a spreadsheet, we get r = 0.80.

Using the formula: df = n - 2.

The sample size (n) is 10, so df = 10 - 2 = 8.

Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).

For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.

Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.

Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.

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help I don't understand ​

Answers

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

What is triangle similarity?

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5


Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.


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What’s the answer to this question? I can’t seem to find the answer.

Answers

You could try factoring.

[tex]6x^2-x-1=(2x-1)(3x+1)\\3x^2+25x+8=(x+8)(3x+1)\\x^2+4x-32=(x+8)(x-4)\\2x^2+7x-4=(x+4)(2x-1)[/tex]

So your expression becomes...[tex]\frac{(2x-1)(3x+1)}{(x+8)(3x+1)}*\frac{(x+8)(x-4)}{(x+4)(2x-1)}=\frac{x-4}{x+4}[/tex].

change 3 5 to a decimal fraction

Answers

Answer:

7/20

its the answer to your question

in which place is the first digit of the quotient: 3,587 ÷ 18

Answers

Answer: The quotient is 199.277777778, the answer is the hundreds place

Step-by-step explanation:

199.277777778, the 1 in 199 is in the hundreds place :)

when interest is compounded n times a year, the accumalated amount(A) after t years.approximately how long will take $2000.00 to double at an annual rate of 5.25% compounded monyhly?

Answers

Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

What is percent?

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

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help! find the area of the trapezoid using 30-60-90 special right triangles theorem

Answers

AFE triangle,

FE= 6cos60

    = 3

dc= 3

ae= 6sin60

   = 3*squareroot3

Area= 1/2(10+4)*3*squareroot3

       = 7*3*squareroot3

        = 21*squareroot3

        = 21*1.73

         = 36.33square units

What is 7% as a decimal ?

Answers

Answer: 0.07%

Step-by-step explanation:

Answer:

0.07

Step-by-step explanation:

8) find the values of c that satisfy Rolle's Theorem.
SHOW STEPS

Answers

Hence the value of c = 4 in [3,5] for Rolles theorem.

Rolle's Principle

If a function f is defined in the closed interval [a, b] in a manner that meets the requirements listed below.

The interval [a, b] is closed and the function f is continuous.

ii) On the open interval, the function f can be differentiated (a, b)

iii) If f (a) = f (b), then at least one value of x exists; in this case, let's assume that this value is c, which is situated between a and b, i.e. (a c b), in such a way that f'(c) = 0.

There exists a point x = c in (a, b) such that f'(c) = 0 if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

let f(x)=x²-8x+12 in [3,5]

i) f(x) is continuous in closed interval [3,5] because f(x) is algebraic function.

ii) f(x) is differentiable in the open interval (3,5) since the algebraic function is differentiable.

now f(3)=3²-8*3+12

f(3)= 9-24+12

f(3)= -3

f(5) = 25-40+12

f(5)= - 3

f(3) = f(5)

f'(x)= 2x-8

x=c ,c in [3,5]

f'(c)= 2c-8

2c-8=0

c=4

Hence the value of c = 4 in [3,5] for Rolles theorem.

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Type the correct answer in the box. Use numerals instead of words.

The cone and cylinder below both have a height of 11 feet.


The cone has a radius of 3 feet.


The cylinder has a volume of 310.86 cubic feet.




Complete the statements using 3.14 for pi. Any non-integer answers in this problem should be entered as decimals rounded to the nearest hundredth.


The volume of the cone is [?]

cubic feet.


The radius of the cylinder is [?]

feet.


The ratio of the volume of the cone to the volume of the cylinder is 1:[?]

.

Answers

Volume of cone: 1/2 π r^2

1/3•3.14 (3) ^2 •11


Solution: 103.62


Volume of cylinder: π r^2 h

310.86/ 3.14 (11)

R^2 = 9

R= 3

Solution: 3


The ratio: 103.62 / 310.86 = 1/3 or 1: 3


Solution : 3

If Marie were to paint her living room alone, it would take 3 hours. Her sister Fran could do the job in 6 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.

Answers

The time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms 2 hours is 2/1.

What is time working together?

Time working together refers to the amount of time that two or more people need to work together to complete a certain task. It is often used in situations where people are working collaboratively or cooperatively to achieve a common goal.

According to question:

Let's denote the time it takes Marie to paint the living room alone by M and the time it takes Fran to paint the living room alone by F.

From the problem, we know that:

M = 3 hours

F = 6 hours

To determine the time it takes them to paint the living room together, we can use the following formula:

1 / (time working together) = 1 / M + 1 / F

Substituting the values we have:

1 / (time working together) = 1 / 3 + 1 / 6

Simplifying the right-hand side of the equation:

1 / (time working together) = 2 / 6 + 1 / 6

1 / (time working together) = 3 / 6

1 / (time working together) = 1 / 2

Therefore, the time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms:

2 hours = 2/1

So the answer is: 1 / (time working together) = 1 / 2, or equivalently, the time working together is 2/1.

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What is the percent change from 310 to 155?​

Answers

Answer: 50% decrease

Step-by-step explanation:

50% of 310 = 155

310-155=155

50% decrease :)

ANSWER: 50% decrease

SOLUTION:

50% of 310 = 155

310-155=155

So in all the answer is.......

50% decrease  :)))))

-XOXOXO:)

If Planet I is 31.1 million miles farther from the sun than Planet​ II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million​ miles, how far away from the sun is Planet​ II?

Answers

After solving the equations e know that Planet II is 35 million miles away from the sun.

What are equations?

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, let x be the separation between planet I and the sun.

Planet II's distance from the sun is x-30.2.

Planet iii's distance from the sun is equal to x+24.8.

x + x-30.2 + x+24.8 = 190.2

Mix related phrases to find x.

3x - 5.4 = 190.2

3x = 195.6

x = 65.2

65.2 million miles separate planet I from the sun.

Planet II is 35 million miles from the sun or 65.2-30.2.

Planet iii is 90 million miles from the sun (65.2 + 24.8 = miles).

Therefore, after solving the equations e know that Planet II is 35 million miles away from the sun.

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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?



Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)

Answers

The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

How to obtain the coordinates of B'?

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

What is a rotation?

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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