7. Use coordinate geometry to find the perimeter and area of a polygon.
Part I: The coordinate grid below displays the stakes and wickets of the croquet
course. Sonja warmed up by putting her ball down at wicket 2. She then hit it through
wicket 9, then wicket 8, then wicket 5, then wicket 3, and finally back to wicket 2. On
the coordinate grid, draw the path of Sonja's ball. (5 points)
feet
y
70
60
50
40
30
20
(15,43)
9
(16,18)
(37,65)
8
●
(40,42)
Stake B
(70,72)
171
(66,68)
(62,64)
●3
(63.19)

Check the picture below.

The graph of the cubic function [tex]f(x)=x^3[/tex] is plotted.

The correct answer is Option C.

Given data:

The graph of a cubic function is a type of polynomial graph that has the form  [tex]f(x) = ax^3 + bx^2 + cx + d[/tex] , where 'a', 'b', 'c', and 'd' are constants.

The graph of the cubic function  [tex]f(x) = x^3[/tex]  is a smooth curve that passes through the origin (0,0) and extends into the four quadrants of the Cartesian coordinate system.

Y-Intercept:

The cubic function passes through the origin (0,0), so it has a y-intercept of (0,0).

X-Intercept:

The x-intercept occurs when f(x) = 0.

On solving for x:

[tex]x^3 = 0[/tex]

x = 0

So, the cubic function has an x-intercept of (0,0).

Hence, the cubic function is [tex]f(x)=x^3[/tex] and is plotted below.

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The combination of the letters will be 60.

When an order or sequence of arrangement is required, permutations are used. Combinations are used when there are only a limited number of possible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of things, permutations are used. Combinations are employed for similar items.

Given that the passcode for a smartphone consists of 3 letters followed by 3 digits.

The number of the vowels is:-

Vowels = { A, E, I, O, U} = 5

Number of letters = 3

The arrangements of the vowels will be:-

Number = ⁵C₃

Number = ( 5 x 4 x 3 )

Number = 60

Hence, the vowels can be arranged in 60 ways.

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The dimensions of the playing field are a length is 99 ft, and a width is 55 ft.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle and L is the length of the rectangle

Given that the length is 44ft longer than the width.

This means L = W + 44  ....(i)

Since the perimeter of a playing field is 308 ft

So 2(L+W) = 308

Substitute the value of the equation (i), and we get

2(W + 44 + W) = 308

2(2W + 44) = 308

4W + 88 = 308

4W = 220

W = 55

Substitute the value of W = 55 in equation (i), and we get

L = 55 + 44 = 99

Thus, the length is 99 ft, and the width is 55 ft.

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The monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.

To calculate the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan.

We'll need to first calculate the amount of the loan and then use the following formula to calculate the monthly payment:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

First, we'll calculate the down payment:

Down payment = 204,000 * 0.10 = $20,400

Next, we'll calculate the loan amount:

Loan amount = 204,000 - 20,400 = $183,600

Now, we'll need to convert the 30 year loan term into the number of payments (n) and the interest rate into the monthly interest rate (r):

n = 30 years * 12 months/year = 360 payments

r = (Annual interest rate) / 12 months/year

Assuming an annual interest rate of 3.5%, the monthly interest rate would be:

r = 0.035 / 12 = 0.002917

Finally, we can plug the values into the formula to calculate the monthly mortgage payment:

M = 183,600 * 0.002917 * (1 + 0.002917)^360 / ((1 + 0.002917)^360 - 1) = $808.44

Therefore, the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.

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It will take Rachel 5 months to pay off her debt at her current monthly payment rate.

Interest rate is a percentage that represents the amount of interest charged by a lender to a borrower for the use of money. It is used to calculate the interest that will accrue on a loan or deposit over a specific period of time, and is usually expressed as an annual rate. It is a key component in determining the cost of borrowing money, and affects the amount that must be paid back to the lender, including the principal amount and any additional interest charges.

Rachel's monthly payment of $320 will only cover the interest on her debt and will not significantly reduce the outstanding balance. She would need to pay more each month or find a way to reduce the interest rate in order to pay off her debt in a reasonable amount of time.

To calculate the time it will take for Rachel to pay off her debt, we can use the following formula:

n = ceil(log(P/A) / log(1 + r))

where n is the number of payments, P is the initial balance, A is the monthly payment, and r is the monthly interest rate (expressed as a decimal).

In this case, P = $8,975, A = $320, and r = 17% / 12 = 0.17 / 12 = 0.01417.

So, n = ceil(log($8975 / $320) / log(1 + 0.01417)) = ceil(log(28.09375) / log(1.01417)) = ceil(4.3626) = 5.

It will take Rachel 5 months to pay off her debt at her current monthly payment rate. This means that it will take her just over 4 years to pay off the debt, assuming no additional purchases are made on the card and the interest rate does not change.

As for shopping for a new card, Rachel should consider a card with a lower interest rate. This will allow her to pay off her debt more quickly and save money in interest charges. She may also consider a balance transfer card with an introductory 0% interest rate, which would give her time to pay off the debt without accruing interest. However, she should be aware of any balance transfer fees that may apply. It is best for Rachel to compare options and read the fine print before making a decision.

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The amount of the fabric is 4 / 3 yards.

Let's call the amount of fabric used to make each pillow "x".

Then, the total amount of fabric used was 12 * x = 16 yards.

Solving for x, we get x = 16 / 12 = 4 / 3 yards.

Since fabric is typically sold in whole yards, the answer lies between 1 and 2 yards.

The answer, 4 / 3 yards,

This can be rounded up to 1 yard or rounded down to 1 1/3 yards.

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The number of students that signed up for only language art is 116

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

n( of Math and language only) = 20-2 = 18

n( of Math and humanities only) = 5-2 = 3

n( of humanities and language only) = 10-2 = 8

n( math only) = 68-(18+2+3)

= 68 - 23 = 45

n( humanities only) = 40-( 8+3+2)

= 40-13 = 27

represent number of student Who signed up for language by x

n( of language only) = x-( 18+2+8)

=x- 28

219 = 45+27+18+2+3+8+x-28

219 = 75 +x

x = 219-75

x= 144

therefore number of students that signed from language art only = 144-28

= 116

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Answer:

2 right, 4 down

Step-by-step explanation:

By subtracting 2 inside the function, the graph is shifted 2 to the right and by subtracting 4, it is shifted 4 down.

To think of this more intuitively, in the original function, inputting 0 would  yield the same output as plugging in a function with (x - 2) inside:

[tex]x^3=0^3=0\\(x-2)^3=(2-2)^3=0^3=0[/tex]

In addition, by subtracting -4, the value would always go down 4 from the original value of x^3:

[tex]x^3 = 0^3 = 0[/tex]  

[tex]x^3-4 = 0^3-4=0-4=-4[/tex]

By putting these together we get the answer above.

Answer: A.

Step-by-step explanation:

Sarah made 6 dozen cupcakes which is (12 x 6)

Then if her co-workers or c ate 3 cupcakes EACH, it will be (c x 3)
and since they ate them it's subtraction with a left over of 45 cupcakes

Answer:

D. All of the above

Step-by-step explanation:

Answer:

D. All of the above

Step-by-step explanation:

If you were to base your reading on one article and nothing else, your chances of possibly misinterpreting information and sending false narratives are more possible. That is why you should always do as much research as you can.

Answer:

x = 28

Step-by-step explanation:

Consider the two triangles ΔAPR and ΔCDR

We see that AP ║ CD

Therefore m∠PAR = m∠CR, m∠APR= m∠CDR
Angle ∠R is common to both triangles

So the triangles are similar

Therefore the ratios of the sides must be the same ratio

[tex]\dfrac{AR}{CR} = \dfrac{PR}{DR}\\\\[/tex]

AR = x + 10

CR = x

PR = 42 + 15 = 57

DR = 42

PR = 42 + 15 = 57

Plugging in the values for these sides:

[tex]\dfrac{x + 10}{x} = \dfrac{57}{42}\\[/tex]

Cross-multiplying we get

[tex]42(x + 10) = 57x\\\\42x + 420 = 57x\\\\420 = 57x - 42x = 15x\\\\15x = 420\\\\x = 420/15\\\\= 28[/tex]

Answer:

Step-by-step explanation:

When someone has a growth mindset they believe that they can continue to learn and become more intelligent with effort.

Answer:

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months. you will have 800,000 after 20 years.

Step-by-step explanation:

rate of return is 5.3% compounded monthly.

number of years = 40.

future value = 800,000

interest rate per month is 5.3% / 12 = .4416666....%

number of time periods if 40 * 12 = 480

payment required at the end of each month is equal to 484.5267545

your total payments are 480 * 484.5267545 = 232,572.8422

total interest earned would be 800,000 minus 232,572.8422 = 567,427.1578

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months.

you will have 800,000 after 20 years.

if you deposit that money for an additional 10 years at the same rate of interest per year compounded annually, then you will have 1,357,560.674.

you can use an online calculator to get the results similar to this.

they might not be right on because of possible rounding errors, but they'll be close.

The amount of money Camilla gave the cashier is

$11.68

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

For example, if there are 20mangoes and 20 oranges are in a basket, the total number of fruit is 20+20 = 40 fruits

Camilla bought a duffel bag for $10.73 and he collected $0.95 as change.

Therefore the total money he gave to the cashier is $10.73+$0.95 = $11.68

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The triangle ABC is vertically translated only. Then the correct option is B.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

We know that;

Reflection does not change the size and shape of the geometry.

Rotation does not change the size and shape of the geometry.

Translation does not change the size and shape of the geometry.

Here, On a coordinate plane, triangle ABC is shifted 5 units up to form triangle A'B'C'.

The diagram is given below.

From the diagram, we can clearly observe that the triangle ABC is vertically translated only.

Then, The correct option is B.

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The total length on each side of the 5 foot painting is given by the equation A = 5 feet each

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total length on each side of the 5 foot painting be A

Now , the equation will be

The length of the painting = 5 feet

The length of the wall = 15 feet

So , when 5 foot wide painting is centered on a 15 foot wide wall , the remaining space will be

2A = length of the wall - length of the painting

Substituting the values in the equation , we get

2A = 15 - 5

2A = 10 feet

Now , total length on each side of the 5 foot painting A = 10 / 2

On simplifying the equation , we get

The total length on each side of the 5 foot painting A = 5 feet

Hence , the equation is A = 5 feet

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Answer:  A; The probability of landing on blue is greater than the probability of landing on purple.

Step-by-step explanation: This statement is true because you need to analyze the problem. Since there is a 3/6 or 1/2 chance of getting a blue, it is higher than getting a purple spot, which is 2/6 or 1/3. So, we can model our answer as:

3/6 > 2/6

or

1/2 > 1/3

I hope this helped!

The wrap has an area of  1.12π square inches.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The net of a cylinder with a diameter of both circles labeled 1.6 inches.

So, The complete circle or the circumference of the circle will be the length of the wrap which is,

= 2π×0.8.

= 1.6π and the height of the wrap is 0.7 inches.

Therefore, the area of the wrap is 1.6π×0.7 square inches.

= 1.12π square inches.

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Answer: The real answer is 2.4π square inches (B)

Step-by-step explanation:

(Get ready for a long explanation)

So, we are trying to find the Surface Area of the cylinder.

We need to use the formula (SA = 2πr^2 + 2πrh)

Looks like a very long formula, but let do it in parts.

So the first part is just finding the area of the circle and multiplying by 2 because there are two bases. The area formula for circles is (πr^2)

But this time put a 2 in there. (2πr^2)

Okay lets get started. The diameter is 1.6. The radius is half the diameter, so divide 1.6 by 2 and you will get 0.8 which is the radius.

Now times the radius by itself (0.8 * 0.8 = 0.64) Now times that by 2 (0.64 * 2 = 1.28) The answer should be in terms of pi so just put the pi symbol next to 1.28  (1.28π)

On to the next part, (2πrh) you are basically taking the circumference of either circle base, and multiplying that by the height, which is (0.7)

The formula for Circumference is (2πr)

We already have the diameter so we don't need times the radius by 2.

So take the diameter of the circle base (1.6) and multiply that by the height, which is (0.7)
(1.6 * 0.7 = 1.12π)

Now for the last part, we need to add the two values together to find the surface area.

The first value we found is (1.28π ) and the second is (1.12π)

Now add (1.28π  + 1.12π = 2.4π)

Answer: 2.4π square inches

Sorry for the really long explanation. I took the same test and I got it right so here is proof that it is correct. Have a great day y'all.

We have compared the given expression using inequalities

[tex]1/4+2/5 > 1/4+1/5[/tex]

[tex]\frac{16}{20} > \frac{9}{20}[/tex].

What is the comparison of factor?

When evaluating a job, factor comparison is a systematic, scientific process that evaluates candidates according to a number of characteristics rather than grading the job as a whole.

Given:

[tex]1/4+2/5 \\ 1/4+1/5[/tex]

Cross multplying the  fractions:

[tex]\frac{1}{4}+\frac{2}{5}[/tex]  = [tex]\frac{4}{20}+ \frac{8}{20}[/tex]

         = [tex]\frac{12}{20}[/tex]

         =[tex]\frac{4}{5}[/tex]

Similarly ,

[tex]\frac{1}{4}+ \frac{1}{5}[/tex]=[tex]\frac{5}{20} +\frac{4}{20}[/tex]

        =[tex]\frac{9}{20}[/tex]

Compare 4/5 and 9/20.

Find the LCD:

The multiples of 5 are 5, 10, 15, 20, 25, etc. The multiples of20 are 20, 40, 60, 80, etc. The lowest common multiple is 20 so we use that as the lowest common denominator.

Convert each fraction to its equivalent fraction using the LCD.

For 4/5, multiply numerator and denominator by 4 to have LCD = 20 in the denominator.

=[tex]\frac{4}{5} *\frac{4}{4}[/tex]=[tex]\frac{16}{20}[/tex]

For 9/20,  20 is the denominator.

Compare the fractions. Because there are like denominators you can compare the numerators.16 is larger and 9 is smaller so,

[tex]\frac{16}{20} > \frac{9}{20}[/tex]

so,

[tex]1/4+2/5 > 1/4+1/5[/tex]

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If you already chopped 4 walnuts and you have only gotten 1/4 cup of the chopped walnuts, it means that each walnut yields 1/4 cup / 4 walnuts = 1/16 cup of chopped walnuts.

To find out how much more chopped walnuts you need, we can subtract the amount you have from the total amount the recipe calls for:

1 cup - 1/4 cup = 3/4 cup

So you need 3/4 cup of chopped walnuts more.

To find out how many more walnuts you should chop, divide the amount you need by the amount each walnut yields:

3/4 cup / (1/16 cup/walnut) = 12 walnuts

So you should chop 12 more walnuts to get the desired amount.

Answer: 0.6

Step-by-step explanation:

Answer: I believe its 6%

Step-by-step explanation:

so sorry if i'm wrong

There are a total of 2285 people in the given town.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, fourteen percent of the town's population is above the age of 65.

Since there are 320 residents who are above the age of 65,

Thus,

14% of the population = 320

So,

1 % of the population = 320 /14

Thus,

Total population = 320/14 * 100

Total population of the town = 2285.71

Therefore, there are a total of 2285 people in the given town.

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Answer:

He includes foreshadowing to indicate events

to come

On solving the provided question, we can say that In rectangle, the two diagonals are in congruence , the diagonals bisect each other. PT=TR=ST=TQ=1/2PR=1/2QS =1/2×22.8=11.4

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Rectangle, two diagonals are in congruence

⇒PR=QS=22.8

The diagonals bisect each other.

⇒PT=TR=ST=TQ=1/2PR=1/2QS

=1/2×22.8=11.4

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Answer:

5, second choice

Step-by-step explanation:

When x is 3, the purple line's y-value is between 4 and 6, which is 5.

Answer:

B

Step-by-step explanation:

You have two black lines with the arrows at the end. The one going left and right is your X-Axis. The one going up and down is the Y-Axis.

What they want to know is what is f(x) when x = 3

f(x) is another term for y

So they want to know, what is the value of the y-axis when x is 3 on the x-axis.

So on the line going left and right you find the line 3, between 2 and 4, then going up until you hit the purple line. Once you hit the purple line, go left until you hit the up and down line. That will give you an answer of 5

Answer:

six hindered twenty seven thousand three hundred ninety one

Step-by-step explanation:

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Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{h(x)}{y}~~ = ~~2x^3+3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^3 + 3} \\\\\\ x-3=2y^3\implies \cfrac{x-3}{2}=y^3\implies \sqrt[3]{\cfrac{x-3}{2}}=y=f^{-1}(x)[/tex]

The Answer is B because we use pemdas (parentheses)(exponents)(multiplication)(division)(addition)(subtraction)

so first is what is inside of the parentheses which is a subtracting equation number b is subtraction so the answer is b