Mathematics High School

Chico is financing a car for $9,550 and an APR 8.9 percent for 3 years. What is his monthly payment if the monthly payment per $100 is $3.52?

A. $336.16

B. $352

C. $251.48

D. $235.24
(I divided 9550 by 100 and then multiplied that by 3.52 and got A but I don't know if that's the right way to do it)

Answers

Answer 1

235.24 is the answer is d

Answer 2

Answer:

A. $336.16

Step-by-step explanation:

The payment per $100 can be set up as a ratio:

[tex]\frac{3.52}{100}[/tex]

Let the unknown payment be x. Now setting up the ratio over the full value:

[tex]\frac{x}{9550}[/tex]

Set them equal and solve for x:

[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]

1[tex]100x=33616[/tex]

This gives x = $336.16

Therefore, the answer is option A.

Related Questions

Nadine is constructing a line perpendicular to KE←→ . She has constructed the arcs as shown. What is the next step in her construction? Use a straight edge to draw a line through D and M. Use a straight edge to draw a line through M and E. Use a straight edge to draw a line through M and K. The image shows a horizontal line with points K, D, and E from left to right. Point D looks halfway between points K and E. An arc is shown at point K turning inwards towards point D. An arc is shown at point E turning inwards towards point D. Above point D is point M. Two arcs go through point M. One arc faces southwest towards point K and one points southeast towards point E.

Answers

Given that Nadine is constructing a line perpendicular to KE←→ and that she has constructed the arcs as shown.

The next step in her construction is "Use a straight edge to draw a line through D and M."

Use a straight edge to draw a line through D and M. Point M is where the two arcs above the line intersect. This is where a line connecting D to M would be perpendicular to line KE.

Math problem : suppose you cut a sheet of papper into fourths and throw away three of the fourths. you cut the reminding fourths into fourths you repeat the process , each time cutting the paper into fourths and throwing away three of the fourths. after the sixth repetition what fraction of the original sheet of paper id left?

Answers

(1/4)^6 = 1/4^6 = 1/4096

Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work.

Answers

The mistake is that given that 6 and 7 are in the place of tenths, 6 tenths + 7 tenths means 13 tenths and that is 1 unit plus 3 tenths.

So 3.6 + 2.7 = 5 units + 1 unit + 3 tenths = 6 units + 3 tenths = 6.3

If you write 5.13 that is 5 units and 13 hundreeths which is wrong.

The procedure used by the student wont work when the addtion of the two digits is 10 or greater than 10. In those cases, you must pass the left digit to the next place and sum it to the other digits that are in that place since the beginning.

Not sure how to do this. (I'm aware this is wrong lol)

Answers

I think the answer is 80 degrees. Think about it like you're moving the chunk with 100 degrees already filled in, to the space where you're trying to find the amount since they're the same. Vertical angles are supplementary and are equal to 180. So, 100+x = 180. x would equal 80 degrees.

Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.

Answers

-5 and 1/4. hope it helps

Write an additional word problem in which the estimated sum is 14,000

Answers

10,000 + 4,000 = 14,000
7,000 + 7,000 = 14,000

Final answer:

The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.

Explanation:

The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?

First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000

This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.

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Markus receives dollar bills from his grandfather for one week on the first day he received $1 on the second day he received $2 on the third day he received $4 and on the fourth day he received $8 if this continues how much money will Marcos have by the end of the week

Answers

Marcos will have $127 by the end of the week

Answer:

127

Step-by-step explanation:

It gas geometric sequence,

We has a sequence: 1, 2, 4, 8, 16, 32, 64.

It can be solved by two method either sum these digits individually or use formula of sum of geometric sequence

We have formula: [tex]S_n=\frac{a_1(1-r^n)}{(1-r)}[/tex]

Here r = Common Ratio = 2 ÷ 1 = 4÷2 = 2

and a = First term = 1

⇒ [tex]S_n= \frac{1\times(1-2^7)}{(1-2)} \\\Rightarrow S_n=\frac{(1-128)}{-1}\\ \Rightarrow S_n=127[/tex]

If 15% of x is 42, what is x?

Answers

"x" is 100%, and 42 is 15% of that, so, what's "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 42&15 \end{array}\implies \cfrac{x}{42}=\cfrac{100}{15}\implies x=\cfrac{42\cdot 100}{15}[/tex]

Write 15% as a fraction= 15/100= 3/20 times x=42 thats one equation.
3/20x=42
x= 42* 20/3 (reciprocal)
x=14*20
x=406

The three interior angle measures of this triangle are x = °, y = °, and z = °.

Answers

x = 180 - 150 = 30
z = 180 - 100 = 80
y = 180 - (30+80) = 180 - 110 = 70

Answer:

30-70-80

Step-by-step explanation:

Write the following statement as a conditional. All flowers are beautiful.

Answers

If something is a flower, then it is beautiful.

Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg. Write an equation to determine the weight, w ww, of each of Carl's checked bags. Find the weight of each of his checked bags.

Answers

Let B equal how many bags

2+4b=35

35-2=33

33/4=8.25kgs

Answer:

15.5 kg (each)

Step-by-step explanation:

Let [tex]w[/tex] be the weight of each checked bag (there are 2). Thus, we can write, from the information given:

[tex]w+w+4=35\\2w+4=35[/tex]

Now we solve this equation for [tex]w[/tex] to find weight of each checked bag:

[tex]2w+4=35\\2w=35-4\\2w=31\\w=\frac{31}{2}\\w=15.5[/tex]

So, the weight of each of his checked bags is 15.5 kg.

Find the x -intercept and the y -intercept. Then use them to graph the line of 6x+2y=-12

Answers

the x intercept is when y=0
6x+0=-12
x=-2, now you have point A with coordinates (-2, 0)
The y intercept is when x=0
0+2y=-12
y=-6, so you have another point with coordinates (0, -6)
Connect those two points, you have your graph. It is a line.

Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?

Answers

First, let's write two expressions, letting x= the number of months which have elapsed:

Bill: 120 + 10x
Phil: 150 + 4x

If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:

120+10x = 150 + 4x [starting equation]
-120 -4x -120 -4x [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]

6x = 30 [divide both sides by 5]
5 5

x=6. They will weigh the same in six months.

Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.

it will take 5 months for Bill to weigh the same as Phil.

Let's represent the number of months they gain extra weight as: m

Step 1

Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :

120 ib + 10 ib x m

120 + 10m ........Equation 1

Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :

150 ib + 4 ib x m

150 + 4m ........Equation 2

Step 2

We equate equations 1 and 2 to each other

Equation 1 = Equation 2

120 + 10m = 150 + 4m

Collect like terms

10m - 4m = 150 - 120

6m = 30

Divide both sides by 6

6m/6 = 30/6

m = 5

Therefore, it will take 5 months for Bill to weigh the same as Phil

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The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].

Answers

Part A:

Given that the game of clue involves 6 suspects, 6 weapons, and 9 rooms.

The number of ways that one of each is randomly chosen is given by:

[tex] ^6C_1\times{ ^6C_1}\times{ ^9C_1}=6\times6\times9=324[/tex]

Therefore, the number of solutions possible is 324.

Part B:

Given that a players is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.

The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are: 6 - s, 6 - w, and 9 - r.

Let x denote the number of solutions that are possible after that player observes his or her three cards, then:

[tex]x={ ^{6-s}C_1}\times{ ^{6-w}C_1}\times{ ^{9-r}C_1}=(6-s)(6-w)(9-r)[/tex]

Therefore, x in terms of s, w, and r is given by x = (6 - s)(6 - w)(9 - r).

Part C:

The expected value E(x) of a data set [tex]x_i[/tex] with probabilities [tex]p(x_i)[/tex] is given by [tex]E(x)=\Sigma xp(x)[/tex]

There are [tex] ^{3+3-1}C_{3-1}={ ^5C_2}=10[/tex] possible combinations s, w and r. They are (3, 0, 0), (0, 3, 0), (0, 0, 3), (2, 1, 0), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (0, 1, 2), (1, 1, 1)

Thus the expected value is given by

[tex]E(x)=3\cdot6\cdot9p(3, 0, 0)+6\cdot3\cdot9p(0, 3, 0)+6\cdot6\cdot6p(0, 0, 3) \\ 4\cdot5\cdot9p(2, 1, 0)+6\cdot4\cdot8p(0, 2, 1)+5\cdot6\cdot7p(1, 0, 2)+4\cdot6\cdot8p(2, 0, 1) \\ +5\cdot4\cdot9p(1, 2, 0)+6\cdot5\cdot7p(0, 1, 2)+5\cdot5\cdot8(1, 1, 1) \\ \\ = \frac{1}{ ^{21}C_3} (162\cdot{ ^6C_3}\cdot{ ^6C_0}\cdot{ ^9C_0}+162\cdot{ ^6C_0}\cdot{ ^6C_3}\cdot{ ^9C_0}+216\cdot{ ^6C_0}\cdot{ ^6C_0}\cdot{ ^9C_3} \\ \\ +180\cdot{ ^6C_2}\cdot{ ^6C_1}\cdot{ ^9C_0}+192\cdot{ ^6C_0}\cdot{ ^6C_2}\cdot{ ^9C_1}[/tex]

[tex]+210\cdot{ ^6C_1}\cdot{ ^6C_0}\cdot{ ^9C_2}+192\cdot{ ^6C_2}\cdot{ ^6C_0}\cdot{ ^9C_1}+180\cdot{ ^6C_1}\cdot{ ^6C_2}\cdot{ ^9C_0} \\ \\ +210\cdot{ ^6C_0}\cdot{ ^6C_1}\cdot{ ^9C_2}+200\cdot{ ^6C_1}\cdot{ ^6C_1}\cdot{ ^9C_1} \\ \\ =\frac{1}{1,330}(324\cdot20+216\cdot84+360\cdot90+384\cdot135+420\cdot216+200\cdot324) \\ \\ =\frac{1}{1,330}(6,480+18,144+32,400+51,840+90,720+64,800) \\ \\ =\frac{1}{1,330}(264,384) \\ \\ =\bold{198.78}[/tex]

Answer:

(a) 324 solutions are possible

(b) (6 - s)(6 - w)(9 - r)

Step-by-step explanation:

Just a pure guess and also give brainliest to the other person

The volume of a cone is 1004.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.)

64
32
8
4

Answers

your answer is 8...........

Which inequality will have a shaded area above its graph?

a
x − 9y ≤ 1
b
4x + 3y < 6
c
2x − y ≥ 4
d
x − 3y > 4

Answers

x − 9y ≤ 1

Because If you solve the equation y will be greater than ...

x − 9y ≤ 1

Solve for y...

Subtract x from both sides...

- 9y ≤ - x + 1

Divide both sides by -9

REMEMBER WHEN DIVIDING OR MULTIPLYING BY A NEGATIVE NUMBER FLIP THE INEQUALITY SIGN....

y ≥ x/9 - 1/9

To find the inequality whose graph is shaded *above* the line, you’ll have to find the inequality in which y is greater than the right side of the inequality. This boils down to isolating y in each of these, but there’s a bit of a shortcut you can take if you know about how multiplying/dividing both sides of an inequality by a negative number flips the inequality.

If the coefficient of y is negative, you’ll have to flip the inequality sign around in the process of isolating y. Which of those options have negative coefficients for y, and how would flipping the inequality sign effect them? Try to find the one option where the inequality ends up facing the y.

Sharon is twice as old as brian, and in 5 years the sum of their ages will be 25 years. find their present ages.

Answers

Answer:

sharon=10

Step-by-step explanation:

The present age of Sharon and Brain is 10 years old and 5 years old.

Given,

Sharon is twice as old as brian.

In 5 years the sum of their ages will be 25 years.

We need to find their present ages.

What are the important terms in solving age problems?

Some of the terms are:

In x years - add x years to the present age

x years ago - Subtract x years with the present age

Before x years - subtract x years to the present age

After x years - add x years to the present age

Find the present age of Sharon and Brain.

Let the present age of:

Sharon - S

Brain - B

Now,

Sharon is twice as old as brian.

We can write this as:

S = 2B ____(1)

In 5 years the sum of their ages will be 25 years.

It can be written as:

(S + 5) + (B + 5) = 25

S + B + 10 = 25

S + B = 25 - 10

S + B = 15 _____(2)

From (1)

We get,

2B + B = 15

3B = 15

B = 5. ______(3)

Putting (3) in (2)

S + 5 = 15

S = 15 - 5

S = 10

We have,

B = 5 and S = 10

Thus the present age of Sharon and Brain is 10 years old and 5 years old.

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Simplify the expression (20-14)^2 divided by 12

A)1

B)3

C)17

D)0.5

Answers

(20-14)^2 / 12

6^2 / 12

36 / 12 = 3

B) 3

Hope this helps!

Answer:

The correct option is B) 3.

Step-by-step explanation:

Consider the provided expression.

(20-14)^2 divided by 12

The above statement can be written as:

[tex]\frac{(20-14)^2}{12}[/tex]

[tex]\frac{(6)^2}{12}[/tex]

[tex]\frac{6\times 6}{12}[/tex]

[tex]\frac{36}{12}[/tex]

3 times 12 is 36,

[tex]3[/tex]

Hence, the simplified form of the provided expression is 3.

Therefore, the correct option is B) 3.

Find the specific formula for the sequence. [−3,1,5,9,13,...]

Answers

x+4 is the specific formula for sequence [−3,1,5,9,13,...]

What is Sequence?

A sequence is defined as an arrangement of numbers in a particular order.

The given sequence is

−3,1,5,9,13,...

-3+4=1

1+4=5

5+4=9

9+4=13

As we can see above, to get from one number to the next it is simply adding 4. So the formula for sequence is x + 4.

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In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.

Answers

Based on the information about side JK = side JL, then we know it is at least an isosceles triangle. Furthermore, ∡K =∡L because they are the base angles in an isosceles triangle.
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
∡K = ∡L = 23

m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.

From the figure attached,

JK and JL are equal sides of the triangle.m(∠J) = 23x - 4m(∠K) = 4x - 1m(∠L) = 9x - 31

Since, two sides JK and JL of ΔJKL are equal in measure,

Therefore, ΔJKL is an isosceles triangle.

By the property of an isosceles triangle, opposite angles of the equal sides are equal.

Therefore, m(∠K) = m(∠L)

4x - 1 = 9x - 31

9x - 4x = 31 - 1

5x = 30

x = 6

By substituting the value of 'x' in the measures of each angle,

m(∠J) = 23x - 4

= 23(6) - 4

= 138 - 4

= 134°

m(∠K) = 4x - 1

= 4(6) - 1

= 24 - 1

= 23°

m(∠L) = 9x - 31

= 9(6) - 31

= 23°

Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.

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The area of a circle is found with the formula a = , where represents 3.14. if a tile artist is placing tiles in a circular mosaic pattern and the area of the circle is 658 square feet, what is the approximate radius of the circle in feet?

Answers

3.14 r^2=658
r=14.47 ft

Answer:

Step-by-step explanation:

Area = 3.14πr^2

We know that the area of the circle is 658. Divide 658 by 3.14 which equals 209.5 ( rounded to the nearest whole number is 210). The square root of 210 is 14.4 and rounding to the nearest whole number is 14.

Deshawn has several dimes and quarters that total $2.05. he has 3 fewer quarters than dimes. how many of each doe he have

Answers

Let
x = the number of dimes
y = the number of quarters

The total sum is $2.05, therefore
0.10x + 0.25y = 2.05
Divide through by 0.05 to obtain
2x + 5y = 41 (1)

There are 3 fewer quarters than dimes, therefore
y = x - 3 (2)

Substitute (2) into (1).
2x + 5(x - 3) = 41
2x + 5x - 15 = 41
7x = 56
x = 8
y = x - 3 = 5

Answer: 8 dimes, 5 quarters

Please help asap!!! I will mark brainliest!

Estimate 27.89 • 10.3 divided by 4.37 using compatible numbers

Answers

original answer: 65.7
if you round your answer= 66.0

i think its 66.7
hope this help!

The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?

Answers

The profit function is given by [tex]$ P(x) = -0.0002x^2 + 26x - 120,000 $.[/tex]

To find the expression for the profit, we need to subtract the cost function from the revenue function.

Given:

Cost function: [tex]$ C(x) = 14x + 120,000 $[/tex]

Revenue function: [tex]$ R(x) = 40x - 0.0002x^2 $[/tex]

The profit function, ( P(x) ), is given by:

[tex]\[ P(x) = R(x) - C(x) \][/tex]

Substitute the given functions into the profit function:

[tex]\[ P(x) = (40x - 0.0002x^2) - (14x + 120,000) \][/tex]

Now, let's simplify:

[tex]\[ P(x) = 40x - 0.0002x^2 - 14x - 120,000 \][/tex]

[tex]\[ P(x) = 26x - 0.0002x^2 - 120,000 \][/tex]

This is the expression for the profit:

[tex]\[ {P(x) = -0.0002x^2 + 26x - 120,000} \][/tex]

So, the profit function is given by [tex]$ P(x) = -0.0002x^2 + 26x - 120,000 $.[/tex]

Write an equation for the line that is parallel to the given line and that passes through the given point.
y equals five halves x minus 10; the point negative 6, negative 29

A. y equals five halves x plus one hundred thirty three halves

B. y equals five halves x minus 14

C. y equals two fifths x minus 14

D. y equals negative two fives x plus 14

Answers

Answer:

The correct option is B.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

The given equation is

[tex]y=\frac{5}{2}x-10[/tex]

It means the slope of the line is 5/2 and y-intercept is -10.

The slope of two parallel lines is same. So, the slope of required line is 5/2.

The equation of required line is

[tex]y=\frac{5}{2}x+b[/tex]

It is given that the line passes through the point (-6,-29).

[tex](-29)=\frac{5}{2}(-6)+b[/tex]

[tex]-29=-15+b[/tex]

[tex]-29+15=+b[/tex]

[tex]-14=b[/tex]

The y-intercept of required line is -14. So the equation of required line is

[tex]y=\frac{5}{2}x-14[/tex]

Therefore the correct option is B.

Answer:

the answer is B. y equals five halves x minus 14

Step-by-step explanation:

hope it helps

For what values of x does 25^x = 5^x^2-3?

Answers

Attached solution with detailed work.

The values of x that satisfy the given equation are -1 and 3

What is an indical equation?

From the question, we are to determine the values of x that satisfy the given equation

The given equation is

25^x = 5^x^2-3

The can be written as

[tex]25^{x} =5^{x^{2} -3}[/tex]

Expressing 25 in index form, we get

[tex]5^{2x} =5^{x^{2}-3 }[/tex]

Now, equate the powers (since the bases are equal)

[tex]2x =x^{2}-3[/tex]

Then, we have that

[tex]x^{2} -2x-3 =0[/tex]

Solve quadratically

Using the factorization method, we get

[tex]x^{2} -2x-3 =0[/tex]

[tex]x^{2} -3x+x-3 =0[/tex]

[tex]x(x-3)+1(x-3)=0[/tex]

[tex](x+1)(x-3) =0[/tex]

∴ x+1 = 0 OR x-3 = 0

x = -1 OR x = 3

Hence, the values of x that satisfy the given equation are -1 and 3.

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Write a function g in terms of f so that the statement is true.

The graph of g is a reflection in the y-axis of the graph of f
g(x)=

Answers

Final answer:

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

Explanation:

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

To reflect a point across the y-axis, we change the sign of the x-coordinate. So, to reflect the graph of f(x) across the y-axis, we need to change the sign of f(x). This can be achieved by multiplying f(x) by -1, giving us g(x) = -f(x).

For example, if f(x) = 2x+3, then g(x) = -(2x+3) = -2x-3.

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Final answer:

The function g(x) that represents a reflection in the y-axis is g(x) = -f(x).

Explanation:

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

To reflect a graph in the y-axis, we replace each x-coordinate with its opposite (negative value) while keeping the y-coordinate unchanged. In this case, since g is the reflection of f in the y-axis, the function g(x) will have the same y-values as f(x), but the x-values will be their negatives.

For example, if f(x) = 2x + 3, then g(x) = -f(x) would be g(x) = -2x - 3, where the graph of g(x) is the reflection of f(x) across the y-axis.

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What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?

Enter your answer in the box. Do not round any side lengths.

Answers

Let A, B, C, D, E be the given points in order.
AB=4-1=3
BC=√((7-4)²+(2-(-2))²)=√(9+16)=√25=5
CD=BC=5
DE=4-1=3
AE=6-(-2)=8
Perimeter=3+5+5+3+8=24.

Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.

What is the Perimeter of a Polygon?

Perimeter = sum of all sides of the polygon.

Name the vertices as follows:

A(−2, 1)B(−2, 4)C(2, 7)D(6, 4) E(6, 1)

Perimeter of the polygon = AB + BC + CD + DE + EA

Use the distance formula, [tex]d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find the length of each segment:

AB = |1 - 4| = 3 units

BC = √[(2−(−2))² + (7−4)²]

BC = 5 units

CD = √[(2−6)² + (7−4)²

CD = 5 units

DE = |4 - 1| = 3 units

EA = |6 - (-2)| = 8 units

Perimeter of the polygon = 3 + 5 + 5 + 3 + 8

Perimeter of the polygon = 24 units

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Solve 4(c + 2) < 4c + 10.

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4(c + 2)< 4c + 10
4c + 8 < 4c + 10
4c - 4c < 10 - 8
0 < 2...no variables
this inequality has no solution

[tex]4(c + 2) \ \textless \ 4c + 10[/tex]

[tex]4c+8\ \textless \ 4c+10 [/tex]

[tex]8\ \textless \ 10 [/tex] [tex]\text{Cancel 4c on both sides}[/tex]

[tex]\text{Since}[/tex] [tex]8\ \textless \ 10 [/tex] [tex]\text{is always true, there are infinitely many solutions}[/tex]

How does finding the square root of a number compare to finidng the cubic root of a number?

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A square root means the number is multiplied by itself twice and a cubic root means the number is multiplied by itself thrice

Final answer:

Square rooting and cube rooting are processes to find a number that, when raised to the second or third power respectively, equals the original number. Square roots are related to squares, and cube roots are related to cubes; both functions are essential in solving various mathematical problems, including equilibrium and Pythagorean Theorem problems.

Explanation:

Finding the square root of a number is the process of determining a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 squared (5²) is 25. This can be expressed using exponents as x¹⁄₂ = √x.

On the other hand, finding the cube root of a number involves determining a number which, when multiplied by itself twice (or cubed), results in the original number. For instance, the cube root of 27 is 3, since 3 cubed (3³) equals 27. The formula for a simple equilibrium problem that involves cubic roots is a³ = M₁ × P², where you would then find the cube root of the result to solve for 'a'.

Both operations are inverse functions: square rooting is the inverse of squaring, and cube rooting is the inverse of cubing. When dealing with equilibrium problems or Pythagorean Theorem applications, it's important to know how to perform these operations, often requiring a calculator. Make sure you are comfortable with your calculator's functions for these operations, or seek assistance from your instructor if needed.

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