The Wertz car rental company charges $45 to rent a Mustang convertible, plus $42 per day. Write the cost of renting the car as a function of the number of days rented. Use your function to find how much it would cost to keep the car for a week

Option C:

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]

Solution:

Given expression is [tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex].

To find the product of the above expression.

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex]

First multiply the numerical coefficients.

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{2} y^{3} x^{5} y^{8}[/tex]

Arrange the terms with same base.

                         [tex]=21 x^{2} x^{5} y^{3} y^{8}[/tex]      

Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

                        [tex]=21 x^{2+5} y^{3+8}[/tex]

                        [tex]=21 x^{7} y^{11}[/tex]

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]

Hence option C is the correct answer.

Answer:

d = 10.630146

Step-by-step explanation:

Formulae for calculating the distance between two points on a graph is

√ (x2 − x1)2 + (y2 − y1)2

Let the given points be (3,-1) where 3 is x1 and -1 is y1 and the other point is (-5,6) where -5 is x2 and 6 is y2

√[(-5-3)^2+(6-(-1))^2]

And on solving, we get d = 10.630146

Answer:

B. 3 g/mL

Step-by-step explanation:

The first thing is to know the density formula:

Density is given as follows:

d = m / V

let m: mass and V: volume.

We have that the mass of the metal is 1800 grams and the volume of 600 milliliters.

Therefore, replacing:

d = 1800/600 = 3 g / mL

That is, the density is 3 grams per milliliter.

Answer: B. 3

Step-by-step explanation: I Just Took the Test

Answer:

32

Step-by-step explanation:

When you multiply 40 by 20% or 0.20, the product will be the amount of games he lost. When you subtract 40-8 you get how many games he won.

Answer:

r = 9ft

h = 4ft

Step-by-step explanation:

Step-by-step explanation:

see.... l is a perpendicular bisector of m.... so line l makes an angle 90° with m

so equation becomes

6(2x+1)= 90

12x + 6 = 90

12x = 90 - 6

12x = 84

x = 7

Hope it helps you

Thank you

Answer:

y = [tex]\frac{1}{3}[/tex] x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 1 ← is in slope- intercept form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex], thus

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (6, 3) into the partial equation

3 = 2 + c ⇒ c = 3 - 2 = 1

y = [tex]\frac{1}{3}[/tex] x + 1 ← equation of perpendicular line

The equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3) is y = 1/3x + 1

To find the equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3), we first need to find the slope of our new line. The slope of a line perpendicular to another is the negative reciprocal of the original slope. Since the slope of the original line is -3, the slope of the new, perpendicular line will be 1/3.

The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We already have the slope, m = 1/3, and a point through which the line passes (6, 3). Substituting these values into the equation gives us 3 = 1/3 * 6 + b. Solving for b gives us b = 1.

Therefore, the equation of the line that is perpendicular to y = -3x + 1 and passes through the point (6, 3) is y = 1/3x + 1.

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Answer:

y= −9.16x²+73.04x+183.3

Values increase till x = 4 and then decrease which means thus curve has a maximum turning point around 4.

Coefficient of x² should be negative

because max to (concave down)

x = -b/2a should be around 4

x = -73.04/(2×-9.16) = 3.987

Answer:

dot plots are best used to show a distribution of data

Answer:

Dot plots are best used for a.Dot plots are best used to show a distribution of data.

Step-by-step explanation:

Answer:

Part 1) [tex]30\ coupons[/tex]

Part 2) [tex]12\ sandwiches[/tex]

Part 3) [tex]60\ push-ups[/tex]

Part 4) [tex]96\ minutes[/tex]

Part 5) [tex]\$95[/tex]

Part 6) [tex]1\frac{7}{8}\ cups\ of\ pretzel[/tex]

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

so

Using proportion

Find out the number of salads you could buy to get $10 in coupons

[tex]\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons[/tex]

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

[tex]\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches[/tex]

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does  15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

[tex]\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups[/tex]

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

[tex]1\ h=60\ min[/tex]

[tex]\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes[/tex]

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

[tex]\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25[/tex]

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

[tex]\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70[/tex]

step 3

Adds the amount earned by Aly plus the amount earned by Janet

[tex]25+70=\$95[/tex]

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

[tex]1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix[/tex]

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

[tex]\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel[/tex]

Convert to mixed number

[tex]\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel[/tex]

Answer:

The answers are as given

4.36 + 2.89 is equal 7.25 and 6.8 - 5.42 is equal 1.38

Step-by-step explanation:

4.36 + 2.89 = 7.25

6.8 - 5.42 = 1.38

Answer:

7.25

1.38

Step-by-step explanation:

a)  For first addition

4.36 + 2.89

Start adding from the right side. Take the last number and add them together.

9+6 = 15.................. write 5 and keep 1

Bring forward the kept "1"

3+8 + 1 = 12............. write 2 and keep 1

Bring forward the kept "1"

4+2 + 1 = 7...............write 7

∴ 7.25

b) For second subtraction

6.8 - 5.42 = 1.38

Start from the right side of each number

0 - 2 requires that you borrow "1" from "8" now turning "0" to "10" and "8" to "7".

now, 10 - 2 = 8...........write 8

         7 - 4 = 3.............write 3

         6 - 5 = 1..............write 1

∴ 1.38

1 1/4 cups to make 1 pie

So,

1 1/4 = 5/4 * 4 pies

=20/4 = 5 cups of sugar.

She has 1/2 cups of sugar so she will need 4 1/2 cups more

Answer:

4x-11(simplified)

x=2.75(solved, if needed)

Step-by-step explanation:

Simplify like terms

4x(-8-3)

4x-11

If you wanted it solved,

4x=11 (adding 11 to both sides)

x=2.75 (divide by 4)

Answer: x=2.75 or without simplifying 4x-11

hope it helps please give brainliest!

Step-by-step explanation:

[tex]4x-8-3\\4x-11\\[/tex]

This is the farthest you can go but you can simplify to...

[tex]4x-11\\x-\frac{11}{4}\\ x-2.75\\-x=-2.75\\/-1 /-1\\x=2.75[/tex]

Answer :

Toby: 4 of the $1.64, 1 of the $0.77, and 1 of the $3.59

Elisa: 3 of the $3.59

Heidi: 3 of the $3.59, and 1 of the $0.77

The question is a math problem about calculating the total cost of purchased fruits within a given budget. It requires us to determine the fruit combinations that match the total spending amount and the number of items bought for each individual.

The problem is a typical mathematics question focusing on money and budgeting. Toby, Elisa, and Heidi each have a budget between $10 and $12 to spend on fruit. Each fruit item's cost is given, and we need to assign a combination of fruits to each person that matches their total spending amount. Toby bought 6 items, Elisa bought 3, and Heidi bought 4.

For example, if Toby bought 6 bananas at 20 cents each, his total would be $1.20. As he needs to spend between $10 and $12, you would continue to mix and match the rest of the fruits until his purchase meets the criteria of total amount spent and number of items bought.

Option C: [tex]a=3, b=4[/tex] is the value of a and b

Explanation:

Given that the expression [tex]\sqrt{648}=\sqrt{2^a\times3^b}[/tex]

We need to determine the value of a and b

Let us consider the term [tex]\sqrt{648}[/tex] and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

[tex]648=2 \cdot 324[/tex]

324 divides by 2,

[tex]648=2 \cdot 2 \cdot 162[/tex]

162 divides by 2,

[tex]648=2 \cdot 2 \cdot 2 \cdot 81[/tex]

81 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27[/tex]

27 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9[/tex]

9 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3[/tex]

Thus, we have,

[tex]\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}[/tex]

Therefore, equating the powers of 2 and 3, we get,

[tex]a=3, b=4[/tex]

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

The values of a and b which make the equation true are; a = 3 and b = 4 respectively.

From the question; the expression given is;

[tex] \sqrt{648} = \sqrt{ {2}^{a} \times {3}^{b} } [/tex]

In essence; we have;

By expression of of 648 as the product of its lowest factors; we have;

In which case; we have;

Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.

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Brady White lost 4 pounds in the first month, leaving him at 193 pounds. To reach his goal weight of 184 pounds, he needs to lose an additional 9 pounds.

(a) To find out how much weight Brady White lost in the first month, we subtract his weight at the end of the month from his initial weight.

Initial weight = 197 pounds

Weight at the end of the first month = 193 pounds

So, the weight lost = Initial weight - Weight at the end of the first month

= 197 pounds - 193 pounds

= 4 pounds

Therefore, Brady White lost 4 pounds in the first month.

(b) To determine how much more weight Brady needs to lose to reach his goal of 184 pounds, we need to find the difference between his current weight and his goal weight.

Current weight = 193 pounds

Goal weight = 184 pounds

So, the amount of weight Brady needs to lose = Current weight - Goal weight

= 193 pounds - 184 pounds

= 9 pounds

Therefore, Brady needs to lose 9 more pounds to reach his goal weight of 184 pounds.

Complete question :- Brady White weighed 197 pounds when he decided to join a gym to lose some weight. At the end of the first month, he weighed 193 pounds. (Enter your answers as 2 simplified mixed numbers.)

(a) How much (in pounds) did he lose that month?

3 (b) If his goal is 184 pounds, how much more (in pounds) does he have to lose?

Answer:

Answer below, let me know if it didn't make sense.  

Step-by-step explanation:

I attached a picture of the scatterplot with a line connecting the points.  There is a definite upside down u type shape, and it doesn't look close to a line at all, so linear is not a good choice.  

an upside down u shape (or right side up u shape for that matter) is exactly what a quadratic is, or any polynomial if you do it right, but quadratic is the simplest, so let's go with that.

A linear representation is not the best way to represent the data from the equation gotten from the regression calculator.

Regression simply means a statistical measurement that is used to determine the strength of the relationship that exists between the dependent and independent variables.

In this case, a linear representation is not the best way to represent the data from the equation. A quadratic equation will have been more appropriate in this case.

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Answer:

The slope is 0/-8 zero

Step-by-step explanation:

To find the slope you use the equation m=Y2-Y1 m= -2-(-2) = 0

X2-X1 -9- (-1) -8

Answer:

For this, we can use the formula

A=P(1+rt).

We know that A=1,000, r=4%=0.04 and t=5, so we can rearrange the formula for P to give

P=A1+rt,

and substituting the known quantities gives

P=1,0001+(0.04)(5)=1,0001.2≈$833.33

to the nearest cent. So, to the nearest dollar she must deposit $833.

Step-by-step explanation:

Final answer:

Mary must deposit approximately $800 today into her account with a simple interest rate of 4% per year to have it worth $1,000 in 5 years.

Explanation:

To find out how much Mary must deposit today to have her account worth $1,000 in 5 years with a simple interest rate of 4% per year, we need to use the simple interest formula.

The formula for simple interest is I = P × r × t, where I is the interest, P is the principal amount (initial deposit), r is the annual interest rate (in decimal form), and t is the time in years.

The total amount A after t years is given by A = P + I. Since we know that A is $1,000, t is 5 years, and r is 0.04, we can rearrange the formula to solve for P:

In this case, the total interest earned in 5 years would be I = $1,000 - P. We can plug this into the interest formula: $1,000 - P = P × 0.04 × 5.

After simplifying, we'll find that P = $1,000 / (1 + 0.04 × 5), which calculates to P being approximately $800. So, Mary would need to deposit $800 today.

Jasmine calculates the selling price of her jewelry by adding a markup percentage to the cost price. The sale price is equivalent to the cost price plus the percentage markup applied to this cost. For example, if the jewelry cost is $10 with a markup of 20%, the selling price will become $12.

Jasmine's method of pricing involves costs and percentage markup into consideration. To determine the selling price, she first calculates the cost to make the jewelry. This could include the cost of beads, thread, and her time. Afterwards, she determines the percentage markup. This is the additional amount on top of the cost price to generate profit. The equation can be written as: Selling price = Cost price + (Percent markup/100 * Cost Price).

For example, if it costs her $10 to make a piece of jewelry and she uses a markup of 20%, the amount of markup added would be $2 (20/100 x $10). Therefore, she would sell the jewelry for $12 ($10 + $2).

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No. It is not true for all similar triangles.

Step-by-step explanation:

The measure of arcWUX in circle V of the given diagram with the circle geometry is; C: 120°

From the complete image as seen online, we can say that;

The measure of ∠WUX is similar to the measure of vertex ∠V.

To get the measure of angle V (∠V), we will use the sum of angles in a triangle theorem to get;

30 + ∠V + ∠X = 180

60 + ∠V = 180

∠V = 180 - 60

∠V = 120°

Since ∠V = arcWUX

Then, measure of arcWUX is 120°

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Answer: C. 120

Step-by-step explanation: First guy wrote out the math cause he's smart like that.

Answer:

16

Step-by-step explanation:

If it is compounded quarterly, that's 4 times a year.

If you do this for 4 years that's 4×4.

That would be 16.

We have been given invest $500 in an account that has a annual interest rate of 5%, compounded quarterly for four years. 16 times will the money be compounded.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We have been given invest $500 in an account that has a annual interest rate of 5%, compounded quarterly for four years.

Since the interest is compounded quarterly so it will be compounded 4 times a year.

Now, 4 x 4 is 16, so it will be compounded 16 times.

Then we have to divide the 5% by four to get how much will be compounded each quarter.

So, (0.05 / 4) = 0.0125, which is 1.25%.

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Answer:

a) rational

b) irrational

Step-by-step explanation:

a) 36 = 6²

So sqrt(36) = 6

b) 72 = 2 × 36

sqrt(72) = sqrt(2) × sqrt(36)

Since 2 is not a perfect square, sqrt(72) is irrational

Final answer:

√36 is a rational number because 36 is a perfect square, which results in a whole number when square rooted. However, √78 is an irrational number as it is not a perfect square and cannot be simplified to a fraction of two integers.

Explanation:

We are tasked with determining whether each given root, √36 and √78, is a rational or irrational number. First, we observe that √36 is the square root of 36. Since 36 is a perfect square (6 x 6), √36 equals 6, which is a rational number because it can be expressed as the quotient of two integers (6/1).

On the other hand, √78 is not a perfect square; its square root cannot be simplified to a whole number or a simple fraction of two integers. Therefore, √78 is an irrational number because it cannot be written exactly as a simple fraction or repeating or terminating decimal.

Answer:

Step-by-step explanation:

P(AUB)=P(A)+P(B)+P(A∧B),P(A∧B)=0 as both the events are independent.

P(AUB)=1/2+1/3=(3+2)/6=5/6

The probability value of P(A u B) is 2/3

The probability values are given as:

P(A) = 1/2

P(B) = 1/3

The required probability is then calculated using:

P(A u B) = P(A) + P(B) - P(A) * P(B)

This gives

P(A u B) = 1/2 + 1/3 - 1/2 * 1/3

Evaluate the product

P(A u B) = 1/2 + 1/3 - 1/6

Take the LCM

P(A u B) = (3 + 2 - 1)/6

Evaluate

P(A u B) = 2/3

Hence, the probability value of P(A u B) is 2/3

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Answer:

24

Step-by-step explanation:

36= 3 equal parts

so: 36/3 =12

One part=12

so 2 parts is 12*2

12*2=24mm is the answer

The measure of the matching side of the smaller triangle is 24 millimeters.

When dealing with similar triangles, the lengths of corresponding sides are proportional. This means that if one triangle has sides that are a constant multiple of the sides of another triangle, we can find the length of a matching side by using that constant multiple. In this case, the sides of the smaller triangle are said to be 2/3 the lengths of the sides of the larger triangle.

To find the matching side of the smaller triangle when a side of the larger triangle is 36 mm, we use the proportionality factor, which is 2/3. Therefore, the length of the corresponding side in the smaller triangle is 2/3 of 36 mm, which can be calculated as:

(2/3) * 36 mm = 24 mm

So, the measure of the matching side of the smaller triangle is 24 millimeters.

Answer:

5

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

C = 5/9 (f - 32)

since f = 68 and substitute it into the equation above

C = 5/9 ( 68 - 32)

C = 5/9 (36)

opening the bracket

C = 5/9 x 36

C = 180/9

C = 20

Step-by-step explanation:

x^3 - 5x^2 - 4x + 20 (I'm assuming this is what you meant)

(1)^3 - 5(1)^2 - 4(1) + 20 = 1 - 5 - 4 + 20 = 12

(-1)^3 - 5(-1)^2 - 4(-1) + 20 = -1 - 5 + 4 + 20 = 18

(2)^3 - 5(2)^2 - 4(2) + 20 = 8 - 20 - 8 + 20 = 0

Now I know (x-2) is a factor of the polynomial.

Synthetic division

2 | 1. -5. -4. 20

| 2. -6. -20

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

1. -3. -10. 0

x^2 -3x -10

Factor -> (x-5)(x+2)

So the factors of the original polynomial are (x-5), (x+2), and (x-2)

f(x) = 0 when x = -2,2,or 5