As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.

Answer:

5 Packages

Step-by-step explanation:

40 / 8 = 5

Answer:

5x + 15 = -5x - 15

10x = -30

x = -3

y = 5(-3) + 15 = -15 + 15 = 0

(-3,0)

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

The function in the graph is an exponential growth function.

Therefore its equation is [tex]g(x)=3^x[/tex]

A transformation that shrinks this graph is of the form: [tex]f(x)=k*3^x[/tex] where [tex]0\:<\:k\:<\:1[/tex]

From the given options, we must have [tex]k=\frac{1}{2}[/tex]

This implies that:

[tex]f(x)=\frac{1}{2} (3)^x[/tex]

Answer:

B

Step-by-step explanation:

Answer:

4+ x/2 =6

Step-by-step explanation:

Let  the number be X

half of the number is 1/2 multiply X= X/2

Four increased by half the number is 4+X/2

Therefore, Four increased by half of anumber is equal to six is written as

4+ x/2 =6

Final answer:

It would have taken Janet about 9.7536 pages to read..

Explanation:

To determine Janet's reading progress, her reading speed is multiplied by the duration she read. With a reading speed of 3.6 pages per minute, if Janet read for 2.71 minutes, the calculation is 3.6 multiplied by 2.71, resulting in 9.7536. Hence, Janet would have read approximately 9.7536 pages. This calculation showcases how the product of reading speed and time provides a quantitative measure of reading accomplishment. It's a straightforward way to estimate the amount of material covered within a specific timeframe, offering insights into reading efficiency and progress.

Total area is 102.3 yd²

Step-by-step explanation:

Total area = area of the parallelogram + area of the right triangle

Calculate the area of the parallelogram.

Base = 11 yd, Height = 6.2 yd

⇒ Area of the parallelogram = Base × Height = 11 × 6.2 = 68.2 yd²

Calculate the area of the right triangle.

Height = 6.2 yd, Base = 11 yd (Since opposite sides of a parallelogram are equal)

⇒ Area of the triangle = 1/2 × base × height = 1/2 × 11 × 6.2 = 34.1 yd²

Calculate the total area.

⇒ Total area = 68.2 + 34.1 = 102.3 yd²

Answer:

Well no cheating not from me

Step-by-step explanation:

Answer:

Step-by-step explanation:

94 dollars

Answer:

The discount would be $94.50 but the final price would be $220.25.

Hope this helps!

a) ASA congruency

b)SAS congruency

c)SSS congruency

d) Not congruent

Step-by-step explanation:

Step 1:

a)

Angle PRQ = Angle RQS

Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.

QR is the common Side

Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.

Step 2 :

b)

Angle IGH = Angle EDF

Side IG = DF and Side GH = DE

Here 2 of the sides of the triangle are same and the Angle which is included are same.

Hence the given triangles are equal

Step 3:

c)

In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.

Step 4:

d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent

Answer:the answer is B

Step-by-step explanation:

The function that represents the exponential growth is

f(x) = 4 x [tex]1.05^n[/tex].

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

An exponential growth function.

Rate of change = 5%

This means,

There is a growth per year of 5%.

The function can be represented as,

f(x) = a [tex](1 +0.05)^n[/tex]

f(x) = a x [tex]1.05^n[/tex]

Where 100% = 1 and 5% = 0.05

Let a = 4

f(x) = 4 x [tex]1.05^n[/tex]

Thus,

The exponential growth function is

f(x) = 4 x [tex]1.05^n[/tex]

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

Answer:

36 batches

Step-by-step explanation:

we know that

Each bath of cookies used 2/9 cup of sugar

so

using proportion

Find out how many batches of cookies Melinda makes for 8 cups of sugar

[tex]\frac{1}{(2/9)}\ \frac{bath}{cups}=\frac{x}{8}\ \frac{bath}{cups}\\\\x=8/(2/9)\\\\x=36\ batches[/tex]

Answer:

The total number of fliers they gave out is 1368.

Step-by-step explanation:

Given:

Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood.

Now, to find the total number of fliers they gave out.

Let the total number of fliers be [tex]x.[/tex]

Number of fliers they gave out for a political campaign:

[tex]\frac{21}{38}\ of\ x[/tex]

[tex]=\frac{21}{38} \times x[/tex]

[tex]=\frac{21x}{38}[/tex]

Number of fliers remaining they gave out in another neighborhood = 612.

Now, to get the total number of fliers by putting an equation:

[tex]x-\frac{21x}{38} =612[/tex]

[tex]\frac{38x-21x}{38} =612[/tex]

[tex]\frac{17x}{38} =612[/tex]

Multiplying both sides by 38 we get:

[tex]17x=23256[/tex]

Dividing both sides by 17 we get:

[tex]x=1368.[/tex]

Therefore, the total number of fliers they gave out is 1368.

Answer:

$19.60

Step-by-step explanation:

$98 is made each week.

80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.

20%=.20

98•.20=19.6

$19.60 is spend on lunches each week.

Answer:

2x-5

remainder of 0

Step-by-step explanation:

Check the image

Answer:

yes

Step-by-step explanation:

well plug it in: y=6x -> y=6(3/9) and solve, yes if theres a slope of 1

Answer:

x=8

NR=5 units

BI=10 units

Step-by-step explanation:

In  a rectangle BRIA

AN=5 units

NR=x-3

We have to solve for x , NR and BI.

We know that

Diagonals of rectangle bisect to each other.

BI and AR are the diagonals of rectangle BRIA and intersect at point N.

AN=NR

[tex]5=x-3[/tex]

[tex]x=5+3=8[/tex]

[tex]x=8[/tex]

Substitute the value of x

NR=8-3=5

By property of rectangle

BI=AR=AN+NR=5+5=10 unit

BI=10 units

Answer:

Step-by-step explanation:

The blank is -8

Step-by-step explanation:

Let us revise some rules of indices:

∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]

∵ All bases are equal

∴ Use the first and third rule above to find x

∵  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]

∴  [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S

∵  [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S

Equate L.H.S and R.H.S

∴  [tex]4^{-3}[/tex] =  [tex]4^{5+x}[/tex]

Equate the indices of the two sides

∴ -3 = 5 + x

- Subtract 5 from both sides

∴ -8 = x

∵ x represents the blank

∴ The blank = -8

The blank is -8

Learn more:

You can learn more about the indices in brainly.com/question/4419221

#LearnwithBrainly

Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.

To solve for the missing exponent, we can use the following properties of exponents:

Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.

Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.

Applying these properties:

4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)

4^5 * 4^x = 4^(5 + x)

Setting these equal to find x:

4^-3 = 4^(5 + x)

Therefore, x = -3 - 5 = -8.

Answer:

9%

Step-by-step explanation:

It is simple because you just count to get to 24 and that is the percentage.

Answer:

[tex]\frac{104}{5}[/tex] weeks or [tex]20\frac{4}{5}[/tex] weeks

Step-by-step explanation:

To do this we can set up a proportion

[tex]\frac{52}{1} *\frac{2}{5}[/tex]

This will tell us how many weeks are in 2/5 of a year

Let's evaluate this

[tex]\frac{104}{5}[/tex]

We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below

[tex]20\frac{4}{5}[/tex] weeks

[tex]\text{We're trying to find how many weeks Ben has lived in London}\\\\\text{We know that there are 52 weeks in a year}\\\\\text{We also know that he's been in London for 2/5 of a year, or 40\%}\\\\\text{To find your answer, you could multiply 52 by 0.40}\\\\52*0.40= 20.8\\\\\boxed{\text{Ben has been in London for 20.8 weeks}}[/tex]

Kate and Will meet at 1 : 09 pm

Solution:

The distance between Quebec City and New York City is 520 miles.

At the point where Kate and Will meet, they would have traveled 520 miles.

Let "t" represent the time it takes Kate to travel a certain distance before they met.

[tex]Distance = speed \times time[/tex]

If Kate drives at 55 mph, the distance covered would be

[tex]Distance = 55 \times t = 55t[/tex]

If Will drives at 75 miles per hour, then the distance covered will be

[tex]Distance = 75 \times t = 75t[/tex]

Since the total distance covered is 520 miles

Which means,

[tex]55t + 75t = 520\\\\130t = 520\\\\t = \frac{520}{130}\\\\t = 4[/tex]

Given that in question,

If Kate leaves Quebec and will leaves New York at 9:09 a.m

4 hours after 9: 09 am, Kate and Will will meet

9: 09 am + 4 hours = 1: 09 pm

Thus they would meet at 1 : 09 pm

Answer:

Akira needs 45 square inches of  gold foil to cover the chair free including the bottom​

Step-by-step explanation:

Total surface  =  surface area of the base square + area of 4 triangles

Step 1: The surface area of the base square

surface area of the base = surface area of the square =  [tex]s^2[/tex]

where s is the side length

The the surface area of the base  = [tex]3^2[/tex] = 9 square inches

Step 2: The surface area of the side triangles

The area of the triangle = [tex]\frac{1}{2}\times \text{side length} \times \text{slant height}[/tex]

On substituting the values,

The area of the triangle =[tex]\frac{1}{2} \times 3 \times 6[/tex]

The area of the triangle = [tex]\frac{18}{2}[/tex]

The area of the triangle = 9 square inches

Now the area of 4 triangles  =  4 x 9  = 36 square inches

Thus the total surface area  =  9 + 36 = 45 square inches

The amount of gold foil needed to cover a trophy in the shape of a square pyramid can be calculated using the surface area formula for square pyramids, which considers the base area and the slant height.

To calculate the amount of gold foil needed to cover the trophy, we need to find the surface area of the square pyramid trophy. The surface area of a square pyramid is calculated by the formula: Surface Area = base area + 1/2 * Perimeter of base * slant height. If we know the length of the base (which is a square here), the slant height, we can substitute them into this formula to get the surface area. This is the amount of gold foil Akira used to cover her trophy, assuming the gold foil perfectly fits the trophy shape with no overlap.

https://brainly.com/question/31800864

#SPJ

Answer:

Step-by-step explanation:

I don't have all the information, but all you need to do it convert 2 hours to minutes (which would be 120 minutes) and setup a proportion.

amount of calories burnt per minute           x (total amount of calories burnt)

____________________________    = ________________

1 minute                                                              120 minutes

Hope this helps!

They would burn 360 calories doing 2 hr of bowling.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that this energy is measured in calories. When you exercise, you use up or burn calories.

The information shows about how many calories a 125-pound person burns each minute bowling.

We need to do it convert 2 hours to minutes which would be 120 minutes and setup a proportion.

The amount of calories burnt per minute  x (total amount of calories burnt)

1 minute  =  120 minutes

Multiply 120 x 3 = 360.

Hence, they would burn 360 calories doing 2 hours of bowling.

More can be learned about proportions at;

brainly.com/question/24372153

#SPJ5

If a number is decreased by 79%, we are left with 21%.

so let's devide by 21 to get down to 1%, then multiply by 100 to get to the origininal number:

13 / 21 * 100 = 61.9047619048

To the nearest tenth it's 61.9

Final answer:

To find the original number when decreased by 79% to result in 13, we solve the equation 0.21x = 13, which gives us 61.9047619. Rounding this to the nearest tenth gives us 61.9.

Explanation:

To find the original number, we need to translate the percentage decrease back into the original number. Here's the step-by-step calculation:

So the original number to the nearest tenth is 61.9.

Answer:

D

Step-by-step explanation:

When Y is a function of X, the graph is a v shape.

Answer:

1st triangle = 1

2nd triange= 3

3rd triangle = 9

4th triangle = 27

A triangle exists a three-sided polygon with three vertices and three edges. The number of triangles in the given figure exists 1, 3, 9, and 27.

A triangle exists a three-sided polygon with three vertices and three edges. It exists one of the major fundamental geometric forms.

The number of shaded triangles in each of the triangles exists shown below, thus, the number of triangles in each triangle can are:

1st triangle = 1

2nd triangle = 3

3rd triangle = 9

4th triangle = 27

Therefore, the number of triangles in the given figure exists 1, 3, 9, and 27.

To learn more about triangle

https://brainly.com/question/27061400

#SPJ2

Answer:

a) $30

b) $8

Step-by-step explanation:

Wayne's savings to Stef's savings were in the ratio 5:6.

Let, Wayne's saving is 5x and Stef's saving is 6x.

Now, given that after spending $28 each the ratio became 1:4.

So, we can write the equation as

[tex]\frac{5x - 28}{6x - 28} = \frac{1}{4}[/tex]

⇒ 20x - 112 = 6x - 28

⇒ 14x = 84

⇒ x = 6

a) Therefore, Wayne's savings before he spends $28 is $(5 × 6) = $30

b) And, Stef's savings after she spends $28 will be $(6x - 28) = $(6 × 6 - 28) = $8 (Answer)

Answer: 20%

Step-by-step explanation:

25 = 100%

25/5 = 5

100/5 = 20

That means 80% passed and 20% didnt.

Answer:

20%

Step-by-step explanation:

If 20 kids passed, that means 5 did not. 5/20 is 0.2. Write that in percentage is 20%.

Answer:

Multiply by 5

-250, 1250

Step-by-step explanation:

2 x -5 = -10

-10 x -5 = 50

50 x -5 = -250

-250 x -5 = 1250

Answer:

6km

Step-by-step explanation:

Area of circle = πr²

Where r = radius,  π= 3.14, A = 28.26km²

A = 3.14 x r²

3.14 r2 = 28.26

Divide both sides by 3.14

r²= 28.26/3.14

r² = 9

Square root both sides

r= √9

r= 3

Radius = 3km

Note : Diameter = 2 x radius

Diameter = 3 x 2

Diameter = 6km

I hope this was helpful, Please mark as brainliest.