This table shows how the amount of money Sadie makes from selling lemonade is related to the number of cups sold. How much does one cup of lemonade cost?

Paolo wrote the following equation for the perimeter of a rectangle.

P=2(l+w)

Which equation is equivalent to the equation Paolo wrote?

The equivalent equations are:

[tex]w = \frac{p-2l}{2}\\\\l = \frac{p-2w}{2}\\\\p = 2l+2w[/tex]

Given that:

The equation for perimeter of rectangle written by Paolo is:

P = 2(l + w)

where

l = length side of rectangle

w = width side of the rectangle

We have to find the equivalent equation

Let us solve the equation for "w"

[tex]P = 2(l + w)[/tex]

Divide by 2 both sides

[tex]\frac{P}{2} = \frac{2(l+w)}{2}\\\\\frac{P}{2} = l + w[/tex]

[tex]\text{Subtract L on both sides of equation }[/tex]

[tex]\frac{P}{2} - l = l + w - l\\\\\frac{P}{2} - l =w[/tex]

[tex]w = \frac{p-2l}{2}[/tex]

Similarly solving for "l" we get,

[tex]l = \frac{P-2w}{2}[/tex]

Also, given equation can be written as,

[tex]P = 2(l+w)\\\\P = 2l + 2w[/tex]

Thus the equivalent equations are found

Final answer:

The equivalent equation to Paolo's originally written P=2(t+W) for a rectangle's perimeter should be P=2t+2u, assuming 't' stands for width and 'u' for length. The area function a(t) for the rectangle based on width and fixed perimeter is valid within the domain 0 <= t <= L/2.

Explanation:

The question pertains to the formation of equivalent equations to express the perimeter of a rectangle. Paolo wrote the equation P=2(t+W). However, it seems there may have been a typographical error as the correct variables should have been 't' for width and 'u' for length. Given this, the equivalent equation to Paolo's should be P = 2t + 2u, also stated as P = 2(t + u) which confirms the relationship between perimeter, length, and width for a rectangle.

From the provided context, it's also understood that the function representing the area of the rectangle, when written in terms of width (t), is a(t) = t(L/2 - t), which is valid within the domain 0 <= t <= L/2. This function helps in determining the maximum area of the rectangle for a given perimeter (L).

Answer:

$112.7

Step-by-step explanation:

15%=0.15

0.15*98=14.7

98+14.7=112.7

Answer:

x = 20

Step-by-step explanation:

    2x + 7x = 180

⇔ 9x = 180

⇔ x = 180/9 = 20

Answer:

  yes, they are

Step-by-step explanation:

y = -5 is a horizontal line.

x = 5 is a vertical line.

Horizontal and vertical lines are perpendicular to each other. These lines are perpendicular.

The sum of the series [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex] is 44.

Step-by-step explanation:

The given series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

To find the sum of the series, we need to substitute the values for k in the series.

[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right][/tex]

Now, simplifying the square terms, we get,

[tex][2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4][/tex]

Multiplying the terms,

[tex][2-4]+[8-4]+[18-4]+[32-4][/tex]

Subtracting the values within the bracket term, we get,

[tex]-2+4+14+28[/tex]

Now, adding all the terms, we get the sum of the series,

[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

Thus, the sum of the series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

Hes right its 44

444444444444444444444

Answer: $22.03

Step-by-step explanation: 15% 67.8= 10.17. 67.8+10.17=77.97. x=remain balance. x=100.00-77.97=22.03.

Answer:

Therefore  40 milliliter of 50% fungicide solution is required

Therfore  60 milliliter of 10% fungicide solution is required

Step-by-step explanation:

i) Let the 10% fungicide solution have x milliliter and the 50% fungicide solution have y milliliter.

ii) Therefore 10x + 50y = 26(x + y)

                      x + y = 100

iii) form the first equation in ii) we get

                   16 x  = 24 y   Therefore [tex]x = \frac{24}{16} y = \frac{3}{2} y[/tex]

iv) substituting the value obtained in iii) in the second equation in ii) we get

      [tex]\frac{3}{2} y + y = \frac{5}{2} y = 100[/tex]

  Therefore y = 100 ÷ 2.5 =  40 milliliter

   Therfore x = 100 - 40 = 60 milliliter

Answer:

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

Step-by-step explanation:

i) the cost of an automobile is given by the equation is

 C(t) = [tex]28000\times(0.73)^{t}[/tex], where C(t) represents the cost and t represents the time in years

ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.

ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.

iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

The question is about comparing Angela's 12% commission structure against her friend's $750 fixed salary plus 5% commission. The answer examines how the volume of sales would affect their respective incomes.

This problem is about comparing commission rates and overall income. If Angela worked on a straight 12% commission, it means that she earns 12% of the total sales she makes. Her friend, however, has a fixed salary of $750, in addition to earning 5% of his total sales as commission. To compare their incomes, we would need to know the total sales each of them makes. Generally, the more sales they make, the more beneficial the commission system becomes.

For example, if Angela made $1000 in sales, she would earn $120 (12% of $1000). If her friend made the same amount in sales, he would earn $800 ($750 salary + $50 from 5% of $1000). However, if they only made $100 in sales, Angela would earn $12, and her friend would earn, $755. So, the best system depends on the volume of sales.

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Answer:

[tex]v = 15 \\ c = v \div 5[/tex]

Step-by-step explanation:

It could be this

Answer:

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Step-by-step explanation:

Consider a Δ ABC with

m∠ B = 53°

BC = a = 10

AC = b = 17    

To Find:  

AC = c = ?  

m∠ A = ?

m∠ C =  ?

Solution:

We know in a Triangle Sine Rule Says that,  

In Δ ABC,

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

substituting the given values we get

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]

[tex]\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°[/tex]

Therefore m∠A = 28°

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

[tex]\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°[/tex]

Therefore m∠C = 99°

Now From Sine rule we have

[tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

Substituting the values we get

[tex]\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit[/tex]

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Answer:

x intercept is 6/13

y intercept is -6

Step-by-step explanation:

x intercepted when y is zero.

y intecepted when x is zero...

Answer:

I would eliminate both of the -4x because they are identical.

Step-by-step explanation:

Cancel out the both of the -4x by eliminating them. Then subtract the 3y - y. Subtract the -19 - 15. You then will be left with 2y = -34. Solve for y. Then plug y back into the equation to solve for the x.

Hope this helped. :^)

Answer:

20 units

Step-by-step explanation:

Let the equal sides of the triangle be x.

Then the third side will be (x+5) units

Since the perimeter is 50, we have:

[tex]x + x + (x + 5) = 50[/tex]

We simplify to get:

[tex]3x + 5 = 50[/tex]

This implies that:

[tex]3x = 50 - 5[/tex]

[tex]3x = 45[/tex]

Divide both sides by 3 to get:

[tex]x = \frac{45}{3} = 15 [/tex]

The length of the third side is:

15+5=20

Answer: 1 hour

Step-by-step explanation: if he travels 12 mph, it will take 1 hour to travel 12 miles.

Answer:

176 square yards

Step-by-step explanation:

The picture of the question in the attached figure N 1

we know that

The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)

see the attached figure N 2 to better understand the problem

step 1

Find the area of the two trapezoids (#1 and #2)

[tex]A=2[\frac{1}{2}(b_1+b_2)h][/tex]

simplify

[tex]A=(b_1+b_2)h[/tex]

we have

[tex]b_1=12\ yd\\b_2=4+12+4=20\ yd\\h=4\ yd[/tex]

substitute

[tex]A=(12+20)(4)=128\ yd^2[/tex]

step 2

Find the area of the two smaller rectangles (#3 and #4)

[tex]A=2[LW][/tex]

we have

[tex]L=4\ yd\\W=6\ yd[/tex]

substitute

[tex]A=2[(4)(6)]=48\ yd^2[/tex]

step 3

Find the area of the walkway around the rectangular pool

[tex]128+48=176\ yd^2[/tex]

Answer:

176 sq yards

Step-by-step explanation:

Answer:

6 shaded squares and 4 unshaded....shaded = 60%

Step-by-step explanation:

a grid with 100 squares, 6 are shaded....6/100 = 0.06 = 6%

a grid with 100 squares, 36 are shaded....36/100 = 0.36 = 36%

6 shaded squares and 4 unshaded...6:4...added = 10

shaded = 6/10 = 0.6 = 60% <====

4 shaded squares and 6 unshaded...4:6...added = 10

shaded = 4/10 = 0.4 = 40%

Answer: The answer is C

Answer:

The value of the given expression -9w+9 when w=15 is -126

Step-by-step explanation:

Given expression is -9w+9

To find the given expression when w=15:

That is put w=15 in the given expression we get

-9w+9=-9(15)+9

=-135+9 ( adding the like terms )

=-126

Therefore the value of the given expression -9w+9 when w=15 is -126

Answer:

Step-by-step explanation:

40 hours per week*20 dollars per hour=800 dollars per week. This job makes 200 more dollars than the other job.  

The amount of generation of the most income in the second job offer will be more which is $800 per week.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

An employee working 40 hours per week earns a salary of $600 per week. Then the rate is given as,

Rate = $600 per week

But gets a second job offer to work 40 hours per week, hourly at $20 an hour. Then the rate is given as,

Rate = $20 x 40

Rate = $800 per week

The amount of generation of the most income in the second job offer will be more which is $800 per week.

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Answer:

$ 1.10

Step-by-step explanation:

p + r = 1.45....p = 1.45 - r

2p + r = 1.80

2(1.45 - r) + r = 1.80

2.90 - 2r + r = 1.80

-2r + r = 1.80 - 2.90

-r = - 1.10

r = 1.10 <=== a ruler costs $ 1.10

p + r = 1.45

p + 1.10 = 1.45

p = 1.45 - 1.10

p = 0.35 .......a pencil will cost $ 0.35

By setting up simultaneous equations based on the purchases of Phoebe and Ioeh and solving them, we find that the cost of the ruler is £1.10.

To determine the cost of the ruler, we need to set up two equations based on the given information about Phoebe and Ioeh's purchases and use the method of simultaneous equations.

Let's assume 'R' represents the cost of the ruler and 'P' represents the cost of one pencil.

According to the question:

To find the cost of the ruler, we can solve these equations simultaneously. Subtract the first equation from the second to eliminate R and find P:

1. R + 2P = £1.80
2. R + P  = £1.45

Subtract equation 2 from equation 1:

2P - P = £1.80 - £1.45
P = £0.35

Now that we know one pencil costs £0.35, we can substitute P back into either equation to find R. Let's use the first equation:

R + P = £1.45
R + £0.35 = £1.45
R = £1.45 - £0.35
R = £1.10

Thus, the ruler costs £1.10.

Final answer:

In the given algebraic expression, 4n³ and 2n³, 2m and 6m, and 5n and 2n are identified as like terms.

Explanation:

The question asks to identify like terms in a given algebraic expression. Like terms in algebra are terms that have the exact same variables raised to the same powers, although they can have different coefficients.

For example, 4n³ and 2n³are like terms because they both contain the variable n to the third power.

On the other hand, 2m and 6m are like terms because they both contain the variable m to the first power.

Lastly, 5n and 2n are like terms because they contain the variable n to the first power.

Answer:

1,500

Step-by-step explanation:

Find x in proportional form.

Answer: 1,500

Step-by-step explanation:

use the is/of = %/100 proportion

Answer:

Part 1)Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .  

If a consistent system has exactly one solution, it is independent .  

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

[tex]x+5y=-2[/tex]

[tex]x+5y=4[/tex]

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

[tex]y=3x+4[/tex]

[tex]-2x+y=4[/tex]

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes )m=3 and m=2)

so

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

[tex]3x+y=4[/tex] ----> equation A

[tex]-6x-2y=-8[/tex] ----> equation B

Multiply equation A by -2 both sides

[tex]-2(3x+y)=-2(4)[/tex]

[tex]-6x-2y=-8[/tex] ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

Answer:

B

Step-by-step explanation:

15% = 0.15

1 - 0.15 = 0.85

[Plug in the p and s]

Answer:

Step-by-step explanation:

2x + 2y = -10

Making y as subject

2y = -2x - 10

Dividing by 2

y = -2x/2 - 10/2

y = -x - 5

Comparing with y = mx + c

Slope m = -1, y intercept c = -5

The equation is first rewritten in slope-intercept form as y = -x - 5, revealing that the slope is -1 and the y-intercept is -5.

To find the slope and y-intercept of the given equation 2x + 2y = -10, you need to rewrite it in the slope-intercept form, which is y = mx + b, where m represents the slope, and b represents the y-intercept. First, let's separate the y-term on one side by subtracting 2x from both sides of the equation:

2y = -2x - 10

Now divide the entire equation by 2 to solve for y:

y = (-2x/2) - (10/2)

y = -x - 5

Comparing this with the slope-intercept form y = mx + b, we can see that the slope (m) is -1, and the y-intercept (b) is -5.

Answer:

Domain : {-2, -1, 0, 4}

Range: {-2, 2, 3, 4}

Answer:

b,c

Step-by-step explanation:

Answer:

Step-by-step explanation:

V=πr²h

=3.14*6*6*10

=1130.4 cm³

New cylinder:

h = 15cm

V= 1130.4  cm³

πr²h = 1130.4

3.14*r²*15=1130.4

r²=1130.4/15*3.14

r²=24

r=√24

r=4.898 = 4.9 cm

The radius be to meet the client's need is 4.9 cm.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

Volume is sometimes referred to as capacity.

We have,

Radius of cylinder (r)= 6 cm

Height of cylinder (h) = 10 cm

and, Height of new cylinder (H)  = 15 cm

Radius of new cylinder = R cm

Now, Volume of cylinder can be compared as

πr²h = πR²H

6 x 6 x 10 = R² x 15

360 / 15 = R²

R² = 24

R= 4.9 cm

Thys, the radius is 4.9 cm.

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Answer:

m > 124

Step-by-step explanation:

switch sides, add 91 to both sides then simplify :)

You need to isolate/get the variable "m" by itself on one side of the equation

33 < m - 91    Add 91 on both sides to get m by itself

33 + 91 < m - 91 + 91

124 < m    [124 is less than m]