Equations with variables on both sides : 17-2p = 2p+5+2p

Peter weighs 156 pounds, but he would like to wrestle in a lower weight class.He loses 4 pounds one week, gains back 2 pounds the next, loses 5 pounds the third week and loses 3 pounds the fourth week.How much does 

Peter weigh now?

Answer:

[tex]\frac{3}{4}[/tex] miles

Step-by-step explanation:

Total length of the trail = [tex]4\frac{1}{2}[/tex] miles = [tex]\frac{9}{2}[/tex] miles

She ran the first [tex]\frac{2}{3}[/tex] of the distance i.e.

The distance for which she ran = [tex]\frac{2}{3} \times \frac{9}{2} = 3\ miles[/tex]

Remaining distance = Total length of trail minus the distance for which she has already run = [tex]\frac{9}{2} - 3 = \frac{3}{2}[/tex] miles

Given that: After running, Annie has to walk due to steep nature of the trail, So, Annie walked for [tex]\frac{1}{2}[/tex] of the remaining distance.

The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] Remaining distance

The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] miles

So, the answer is: [tex]\frac{3}{4}[/tex] miles

Answer:

a) her estimate is wrong, because 22 crates can only contain 704 boxes

b) 23 crates

Step-by-step explanation:

Each crate can hold 32 boxes and there are total of 712 boxes.

Megan thinks she can fit all 712 boxes into 22 crates.

Now multiplying 22 crates 32 boxes to know the number of boxes22 crates can contain

= 22*32

= 704 boxes

The boxes are not all contacts in 22 crates

To pack 712 boxes

She Will need = 712/32 crates

She will need= 22.25 crates

Rounding up to whole number she will need 23 crates

Answer:

10) -1

11) 1/2 or 0.5

12) -1/5 or -0.2

13) -13/6 or -2.166666666

14) -1/8 or -0.125

15) 1/2 or 0.5

hope it helps;)

good luck!

Answer:

3 a^(-2)

3 / a^2

Step-by-step explanation:

(3a) (a^-3)

Multiply

3 a^1 * a^-3

Since we are multiplying, we add the exponents

3 a^ ( 1-3)

3 a^(-2)

If  you are not supposed to leave a negative exponent

x^-b = 1 / x^b

3 / a^2

Answer:

Axis of Symmetry: x = -4

Vertex: (-4, 54)

Step-by-step explanation:

We use a graphing calc.

Answer:

the equation of the axis of symmetry is [tex]x=-4[/tex]

Step-by-step explanation:

Recall that the x-value of the vertex of a parabola of the form:

[tex]y=ax^2+bx +c[/tex]

is given by the expression:

[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]

therefore, in our case the x-position of the vertex becomes;[tex]x_{vertex}=-\frac{b}{2\,a}=\frac{32}{-8} =-4[/tex]

and since the equation of the axis of symmetry is [tex]x=x_{vertex}[/tex]

Then, the equation of the axis of symmetry is [tex]x=-4[/tex]

Answer:

15

Step-by-step explanation:

if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten

Answer:

D): 15

Step-by-step explanation:

if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten

Answer:

See graph attached

Step-by-step explanation:

Our life is simple because the equation [tex]y=2x+2[/tex] is already put in slope-intercept form.

This form is called slope-intercept because it states exactly what it's called: The number multiplied by [tex]x[/tex] (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)

With this info, we can start graphing.

We know that the y-intercept is 2, meaning one point will be (0,2).

We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.

Hope this helped!

The graph of the function y = 2x + 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 2x + 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ6

Answer:

Step-by-step explanation:

The time for each canoe is 3.5 hours

The total distance traveled by the first canoe is not known. Nor is the distance for the second canoe. We do know that the difference is 5.25 miles.

So let the rate of the slower canoe = x

Let the rate for the second canoe = 2x

The first canoe goes a distance of 2*x * 3.5 = 7x

The second canoe goes a distance of 3.5x

The difference = 7x - 3.5x = 5.25

3.5x = 5.25                                       divide by 3.5

x = 5.25/3.5

x = 1.5 which is the rate of the slower canoe

2x = 3  which is the rate of the faster canoe    

Answer:

13 playing cards

Step-by-step explanation:

Thomas = 19 playing cards

Brother = 6 playing cards (which give Thomas)

Thomas = 19 playing cards - 6 playing cards = 13 playing cards

Answer:

[tex]\huge\boxed{\sf 13\ cards}[/tex]

Step-by-step explanation:

Thomas has total = 19 playing cards

He gave away = 6 cards

Thomas have now:

=> 19-6

=> 13 cards

Answer:

22.4cm

Step-by-step explanation:

Opposite side of the triangle is x

Adjacent side of the triangle is 10

Tangent 20° = x/10

2.237 = x/10

x = 2.237 × 10

x = 22.37cm

x = 22.4cm to the nearest tenth

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

y = 4/3x - 5

Comparing with the general equation above

Slope/ m = 4/3

Since the lines are parallel their slope are also the same

So we have

Slope of parallel line = 4/3

Equation of the line using point (−6,−5) and slope 4/3 is

We have the final answer as

Hope this helps you.

Answer: LOL

Step-by-step explanation:

Answer:

K-273=C

Step-by-step explanation:

K=C+273

Subtract 273 from each side

K-273=C+273-273

K-273=C

Answer:

a. x=9, b. x=6

Step-by-step explanation:

In a the triangle is cut in half. the sides are equal even though the triangle is slanted.

In b the triangles are similar if you flip the big one. Since the smaller triangle is smaller it is a reduced form of the larger one.

Answer:

The weekly profit function P(x,y) = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

3.5 oz bars = 3560

5 oz bars = 80

The maximum weekly profit = 119680

Step-by-step explanation:

Given that:

the demand functions are p and q

the variable cost of x = 8x and the variable cost of y = 12y

Since the  fixed cost attributed to the division is exist 10,000/week

∴ the total cost C = 8x + 12y + 10000

R(x,y) = p(x) + q(y)

where ;

xp(x) = 80x -0.01x² -0.005y

yqz(y) = 50 -0.005x -0.015y²

R(x,y) = 80x -0.01x² -0.005xy +  50y -0.005xy -0.015y²

The weekly profit function P(x,y) = R(x,y) - C

P(x,y) = 80x -0.01x² -0.005xy + 50 -0.005xy -0.015y² - ( 8x + 12y + 10000)

P(x,y) = 80x -0.01x² -0.005xy + 50 - 0.005xy -0.015y² - 8x -12y - 10000

P(x,y) = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

(b) How many of the 3.5-oz size bars and how many of the 5-oz bath size bars should the division produce per week to maximize its profit?

profit will be  maximized if:

[tex]\dfrac{\partial P}{\partial x} =0 \ and \ \dfrac{\partial P}{\partial y} =0[/tex]

given  that:

[tex]\dfrac{\partial^2 P}{\partial x^2} < 0 \ and \ D >0[/tex]

where;

D = Px Py -Pxy²

Now;

[tex]\dfrac{\partial P}{\partial x} =(-0.02 x -0.01 y +72)[/tex]

[tex]\dfrac{\partial P}{\partial y} =(-0.03 x -0.01 y +38)[/tex]

[tex]\dfrac{\partial P}{\partial x} =0 \to 2x+y = 7200[/tex]

[tex]\dfrac{\partial P}{\partial y} =0 \to x+3y = 3800[/tex]

2x + y   = 7200

2x + 6y = 7600  

5y = 400

y = 400/5

y = 80

From

x + 3y = 3800

x + 3(80) = 3800

x = 3800 - 240

x =  3560

∴ 3.5 oz bars = 3560

5 oz bars = 80

What is the maximum weekly profit?

The maximum weekly profit = 72x  - 0.01x² -0.005xy + 38y -  0.005xy -0.015y²  - 10000

The maximum weekly profit = 72(3560)  - 0.01(3560)² -0.005(3560)(80) + 38(80) -  0.005(3560)(80) -0.015(80)²  - 10000

The maximum weekly profit =  256320 - 126736 - 1424  + 3040 -  1424 -96  - 10000

The maximum weekly profit = 119680

Answer:

  $2611.05

Step-by-step explanation:

  earnings = lane rentals + concessions

Friday:

  earnings = $842.72 +412.38 = $1255.10

Saturday:

We assume "down by 1/8" means the value was 1 -1/8 = 7/8 that of the previous day. Likewise, "increased by 1/2" is assumed to mean the value was 1 + 1/2 = 3/2 that of the previous day.

  earnings = 7/8×$842.72 + 3/2×412.38 = $1355.95

__

Then the total earnings for both days were ...

  $1255.10 +$1355.95 = $2611.05

Answer:

$1,355.95

$1,580.10

$1,992.48

$2,611.05

Step-by-step explanation:

 $2611.05  

plz give him a heart and a rating.     c'mon do it for him

༼ つ ◕_◕ ༽つ

Answer:

-9

Step-by-step explanation:

Simplify the following:

7 - 8/4 (3^2 - 1)

Hint: | Evaluate 3^2.

3^2 = 9:

7 - 8/4 (9 - 1)

Hint: | Subtract 1 from 9.

9 - 1 = 8:

7 - 2×8

Hint: | Divide 8 by 4.

8/4 = (4×2)/4 = 2:

7 - 2×8

Hint: | Multiply -2 and 8 together.

-2×8 = -16:

7 + -16

Hint: | Subtract 16 from 7.

7 - 16 = -9:

Answer:  -9

Answer:

0.285

Step-by-step explanation:

To do this, divide 28 1/2% by 100%, obtaining:

28.5%

---------- = 0.285

100%

Answer: Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other

Hope it helps:) I got it right on my test btw

Step-by-step explanation:

Answer:

$35.2

Step-by-step explanation:

I’m assuming you meant the total of the dress after tax.

1. 32 * 1.1 = 35.2

OR

1. 32 * 0.1 = 3.2

2. 32 + 3.2 = 35.2

You could do it either way.

Answer:

[tex]77\div.77\cdot1[/tex]

Step-by-step explanation:

What we're basically looking for here are ways to get 100 using these numbers.

My immediate first thought was "can we divide the 7's by some 7's to get 100?"

I know that [tex]7 \div .7=10[/tex], so I had the idea to make it [tex]77 \div .77 = 100[/tex]. This means that we can use the number 7 four times in the equation [tex]77 \div .77=100[/tex].

However, we're still missing a 1 that we need to include. This is easy, we can just multiply [tex]77 \div .77[/tex] by 1.

So in conclusion, we get [tex]77 \div .77\cdot1[/tex]

Hope this helped!

Answer:

177 - 77 = 100

Step-by-step explanation:

there are basically 4 7s

77-77 = 00

177 - 77 = 100

hope this helps （＾▽＾）

Answer:

3x+3

plz mark brainliest

Answer:

3x + 3

Step-by-step explanation:

Combine like terms. Like terms are terms with the same amount of variables.

10x - 7x + 3

(10x - 7x) + 3

Subtract:

10x - 7x = 3x

Remember to bring the constant down.

3x + 3 is your answer.

~

Answer:

a)after 1,000 years?

1 meter

b) 10 million years?

10,000 meters

c) 50 million years?

50,000 meters

Step-by-step explanation:

We are told in the question that mountains rise 1 mm per year.

a) After 1000 years

1 year = 1 mm

1000 years =

Cross Multiply

1000 × 1 mm

= 1000mm

Converting to meters

1 mm = 0.001 m

1000 mm =

1000 × 0.001m

= 1 meter

b) After 10 million (10,000,000) years

1 year = 1 mm

10000000years =

Cross Multiply

10000000 × 1 mm

= 10,000,000mm

Converting to meters

1 mm = 0.001 m

10,000,000mm =

10,000,000 × 0.001m

= 10,000 meters

c) After 50 million years(50,000,000)

After 50,000,000 years

1 year = 1 mm

50,000,000years =

Cross Multiply

50,000,000 × 1 mm

= 50,000,000mm

Converting to meters

1 mm = 0.001 m

50,000,000mm =

50,000,000 × 0.001m

= 50,000 meters

Answer:

The cosine of angle C is 5/13, or approximately 0.38.

Step-by-step explanation:

To solve this problem, we must remember what the cosine of an angle represents.  The cosine of an angle is equal to the ratio of the adjacent side divided by the hypotenuse.

From the diagram, we can determine that the adjacent side length is 10 and the hypotenuse is 26.

Therefore, the cosine of angle C is:

10/26 = 5/13 (simplified)

Hope this helps!

Answer:

6

because a dozen is 12 and a half dozen is 6.

Answer:

the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x)

Step-by-step explanation:

To find the equation of a line given two points, we use the formula:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

The standard equation of a line is given by:

y = mx + c; where m is the slope of the line and c is the intercept on the y axis

For the function f(x), we have to select two points, let us select (-6, 9) and (0, 27)

Hence the equation of the line f(x) is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-9=\frac{27-9}{0-(-6)}(x-(-6))\\ \\y-9=\frac{18}{6} (x+6)\\\\y-9=3(x+6)\\\\y-9=3x+18\\\\y=3x+18+9\\\\y=3x+27\\[/tex]

Comparing y = 3x + 27 with y = mx + c, we can see that the slope (m) = 3 and the y intercept is 27

For the inverse function f⁻¹(x), let us use the points (-3, -10) and (0, 9)

Hence the equation of the line f⁻¹((x) is:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-10)=\frac{-9-(-10)}{0-(-3)}(x-(-3))\\ \\y+10=\frac{1}{3} (x+3)\\\\y+10=\frac{1}{3}x+1\\\\y=\frac{1}{3}x+1-10\\\\y=\frac{1}{3}x-9\\[/tex]

To find the x intercept put y = 0

0 = (1/3)x - 9

(1/3)x = 9

x = 27

Comparing y = (1/3)x - 9 with y = mx + c, we can see that the slope (m) = 1/3 and the y intercept is -9

Hence, the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x) (i.e reciprocal of 3 = 1/3)

Answer: A

The reciprocal of the slope of f(x) is the same as the slope of f–1(x).

Step-by-step explanation:

Answer:

2a-6b+6c

Step-by-step explanation:

Combine like terms

Answer: -2a + 2c

Step-by-step explanation:

The situation is saying that subtract  4a-3b+2c from 2a-3b+4c.

(2a-3b+4c) - (4a - 3b +2c) Subtract by terms

-2a + 2c