Solve the equation.

3n + 2= 8 + 2n
A. 3
B. 4
C. 5
D. 6

Answer:

D. 1/3^3

Step-by-step explanation:

Divide 3/3 as usual and get 1.

When dividing exponents, you are actually subtracting them. 5-8 = -3.

D is the answer because positive exponents in the denominator of the fraction is the same as a negative exponent in the numerator.

The rule with exponents is that when dividing similar bases with different exponents (or power), you subtract the exponents respectively.

3⁵ / 3⁸ = 3⁽⁵ ⁻ ⁸⁾ = 3⁻ ³ = 1 / 3³

So the answer is

D) 1/3³

Answer:

5050 and 100 pairs

Step-by-step explanation:

Answer:

First situation

More than 3 hours

At least 10

15

75

Step-by-step explanation:

Let x be the number of hours

The equation will be

[tex]5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3[/tex]

So, she needs to work more than 3 hours in order to make more than $15.

The situation that represents [tex]5x>15[/tex] is the first one.

Let x be the additional number of cans

The inequality will be

[tex]x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10[/tex]

So, the additional number of cans to be bought is at least 10.

Let x be the number of comic books Clarice has.

[tex]x>15[/tex]

So, Clarice needs to have more than 15 comic books.

Let x be age of Elizabeth

The equation will be

[tex]x=5\times 15\\\Rightarrow x=75[/tex]

So, Elizabeth is 75 years old.

Answer:

I have a feeling it's 5.36, 275, 336, 535.

Sorry if I'm wrong.

Step-by-step explanation:

Answer:

C is the answer........

Answer:

1 page every 0.5hours, or 1 page every 30 minutes. The equation is

2x = y

The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Madelyn has a total of 15 dimes and quartets in her piggy bank. The total amount of money in her piggy bank is $2.85.

Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,

0.10x + 0.25y = 2.85       ....1

x + y = 15                         ....2

From equations 1 and 2, then we have

0.10(15 - y) + 0.25y = 2.85

1.5 - 0.10y + 0.25y = 2.85

0.15y = 1.35

y = 9

Then the value of the variable 'x' is given as,

x + 9 = 15

x = 6

The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ5

Answer:

1-1/4 cups (1 and 1/4 cups) or 1.25 cups

Step-by-step explanation:

To find the answer you need to take the total volume (5-5/8 cups) and divide it by the number of bottles you have:

5-5/8 divided by 4-1/2

There are two easy ways to do this: you can convert the mixed fractions into decimal form (A) or into improper fractions (B).

A)

First, convert to decimal form:

5-5/8 = 5.625 and 4-1/2 = 4.5

Then, you divide them:

5.625 / 4.5 = 1.25 (converted back to fraction form, if thats what you need, is 1-1/4)

B)

First, convert to mixed numbers:

5-5/8 = 45/8 and 4-1/2 =9/2

Then, you divide them:

45/8  /  9/2

When you divide fractions, you multiply by the inverse of the number you're dividing by (that means swapping the numerator and denominator):

45/8  *  2/9  =  90/72 (converted back to a mixed fraction, this equals 1-1/4)

Answer:

All systems have 2 real solutions.

Explanation: there are X and Y unknowns.

Answer:

cotA. cos(30° - A) - sin(30° - A) = √3/2

⇔

Step-by-step explanation:

9514 1404 393

Answer:

  $90

Step-by-step explanation:

Let's consider the remaining money. If x represents the amount Arlene started with, then the remaining amounts are ...

  after first store: x -(0.4x +4) = 0.60x -4

After spending 50% of her money, the amount remaining will be 1-50% = 50%. Then spending 5 more dollars reduces the amount remaining by another 5.

  after second store: (0.60x -4)(0.50) -5 = 0.30x -2 -7 = 0.30x -7

After spending 60% of her money, the amount remaining will be 1-60% = 40%. Then spending 6 more dollars reduces the amount remaining by another 6.

  after third store: (0.30x -7)(0.40) -6 = 0.12x -2.80 -6 = 0.12x -8.80

This is reported to be $2, so we have ...

  0.12x -8.80 = 2

  0.12x = 10.80

  x = 90

Arlene started shopping with $90.

_____

Check

At the first store, Arlene spent 0.40×$90 +$4 = $40, so she had $90-40=$50 remaining.

At the second store, Arlene spent 0.50×$50 +$5 = $30, so she had $50-30=$20 remaining.

At the third store, Arlene spent 0.60×$20+$6 = $18, so she had $20-18 =$2 remaining.

Answer:

15

Step-by-step explanation:

First do, 30% + 45% = 75%. Then do, 100-75=25.

Lastly,

proportions:

   x/60 = 25/100

So your answer is, 15.

Step-by-step explanation:

do 590 divided by 90 if that doesn't work multiply it

Answer:

29/22

Step-by-step explanation:

Let x = 1.31818181818....

Then, 10x = 13.18181818..., and 1000x = 1318.18181818..... Subtracting the first equation from the second, we get that 990x = 1305. This means that x = 1305/990. In lowest terms, this is 29/22.

Answer:

2540

Step-by-step explanation:

25% is a quarter of 100% so if 635 is 25% you multiple 635 x 4 to get your final answer concluding in 2540. if i'm wrong let someone else correct me :b

Volume = 13in * 9in * 2in = 234in³.

Answer:

234 inches³

Step-by-step explanation:

Formula for volume of a prism = [tex]L \times W \times H[/tex] (L = length, W = width, H = height)

[tex]\therefore[/tex] volume for baking dish = 13 × 9 × 2

                                          = 234 inches³

Hope this helps :)

Step-by-step explanation:

Initial dimension of a sand castle is 54 inches by 77 inches. Mike decided to change the size, making it 112 inches by 38 inches.

He wanted to dug a moat around it.

The perimeter of moat with initial dimensions,

P = 2(54+77)

= 262 inches

The perimeter of moat with new dimensions,

P = 2(112+38)

= 300 inches

Difference in perimeter = 300 - 262

= 38 inches

Hence, the new dimension is 38 inches longer than the initial dimensions.

1. Geneva has 24 points. Then her spin lands on blue. What is her score now? Explain.

Blue = + 4. This means that you will need to add 4 to 24, causing Geneva's new amount of points to be 28. You could put down,

Geneva now has 28 points. Blue is equal to +4, so I added 24 + 4 to get 28.

2. Geneva and Juan start a new game. Each player has 0 points.

a. Geneva's first two spins are yellow and red. What is her score now? Explain.

Geneva's score is now -2. Yellow is equal to -4, red is equal to +2. -4 + 2 = -2.

b. Juan's first two spins are red and green. What is his score now? Explain.

Red is equal to +2 and green is equal to -1. That means that Juan has 1 point because 2 + -1 = 1.

c. Which player has a greater score now? Explain.

Juan has a greater score. He has a greater score because 1 is greater than -2.

Answer:

Candy = $ 0.5

Soda = $ 4.0

Step-by-step explanation:

x + 2y = 5

x + 4y = 6

2y = 1

y = 1/2

= two candies were added and the price increased by 1 dollar, meaning that the a single candy is 0.5 dollar

1 candy = 0.5

x + 2(0.5) = 5

x + 1 = 5

x = 4

Answer:

Infinite/many

Step-by-step explanation:

3x + 7 + 2x = 5x + 7

3x + 2x + 7 = 5x + 7

5x + 7 = 5x + 7

5x - 5x + 7 = 7

7 = 7

Infinite solutions

Answer: many (all real numbers)

Step-by-step explanation:

1) add 2x and 3x to give you 5x

You now have 5x+7=5x+7

2) you can simplify this by subtracting 7 on both sides and dividing by 5

3) you are then left with x=x

Answer:

Option F is true.

Step-by-step explanation:

The rule of reflection across the x-axis

P(x, y) → P'(x, -y)

For example, when a point P with coordinates (1, 2) is reflected across the x-axis, the coordinates of the image of point P will be: P'(1,-2).

i.e.

P(x, y) → P'(x, -y)

P(1, 2) → P'(1, -2)

Now, given FGH with vertices F(-1, 3), G(-5, 1), and H(-3, 5) reflected by Rx-axis.

Using the  rule of reflection across the x-axis

Thus, the coordinate of vertices F'G'H the image of FGH will be:

F(-1, 3) → F'(-1, -3)

G(-5, 1) → G'(-5, -1)

H(-3, 5) → H'(-3, -5)

Hence, option F is true.

Answer:

649

Step-by-step explanation:

Given the expression :

__ ÷ 18 > 86

Let blank = y

y ÷ 18 > 36

y / 18 > 36

Multiply both sides by 18

(y / 18) * 18 > 36 * 18

y > 648

Hence, the least whole number which can make the statement true is (648 + 1) = 649

Answer:

625 cm³ and 64000 cm³

Step-by-step explanation:

Given

x = [tex]\sqrt[3]{V}[/tex] ( cube both sides )

x³ = V

(a)

x = 25 cm , then

V = 25³ = 625 cm³

(b)

x = 40 cm , then

V = 40³ = 64 000 cm³

Answer:

(6x^4-7)(6x^4+7)

Step-by-step explanation:

36x^8-49

1. look for a gcf. since there isn't one, you move on to the next step.

2. what multiplies to what you need. you can do box method or diamond method.

3. (6x^4-7)(6x^4+7)

Answer:

C

Step-by-step explanation:

Answer:

one and fifty-four thousandths

Step-by-step explanation:

The 1 is easy.

The 4 is in the thousandths place, so the decimal part is 54/1000.

Answer: one and fifty-four thousandths

Answer:

55

Step-by-step explanation:

12 x 5 = 60

60-5 = 55

55 is not prime

Answer:

There are 26.75 gallons in the pool.

Step-by-step explanation:

Divide 42.8 by 8, multiply the quotient by 5.

Answer:

26.75

Step-by-step explanation:

42.8 * 5/8 = 26.75

Answer:

a) The maximum height of the ball is 272.25 feet

b) The balls take 8 seconds to hit the ground.

Step-by-step explanation:

a) You know that the quadratic function h(t)=−16*t²+124*t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.

Being a quadratic function of the form:

f (x) = a*x² + b*x + c

The vertex of a quadratic or parabola equation is the highest or lowest point on the graph corresponding to that function. When a> 0, the vertex of the parabola is at the bottom of it and indicates the minimum of the function. When a <0 the vertex is at the top and indicates the maximum of the function.

The value of x at the vertex is calculated by the expression:

[tex]x=\frac{-b}{2*a}[/tex]

The value of y at the vertex is calculated by substituting the value of x at the vertex into the quadratic function.

In this case, being a=-16, b=124 and c=32  you get that the maximum time is:

[tex]x=\frac{-124}{2*(-16)}=3.875[/tex]

Then a maximum height of:

h(3.875)=−16*(3.875)²+124*3.875+32

h(3.875)= 272.25

The maximum height of the ball is 272.25 feet

b) When the ball hits the ground the height is zero. So h (t) = 0:

0=−16*t²+124*t+32

Applying the resolvent:

[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a} =\frac{-124+-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)}[/tex]

you get:

[tex]\frac{-124+\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =-0.25[/tex]

[tex]\frac{-124-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =8[/tex]

Since the time cannot be negative, the balls take 8 seconds to hit the ground.