Mateo wrote the equation 8-2(3-x)=4x-2(x+1).How many solutions are there to Mateo’s equation?

A. No solution
B. exactly one solution
C. exactly two solutions
D. exactly many solutions

Answer:

[tex](3x+5)+\frac{28}{2x-4}[/tex]

Step-by-step explanation:

Since,

The volume of a rectangular prism = Base area × Height,

Given,

Volume of the rectangular prism = [tex]6x^2-2x+8[/tex]

Base area = 2x - 4

Let h be the height,

[tex]\implies 6x^2-2x+8=(2x-4)h[/tex]

[tex]\implies h = \frac{6x^2-2x+8}{2x-4}[/tex]

By long division ( shown below ),

[tex]h=(3x+5)+\frac{28}{2x-4}[/tex]

Which is the required expression that represents the height.

Answer:

[tex](3x+5) + \frac{14}{x-2}[/tex]

Step-by-step explanation:

We are given the following information in the question:

Volume of rectangular prism =

[tex]6x^2 - 2x + 8[/tex]

Area of base of prism =

[tex]2x -4[/tex]

Formula:

[tex]\text{Volume of Prism} = \text{Area of base}\times \text{Height of prism}\\\\\text{Height of prism} = \displaystyle\frac{\text{Volume of Prism} }{\text{Area of base}}[/tex]

Putting the values we, get,

[tex]\text{Height of prism} = \displaystyle\frac{6x^2 - 2x +8}{2x-4} = \frac{2(3x^2-x+4)}{2(x-2)}= (3x+5) + \frac{14}{x-2}[/tex]

Hence, the height of the prism is given by the expression [tex](3x+5) + \frac{14}{x-2}[/tex]

The formula of a circumference is:

[tex]C=2\pi r[/tex]

r - radius

or

[tex]C=d\pi[/tex]

d - diameter

We have d = 12cm. Substitute:

[tex]C=12\pi\ cm[/tex]

One-fourth of the circumference:

[tex]\dfrac{1}{4}C=\dfrac{1}{4}\cdot12\pi=3\pi\ cm\approx3\cdot3.14=9.42\ cm[/tex]

Answer:

1.A =113.04  cm^2

2.A =616  in^2

Step-by-step explanation:

To find the area of a circle we use the formula

A = pi * r^2  if we know the radius or

A = pi * (d^2/4) if we know the diameter

In problem 1 we know the radius

A = pi * r^2

A = pi * (6)^2

A = 36*pi

Using 3.14 for pi

A = 36* 3.14

A =113.04  cm^2

In problem 2 we know the diameter

A = pi * d^2/4

A = pi * (28)^2/4

A = pi 784/4

A = 196

Using 22/7 for pi

A = 196*22/7

A =616  in^2

Answer:

1. Area of the circle with 6 cm radius is [tex] 113.14 cm^2[/tex].

2. Area of the circle with 28 cm diameter is [tex] 616 cm^2[/tex].

Step-by-step explanation:

1. Radius of the circle ,r=  6 cm

Area of the circle , A= [tex]\pi r^2[/tex]

[tex]A=\pi (6 cm)^2=\frac{22}{7}\times 6 cm\times 6 cm=113.14 cm^2[/tex]

Area of the circle with 6 cm radius is [tex] 113.04 cm^2[/tex].

2. Diameter of the circle = d = 28 cm

Radius of the circle , r = [tex]\frac{28 cm}{2=14 cm[/tex]

Area of the circle , A= [tex]\pi r^2[/tex]

[tex]A=\pi (14 cm)^2=\frac{22}{7}\times 14 cm\times 14 cm=616cm^2[/tex]

Area of the circle with 28 cm diameter is [tex] 616cm^2[/tex].

Answer: The plan with 250 minutes is best because she Maximus uses only 245 minutes per month so just 5 min to spare. Also i used mental math

Step-by-step explanation:

1470 divided by 6 equals= 245 minutes exactly unless Katherine had rounded her answer

Final answer:

To determine the best cell phone plan for Katherine, compare the cost per minute for each plan. The second plan, which allows up to 350 minutes per month for $65, has a lower cost per minute.

Explanation:

To determine the best cell phone plan for Katherine, we need to compare the cost per minute for each plan.

For the first plan, Katherine gets 250 minutes for $49, which means the cost per minute is $49/250 = $0.196 per minute.

For the second plan, Katherine gets 350 minutes for $65, which means the cost per minute is $65/350 = $0.1857 per minute.

Since the cost per minute is lower for the second plan, Katherine should choose the plan that allows up to 350 minutes per month for $65.

Answer:

-88

Step-by-step explanation:

Let N(x) be the number of students at NMS for a certain number of years.

Let S(x) be the number of students at SMS for a certain number of years.

Let x be the number of years.

N(x)=1240-25x

S(x)=800-30x

When # of students is equal, N(x)=S(x). Therefore, we are looking for the value of x (# of years) when 1240-25x=800-30x

Subtract 1240 from each side

-25x=-440-30x

Add 30x

5x=-400

x=-88 years

Check your numbers.

Answer:

$20.00

Step-by-step explanation:

"$25 pants, 20% off" is equivalent to (1.00 - 0.20)($25), or:

0.80($25) = $20.00

This is the total cost to the nearest cent.

Answer:

$20

Step-by-step explanation:

Lets find the discount

25 * .2 = 5

You get $5 off

Price - discount = price you pay

25-5 = 20

Answer:

Answer:  2 a + 11

Step-by-step explanation:

Simplify the following:

5 a - a - 2 a - 6 + 17

Grouping like terms, 5 a - a - 2 a - 6 + 17 = (-a - 2 a + 5 a) + (17 - 6):

(-a - 2 a + 5 a) + (17 - 6)

-a - 2 a + 5 a = 2 a:

2 a + (17 - 6)

17 - 6 = 11:

Answer:  2 a + 11

The expression 17-a-2a-6+5a simplifies to 2a+11. This involves combining similar terms and simplifying the arithmetic.

Explanation:

In order to simplify the expression 17-a-2a-6+5a, we first need to gather like terms. In this expression, the like terms are -a, -2a, and +5a. When you add these together, you get 2a. Now, substitute this back into the expression. You now have 17+2a-6. If you simplify further by adding the plain numbers together, you get 2a+11. Therefore, the simplified expression is 2a+11.

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Answer:

Step-by-step explanation:

A proportional relationship is a straight line through the origin that grows at a constant rate

For table C

The constant of proportionality is y/x

2/1 = 4/3 = 6/5 = 8/7   This is not true so this is not proportional

For table D

The constant of proportionality is y/x

1/2 = 3/6 = 4/8 = 5/10   This is  true so this is  proportional

Answer:

The unit rate is 0.14 cents per ounce.

Step-by-step explanation:

Divide 3.92 by 28 to find out how much the trail mix is per ounce.

The unit rate of Dmitri's trail mix purchase is $0.14 per ounce, calculated by dividing the total cost by the total weight.

To find the unit rate of Dmitri's trail mix purchase, we divide the total cost of the trail mix by the total weight of the trail mix. Dmitri bought 28 ounces of trail mix for $3.92, so we perform the following calculation:

Unit Rate = Total Cost / Total Weight

Unit Rate = $3.92 / 28 ounces

Unit Rate = $0.14 per ounce

Therefore, the unit rate is $0.14 per ounce. This means that for every ounce of trail mix, Dmitri paid $0.14.

Answer:

Total cost of boots = $56.02

Step-by-step explanation:

$59 x 0.90 = $53.10

$53.10 x 1.055 = $56.02

or

59 x 0.10 = 5.9

59 - 5.9 = $53.10

53.10 x 0.055 = $2.92 tax

$53.10 + $2.92 = $56.02

Answer:

c.2

Step-by-step explanation:

6x+18=h(3x+9)

To have an infinite number of solutions, the left and right side must be equal

Distribute the h

6x+18 = 3xh +9h

6x = 3xh

Divide by x

6x/x = 3xh/x

6 = 3h

Divide by 3

6/3 =3h/3

2 =h

Lets verify

18 = 9h

Divide by 9

18/9 = 9h/9

2 =h

h must be 2

Answer:

4.6

Step-by-step explanation:

8.1 + (-3.5) = 8.1 - 3.5

4.6

Answer:

z = 7

Step-by-step explanation:

9z + 4 / 5 - 8 = 5.4

Add 8 to both sides.

9z + 4 / 5 = 13.4

Multiply 5 by both sides.

9z + 4 = 67

Subtract 4 from both sides.

9z = 63

Divide both sides by 9.

z = 7

Answer:

7 (rounded up)

Step-by-step explanation:

9z+4/5=13.5

Multiply both sides by 5

9z+4=67.5

Subtract both sides by 4

9z=63.5

Divide both sides by 9

z=7 (rounded up)

Answer:C

Step-by-step explanation:If she studies for 10 munites and t equals munite t would go next tp 10 then d would go under it.

Answer:

1/28

Step-by-step explanation:

think what two can be divided by it can only be divided by two

think if 56 can, it could so 2 divided by 2 is 1 and 56 divided by two is 28 so the answer is 1/28

Answer:

Option C) graph of line going through 1, 4 and 3, 10

Step-by-step explanation:

Let y equal to Margo's coin collection

Let x equal to number of years

At the begining x=0, y=1 → Point=(x,y)→Point=(0,1)

She adds 3 coins per year, then y=1+3x

At x=1, y=1+3(1)=1+3→y=4→Point=(x,y)→Point=(1,4)

At x=3, y=1+3(3)=1+9→y=10→Point=(x,y)→Point=(3,10)

The graph of line going through (1, 4) and (3, 10), then the option C is the correct.

Answer:

225 m

Step-by-step explanation:

Since we know they are similar triangles

8                15

---------- = -----------  

120              bridge

Using cross products

8 * bridge = 15* 120

8* bridge = 1800

Divide each side by 8

8/8* bridge = 1800/8

bridge = 225

Answer:

225m

Step-by-step explanation:

the 2 triangles shown are similar by AAA

so their sides are in the same ratio

bridge/15 = 120/8

bridge length = 15*15 = 225m

check the picture below.

Answer:

The answer is PQ is the diameter

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

45 divided by 9 is 5. So you multiply 4 times 5. Which equals 20. So 20 plus 45 is 65. Hope you understand it.

An integer is any whole number and it can be positive or negative. Integers cannot be fractions!

A few examples of integers are...

21, 4, -6666

Answer: (3√14)/14

Step-by-step explanation: you should go buy a scientific calculator Casio or a TI calculator not much about $10 i will help a lot

Answer:

[tex]\frac{c-a}{2}[/tex]

Step-by-step explanation:

given [tex]\frac{a}{2x-c}[/tex] = - 1 ( cross- multiply )

- (2x - c ) = a ( distribute left side )

- 2x + c = a ( subtract c from both sides )

- 2x = a - c ( multiply both sides by - 1 )

2x = c - a ( divide both sides by 2 )

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

Answer:

x = [tex]\frac{(a - c)}{-2}[/tex]

Step-by-step explanation:

a/(2x-c) = -1

The first step is to multiply both sides by (2x - c)

(2x - c)a/(2x-c) = -1(2x - c)

a = -2x + c

a - c = -2x + c - c

a - c = -2x

Divide both side by -2

(a - c)/-2 = x

∴ x = [tex]\frac{(a - c)}{-2}[/tex]

Answer:

[tex]x=2.8[/tex]

Step-by-step explanation:

we are given that

line passes through (2,-1) and (6,4)

Firstly, we will find equation of line

First point is (2,-1)

x1=2, y1=-1

second point is (6,4)

x2=6 , y2=4

now, we can find slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

now, we can plug values

[tex]m=\frac{4+1}{6-2}[/tex]

[tex]m=\frac{5}{4}[/tex]

now, we can use point slope form of line

[tex]y-y_1=m(x-x_1)[/tex]

now, we can plug values

[tex]y+1=\frac{5}{4}(x-2)[/tex]

since, we have to solve for x from (x,0)

so, we can set y=0

and then we can solve for x

[tex]0+1=\frac{5}{4}(x-2)[/tex]

[tex]5\left(x-2\right)=4[/tex]

[tex]x-2=\frac{4}{5}[/tex]

[tex]x=\frac{14}{5}[/tex]

[tex]x=2.8[/tex]

Answer:

( [tex]\frac{11}{2}[/tex], 8)

Step-by-step explanation:

Find the midpoint using the midpoint formula

midpoint = [ [tex]\frac{1}{2}[/tex](3 + 8), [tex]\frac{1}{2}[/tex](2 + 14)] = ( [tex]\frac{11}{2}[/tex], 8)

Answer: (5.5, 8)

Step-by-step explanation:

We know that midpoint (x,y) of a line XY having points having points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by :-

[tex]x=\dfrac{x_1+x_2}{2}\ ;\ y=\dfrac{y_1+y_2}{2}[/tex]

Then similarly, the midpoint of AB with endpoints A(3,2) and B (8,14)  will be :_

[tex]x=\dfrac{3+8}{2}\ ;\ y=\dfrac{2+14}{2}\\\\\Rightarrow\ x=\dfrac{11}{2}\ ;\ y=\dfrac{16}{2}\\\\\Rightarrow\ x=5.5\ ;\ y=8[/tex]

Hence, the midpoint of AB with endpoints A(3,2) and B (8,14) = (5.5, 8)

Answer:3.25$

Step-by-step explanation:

If one paperback book is 0.25 and you buy 3 of them, (0.25 x 3) is 0.75 and a hardcover is 0.50 per book, (0.50 x 5) is 2 dollars and 50 cents and if you add the two, you will get 3.25$

The amount of money to spend to buy 3 paperback books and 5 hardback books is,

⇒ $3.25

Given that,

The cost of Used paperback books is $0.25.

And, cost of hardback books is $0.50

Here, the cost to buy 3 paperback books is,

⇒ [tex]3 \times 0.25[/tex]

⇒ $0.75

And, the cost of 5 hardback books is,

⇒ [tex]5 \times 0.50[/tex]

⇒ $2.50

So, the total cost of 3 paperback books and 5 hardback books is,

⇒ $0.75 + $2.50

⇒ $3.25

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Answer:

6 units away from 0.

Step-by-step explanation:

when move to 6 you count the units.

Answer:

Marcia can make a total of 80 batches of soup

Step-by-step explanation:

400(total ounces)/5(ounces per batch)=80 batches

Answer:

80 batches of soup can Marcia .

Step-by-step explanation:

Given  : Marcia uses 5 ounces of chicken stock to make one batch of soup.She has a total of 400 ounces of chicken stock.

To find : How many batches of soup can Marcia make.

Solution : We have given

Marcia uses 5 ounces of chicken stock  =  1. batch of soup

Marcia uses 1 ounces of chicken stock = [tex]\frac{1}{5}[/tex].

Marcia uses 400 ounces of chicken stock =  [tex]\frac{400}{5}[/tex].

                                                                      = 80 batch of soup.

Therefore, 80 batches of soup can Marcia .

Answer:

y = 5x + 29

Step-by-step explanation:

y=5x+2

Given equation is in the form of y=mx+b

Where m is the slope = 5

and b is the y intercept = 2

When the lines are parallel then their slopes are equal

So the slope of parallel line is also 5 (m=5)

Given that the line passes through (-6,-1)

We use point slope formula

y-y1= m (x-x1)

m=5, x1= -6, y1=-1

Plug in all the values

y - (-1) = 5(x-(-6))

y + 1= 5 (x+6)

y + 1= 5x + 30

Subtract 1 on both sides

y = 5x + 29