How much did it cost Mark to drive 775 miles? If his car makes 31 mpg and fuel cost $2.00 per gallon.

Step-by-step explanation:

We need to say that [tex]9^{3/4}[/tex] is equivalent to what.

We know that, (3)² = 9

So,

[tex]9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}[/tex]

We can write [tex]3^{3/2} =3\times 3^{1/2}[/tex]

And [tex]3^{1/2}=\sqrt{3}[/tex]

So,

[tex]3\times 3^{1/2}=3\sqrt{3}[/tex]

So, [tex]9^{3/4}[/tex] is equivalent to [tex]3\sqrt{3}[/tex].

Hence, this is the required solution.

Answer:

c = 7

Step-by-step explanation:

ax^2 + bx + c = 0

3x^2 + 5x + 7 = 0

c = 7

Answer:

[tex]\large\boxed{z}[/tex]

Step-by-step explanation:

What is square root of the product of the number z and itself?

Break down into smaller parts

What is the product of the number z and itself?

Product = multiply

Write an equation multiplying z by itself

z * z

Bring back the full question: What is the square root of the product of the number z and itself?

Now we can just add a [tex]\sqrt{}[/tex] to the front of our equation to solve the problem.

[tex]\sqrt{z * z}[/tex]

Simplify

z * z = [tex]z^{2}[/tex]

[tex]\sqrt{z^{2} }[/tex]

In this case, the square root cancels out the exponent ([tex]z^{2}[/tex]), so [tex]\sqrt{z^{2} }[/tex] can simplify to z.

Hope this helps :)

Step-by-step explanation:

Total Surface Area of original cylinder

= (2×(22/7)×9)(9+24)

=18×22/7×33

=1,866.8

Total Surface Area of new cylinder

=(2×(22/7)×9/3)(9/3+24/3)

=(2×(22/7)×3)(3+8)

=6×22/7×11

=207.4

Change or Ratio of org. cylinder to new cylinder

=1,866.8/207.4

=9.0009

Answer:

43

Step-by-step explanation:

Using Thales theorem:

● SP/LN = RP /RN

Notice that RN = 2×RP

● SP/LN = RP/2RP

● SP /LN = 1/2

● SP / (5x-14) = 0.5

● (2x+3)/(5x-14) = 0.5

● 2x+3 = 0.5(5x-14)

● 2x+3 = 2.5x -7

Add 7 to both sides

● 2x+3+7 = 2.5x-7+7

● 2x+10 = 2.5x

Sustract 2x brom both sides

● 2x+10-2x = 2.5x-2x

● 10 = 0.5x

Multiply both sides by 2

● 10×2 = 0.5x×2

● 20 = x

Replace x with 20 in Sp expression:

● SP = 2x+3

● SP = 2×20+3

● SP = 43

Answer:

The maximum number of boxes that will fit on the shelf = 189 boxes

Step-by-step explanation:

First, to harmonize the units of the dimensions given, let us convert the unit of the Pick-Me-Up teabags to cm.

1 cm = 10mm

1mm = 0.1cm

∴ 120mm = 0.1 × 120 = 12cm

Therefore, the base of each box is 12cm²

Next, let us calculate the area of the shelf.

Dimension of shelf = 65cm × 35cm

∴ Area of shelf = 65 × 35 = 2275cm²

Therefore, to calculate how many boxes will fit into the shelf, we will divide the area of the shelf by the area of the boxes of Pick-Me-Up teabag. This is shown below.

Area of shelf = 2275cm²

Area of boxes = 12cm²

Number of boxes that will fit on the shelf = Area of shelf ÷ Area of boxes

= 2275 ÷ 12 = 189.58 boxes

since there are no fractional boxes, we will round down to the nearest whole number of boxes.

Hence, the maximum number of boxes that will fit on the shelf = 189 boxes

Answer:

32 adulta

Step-by-step explanation:

96÷6 = 16 number of families

now we need to see how many adults there are in 16 families.

and the number is 32 adults.

Answer:

32 adults.

Step-by-step explanation:

At the very least, there are 4 children for every 2 adults. That means that, at the very least, there are 6 people in one group to get into the fun fair.

96 / 6 = 16

So, there are 16 groups trying to get into the fun fair, with 2 adults in each group. 2 * 16 = 32 adults are in the queue.

Hope this helps!

Answer:

Step-by-step explanation:

25x(4x -10y + 3)

the solution is C. 25x

Answer:

First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.

The functions here are:

A.f(x) = 2 + 1

B.f(x) = x^2 + 1

c.f(x) = x^2 - 1

D.f(x) == +1

The functions are really poorly written, but i will try to answer this.

first:

"a root at x = -1"

Means that f(-1) = 0,

The only function that is zero when x = -1, is the option c.

f(-1) = (-1)^2 - 1 = 1 - 1 = 0.

Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:

[tex]f(x) = \frac{something}{x - 2}[/tex]

So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.

I can not see this in the options provided, so i guess that the functions are just not well written.

For a horizontal asymptote, we have something like:

[tex]f(x) = \frac{something}{x} + 1[/tex]

So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.

Answer:

18y^3 + 24y^5.

Step-by-step explanation:

6y^3(3 + 4y^2)

= 6*3 y^3 + 6*4 y^(3+2)

= 18y^3 + 24y^5.

Answer:

the ansser is $12

Step-by-step explanation:

becases 10 *6 is equal  to 60 so if 1 person  can not pay then you divide 60 by the remaineing 5 to get 12

A group of 6 people planned to spend $10.00 each to rent a boat for an outing. Each person have to pay 12 dollars.

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

A group of 6 people planned to spend $10.00 each to rent a boat for an outing. At the last minute, 1 person could not go on the outing.

10 x 6 = 60

So if 1 person can not pay then

We will divide 60 by the remaining 5

60/ 5 = 12

Therefore, Each person have to pay 12 dollars.

Learn more about unit price here:

https://brainly.com/question/945712

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Answer: Choice B)

The relation is a function because there are no vertical lines that can be drawn on the graph that pass through more than one point.

This graph passes the vertical line test. Any input (x) leads to one and only one output (y). An example of a graph failing the vertical line test would be a graph that is a sideways parabola.

Answer:

(-4,7)

Step-by-step explanation:

solved by graphing

Answer:

5.08 cm

Step-by-step explanation: You dont have the choices for answers.

2inches is also 1/6 of a foot, etc

Answer:

It would be y = -x + 9

Step-by-step explanation:

Answer:

Y=-x+9

Step-by-step explanation:

Answer:

slope = 2 : 8 or 1:4

Step-by-step explanation:

a(-3, 4)

b(5, 6)

slope = rise / run

slope (6-4, 3+5))

slope = 2 : 8 or 1:4

Answer:

Slope =¼

Step-by-step explanation:

[tex](-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} [/tex]

Answer:

5.2 inches

Step-by-step explanation:

Let a be the side of the square poster.

The area of it is:

● A = a^2

● 27 = a^2

● a = √27

● a = √(9×3)

● a = 3√3

● a = 5.19

Round it to the nearest tenth

● a = 5.2 inches

The length of one side of the poster is approximately 5 inches rounded to nearest tenth.

We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.

According to the given question the area of a square poster is 27inch².

We have to determine the length of one side of the poster.

We know area of a square is (side)².

∴ (side)² = 27.

side = [tex]\sqrt{27}[/tex].

We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.

learn more about rounding of numbers here :

https://brainly.com/question/15235224

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Answer:

x = 16

Step-by-step explanation:

The figure shown shows an inscribed angle F and central angle E. Both angles intercept the same arc.

Therefore, angle E is twice the measure of angle F, according to the central angle theorem of a circle.

Thus,

m<E = 2 * m<F

(x + 94)° = 2(55)

We can find the value of x with this equation.

x + 94 = 110

Subtract 94 from both sides

x = 110 - 94

x = 16

the graph will shift 3 units to the right

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope / gradient

c is the y intercept

y = 3x + 7

Comparing this equation with the general form above

Gradient of the line = 3

2y - 6x = 8

Divide both sides by 2

We have

y - 3x = 8

To make y the subject move 3x to the right side of the equation

That's

y = 3x + 8

Comparing with the general form above that's y = mx + c

The gradient = 3

y = 3x + 7

A(2 , y ) , B( x , 4)

Since they lie on the line we can substitute their values into the equation to find the missing points

For A(2 ,y)

We have

y = 3(2) + 7

y = 6 + 7

For B( x , 4)

4 = 3x + 7

3x = 4 - 7

3x = - 3

Divide both sides by 3

Hope this helps you

Answer:

2n+7

Step-by-step explanation:

First lets find the common difference which is 2, now we can use this formula to find the nth term.

an = a1 + (n - 1 ) d

an= 9+(n-1)2

=9+2n-2

=2n+7

To check let's insert n=5, 2(5)=10+7=17.

15+2=17!

Answer:

=x(x-1) +3x

= x^2-x+3x

=x^2 +2x

=x(x+2)

Step-by-step explanation:

Answer:

7³

Step-by-step explanation:

Using PEMDAS, we see that E (which stands for exponents) comes before M (which stands for multiplication) and A (which stands for addition) so the first operation you should do is 7³.

Answer:

.83

Step-by-step explanation:

If you take 100 shows 60 shows got favorable response and in that 50 shows were successful.

So probability for a show to be successful if it got a favorable response is = 50/60 = 0.83

Answer:

Ty for the free points

Step-by-step explanation:

✊✊✊

Answer:

243 as a power of 3

= 3^5

=243

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

Answer:

5.2/0.052 is 100, and 100 is 10^2, so the missing divisor is 10^2

Answer:

100

Step-by-step explanation:

5.2/x = 0.052

Since the decimal place moves 2 places to the left from 5.2 to 0.052, the divisor is 100.

5.2/100 = 0.052

Answer:

43y

Step-by-step explanation:

31y+12y

combine like terms

Factor out y

y( 31+12)

y (43)

43y

Since we are dealing with two numbers with the same variable (y), all we need to do is combine like terms.

31y + 12y = 43y

Best of Luck!

Answer:

Step-by-step explanation:

Given the  ratio of  the profit, cost of  materials and labour  in the production of

an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25

If the cost of labour is x, the cost of material will be 840+x (since the  cost of materials is Le  840 more than that of  labour)  .

Let the total cost of producing the article be y.

Cost of labour = 13/25 * y = x

Cost of labour  = 13y/25 = x.................... 1

Cost of material = 7/25*y = 840+x

Cost of material = 7y/25 = 840+x ..................... 2

From 1, 13y = 25x

x = 13y/25 ................... 3

Substituting equation 3 into 2:

7y/25 = 840+x

7y/25 = 840+13y/25

collect the like terms:

7y/25 - 13y/25 = 840

-6y/25 = 840

-6y = 25*840

y = 25*840/6

y = 3,500

Hence the total cost of producing the article is 3500