Which input value produces the same output value for the two functions on the graph?
a)-1
b)0
c)3
d)4

Answer:

[tex]h=8\frac{1}{2}\text{ inch}[/tex]

Step-by-step explanation:

Let h represent height of prism.

We have been given that Tana fills the prism with base lengths [tex]3\frac{1}{4}[/tex] inch and [tex]4[/tex] inch with a [tex]110\frac{1}{2}\text{ inch}^3[/tex].

We know that volume of prism is area of base times height, so we can set an equation as:

[tex]\text{Volume of prism}=\text{Base length}\times\text{Base width}\times \text{Height of prism}[/tex]

[tex]110\frac{1}{2}\text{ inch}^3=3\frac{1}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]

[tex]\frac{221}{2}\text{ inch}^3=\frac{13}{4}\text{ inch}\times 4\text{ inch}\times h[/tex]

[tex]\frac{221}{2}\text{ inch}^3=13\text{ inch}^2\times h[/tex]

[tex]\frac{221}{2*13\text{ inch}^2}\text{ inch}^3=\frac{13\text{ inch}^2\times h}{13\text{ inch}^2}[/tex]

[tex]\frac{221}{26}\text{ inch}=h[/tex]

[tex]8\frac{13}{26}\text{ inch}=h[/tex]

[tex]8\frac{1}{2}\text{ inch}=h[/tex]

Therefore, the height of the prism is [tex]8\frac{1}{2}\text{ inch}[/tex].

34x +14 = 30x +22

34x = 30x + 8

4x =8

x = 8/ = 2

 each question was worth 2 points

Christian's home is 10 miles away from the airport. He paid for one mile at the initial fare and 60 sets of 1/6 mile at the per-set rate, totaling 10 miles including the first mile.

The taxi fare Christian paid was $12.50, including a $1.60 tip. The initial charge by the cab company is $1.90 for the first mile. Therefore, without the tip, the fare for the distance traveled is $12.50 - $1.60 = $10.90. The first mile costs $1.90, so the remaining $9.00 covers the additional miles. As the company charges $0.15 for each additional 1/6 of a mile, we need to calculate how many sets of 1/6 mile are covered by $9.00.

To find out how many 1/6 miles can be covered by $9.00, we divide $9.00 by $0.15, which gives us 60. This means Christian traveled 60 sets of 1/6 mile beyond the first mile. Therefore, the total distance is the first mile plus 60 times 1/6 mile, which equals 10 miles in total.

So, Christian's home is 10 miles away from the airport.

The required time that spent on the Act II in the rehearsal is 1 3/4 hours.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The rehearsal for Acts I and II of the school play lasted 5 1⁄2 hours.
3 3⁄4 hours were spent rehearsing Act I,
let the time spent on the Act II be x,
According to the question,
x  = 5 1/2 - 3 3/4
x = 5 - 3 + 1/2 - 3/4
x = 2 -1/4
x = 1 3/4

Thus, the required time that spent on the Act II in the rehearsal is 1 3/4 hours.

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Answer:

100 boys at the concert

Step-by-step explanation:

At a country concert, the ratio of the number of boys to girls is 2:7

Let 'b' be the number of boys in the concert

there are 250 more girls than boys

so b+250 are the number of girls in the concert

the ratio of boys to girls is b: b+250

Now make a proportion using the ratio

[tex]\frac{2}{7} =\frac{b}{b+250}[/tex]

Now solve for b . cross multiply the fraction

[tex](b+250) \cdot 2= 7 \cdot b[/tex]

[tex]2b+500= 7b[/tex]

Subtract 2b from both sides

[tex]5b= 500[/tex]

Divide both sides by 5

b=100

So there are 100 boys at the concert

Answer:

7x+x^-16x+

Step-by-step explanation:

Steve washed 15 cars in 3 hours and can wash 35 cars in 7 hours.

We have given that Steve washed 15 cars in 3 hours.

We have to determine if the cars can be Washed in 7 hours.

15/3 = x/7.

Use cross products and multiply 15*7

= 105/3

= 35.

He can wash 35 cars in 7 hours

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The answer would be B!

To find the total number of candies, square 108 and then multiply by 100. The steps result in a total of 1,166,400 candies in the store.

Calculating the Total Number of Candies

The expression provided is (108) 2 × 100. To calculate this, first square 108, which means you multiply 108 by itself, and then multiply the result by 100. So the calculation will look like this: 108 × 108 × 100.

To carry out this multiplication, the steps are:

Square 108: 108 × 108 = 11,664.

Multiply the result by 100: 11,664 × 100 = 1,166,400.

Therefore, the total number of candies in the store is 1,166,400.

To find the total number of candies in the store given the expression [tex](108)^2[/tex] times 100, you first square 108 to get 11,664 and then multiply that by 100, resulting in 1,166,400 candies.

The student's question asks for the total number of candies in a store given the expression [tex](108)^2[/tex]  times 100.

To find the total, we need to calculate the square of 108 and then multiply the result by 100.

First, 1082 equals 11,664 (108 multiplied by itself).

Next, we multiply 11,664 by 100 to find the total number of candies, which gives us 1,166,400 candies.

Hence, there are 1,166,400 candies in the store.

Step-by-Step Solution:

Therefore, the store has 1,166,400 candies in total.

Answer:

[tex]x = \frac{8}{3}[/tex] is the solution to  [tex]\log_2 9x - \log_2 3 = 3[/tex]

Step-by-step explanation:

Using the logarithmic rules:

[tex]\log \frac{m}{n} = \log m -\log n[/tex]

if [tex]\log_b x = a[/tex] then;

[tex]x = b^a[/tex]

Given the equation:

[tex]\log_2 9x - \log_2 3 = 3[/tex]

Solve for x:

Apply the logarithmic rules:

[tex]\log_2 \frac{9x}{3} = 3[/tex]

⇒[tex]\log_2  3x = 3[/tex]

Apply the logarithmic rules;

[tex]3x = 2^3[/tex]

⇒[tex]3x = 8[/tex]

Divide both sides by 3 we have;

[tex]x = \frac{8}{3}[/tex]

Therefore, the solution for the given equations is, [tex]x = \frac{8}{3}[/tex]

Answer: B or option two on edg

X = 8/3

Step-by-step explanation: