Ellen thinks that if a line has no slope, then it never touches the y-axis. Which line proves that her statement is incorrect?

A rectangular conatainer with a square base is 2/3 full of water. This water is used to fill some small containers how many smal

vivado [14]

Answer:

5 small containers will be required and used.

This water is used to fill four and half small containers exactly.

4.5 small containers

Step-by-step explanation:

The rectangular container has dimensions 12*12*45 cm and the small container has dimensions 6*5*8 cm

The rectangular container with a square base is 2/3 full of water.The height is used up to 45*2/3= 7.5 cm

The volume of the water in the rectangular container with a square base is

12*12*7.5= 1080 cm³

The volume of the water in the smaller container is

6*5*8= 240 cm³

Number of smaller containers required = Volume of large container / Volume of smaller container

Number of smaller containers required =1080 cm³/240 cm³= 4.5

This water is used to fill four and half small containers exactly.

6 0

3 years ago

1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

1.

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

2.

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

3.

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

4.

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

7 0

3 years ago

Can Someone help me I'll do 15 points! I don't know if im correct

Ahat [919]

Answer:

No your answer is incorrect the correct answer is y=1x

Step-by-step explanation:

The answer is y=1x because starting from the origin you do rise over run so since the slope is 1 you would rise 1 and because x=1 you would "run" over 1 sorry i am bad at explaining but the answer is y=1x im pretty sure

6 0

3 years ago

What is 10/14 divided by 2 equal

alexandr402 [8]

10/14 divided by 2 = 0.35714285714

4 0

4 years ago

How did the transformation of ()=f of , open x close . equals , x squared to ()=−g of , open x close . equals , x squared , minu

Nikolay [14]

The intercepts are the points where the graph crosses the x or y-axis

The x-intercepts changed from 0 to $\±\sqrt 3$ .
The y-intercepts changed from 0 to 3

The functions are given as:

$f(x) = x^2$

$g(x) = x^2 - 3$

Function f(x)

$f(x) = x^2$

The x-intercept is calculated as follows:

Set f(x) to 0

$x^2 = 0$

Solve for x

$x = 0$

The y-intercept is calculated as follows:

Set x to 0

$f(0) = 0^2$

$f(0) = 0$

Hence, the intercepts are 0

Function g(x)

$g(x) = x^2 - 3$

The x-intercept is calculated as follows:

Set g(x) to 0

$x^2 - 3 = 0$

Solve for x

$x^2 = 3$

$x = \±\sqrt 3$

The y-intercept is calculated as follows:

Set x to 0

$g(x) = x^2 - 3$

$g(0) = 0^2 - 3$

$g(0) = - 3$

The x-intercepts are $\±\sqrt 3$ , while the y-intercept is -3

By comparing the intercepts of f(x) and g(x),

The x-intercepts changed from 0 to $\±\sqrt 3$ .
The y-intercepts changed from 0 to 3