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MariettaO [177]
3 years ago
10

From his last trip, Carl knows that his car's mileage is 22 miles per gallon of gas. How many gallons will he use if he is plann

ing a 668-mile roundtrip? Use the formula d= rg. Where d is the distance, r is the rate in miles per gallon, and g is the number of gallons of gas
Mathematics
1 answer:
Rzqust [24]3 years ago
7 0

Answer:

He would need 31 gallons

also I rounded it

Step-by-step explanation:

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The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the
Ivenika [448]

Answer:

26; the cheetah's rate in miles per hour

Step-by-step explanation:

4 0
3 years ago
There is a spinner with 10 equal areas, numbered 1 through 10. If the spinner
Ksenya-84 [330]

Answer:

10%

Step-by-step explanation:

The multiples of 2 are 2,4,6,8,10, and so on

The multiples of 5 are 5, 10, 15, 20 , 25, and so on

It is evident that the only one that matches up between 1-10 is 10.

There are 10 options, and our chances are random. There is only 1 option for it to be a multiple of both 2 and 5. Therefore, the probability is 1/10, or 10%

3 0
3 years ago
56 times a number minus 13 is equal to 6 less than the number.
Eddi Din [679]

Answer:

<h2>Z = 19/56</h2>

<h2>OR Z = 0.34</h2>

Step-by-step explanation:

The steps in the photo above

I hope that is useful for you :)

4 0
3 years ago
If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?
deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0
2 years ago
A rectangular container has a base that is 12 inches long and 8 inches wide. The container is filled with water to a height of 6
valina [46]

Answer: the length of one edge of the square base of the second container is 6 inches.

Step-by-step explanation:

The formula for determining the volume of a rectangular container is expressed as

Volume = length × width × height

Considering the first container,

Length = 12 inches

Width = 8 inches

Height to which the water is filled is 6 inches.

Therefore, volume of water in the container is

12 × 8 × 6 = 576 inches³

Considering the second container,

Height of water = 16 inches

Let L represent the length of the square base. Then the area of the square base is L²

Volume of water would be 16L²

Since the water in the first container was poured into the second container, then

16L² = 576

L² = 576/16 = 36

L = √36

L = 6 inches

7 0
3 years ago
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