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muminat
3 years ago
8

Given f (x) = -12x + 72, find x when f(x) = 24.

Mathematics
1 answer:
Neko [114]3 years ago
4 0

Answer:

x = 4

Given:

f(x) = -12x + 72

f(x) = 24

Step-by-step explanation:

=  >  - 12x + 72 = 24 \\  \\  =  >  - 12x = 24 - 72 \\  \\  =  >   \cancel{- }12x =   \cancel{-} 48 \\  \\  =  > 12x = 48 \\  \\  =  > x =  \frac{48}{12}  \\  \\  =  > x = 4

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You have been asked to build a scale model of a restaurant out of bottle caps. The restaurant is 20 feet tall. Your scale is 2.4
Amanda [17]

Answer:

40\ bottle\ caps

Step-by-step explanation:

we know that

The scale is \frac{2.4}{1}\ \frac{cm}{ft}

That means

2.4 cm in the model represent 1 foot in the real

In this problem

The restaurant is 20 feet tall

Find the height of the model

Multiply the actual height of the restaurant by the scale 2.4

20\ ft=20(2.4)=48\ cm

A bottle cap is 1.2 cm tall

To find out the number of bottle caps divide the height of the model by 1.2

\frac{48}{1.2}= 40\ bottle\ caps

8 0
3 years ago
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). [infinity] 6 n2
vekshin1

Answer:

Step-by-step explanation:

given

\sum\limits^\infty_{n=3}\frac{6}{n^2-1}=\sum\limits^\infty_{n=3}\frac{6}{(n-1)(n+1)}\\\\=\sum\limits^\infty_{n=3}\frac{6}{2}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=\frac{6}{2}\sum\limits^\infty_{n=3}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=3[(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+(\frac{1}{4}-\frac{1}{6})+(\frac{1}{5}-\frac{1}{7})+...]\\\\=3[\frac{1}{2}+\frac{1}{3}]=3[\frac{3+2}{6}]=3[\frac{5}{6}]\\\\=\frac{15}{6}=\frac{5}{3}

5 0
3 years ago
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Step-by-step explanation:

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3 years ago
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8 0
3 years ago
Read 2 more answers
A certain company manufactures skateboards and rollerskates. It takes them 2 units of labor and 1 unit of materials to produce a
Alisiya [41]

Answer: The company should produce 7 skateboards and 16 rollerskates in order to maximize profit.

Step-by-step explanation: Let the skateboards be represented by s and the rollerskates be represented by r. The available amount of labour is 30 units, and to produce a skateboard requires 2 units of labor while to produce a rollerskate requires 1 unit. This can be expressed as follows;

2s + r = 30 ------(1)

Also there are 40 units of materials available, and to produce a skateboard requires 1 unit while a rollerskate requires 2 units. This too can be expressed as follows;

s + 2r = 40 ------(2)

With the pair of simultaneous equations we can now solve for both variables by using the substitution method as follows;

In equation (1), let r = 30 - 2s

Substitute for r into equation (2)

s + 2(30 - 2s) = 40

s + 60 - 4s = 40

Collect like terms,

s - 4s = 40 - 60

-3s = -20

Divide both sides of the equation by -3

s = 6.67

(Rounded up to the nearest whole number, s = 7)

Substitute for the value of s into equation (1)

2s + r = 30

2(7) + r = 30

14 + r = 30

Subtract 14 from both sides of the equation

r = 16

Therefore in order to maximize profit, the company should produce 7 skateboards and 16 rollerskates.

6 0
3 years ago
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