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posledela
3 years ago
10

A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 95% pure anti

freeze. In order to obtain 70 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Mathematics
1 answer:
Dimas [21]3 years ago
7 0

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

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Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12? O X= -2. x = 1 O x= -2 x = 4 O x = 2. x = 4 O x = 2
puteri [66]

The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3

<h3>What is function?</h3>

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

According to the question,

The given function is

f(x) = -5|x + 1| + 3

Here f(x) = -12

Substitute f(x) and solve for x

- 12 = -5|x + 1| + 3

By subtracting 3 on both sides

- 12 - 3 = -5|x + 1| + 3 - 3

- 15 = -5|x + 1|

By dividing -5 on both sides

3 = |x + 1|

We get absolute values for the function.

x + 1 = 3 , x + 1 = -3

By subtracting 1 on both sides

x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 ,  x = - 4

Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3

Learn more about function here: brainly.com/question/12431044

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2 years ago
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Step-by-step explanation:

6 0
2 years ago
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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
In-s [12.5K]

Answer:

For x∈ {-∞,-3} y<0, below x-axis

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Step-by-step explanation:

f(x)=2x^{3}-26x-24

2x^{3}-26x-24=0

2x^{3}-26x-24=0\\2x^{3}-2x-24x-24=0\\2x(x^{2} -1)-24(x+1)=0\\2x(x+1)(x-1)-24(x+1)=0\\(x+1)(2x^{2} -2x-24)=0\\=> x+1=0 => x_{1}=-1\\

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x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis



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3 years ago
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