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salantis [7]
3 years ago
5

Last year, Lien earned $1,600 more than her husband. Together they earned $51,000. How much did each of them earn?

Mathematics
1 answer:
jok3333 [9.3K]3 years ago
3 0

Answer:

Lien: $26300 Her husband: $24700

Step-by-step explanation:

x+(x+1600)=51000

2x+1600=51000

2x=49400

x=24700

Her husband earned 24700

24700+1600=26300

Lien earned 26300

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7. If F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6.. Find F'(5) <br>​
serious [3.7K]

Answer:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

x | f (x) | f ' (x) | g (x) | g ' (x)

--------------------------------------

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

(f (g (x))) ' = g ' (x) f ' (g (x))

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

by jannat <33

7 0
3 years ago
Read 2 more answers
Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge
exis [7]

Answer:

Options A and D are correct choices.

Step-by-step explanation:

We have been given an inequality x\leq -7 and we are asked to find the correct options from our given choices.

Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.

(A) 3x\leq -21  

x\leq \frac{-21}{3}

x\leq -7

We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.

(B) 3x\geq -21

x\geq \frac{-21}{3}

x\geq -7

This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.

(C) -3x\leq 21

Dividing inequality by a negative number swaps inequality sign.

x\geq \frac{21}{-3}

x\geq -7

This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.

(D) -3x\geq 21  

Dividing inequality by a negative number swaps inequality sign.

x\leq \frac{21}{-3}

x\leq -7

We can see that option D gives the same answer as our given inequality, therefore, option D is the correct choice.  

8 0
3 years ago
What is the distance between between 120 and -50 on the number line
Otrada [13]
170

Because you have to add
120 + 50 = 170
4 0
3 years ago
5 equivalent fractions of 4/8​
qwelly [4]

Answer:

2/4 1/2 5/10 6/12 10/20

Step-by-step explanation:

just pick an even denominator and take half of that number for the numerator. This only works because the most basic form of 4/8 is 1/2. This method only works if your selected fraction is equivalent to 1/2.

7 0
3 years ago
Read 2 more answers
Find the volume. Answer without units. *<br> 2<br> 4- in<br> 5<br> 3 in<br> 3<br> 16 - in<br> 4
Harman [31]

Answer:

the answer is 221.1

Step-by-step explanation:

8 0
3 years ago
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