If f(x)= x^3 - 2x^2, find f(-2)

the combined age of april and laura is 23 years. laura's age is two years more than half of april's age. what is laura's age

Kipish [7]

Laura's age is 9 years.

Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

<u>Convert statement into algebraic expression:</u>

Half of April's age = $\frac{x}{2}$

2 years more than half of April's age = $\frac{x}{2}+2$

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

$$\Rightarrow \ \ x+(\frac{x}{2}+2) =23$

$$\Rightarrow \ \ x+\frac{x}{2}+2 =23$

$$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23$

To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

$$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23$

$$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23$

Denominators are same, now add the fractions.

$$\Rightarrow \ \ \frac{2x+x+4}{2} =23$

Do cross multiplication.

$$\Rightarrow \ \ 2x+x+4=23\times2$

$$\Rightarrow \ \ 3x=46-4$

$$\Rightarrow \ \ 3x=42$

$$\Rightarrow \ \ x=14$

Aprils's age = 14 years

Laura's age = $\frac{14}{2}+2$

= 7 + 2

Laura's age = 9

Hence Laura's age is 9 years.

8 0

2 years ago

Which of the following changes gives no evidence that a chemical reaction has taken place?

grigory [225]

I think the correct answer for this is
a cube of solid forms a puddle of liquid
but i am no sure it's correct or no

5 0

2 years ago

Can someone see if these are right?

qwelly [4]

I didn't get the same answers.

In this problem, 25 is your constant (the number of baby hats you already started out with).
26 will be affected by your variable, d, the number of days. With each day that passes, 26 more hats will be knit, so the expression 26d can be used.

Set h equal to the constant + hats made per day to create an expression that you can use to solve for h:
h = 26d + 25

Now, just plug the numbers in for d to get h:
When d = 2, h = 26d + 25 = 26(2) + 25 = 77
When d = 4, h = 26d + 25 = 26(4) + 25 = 129
When d = 7, h = 26d + 25 = 26(7) + 25 = 207
When d = 9, h = 26d + 25 = 26(9) + 25 = 259

Your answers should be:
77
129
207
259

5 0

2 years ago

Which of the following statements are true about the function y = 3x?

dolphi86 [110]

Answer:

I believe the answer is The constant of variation is y is 6 when x is 2.

6 0

2 years ago

What do the letters I and P and R mean in "IPRT"?

cupoosta [38]

So P stands for principle which is the amount of the original investment, R stands for rate which is the percent but must be turned into a decimal, T stands for time for example if the time was in a certain amount of months then you plug that in with x/12, and lastly I stands for interest which is the original investment outcome ^_^

6 0

2 years ago