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harina [27]
3 years ago
8

Use these functions to answer the questions.

Mathematics
1 answer:
Elenna [48]3 years ago
4 0
Part A
We have f\left(x\right)=\left(x+3\right)^2-1. To solve for the x-intercept, we set f(x) equal to 0.  That is
     \left(x+3\right)^2-1=0

     \left(x+3\right)^2=1

Take the square root of both sides, 
     x+3=1

     x=-2

The x-intercept is (-2,0). 

To solve for the y-intercept, we set x=0. That is 
     y=\left(0+3\right)^2-1=3^2-1=9-1=8

The y-intercept is (0, 8) 

The coordinates of the optimum point are actually the vertex which can be easily seen from the vertex form equation given above. The minimum point is (-3, -1).

Part B.
We have g\left(x\right)=-2x^2+8x+3.
Factor out -2
     =-2\left(x^2-4x\right)+3

Complete the square
     =-2\left(x^2-4x+4\right)+3-2\left(4\right)

Simplify
     g(x)=-2\left(x-2\right)^2-5

Part C
We have h\left(t\right)=-16t^2+28t.
The maximum height is 12.25 feet after 0.875 seconds from the time of the jump. The dolphin will be back in the water after 1.75 seconds. The graph of the jump is shown in the photo. 
     
    

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See attachment below
KatRina [158]

Answer: Third Option

x=1.469743

Step-by-step explanation:

We have the following exponential equation

3^{x+1}=15

We must solve the equation for the variable x

To clear the variable x apply the log_3 function on both sides of the equation

log_3(3^{x+1})=log_3(15)

Simplifying we get the following:

x+1=log_3(15)

To simplify the expression log_3 (15) we apply the base change property

log_b(y)=\frac{log(y)}{log(b)}

This means that:

log_3 (15)=\frac{log(15)}{log(3)}

Then:

x+1=\frac{log(15)}{log(3)}

x=\frac{log(15)}{log(3)}-1

x=1.469743

6 0
2 years ago
Expressions equivalent to 6x+4
stiv31 [10]
2(3x+2) I couldn’t find any other ones, your best bet would be to go into decimals or fractions if you want to find more.
6 0
3 years ago
What percent of 80 is 25
JulsSmile [24]

Answer: 31.25%

Step-by-step explanation: To answer the question <em>what percent of 80 is 25</em>, we translate the question into an equation.

So we have "what percent" that's x, "of 80" means times 80, "is 25" = 25.

Now to solve for <em>x</em>, since <em>x</em> is being multiplied by 80, we need to divide by 80 on both sides of the equation. On the left side of the equation the 80's cancel and we have <em>x</em> and on the right side of the equation, we have 25 ÷ 80 which gives us 0<em>.</em>3125. Now, remember that we want to right our answer as a percent so to write 0.3125 as a percent, we move the decimal point 2 places to the right and we get 31.25%.

Therefore, 31.25% of 80 is 25.

8 0
3 years ago
PLEAS EHELP, NO LINK ANSWERS I WILL GIVE BRAINLY THING ​
Agata [3.3K]

Answer:

H2O and CO2 are examples of compounds

as the have different elements combined in them, and they don't show properties of combining elements..

4 0
3 years ago
What is the sum of 5.3 x 10 to the fifth power and 3.8 x 10 to the fourth power in scientific notation
sweet-ann [11.9K]

Answer:5.6 x 10^5

Step-by-step explanation:

When ever we hear sum, what comes to our mind must be addition

Here we are Adding 5.3 x 10 to the fifth power= 5.3 x 10^5 to

3.8 x 10 to the fourth power = 3.8 x 10^4

First,

Expanding the scientific notation we have that

5.3 x 10^5 = 530,000

3.8 x 10^4=     38,000

Add           = 568,000

Putting back in Scientific notation  we have 568000 = 5.6 x 10^5

8 0
3 years ago
Read 2 more answers
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