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SVETLANKA909090 [29]
3 years ago
7

Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?

Mathematics
2 answers:
vivado [14]3 years ago
7 0
Hello there!

To find the increasing intervals for this graph just based on the equation, we should find the turning points first.

Take the derivative of f(x)...
f(x)=-x²+3x+8
f'(x)=-2x+3

Set f'(x) equal to 0...
0=-2x+3
-3=-2x
3/2=x

This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity.
Since the leading coefficient is -1, as x approaches ∞, f(x) approaches -∞ Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -∞ is also -∞.

This means that the interval by which this parabola is increasing is...
(-∞,3/2)

PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.

I really hope this helps!
Best wishes :)
Mashcka [7]3 years ago
6 0

Answer:

C

Step-by-step explanation:

the answer is C

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Find the surface area of a square pyramid with a length of 5 cm and a slant height of 8cm.
Tems11 [23]
Area of the square base = 5^2 = 25 cm^2
Area of one of the triangular side = 1/2 * 5 * 8 = 20 cm^2 and there are 4 sides
So the surface area  of while pyramid = 4 * 20 + 25 = 105 cm^2

Volume of the cone = (1/3) pi r^2 h
  = (1/3) pi * 5^2 * 8
  =  209.44  ft^2
8 0
3 years ago
A random sample of 5120 permanent dwellings on an entire reservation showed that 1627 were traditional hogans.
krek1111 [17]

Answer:

a) \hat p=\frac{1627}{5120}=0.3178

b)The 99% confidence interval would be given by (0.301;0.355)

Step-by-step explanation:

1) Notation and definitions

X=1627 number of permanent dwellings on the entire reservation that are traditional hogans.

n=5120 random sample taken

\hat p=\frac{1627}{5120}=0.318 estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.

p true population proportion of permanent dwellings on the entire reservation that are traditional hogans.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

Part a

The point of estimate for p=the proportion of all permanent dwellings on the entire reservation that are traditional hogans is given by:

\hat p=\frac{1627}{5120}=0.3178

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values obtained we got:

0.318 - 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.301

0.318 + 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.335

The 99% confidence interval would be given by (0.301;0.355)

8 0
3 years ago
Match the equation with its corresponding solution for x. 4x + 7 = 35
lyudmila [28]
Are you wanting to solve for x? If so:
4x + 7 = 35
We want to isolate the variable, so subtract 7 from both sides.  You will get:
4x = 28
Now, divide each side by 4 to get X by alone. This will give you:
x = 7
I hope this helped.
8 0
3 years ago
Your state charges 5% sales tax on nonfood items. You're buying a light bulb for $3.00, cereal for $2.50, and an orange for $.50
nekit [7.7K]
Your grand total will be $6.15
3 0
3 years ago
Urgent will mark brainliest
Luda [366]

First, isolate the variable:

x>-33

The answers would be 25, 14, -25.

I am not sure if that is a more than sign or a more than or equals sign; if it is a more than sign the answers mentioned above are the only answers, but if it a more than or equals sign, the answers are 25, 14, -25, -33.

If it helped please consider giving be brainliest :)

7 0
3 years ago
Read 2 more answers
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