The is 12,000ft what the diameter

Use the functions to answer the question.

Lelechka [254]

Answer:

3 and 9

if f(x)=x^2+13 and g(x)=12x-14

Step-by-step explanation:

So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).

So we want to find when f(x)=g(x) for x.

f(x)=g(x)

$x^2+13=12x-14$

Let's get everything to one side.

Subtracting 12x and adding 14 to both sides.

$x^2+13+14-12x=0$

I'm going to reorder the left hand side and also simplify the 13+14 part:

$x^2-12x+27=0$

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.

Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.

So the factored form of our equation is

$(x-3)(x-9)=0$

Since the product is 0, then at least one of the factors must be 0.

So we want to solve both x-3=0 and x-9=0.

x-3=0 can be solved by adding 3 on both sides. This gives us x=3.

x-9=9 can be solved by adding 9 on both sides. This gives us x=9.

The intersection of f and g happens at x=3 or x=9.

5 0

2 years ago

Read 2 more answers

A line has the equation 3x-2y=6, any line parallel to this line has slope (?)

vitfil [10]

Answer:

Slope is 3/2

Step-by-step explanation:

3x-2y=6

-2y=-3x+6

y=3/2-3

5 0

3 years ago

Alex lady sketch for a homemade soccer goal he plans to build . Do you go will be in the shape of a triangular prism . The legs

Otrada [13]

The triangular prism has a volume of
.. V = Bh = (1/2)*(4ft *8 ft)*(24 ft) = 384 ft^3

7 0

3 years ago

Evaluate, 2x-6 if x=.5

kkurt [141]

Answer:

-5

Step-by-step explanation:

2x-6

2(.5)-6

1-6

-5

6 0

3 years ago

A psychologist obtains a random sample of 2020 mothers in the first trimester of their pregnancy. The mothers are asked to play

leva [86]

Answer:

First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.

In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.

According to the problem, the null hypothesis must be: $H_{o} : u = 100$ ; because it says that 100 is the normal mean that is used.

The alternative hypothesis must be: $H_{a} : u > 100$ ; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.

Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: $Z=\frac{x-u}{\frac{o}{\sqrt{n} } }$ ; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.

Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.

Applying all values to the formula: $Z=\frac{104.3 - 100}{\frac{14}{\sqrt{20} } } = \frac{4.3}{\frac{14}{ 4.5} }=\frac{4.3}{3.1}=1.4$

Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.

<em>In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.</em>

Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).

5 0

2 years ago