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Lelechka [254]
3 years ago
14

F(x)=-2x-1 and g(x)=x^2-1. Find (fog)(-5).

Mathematics
1 answer:
serg [7]3 years ago
7 0

Answer: - 49

Step-by-step explanation:

f(x) = -2x - 1

g(x) = x^{2} - 1

fg(x) = f (x^{2} - 1) , we just put in the value of g(x) , the next thing is to substitute x^{2} - 1 for the value of x in f(x) , that is

fg(x) = -2(x^{2} - 1) - 1

fg(x) = -2x^{2} + 2 - 1

fg(x) = -2x^{2} + 1

Therefore : fg(-5) means we will substitute -5 for x in fg(x) , that is

fg(-5) = -2 ((-5)^{2} + 1

fg(-5) =  -2(25) + 1

fg(-5) = -50 + 1

fg(-5) = -49

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Find the critical value of t for a sample size of 23 and a 99% confidence level. choose the correct value from below:
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We can find critical value by using t - table.
For using t - table we need degree of freedom and alpha either for two tailed test or one tailed test.
We can determine degree of freedom by subtracting sample size from one.
So in given question sample size is 23. So we can say degree of freedom(df) for sample size 23 is
df = 23 - 1= 22
Now we have to go on row for degree of freedom 22.

After that we need to find alpha either for two tailed test or one tailedl test.
Confidence level is 99%. We can convert it into decimal as 0.99.

So alpha for two tailed test is 100 - 0.99 = 0.01

Alpha for one tailed test is 0.01/2 = 0.005.

So we will go on column for 0.01 for two tailed test alpha or 0.005 for one tailed test alpha.
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8 0
3 years ago
PQ and QR are two sides of a regular 12-sided polygon. PR is the diagonal of the polygon.
skelet666 [1.2K]

The size of angle PRQ is 15°

Step-by-step explanation:

In any regular polygon of n-sided

  • All sides are equal in length
  • All angles are equal in measure
  • The measure of each interior angle is \frac{(n-2)*180}{n}
  • The measure of each exterior angle is \frac{360}{n}
  • The sum of the measures of the interior and exterior angle at the same vertex is 180°

∵ PQ and QR are two sides of a regular 12-sided polygon

∴ PQ = QR

∵ PR is a diagonal

∴ ∠PQR is an interior angle of the polygon

- By using the rule of the interior angle above

∵ n = 12

∴ m∠PQR = \frac{(12-2)*180}{12}

∴ m∠PQR = 150°

In Δ PQR

∵ PQ = QR ⇒ sides in a regular polygon

- Δ PQR is an isosceles Δ

∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ

The sum of the measures of the interior angles of a triangle is 180°

∵ m∠PQR + m∠PRQ + m∠RPQ = 180°

∴ 150 + m∠PRQ + m∠RPQ = 180°

- Subtract 150 from both sides

∴ m∠PRQ + m∠RPQ = 30

∵ m∠PRQ = m∠RPQ

- Divide their sum by 2 to find the measure of each one

∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°

∴ m∠PRQ = 15°

The size of angle PRQ is 15°

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

#LearnwithBrainly

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6 0
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Solve the simultaneous equation:<br> 2x - y= 2<br> 3y= 4x - 5
Ronch [10]

Answer:

x = \frac{1}{2} , y = -1

<u>Explanation</u>:

2x - y= 2

3y= 4x - 5

<u>Make y the subject:</u>

2x - y= 2

-y = 2 - 2x

y = 2x - 2  <em>.........equation 1 </em>

3y= 4x - 5

y = (4x - 5)/3<em> ........equation 2</em>

From equation 1 and 2 solve them simultaneously:

→ (4x - 5)/3 =  2x - 2

→ 4x - 5=  3(2x - 2)

→ 4x - 5 = 6x - 6

→ 6x - 4x = -5 + 6

→ 2x = 1

→ x = 1/2

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                              →  2(1/2)-2

                              →  -1

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