If ƒ(x ) = x 2 + 1, find ƒ(a + 1).

Factor the algebraic expression below in terms of a single trigonometric function. sin 2x + sin x - 2

Pie

Answer:

The factored form is (sin x +2)(sin x-1)

Step-by-step explanation:

We have been given the trigonometric function $\sin^2 x +\sinx-2$

We can factor this by AC method. In AC method we multiply the term a and c and then write the middle term b in such a way that the sum/difference is equal to the product 'ac'

Using the method, we can write sinx as 2sinx -sinx

$\sin^2 x +2\sinx-\sin x-2$

Now, we group the first two terms and the last two terms

$(\sin^2 x +2\sinx)+(-\sin x-2)$

Now, we take GCF from each group

$\sin x(\sin x +2)-1(\sin x+2)$

Factor out (sinx+2)

$(\sin x +2)(\sin x-1)$

Therefore, the factored form is (sin x +2)(sin x-1)

7 0

3 years ago

Read 2 more answers

An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0

3 years ago

Complete the ratio table. 16 17 32 51 64 68 80 85

aksik [14]

Answer:

32 34

51 54

Step-by-step explanation:

You add +1 by every line more than the last line

3 0

3 years ago

Express the fractions 1/2, 3/16, and 7/8 with an LCD

12345 [234]

You first need to find the LCD (lowest common denominator). You will need to find the smallest number that is a multiple of all numbers that is the denominator (2, 16, 8). Or, to say it another way, all the numbers in the denominator need to be a factor of this number.

You can find this by first checking if the largest number that is the denominator-- in this case 16-- is already the LCD, which means 16 is divisible by all the other numbers.

If this does not work, then multiply all the numbers together to get the LCD-- since you multiplied them together, you know that they will all be factors of the product.

However, you will be able to see that 16 is indeed the lowest common denominator:

2 × 8=16

8 × 2=16

16 × 1=16

So, after you find the LCD, multiply both the numerator and the denominator by the number that you would need to multiply the denominator to get the LCD (the whole point is that you want to get the denominator to be the LCD, but to do that you need to multiply both the top and bottom by the same number to keep the fraction the same).

(1/2) x (8/8)= 8/16

(3/16) x (1/1)= 3/16

(7/8) x (2/2)= 14/16

6 0

3 years ago

What is the answer i cant solve it 6.4u-5.1u=-3.25?

Marta_Voda [28]

I hope this helps you

1,3 u = -3,25

1,3u ÷1,3 = -3,25 ÷ 1,3

u = -2,5

7 0

3 years ago