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2 years ago

Find two acute angles that satisfy the equation sin(2x + 7) = cos(x + 23). Check that your answers make

Mathematics

1 answer:

Vera_Pavlovna [14]2 years ago

3 0

Answer:

The smaller angle is 43 and the larger angle is 47

Step-by-step explanation:

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Can someone help me with number 2. Please explain your answer.

yKpoI14uk [10]

4x+y = 20
3x+y = 2
4x+y-3x-y = 20-2
x = 18

3x+y = 2
3.18 + y = 2
54 + y = 2
y = -52

6 0

3 years ago

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 10.3

user100 [1]

Answer:

Confidence interval for the true mean number of reproductions per hour for the bacteria is (10.1,10.5).

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 10.3

Population standard deviation, σ = 2.1

Sample size, n = 728

Alpha, α = 0.01

Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58$

$10.3 \pm 2.58(\frac{2.1}{\sqrt{728}} ) = 10.3 \pm 0.2008 = (10.0992,10.5008) \approx (10.1,10.5)$

6 0

3 years ago

What is the lcm of 13 and 9

telo118 [61]

Answer:

LCM = 117

Step-by-step explanation:1. Find the prime factorization of 9. 9 = 3 x 3 2. find the prime factorization of 13. 13 = 13 3. Multiply each factor the greater number of times it occurs in steps 1) or 2) above to find the lcm: 3 x 3 x 13 = 117. Hope it helped.

8 0

3 years ago

Which table as a consistent of proportionately between Y and X of two?

Vikki [24]

Answer:

The table that has a consistent proportionality between Y and X of 2 is choice 2.

Step-by-step explanation:

Because the proportionality between X and Y is 2, that means for each x value, the corresponding y value will be twice as big. The only option that meets this requirement is choice 2, so that is the correct answer.

8 0

3 years ago

Please help!!

Soloha48 [4]

Step-by-step explanation:

Given points are:

$(-1,\:3)=(x_1,\: y_1) \:\&\:(1, \:7)=(x_2,\:y_2)$

Equation of line in two point form is given as:

$\frac{y-y_1 }{y_1 - y_2} = \frac{x-x_1 }{x_1 - x_2} \\ \\ \therefore \: \frac{y - 3}{3 - 7} = \frac{x - ( - 1)}{ - 1 - 1} \\ \\ \therefore \: \frac{y - 3}{ - 4} = \frac{x + 1}{ - 2} \\ \\ \therefore \: \frac{y - 3}{ 2} = \frac{x + 1}{ 1} \\ \\ \huge \purple{ \boxed{\therefore \:y - 3 = 2(x + 1)}} \\ this \: is \: the \: equation \: of \: line \: in \: \\ point - slope \: form.\\simplifying \: it \: further \: we \: find: \\ y - 3 = 2x + 2 \\ \\ \therefore \:y = 2x + 2 + 3 \\ \\ \huge \red{ \boxed{\therefore \:y = 2x + 5}} \\ this \: is \: the \: equation \: of \: line \: in \: \\ slope - intercept \: form.$

3 0

3 years ago