Write the expression as either the sine, cosine, or tangent of a single angle. sin(pi/2)cos(pi/7)+cos(pi/2)sin(pi/7)

Answers

Answer 1

Answer: I will use the sin (a + b) identity:
sin (a + b) = sina cosb + cosa sinb and
here a = π/2 and b = π/7

so sin (π/2 + π/7)
= sin (9π / 14)

Answer 2

Answer:

Answer:

$\text{sin}((9\pi)/(14))$ .

Step-by-step explanation:

We have been given a trigonometric expression $\text{sin}((\pi)/(2))\text{cos}((\pi)/(7))+\text{cos}((\pi)/(2))\text{sin}((\pi)/(7))$ . We are asked to write our given expression as either the sine, cosine, or tangent of a single angle.

Using identity $\text{sin}(a)\text{cos}(b)+\text{cos}(a)\text{sin}(b)=\text{sin}(a+b)$ , we can rewrite our given expression.

Let $a=(\pi)/(2)$ and $b=(\pi)/(7)$ .

Upon substituting these values in above identity, we will get:

$\text{sin}((\pi)/(2))\text{cos}((\pi)/(7))+\text{cos}((\pi)/(2))\text{sin}((\pi)/(7))=\text{sin}((\pi)/(2)+(\pi)/(7))$

Upon simplifying right side of our equation, we will get:

$\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((\pi*7)/(2*7)+(\pi*2)/(7*2))$

$\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((7\pi)/(14)+(2\pi)/(14))$

$\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((7\pi+2\pi)/(14))$

$\text{sin}((\pi)/(2)+(\pi)/(7))=\text{sin}((9\pi)/(14))$

Therefore, our required expression would be $\text{sin}((9\pi)/(14))$ .

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If three dozen cookies cost $9, what is the cost per cookie?

Answers

Answer:

$0.25 is the cost per cookie

Step-by-step explanation:

Unit rate defined as the rate are expressed as a quantity as 1 such as 4 meter per second or 4 miles per hour

As per the statement:

If three dozen cookies cost $9.

Use conversion:

1 dozen = 12

then;

3 dozen = 36

then;

36 cookies cost $9.

Cost of cookies = $9

Number of cookies = 36

Then by unit rate definition we have;

$\text{Cost per cookies} = \frac{\text{Cost}}{\text{Number of cookies}} = (9)/(36)$

⇒ $\text{Cost per cookies} = (1)/(4) = \$ 0.25$

Therefore, $0.25 is the cost per cookie

25 cents per cookie

Point B is located at _____.

(3, 0)
(0, 3)
(0, -3)
(-3, 0)

Answers

The point B is located at (3, 0). Therefore option B is the correct answer.

On graph A, B, C, D and E points are given.

What is the graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The numbers on a coordinate grid are used to locate points. Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate).

Here, on the point B is located at (3, 0).

The point B is located at (3, 0). Therefore option B is the correct answer.

To learn more about the graph visit:

brainly.com/question/14375099.

#SPJ2

Point B is located at (0, -3). When both x and y coordinates are positive,it lies in the first quadrant. If both are negative, it lies in the thirdquadrant. If x is negative and y is positive, it is in the second quadrant. If xis positive and y is negative, it is in the fourth quadrant.

Six blood pressure readings are 115, 120, 123, 121, 121, and 112 mm Hg. What is the average (mean) value?

Answers

Answer:

118.666666667 mmHg

Step-by-step explanation:

To find the average/mean of a set of values, you add all the values together, then divide them by the amount of values in the set.

115+120+123+121+121+112 = 712

Since there is 6 values, you divide this by 6.

712÷6 = 118.666666667 mmHg

Hope this helps!

Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value of the house after 10 years?

Answers

This problem can be solved using the formula for interest which is: F = P (1 + i)^n where:

F = future value
P = principal value
i = interest per year
n = interest period

Since we are already provided with the values of each, direct substitution should be done. This is shown below:

F = P(1 + i)^n
F = 125000(1 + 0.035)^10
F = 176324.85

Therefore, the value of the house after 10 years will be $176,324.85

Fishing is allowed in 36 out of the 40 lakes in . What percent of the lakes allow fishing?

Answers

90% of lakes!

36 divided by 40 times 100 is how I got the percentage.

Hope this helps!

A pair of angles whose sum is 90 degrees are called _____ angles.

Answers

Answer:

complimentary

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