MATHEMATICS HIGH SCHOOL

Help please?If sin O = -sqrt3 over 2 and n < O < 3 pi over 2, what are the values of cos O and tan O?

Answers

Answer 1

Answer:

Answer:

cos(θ) = -1/2
tan(θ) = √3

Step-by-step explanation:

You know that ...

cos(θ)² = 1 - sin(θ)²
tan(θ) = sin(θ)/cos(θ)
cosine is negative in the third quadrant (where π < θ < 3π/2)

Using what you know about the relationships of these trig functions, you can find ...

cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4

cos(θ) = -1/2 . . . . . negative square root of 1/4

tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)

tan(θ) = √3

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What quadrant would the ordered pair (–4,–6) fall in?

Answers

Answer:

The ordered pair (-4,-6) is in the 3rd quadrant

Step-by-step explanation:

If we have an ordered pair (a,b), they would fall in:

1st quadrant: if a and b are positive
2nd quadrant: if a is negative and b is positive
3rd quadrant: if a and b are negative
4th quadrant: if a is positive and b is negative

Then, taking into account that -4 and -6 are negative numbers, the ordered pair (-4,-6) belong to the 3rd quadrant

QUADRANT 3 IS the right answer

Steve is turning half of his backyard into a chicken pen. His backyard is a 242424 meter by 454545 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?

Answers

Answer:

51 meters

Step-by-step explanation:

The shape of the backyard is rectangular having a length, l=45 meters, and a width, w=24 meters as shown in the figure.

As wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. So,

The length of fencing = The length of the diagonal AC or BD

As the length of both the diagonals of a rectangle are equals, AC=BD.

The length of fencing $=√(l^2+w^2)$ [length of the diagonal]

$=√(45^2+24^2)=51$ meters

Hence, Steve needs 51 meters of fencing.

Boris Heban is single and pays into an HMO. The total cost is $8,190 annually, and the employer pays 90 percent of the total cost. He also pays 50 percent of the optional annual dental premium of $662 and 50 percent of the optional vision premium of $188. How much is deducted each week from his paycheck?

Answers

so Boris has to pay:
10% * 8190 = 819
50% * 662 = 331
50% * 188 = 94

so in total he pays: 819 + 331 + 94 = 1244

deducted each week is (52 weeks in a year):
1244/52 = 23.92

so each week $23.92 are deducted from his paycheck

Bradley is in a class of 15 boys and 10 girls. 40% of the class takes the bus to school. How many students do not take the bus to school?

Answers

Answer:

30 Students

Step-by-step explanation:

As given

Bill is in a class of 15 boys and 35 girls.

Total number of students in the class = Number of boys + Number of girls

= 15 + 35

= 50

As given

40% of the students in the class take the bus to school.

40% is written in the decimal form.

= 0.40

Number of students take bus to school = 0.40 × Total students in class.

= 0.40 × 50

= 20

.Thus

Students not take bus to school = Total students - Number of students take bus to school

= 50 - 20

= 30

Therefore 30 students not take bus to school .

Answer:

15 students

Step-by-step explanation:

First of we have to calculate how many students there are in the class. There are 15 boys and 10 girls, whish means there are 25 people in total (15+10=25).

Since 40% takes the bus to school, 60% of the sudents do not take the bus to school. The easiest way to calculate how many students is 60% is to first divide the students with 10. 25/10 is 2.5. 2.5 students is 10% of 25 students (100% divided by 10 is 10%).

To get 60%, the number of students has to be multiplied with 6, because 10% times 6 is 60%.

2.5 (10%) times 6 is 15, so the answer is 15.

For the coordinates of P and M (the midpoint) are given. Find the coordinates for Q.P(-2, 3) and M (5, 1)

Answers

Given an endpoint and a midpoint, to look for the other endpoint, the midpoint formula is merely manipulated. The average of the x-coordinates for P and Q have to equate to the x-coordinate of M. The same is applied to the y-coordinates. This is shown below:

X-coordinates:

(-2 + Qx)/2 = 5
(-2 + Qx) = 10

Qx = 12

Y-coordinates:

(3 + Qy)/2 = 1
3 + Qy = 2

Qy = -1

Therefore, Q has the coordinates (12 , -1)

Which graph represents a proportional relationship? A.

B.

C.

D.