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satela [25.4K]
3 years ago
6

In triangle abc, angle A is the right angle. What is the value of y?

Mathematics
2 answers:
Nesterboy [21]3 years ago
4 0

Answer:

7sinΠ/6 (A)

Step-by-step explanation:

Since the triangle given is a right angled triangle, the SOH CAH TOA method will be employed.

Given opposite side to be 'y' (the side facing the acute angle)

The hypotenuse = 7feet(the longest side)

Any the angle theta = 30°

According to SOH;

sin(theta) = opposite/Hypotenuse

Sin30° = y/7

y = 7sin30°

Note that 180°=Πrad

30° = Π/6rad

y = 7sinΠ/6 (A)

Natalka [10]3 years ago
3 0

Answer:

A

Step-by-step explanation:

In a right triangle, the side opposite to the 90 degree angle (here, side opposite to angle A) is known as the hypotenuse.

Also, the side that is "opposite" to the angle given (here side opposite is y to angle given 30 degrees) is the opposite side.

Since we want to find "opposite" and have "hypotenuse" , recalling trig ratios, we can say opposite/hypotenuse is the ratio SINE, so we can write:

Sin(30)=\frac{y}{7}

We solve for y:

Sin(30)=\frac{y}{7}\\y = 7 Sin(30)

Since the answer choice has angles in radians, we recall 30 degrees is \frac{\pi}{6} radians.

Thus, the correct answer is  7Sin(\frac{\pi}{6}), or option A

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Last year at a certain high school, there were 125 boys on the honor roll and 80 girls on the honor roll. This year, the number
Elodia [21]

Answer:

6.8% decrease

Step-by-step explanation:

a drop of 8% means that only 92% of 125 boys remained on honor roll from last year; .92 x 125 = 115

a drop of 5% means that only 95% of 80 girls remained on honor roll from last year; .95 x 80 = 76

total number of students on honor roll last year = 125 + 80 = 205

total number of students on honor roll this year = 115 + 76 = 191

percent of change = (191 - 205) ÷ 205 = -14/205 = -.068

-.068, which represents a 6.8% decrease

3 0
2 years ago
Two 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice will be greater than 8?
Serhud [2]

Answer: 5/18

Step-by-step explanation:

The sample space when two 6- sided dice are rolled is given below:

(+) 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11  12

The total sample space is 36.

Sum greater than 8 are : {9,10,11,12}

which are 10 in number:

Therefore : the probability that the sum of the two numbers on the dice will be greater than 8 will be :

number of the sum greater than 8 / Total sample space

That is ;

P(sum greater than 8) = 10/36

P(sum greater than 8) = 5/18

6 0
2 years ago
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population
frez [133]
The equation
                                            P(t) = 1405233 * (1 - 0.011)^(t)
models the population at t years after 2010. Then, when P(t) = 1,200,000, we have
                                 1200000 = 1405233 * (0.989)^t
                                  (0.989)^t = 1200000/1405233
                                                t = log(1200000/1405233)/log(0.989)
                                                t = 14.27 years
This means 14.27 years after 2010. Therefore, the answer to this question is 2024.
7 0
3 years ago
What is the measure of angle 6, if lines x and y are parallel, and angle 7 measures 121°? 121° 69° 59° 49°
Marianna [84]

Answer:

59°

Step-by-step explanation:

From the diagram, shown in the attachment line x and y are parallel lines.

Angle 7 and angle 6 are angles on a straight line.

The two angles will add up to 180 degrees.

\angle 7+\angle 6=180

But angle 7 measures 121°.

This implies that:

121+\angle 6=180

Solve for angle 6 to get;

\angle 6=180-121\

\angle 6=59\degree

7 0
3 years ago
5e^5x =20<br> What is the approximate solution to this equation<br><br> Answers provided
Zepler [3.9K]

Answer:

i think its B

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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