Answers
We know that ,
[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} [/tex]
and
[tex] \cos( \alpha ) = \frac{adjacent}{hypotenuse} [/tex]
where 'alpha' is an angle of triangle ; 'opposite' denotes the side opposite to alpha & 'adjacent' refers to the side next to the angle (but not hypotenuse)
Similarly ,
[tex] \sin(q) = \frac{opposite}{hypotenuse} = \frac{4}{5} [/tex]
Let the length of the opposite side be 4x and the length of hypotenuse be 5x. By using Pythagorean Theorem , we can find the length of base.
[tex] {base}^{2} + {(4x)}^{2} = {(5x)}^{2} [/tex]
[tex] = > {base}^{2} = 25 {x}^{2} - 16 {x}^{2} = 9 {x}^{2} [/tex]
[tex] = > base = \sqrt{9 {x}^{2} } = 3x[/tex]
Now , we have got the length of all the sides of the triangle. So,
[tex] \cos(q) = \frac{adjacent}{hypotenuse} = \frac{3x}{5x} = \frac{3}{5} [/tex]
and
[tex] \cos(p) = \frac{adjacent}{hypotenuse} = \frac{4x}{5x} = \frac{4}{5} [/tex]
So,
[tex] \cos(p) + \cos(q) = \frac{4}{5} + \frac{3}{5} = \frac{7}{5} [/tex]
Related Questions
Solve the system of linear equations by substitution. Check your solution.
Answers
Answer:
[tex]x = 1.5[/tex]
[tex]y =1[/tex]
Step-by-step explanation:
Given
[tex]4x + 2y = 8[/tex]
[tex]6x - 4y = 5[/tex]
Required
Solve for x and y
[tex]4x + 2y = 8[/tex] --- (1)
[tex]6x - 4y = 5[/tex] --- (2)
Divide equation (1) through by 2
[tex]\frac{1}{2}(4x + 2y) = 8*\frac{1}{2}[/tex]
[tex]2x + y = 4[/tex]
Make y the subject
[tex]y = 4 - 2x[/tex]
Substitute 4 - 2x for y in equation (2)
[tex]6x - 4y = 5[/tex]
[tex]6x - 4(4- 2x) = 5[/tex]
Open bracket
[tex]6x - 16+ 8x = 5[/tex]
Collect Like Terms
[tex]6x + 8x = 5+16[/tex]
[tex]14x = 21[/tex]
Solve for x
[tex]x = \frac{21}{14}[/tex]
[tex]x = 1.5[/tex]
Substitute 1.5 for x in [tex]y = 4 - 2x[/tex]
[tex]y = 4 - 2(1.5)[/tex]
[tex]y = 4 - 3[/tex]
[tex]y =1[/tex]
To check the solution:
Substitute the values of x and y i the equations
[tex]4x + 2y = 8[/tex]
[tex]4 * 1.5 + 2 * 1 = 8[/tex]
[tex]8 = 8[/tex]
[tex]6x - 4y = 5[/tex]
[tex]6 * 1.5 - 4 * 1 = 5[/tex]
[tex]5 = 5[/tex]
Hence, the solution is true
When Ms. Lawrence goes to the doctor’s office, they have patients wait 30 minutes. She found a new doctor that has 15% less wait time. What is the wait time at the new doctor’s office?
Does anyone know the answer?? Idk how to solve
Answers
Answer:
25.5 minutes
Step-by-step explanation:
Arturo can walk 4 miles in 1 hour. How many miles can he walk 3 hours?
Answers
Answer:
12
Step-by-step explanation:
In a class of 100 half the students are science majors and half are liberal art majors. A student who is a science major has a 0:9 probability of passing a given test whilst a student who is liberal art major has only a probability of 0:7. We pick 2 students at random without replacement and give them the test. What is the probability that both students pass the exam
Answers
Answer:
P(both students passed the exam) = 0.61948
Step-by-step explanation:
From the given information:
P(both students passed the exam) = P(both are science students or both are art major students or one is from each group)
= P (both are science students) + P(both are art students) + P(one from each group)
where;
P (both are science students) = (50/100) (0.9) × (44/99) × (0.9) = 0.18
P(both students are art) = (50/100) (0.7) × (49/99) 0.7 = 0.1213
P(one of the student are from each group) = (50/100) (0.9) ×(50/99) (0.7) + (50/100) (0.7)× (50/99)(0.9) =0.3182
P(both students passed the exam) = 0.18 + 0.1213 + 0.3182
P(both students passed the exam) = 0.61948
HELPP PLZZZ I put a picture
Answers
Answer:
The first one
Step-by-step explanation:
Dont have time to explain sry
Bill is playing a board game that has a spinner divided into equal sections numbered 1 to 20.
The probability of the spinner landing on an even number or a multiple of 5 is?
Select one:
a. 12/20
b. 3/5
c. 7/15
d. 1/5