part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.
Answers
Answer: [tex]\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}[/tex]
Step-by-Step Explanation:
Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse
[tex]5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]
Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18
[tex]6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}[/tex]
Note: 8² + 15² = hypotenuse² → hypotenuse = 17
[tex]7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}[/tex]
Note: hypotenuse not needed for tan
[tex]8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}[/tex]
Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10
5) cosθ = [tex]\frac{\sqrt{11} }{6}[/tex] , 6) cosθ = [tex]\frac{8}{17}[/tex] , 7) tanθ = [tex]\frac{4}{3}[/tex] , 8) cosθ = [tex]\frac{1}{\sqrt{10} }[/tex]
What is pythagorean theorem ?If, a be the perpendicular, b be the base & c be the hypotenuse of a right angle triangle.
Then, [tex]c=\sqrt{a^{2}+ b^{2} }[/tex]
What are the trigonometric functions ?cosθ = (Side adjacent to θ)/(Hypotenuse)
sinθ = (Side opposite to θ)/(Hypotenuse)
tanθ = (Side opposite to θ)/(Side adjacent to θ)
What are the values of required trigonometric functions ?5) Hypotenuse = [tex]\sqrt{(3\sqrt{11}) ^{2} +15^{2} }[/tex]
= [tex]\sqrt{99+225}[/tex]
= [tex]\sqrt{324}[/tex] = 18
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{3\sqrt{11} }{18}[/tex] =[tex]\frac{\sqrt{11} }{6}[/tex]
6) Hypotenuse = [tex]\sqrt{8^{2} +15^{2} }[/tex]
= [tex]\sqrt{64+225}[/tex]
= [tex]\sqrt{289}[/tex] = 17
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{8}{17}[/tex]
7) tanθ = (Side opposite to θ)/(Side adjacent to θ)
= [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex]
8) Hypotenuse = [tex]\sqrt{2^{2} +6^{2} }[/tex]
= [tex]\sqrt{4+36}[/tex]
= [tex]\sqrt{40}[/tex] = [tex]2\sqrt{10}[/tex]
∴ cosθ = (Side adjacent to θ)/(Hypotenuse)
= [tex]\frac{2}{2\sqrt{10} }[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]
Learn more about trigonometric functions here :
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Related Questions
Segment AC bisects angle BAD if the measure of angle BAC is 20 degrees what’s is the measure of angle BAD
Answers
Answer:
40°
Step-by-step explanation:
An angle bisector divides an angle into 2 equal angles. 20° x 2 = 40°.
2) solve for h: a = 1/2 bh
(area of triangle)
Answers
Answer:
h = 2a/b
Step-by-step explanation:
a = 1/2 bh
2*a = 2* 1/2 bh
2a = bh
2a/b = bh/b
2a/b = h
When cut into 16 equal slices, each slice is 1/16 of the pizza. Express how much of the pizza 8 of these slices would be in decimal form.
Answers
Answer:
0.5
Step-by-step explanation:
If one part = 1/17
Then, 8 parts = 1/16 x 8 = 1/2
1/2/as a decimal is 0.5
Hope this helps
16.) The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 adult tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 adult tickets and 5 student tickets. What is the price of the adult and the student ticket?
Answers
Answer:
adult tickets are $8 and student tickets are $14
Step-by-step explanation:
to find the price of adult and student tickets, first look at all the given values:
a = adult tickets
s = student tickets
so: 4a + 5s = 102
and : 7a + 5s = 126
since in both equations the number of student tickets are the same, we have to find the difference of value to determine how much adult tickets are:
126-102 = 24
there are 3 more adult tickets in the equation with a total of 126, therefore:
24 / 3 = 8
that means each adult ticket is work 8 dollars.
now substitute this value:
4(8) + 5s = 102
32 + 5s = 102
you can solve this by concluding that 102- 32 is 70
that means 5(s) has to equal 70
so 70 / 5 = s
70/5 = 14
so the value of s = 14 and the value of a = 8
Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, they increases by a common difference of 3.
For each x increase of 1, the y increases by a common factor of 3.
For each x increase of 1, the y increases by 4 more than the previous increase.
For each x increase of 1, they increases by doubling and then adding 1.
Answers
Answer:
For each x increase of 1, the y increases by a common factor of 3. (second answer listed)
Step-by-step explanation:
Notice that you have not provided the graph that the problem involves, but from the description of what the y behavior is when x increases by one, one can deduct if an exponential pattern applies.
Out of the four examples given, only one of them represents an exponential growth. Such type of growth has to include a common multiplicative factor (the base of the exponent), since the function has to be of the form:
[tex]f(x)=a\,\,b^x[/tex]
to be called exponential.
So every time that x increases by one unit, the following happens:
[tex]f(x+1)=a\,\,b^{(x+1)}\\f(x+1)= a\,\,b^x\,\,b[/tex]
So notice that the original function ends up being just multiplied by the common factor "b".
The other options don't describe such behavior.
Answer:
For each x increase of 1, the y increases by a common factor of 3.
Step-by-step explanation: hope it helps ^w^
What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)? (1 point) Select one: a. 0 b. 5 c. 10 d. 15
Answers
Answer: C. / 10
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given a polynomial divided by a factor (x + h) then the remainder is f(- h)
Given
f(x) = 3[tex]x^{4}[/tex] + 2x³ - x² + 2x - 19 divided by (x + 2)
To find remainder evaluate f(- 2)
f(- 2) = 3[tex](-2)^{4}[/tex] + 2(- 2)³ - (- 2)² + 2(- 2) - 19
= 3(16) + 2(- 8) - 4 - 4 - 19
= 48 - 16 - 4 - 4 - 19
= 5 → B
factorise: 2x + 6y 2x-4 t + 2t squared
Answers
what is the middle product of (-2x+1)(-3-5)?
Answers
Answer:
7x
Step-by-step explanation:
Share £90 in the ratio 1:5
Answers
Answer:
the answer is
Step-by-step explanation:
if we take a and b as two pupil to share the money,then a gets
$15 and b gets $75
sum of the ratio is=6
a =1/6×$90
=$15
b=5/6×$90
=$75
Which statement best describes the function below
Answers
Answer:
Option D. will be the answer.
Step-by-step explanation:
Given function is f(x) = 2x³ + 2x² - x
Table of input and output:
Input (x) -2 -1 0 1 2
Output (y) -6 1 0 3 22
Option (A).
From the graph attached,
It passes the vertical line test.
Option (B).
Since every input value gives a unique output value, it's not a many-to-one function.
Option (C).
It's a function.
Option (D).
It's a one-to-one function.
Answer: It is a many-to-one function.
Step-by-step explanation:
just did the test
Monty has a total of $290 in ten dollar and five dollar bills. This can be represented by the function 10x + 5y = 290. Interpret the x- and y-intercepts.
Answers
Answer:
The x-intercept indicates that he has 29 ten dollar bills
and no five dollar bills. The y-intercept indicates that he has 58 five
dollar bills and no ten dollar bills.
Step-by-step explanation:
find the length of each side of a square field whose area is 608 sq.m
Answers
Answer:
a=24.65 sq.m
Step-by-step explanation:
A=[tex]a^{2} or l^{2}[/tex]
608=[tex]a^{2}[/tex]
[tex]a=\sqrt{608}[/tex]
[tex]a=24.65[/tex]
To check your answer
[tex]A=a^{2} \\A=24.65^{2}\\A=24.65*24.65\\A=607.6225=608[/tex]
which best decribes how to slove the equation below 26x=74
Answers
Which similarity postulate or theorem can be used to verified that the two triangles shown below are similar? PLEASE HELP ASAPP
Answers
Answer:
Correct option: A -> AA postulate
Step-by-step explanation:
In the figure we can see that in triangle ABC we have:
A = 53°
B = 72°
And we can see in the triangle LMN that:
L = 53°
M = 72°
We have two pairs of angles (A - L and B - M) that are congruent, and therefore we can use the case AA (angle-angle) to affirm that these triangles are similar.
So the correct option is A: AA postulate.
I hate math bro please help me ill mark u brainliest
Answers
Please help me with my question!!
Answers
Answer:
B,C
Step-by-step explanation:
The sum of B is 1
The sum of C is -1/2
Let's try each option.
Option A:
-3 + 5 + (-1) = 2 + (-1) = 1
FALSE
Option B:
5 + (-8) + 4 = -3 + 4 = 1
TRUE
Option C:
-19/2 + 9 = -9.5 + 9 = -0.5
TRUE
Option D:
-17 + 36/2 = -17 + 18 = -1
FALSE
So, the correct answers are B and C
Best of Luck!
Solve the system.
2x + y = 3
−2y = 14 − 6x
Answers
2x+y=3
6x-2y=14
Then the 6x and 2x would turn into a -4x and the -2y and y would turn into 3y and the 14 and 3 would turn into a -11
Answer:
y= -2 x= 3
y= 3 x= -7
Step-by-step explanation:
Sam read 20 pages, which is 2/3 of the book. How many pages are there in the book?
Answers
Answer:
30pages
Step-by-step explanation:
20 is 2/3 so 10 is 1/3 so 3/3 is one book
Answer:
30 pages
Step-by-step explanation:
What is the product (40 + (-10))((36 + (-9))(32 + (-8))...(-32 + 8)(-36 + 9)(-40 + 10) where the first number in each factor is decreasing by 4 and second number in each factor is increasing by 1?
Answers
Answer:
0
Step-by-step explanation:
The first number is 40 and decreases by 4 in each factor, and the second number is -10 and increases by 1 in each factor.
The first number is positive and decreases by 10% its value in each factor, and the second number is negative and increases by 10% its absolute value in each factor. That means we will have a factor where both numbers are 0 (in the 11th value, we will have the first number 40 - 4*10 = 0 and the second number -10 + 1*10 = 0), so the factor will be 0 + 0 = 0, and then whole product will be zero.
9y + 6 + 2(5 + y) = blank y + blank
Answers
Answer:
11y+16Solution,
[tex]9y + 6 + 2(5 + y) \\ = 9y + 6 + 10 + 2y \\ combine \: like \: terms \\ = 9y + 2y + 6 + 10 \\ simplify \\ = 11y + 16[/tex]
hope this helps...
Good luck on your assignment..
Answer:
11y+16
Step-by-step explanation:
9y+6+2(5+y)=
9y+6+10+2y=
Combine like terms
11y+6+10=
11y+16
Can someone pls help me solved this problem plz! I really need help plz someone help me solved it! I need help ASAP!
Answers
Answer:
a) 0
b) 4.5
c) 3
d) 6
Step-by-step explanation:
Formula: 3x + 4y = 12
The questions contains the values of x. So here's an example of:
d) x = -4, y = ?
Using the formula: 3(-4) + 4y = 12
-12 + 4y = 12
4y = 24
y = 6
Do the same for the others!
If Colin tosses a normal die from a board game, what is the probability that the result will be prime?
A. 2/3
B. 5/6
C. 1/2
D. 1/6
Answers
Do you need working out?
Can anyone help 9th-grade geometry
Answers
Answer:
5 < x < 23
Step-by-step explanation:
let the third side be x , then
difference of 2 sides < x < sum of 2 sides
14 - 9 < x < 9 + 14 , that is
5 < x < 23
What is the value of cos(150°)?
OF
22
-
V3
2.
1500
30
-
Answers
Answer:
[tex]cos(150^o)=-\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Recall that the value of the cosine of an angle in the unit circle is the horizontal value (x-coordinate) read-out for the point on the circle's circumference that represents the given angle.
in this case, notice that [tex]150^o[/tex] corresponds to an angle in the second quadrant, and the actual coordinate values for it are given to you. therefore, use the value you read for the x-coordinate: [tex]-\frac{\sqrt{3} }{2}[/tex]
c) A triangle has one pair of equal sides and one pair of equal angles
What is it called?
Answers
Answer:
The answer is Isosceles Triangle.
Answer fast pleaseee, Solve the following system of equations: y= -5x +1 and y= -x-3
Answers
Answer:
x=1 y=-4
Step-by-step explanation:
Answer:
(1, - 4 )
Step-by-step explanation:
Given the 2 equations
y = - 5x + 1 → (1)
y = - x - 3 → (2)
Since both are expressed in terms of y, equate the right sides, that is
- x - 3 = - 5x + 1 ( add 5x to both sides )
4x - 3 = 1 ( add 3 to both sides )
4x = 4 ( divide both sides by 4 )
x = 1
Substitute x = 1 into either of the 2 equations and evaluate for y
Substituting into (2)
y = - 1 - 3 = - 4
Solution is (1, - 4 )
The volume of a cube depends on the length of its sides. This can be written
in function notation as ws). What is the best interpretation of v(4) = 64?
Answers
Answer:
46=-76.333(6×7)-÷45%€7*÷00.0001×6÷45+2
Simplify
(2 Points)
2a xa x 3a + b x 45
Answers
Answer:
[tex]6a^3+45b[/tex]
Step-by-step explanation:
[tex]2a\times a\times 3a+b\times 45[/tex]
[tex]2a\times 1a\times 3a+b\times 45[/tex]
[tex]2\times 1\times 3 \times a \times a \times a+b\times 45[/tex]
[tex]6a^3+b \times45[/tex]
[tex]=6a^3+45b[/tex]
Answer:
6a^3 + 45b
Step-by-step explanation:
=2a × a × 3a + b × 45
=2a × 1a × 3a + b × 45
=2 × 1 × 3 × a × a × a + b × 45
=6a^3 + b × 45
= 6a^3 + 45b
A rectangle is 6 inches longer than it is wide. Write and simplify an expression for
the perimeter of the rectangle in terms of the width w.
Answers
Answer:
L+6=W
Step-by-step explanation:
Answer:
4w + 12
Step-by-step explanation:
w + (w+6) + w + (w+6) = 4w + 12
for perimeter you add all the sided together
w = width
w + 6= length
anyone know the answer ? :(
Answers
The smallest x value allowed is x = 0, as shown as the leftmost point on the graph at (0,0).
The largest x value allowed is x = 11 because of the right-most point (11,100).
The domain is the set of any real number between those endpoints. We can pick any fractional or decimal number in this interval since time can be subdivided however you want, so the set of integers isn't enough.
