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Damm [24]
3 years ago
12

If line j is parallel to line k, what is the value of x?

Mathematics
1 answer:
Licemer1 [7]3 years ago
6 0

Answer:

x=14

Step-by-step explanation:

two named angles are equal because they are known as corresponding angles; therefore, set them equal to each other

6x+3=87

6x=84

x=14

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If g^-1(x) is the inverse of g(x) which statements must be true
stellarik [79]

Answer:

  A, B, D, F

Step-by-step explanation:

The domain of a function is the range of its inverse.

The composition of a function and its inverse is an identity.

5 0
3 years ago
Express the function y(t)= 4 sin 2πt + 15 cos 2πt in terms of (a) a sine term only. (b) Determine the amplitude, the period, the
Bond [772]

Answer:

See the step by step solution

Step-by-step explanation:

Consider a more general case of the form a\sin(x)+b\cos(x). We want to express it as a sine term only by using the following formula \sin(\alpha+\beta) = \sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)

The trick  consists on find a number \beta \in [0,2\pi] such that \cos(\beta) = a, \sin(\beta)=b . But, note that since \cos^2(\beta)+\sen^2(\beta)=1 it is most likely that a^2+b^2neq 1. Then, we will use the following equations:

\cos(\beta) =\frac{a}{\sqrt[]{a^2+b^2}=A,\sin(\beta) =\frac{b}{\sqrt[]{a^2+b^2}=B

Then, problem turns out to be

a\sin(x)+b\cos(x)= \sqrt[]{a^2+b^2}(A\sin(x)+B\cos(x)) =\sqrt[]{a^2+b^2}(\sin(x)\cos(\beta)+\sin(\beta)\cos(x))=\sqrt[]{a^2+b^2}\sin(x+\beta),

where \beta = \tan^{-1}(\frac{B}{A})= \tan^{-1}(\frac{b}{a}). So, note that the frequency is the same. Then, a) Taking a=4 and b= 15 we have that 4 sin 2πt + 15 cos 2πt= [tex]\sqrt[]{15^2+4^2}\sin(2\pi t + \tan^{-1}\frac{15}{4})

b) The amplitude is \sqrt[]{15^2+4^2} = \sqrt[]{241}. Since 2\pi rad/s = 1 Hz the frequency is 1 Hz. The period is given by \frac{2\pi}{2\pi} = 1.

c) The function's graph is attached

7 0
3 years ago
Read 2 more answers
A manufacturer earns Rs4500 in the first month and Rs 6000 in second month. On plotting these points a manufacturer observes a l
UkoKoshka [18]

Answer:

f(x) = 1500x +3000

Step-by-step explanation:

Given

Represent the months with x and the earnings with y.

So:

(x_1,y_1) = (1,4500)

(x_2,y_2) = (2,6000)

Required

Determine the linear function

First, calculate slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{6000 - 4500}{2 - 1}

m = \frac{1500}{1}

m = 1500

The equation is then calculated using:

y = m(x - x_1) + y_1

y = 1500(x - 1) + 4500

y = 1500x - 1500 + 4500

y = 1500x +3000

As a function, we have:

f(x) = 1500x +3000

7 0
2 years ago
What is the area of this irregular shape 28in 7in 20in 30in 25in
Alex777 [14]

Answer:

b1=1b2=1h=7b1=1b2=6h=2b1=6b2=9h=2

7 0
2 years ago
Math help please, thx
pogonyaev
The answer is radical 9
5 0
3 years ago
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