What is the value of x? sin(x 37)°=cos(2x 8)° enter your answer in the box. x =

Answers

Answer 1
Applying the trig formula: sin a = cos (90 - a)
cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x)
Property of the cosine function -->
(
2
x
+
8
)
=
±
(
53

x
)

a. 2x + 8 = 53 - x
3x = 45
x
=
15


b. 2x + 8 = - 53 + x
x
=

61


For general answers, add
k
360


Check by calculator.
x = 15 --> sin (x + 37) = sin 52 = 0.788
cos (2x + 8) = cos (38) = 0.788. Proved
x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407
cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved
Answer 2

The value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15.

How to convert sine of an angle to some angle of cosine?

We can use the fact that:

[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]

to convert the sine to cosine (but the angles won't stay same unless its 45 degrees).

For this case, we're specified the equation sin(x+37)°=cos(2x+8)°.

Converting sine to cosine, we get:

[tex]\cos(90 - x - 37)^\circ = \cos(2x + 8)^\circ\\[/tex]

Since cosine is a periodic function with period of [tex]360^\circ[/tex], thus, we get:
[tex]90 - x - 37= 2x + 8 +360 n[/tex]

where n = an integer (positive, negative, or zero).

or

[tex]90 - 37 - 8= 3x + 360 n\\\\x = \dfrac{45 - 360n}{3} = 15 - 120n[/tex]

This is the general solution of the considered equation.

Assuming that only principal values (from 0 to 360 degrees) angles are allowed, we need:

[tex]0 \leq x + 37 \leq 360\\\\and\\\\0 \leq 2x+8 \leq 360[/tex]

The first inequality gives:

[tex]-37 \leq x \leq 323[/tex]

The second inequality gives:

[tex]-4 \leq x \leq 176[/tex]

We need to satisfy both the inequalities, so the final boundaries on x are:

[tex]-4 \leq x \leq 176[/tex] (the minimum ones for which both inequalities stay true).

n = -2 gives x = 255n = -1 gives x = 135n = 0 gives x = 15n = 1 gives x =  -105

n < -2 gives x > 255, and n > 1 gives x < -105

So, values of n for which [tex]-4 \leq x \leq 176[/tex] is true are n = -1, or n = 0

Thus, x = either 135 or 15

sin

Thus, the value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15

Learn more about sine to cosine conversion here:

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Related Questions

3x - 12y = 6
x - 4y = 2
solve by elimination

Answers

3x-12y=6

x-4y=3--(1)x-4y=2--(2)

Lets convert to slope intercept form

4y=x-34y=x-2

Slopes are equal so lines are parallel

Hence no solutions

1) the height is 11 ft
2) base is 9 in and the height is 3 in
I just need to know the area ​

Answers

1. All 4 sides are the same length

Area = 11 x 11 = 121 square ft.


2. area = 9 x 3 = 27 square in.

what is the slope-intercept form of the equation of the line that contains the points (-3,-3) and (4,5)

Answers

Answer:

[tex]y=1.14x+0.420[/tex]

Step-by-step explanation:

Given the following question:

Point A = (-3,-3) = (x1, y1)
Point B = (4, 5) = (x2, y2)

To write the points in slope intercept form we must first calculate the slope using rise over run. Once we have the slope, we substitute the values into the formula for slope intercept which is y = mx + b and then solve for b to have our answer.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{5--3}{4--3} =\frac{8}{7}[/tex]
[tex]8\div7=1.14[/tex]
[tex]m=1.14[/tex]

Now that we have the slope substitute the values:
[tex]y=mx+b[/tex]
[tex]y=-3[/tex]
[tex]m=1.14[/tex]
[tex]x=-3[/tex]
[tex]-3=1.14(-3)+b[/tex]
[tex]1.14\times-3=-3.42[/tex]
[tex]-3=-3.42+b[/tex]
[tex]-3.42+3.42=0[/tex]
[tex]-3+3.42=0.42[/tex]
[tex]0.42=b[/tex]
[tex]b=0.42[/tex]
[tex]y=1.14x+0.420[/tex]

Your answer is "y = 1.14x + 0.420."

Hope this helps.

Erik rides his motorbike 26/23 miles in 23 hour. What is Erik’s average speed in miles per hour?

Answers

Answer:

Average speed = 40 mph.

Step-by-step explanation:

Which term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line?

Answers

Answer: C

Step-by-step explanation:

Jim has some socks in two drawers. In one drawer he has 3 red and 6 green socks. In the other drawer he has 2 red and 2 green socks. If jim takes one sock out of each drawer, how probable is it that both will be red?

Answers

Answer:

5/6

Step-by-step explanation:

There are 5 steps to solving this problem:

Calculate the number of marbles in each drawerCalculate the fractional number of red marbles in each drawerThe answer is the number of red marbles in both drawers added together.

Using these steps, we see that:

9 in the first drawer and 4 in the other drawer  3/9 or 1/3 of the socks in the first drawer are red, and 1/2 of the socks in the second drawer are redAdding 1/3 and 1/2 together equals 5/6Therefore, the answer is 5/6!

7x+ 8=29 how to solve it

Answers

Answer:

the correct answer is x = 3

Step-by-step explanation:

you solve this by moving all the terms that dont contain x to the right side and solve the equation.

hope this helps

have an awesome day -TJ

pls mark brainliest if this helps you :)

X + Y-2 (3X-4Y+3) please simplify this
thanks

Answers

Answer:

-5x+9y-6

Step-by-step explanation:

Step 1:

Remove bracket,  

x+y-6x+8y-6

collect like terms and simplify,

x-6x+y+8y-6= -5x+9y-6

There is an isosceles triangle which is also a right triangle. Its area is 50 square inches. Find the length of the base of the triangle

Answers

Answer: 10 inches

Step-by-step explanation:

find ml 2x+5 5x-4 Brainliest HURRY RN

Answers

Answer:

11

Step-by-step explanation:

5x + -4 = 2x + 5

-2x  +4   -2x  +4

3x = 9

x = 3

5(x) - 4 = ML

5(3) - 4 = ML

15 - 4 = ML

11 = ML

A plane takes off from an airport at an angle of 14.5°. If the plane is traveling at a velocity of 220 feet per second, how high off of the ground is the plane at 10 seconds?

Answers

The distance of the plane travelling at 220 feet per second off the ground is 151.71feet

How to calculate the maximum height of an object

Maximum height of the plane is expressed as:

[tex]M=\frac{u^2sin^2\theta}{2g}[/tex]

u  is the velocity = 220ft/s

θ is the angle of elevation = 14.5°.

g is the acceleration due to gravity

Substitute

[tex]M=\frac{u^2sin^2\theta}{2g}\\M=\frac{220^2sin^2(14.5)}{2(10)}\\M=151.71feet[/tex]

Hence the distance of the plane off the ground is 151.71feet

Learn more on maximum height here: https://brainly.com/question/12446886

Find the 53rd multiple of 62, if the 54th multiple is 3348.

Answers

Answer:

[tex]\displaystyle 3286[/tex]

Explanation:

Just multiply 62 and 53 to get 3286.

I am joyous to assist you at any time.

How much of a radioactive substance must be presented to decay to 80 grams in 12 years if the half-life of the substance is 7.6 years?

Answers

Answer:

Radioactive in half life is 51gram

Step-by-step explanation:

80grams:12years

X :7.6years

12x÷x=x

7.6×80÷12=51gram

Answer:

239 grams.

Step-by-step explanation:

Half life t(1/2) = ln 2 / k

So 7.6 = ln 2 / k

k = ln 2 / 7.6 = 0 0901204

N = No e^-kt

So after 12 years

80 = No / e^(-0.0901204*12)

No = 80 / e^(-0.0901204*12)

= 239.

Find the domain over which the function y = x + 6x is monotonic increasing.

Answers

Answer:

x > -3

[tex]\sf (-3, \infty)[/tex]

Step-by-step explanation:

Domain: input values (x-values)

Monotonic increasing:  always increasing.  
A function is increasing when its graph rises from left to right.

The graph of a quadratic function is a parabola.  If the leading term is positive, the parabola opens upwards.  The domain over which the function is increasing for a parabola that opens upwards is values greater than the x-value of the vertex.

Vertex

Standard form of quadratic equation:  [tex]\sf y=ax^2+bx+c[/tex]

[tex]\textsf{x-value of vertex}=\sf -\dfrac{b}{2a}[/tex]

Given function:

[tex]\sf y=x^2+6x[/tex]

Therefore, x-value of function's vertex:

[tex]\sf \implies x= -\dfrac{6}{2}=-3[/tex]

Final Solution

The function is increasing when x > -3

[tex]\sf (-3, \infty)[/tex]

you go to the pet store and see 9 cats and 12 dogs.if this ratio stays the same and there are 108 cats in the store,how many dogs would be in the store?

Answers

Answer:

144

Step-by-step explanation:

Because if you multiply 9*12=108 and 12*12=144

Plot the points A(7,1), B(-2, 3), C(1, -7) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a parallelogram.
(Plotting point D is optional.)

Answers

      A             B

D              C

vectors

AB = DC

AB (-2-7 ; 3-1) => AB (-9 ; 2)

DC (1-x : -7-y)

1 - x = -9 => x = 10

-7-y = 2 => y = -9

D(10 ; -9)

Answer:

D = (10, -9)

Step-by-step explanation:

If ABCD is a parallelogram, then AB = DC and BC = AD

Therefore,

[tex]\sf x_A-x_B=x_D-x_C[/tex]

[tex]\sf \implies 7-(-2)=x_D-1[/tex]

[tex]\sf \implies x_D=10[/tex]

[tex]\sf y_A-y_B=y_D-y_C[/tex]

[tex]\sf \implies 1-3=y_D-(-7)[/tex]

[tex]\sf \implies y_D=-9[/tex]

Therefore, D = (10, -9)

Help assappp

Line L is a line that passes through (-4,5)
and is parallel to the line described by
y-7=-2(x+1). Write the equation
of line l in point-slope form

Answers

Answer:

y-5=-2(x+4)

Step-by-step explanation: All you need to do is remember the point-slope form equation y-y1=m(x-x1), parallel slope (-2), then (-4,5). Plug in (-4,5) and -2 into the point slope form equation y-5=-2(x+4). That's all.

What is the sale price of jeans which regularly cost $32, but now are 10% off?

Answers

Answer:

$28.80

Step-by-step explanation:

32 x 0.1 = 3.2
32 - 3.2 =28.8

Hope this helps :)

Answer:

$28.8

Step-by-step explanation:

10% of 32 is 3.2

32 - 3.2 = 28.8

Which equation can be used to calculate the surface area of the triangular prism net show below? The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters. [Not drawn to scale] Surface Area = (one-half) (5) (12) (5) (10) (12) (10) (13) (10) Surface Area = (one-half) (5) (13) (one-half) (5) (13) (13) (10) (12) (10) Surface Area = (2) (5) (13) (5) (10) (13) (10) (12) (10) Surface Area = (one-half) (5) (12) (one-half) (5) (12) (5) (10) (12) (10) (13) (10).

Answers

The  [tex]13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex]  equation can be used to calculate the surface area of the triangular prism.

It is given that the triangular prism net showing in the figure with dimensions.

It is required to find which equation can be used to find the surface area of the triangular prism net.

What is surface area?

It is defined as the area of 3-dimensional geometry surfaces area sum which is occupying the outer area of the object.

We know the area of a rectangle = length × width

Area of the top rectangle = 13×10

Area of the middle rectangle = 12×10

Area of bottom rectangle=  5×10

The formula for finding the area of a triangle:

[tex]\rm A=\frac{1}{2} \times bh[/tex]

Area of right triangle = [tex]\rm \frac{1}{2} \times 5 \times12[/tex]

Area of left triangle = [tex]\rm \frac{1}{2} \times 5 \times12[/tex]

The surface area = Area of top+ Area of middle+ Area of bottom+ Area of    

                                a right triangle+ Area of the left triangle  

[tex]=13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex]

Thus, the [tex]13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12[/tex]  equation can be used to calculate the surface area of the triangular prism.

Learn more about the surface area here:

https://brainly.com/question/1196953

If tan 0 = 8/15, what is sin 0?

Answers

Tan0 = opposite/adjacent =8/15
Therefore opposite(o)= 8
adjacent(a)= 15
Considering Hypotenuse
= √(o2 + a2)
= √[(8)2 + (15)2]
= √289 = 17
Sin0 = opposite/ Hypotenuse
= 8/17
Sin0=8/17

If (x − 5) is a factor of the polynomial function f(x) = 3x2 − 23x + 40, which of the following is another factor?

Answers

Answer:

3x-8

Step-by-step explanation:

Use synthetic division:

5 | 3 -23 40

____ 15 -40_

    3  -8 | 0

Hence, another factor of the polynomial is 3x-8

Write -1.7 repeating as a fraction

Answers

Answer:

-1 7/10

Step-by-step explanation:

Hope that helps!!!

In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town.

Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x, the number of left-handed females?
6
24
96
108

Answers

Answer:

  (b)  24

Step-by-step explanation:

The given variable definitions and the given relationships let us write these statements:

  LH males = 4 × LH females = 4x

  RH females = 3 × RH males = 3y

  LH males + RH males = 204 = 4x +y

  RH females + LH females = 348 = 3y +x

Your favorite method of solving equations of this sort can tell you ...

  (x, y) = (24, 108)

There are 24 left-handed females.

__

Additional comment

Other numbers involved here are ...

  y = 108 . . . . right-handed males

  204-108 = 96 . . . . left-handed males (=4×24)

  348-24 = 324 . . . . right-handed females (=3×108)

__

If you want to solve the equations by hand, you can use substitution for y to get an equation in x:

  3(204 -4x) +x = 348   ⇒   -11x = -264   ⇒   x = 24

Draw a number line to represent the street sign below

Answers

Its kind of like how it is on a car to tell how fast your going i hoped this helped!

marked price an article is 20% above its cost price. it is sold for rs 1100 at 10% profit find its marked price​

Answers

Hey there!

Marked price (MP) = 1100 + Cost price (CP) ----(1)

If the watch was sold at discount of 20%, profit = Rs. 400

⇒ Selling price = MP - 20% of MP = 0.8MP

Also, Selling price = CP + 400

⇒ CP + 400 = 0.8MP

Substituting from (1),

⇒ CP + 400 = 0.8(1100 + CP)

⇒ CP + 400 = 880 + 0.8CP

⇒ 0.2CP = 480

⇒ CP = Rs. 2400

∴ To earn a profit of 30%, Selling price = 2400 + 30% of 2400 = 2400 + 720 = Rs. 3120

What does the 6 in 2/6 mean?

Answers

Hey there!

Here we have a fraction

2/6.

The 2 is the numerator, and 6 is the denominator.

How to remember where the numerator and the denominator is?

Well, please remember the following:

The Denominator is Down

Hence, 6 is the denominator of this fraction.

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

HELP ASAP
I WILL GIVE BRAINIST

Answers

answer:

jesus know the answer

What is the value of x

Answers

Answer:

The answer would be 7

36/6=6

so it would be

42/x=6

x=7

Is the following function even, odd, or neither f(x)=x^3/x+1

Answers

Answer: Odd

Step-by-step explanation:

Odd functions are functions where the exponent of the leading term is odd. In this case, the exponent of 3 is odd, so the function is odd.

Please Help! will give brainlest!

Answers

Answer:

No, because triangle XYZ is not a right triangle.

Step-by-step explanation:

SOHCAHTOA (sin, cos, tan) can only work on right triangles. If a triangle is not a right triangle, you cannot use sin cos tan on it. This triangle is not a right triangle, so this is why you cannot fin the tangent ratio.

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