Which values represent solutions to Cosine (StartFraction pi Over 4 EndFraction minus x) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction sine x, where x Is an element of [0, 2Pi)?
Left-brace 0, pi right-brace
Left-brace 0, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Left-brace pi, StartFraction 3 pi Over 2 EndFraction
Answers
Answer:
C.
Step-by-step explanation:
got it right on edge :)
The given trig function consist of trig values of common angles;
The values that represent the solution to [tex]\mathbf{cos \left(\dfrac{\pi}{4} - x\right)} = \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex], x ∈ [0, 2·π) are;
[tex]x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}[/tex]
Reason:
The given function is presented as follows;
[tex]cos \left(\dfrac{\pi}{4} - x\right) = \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex]
Where;
x ∈ [0, 2·π)
We have;
cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)
[tex]cos \left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}, \ sin\left(\dfrac{\pi}{4} \right) = \dfrac{\sqrt{2} }{2}[/tex]
Which gives
[tex]cos \left(\dfrac{\pi}{4} - x\right) =\dfrac{\sqrt{2} }{2} \cdot cos \, x + \dfrac{\sqrt{2} }{2} \cdot sin \, x[/tex]
Therefore, we get;
[tex]\dfrac{\sqrt{2} }{2} \cdot cos \, x = \dfrac{\sqrt{2} }{2} \cdot sin \, x - \dfrac{\sqrt{2} }{2} \cdot sin \, x = 0[/tex]
cos x = 0
[tex]cos \left(\dfrac{\pi}{2} \right) = 0[/tex]Therefore;
The possible solutions (x-values) to cos x = 0 are; [tex]0 \leq \dfrac{n \cdot \pi}{2} \leq 2 \cdot \pi[/tex]Where;
n = 1, 3, 5, ...
x ∈ [0, 2·π)
We get;
[tex]x = \left\{\dfrac{\pi}{2} , \, or \ \dfrac{3 \cdot \pi}{2} \right \}[/tex]Learn more here:
https://brainly.com/question/12774575
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Answer:
7 * x = 5 + y
Step-by-step explanation:
hope this helps!, you can correct me if I'm wrong.
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What is the difference in the steps you take to evaluate (-7)2 and -72 ? What is the
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58
Step-by-step explanation:
because it is
Answer:
Sample Response:
To find (–7)2, the base –7 is multiplied by itself: (–7)(–7) = 49. To find –72, the base 7 is multiplied by itself: 7 • 7 = 49. The negative sign is then applied to get –49.
Translate sentence into an equation.
Thirteen is 7 more than one-fifth of a number
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Answer:
[tex]13=7+\frac{1}{5}x[/tex]
Step-by-step explanation:
The answer would be 30
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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13. A square has a side length of 4 centimeters. What is the length of the diagonal of the
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The table represents a function.
What is f(5)?
A. -8
B. -1
C. 1
D. 8
Answers
Answer:
A. -8
Step-by-step explanation:
We can look at the table and figure out how we get f(5)
really its just the x value pugged into the x value for the function
after that we look on the table, f(5) is -8 because at the bottum of the table it shows 5 and -8
High Hopes^^
Barry-
What is the slope and equation of a line parallel to the x-axis passing through (3,7)?
Answers
Answer:
We know that the equation is y=7 because it passes through point (3,7), and 7 is the y-coordinate of that point (remember we don't really care about the 3 because since the line is parallel to the x-axis, it will pass through all values of x, so the 3 is irrevalent).
Step-by-step explanation:
The equation of the line passing through the point (3,7) and parallel to the x-axis is y =7.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
We know that the equation is y=7 because it passes through the point (3,7), and 7 is the y-coordinate of that point (remember we don't really care about the 3 because since the line is parallel to the x-axis, it will pass through all values of x, so the 3 is prevalent.
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Answers
Answer:
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A recipe uses 834 cups of milk for every 312 cups of oatmeal.
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Answer:
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Answer:
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Step-by-step explanation:
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Answer:
2
Step-by-step explanation:
hi! to find the perpendicular slope, you have to flip the fraction to its reciprocal and use the opposite sign (- or +).
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Answer:
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Step-by-step explanation:
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Answers
Answer:
x=9
Step-by-step explanation:
Subtract 8 from both sides.
−5x=−37−8
Subtract 8 from −37 to get −45.
−5x=−45
Divide both sides by −5.
x= -45/-5
Divide −45 by −5 to get 9.
x=9
Answer:
9
Step-by-step explanation:
Step 1:
8 - 5x = - 37 Equation
Step 2:
8 = - 37 + 5x Add 5x on both sides
Step 3:
45 = 5x Add 37 on both sides
Step 4:
x = 45 ÷ 5 Divide
Answer:
x = 9
Hope This Helps :)
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Answer:
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Answer:
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
y=10x+28
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Answer:
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Answers
Answer:
5
Step-by-step explanation:
Because 5 is greater than 3 by 2
(5-3=2)
Answer:
5 is greater than 3
Step-by-step explanation:
cause the is the third number
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Answers
Answer:
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Step-by-step explanation:
Hope this helps. Plz give brainliest
If you need work tell me
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Answers
Answer:
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Step-by-step explanation:
Answer:
-10. is the answer
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i just answered the question on edge.
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Answers
Answer:
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Step-by-step explanation:
-2x + 8x - 9 + 4x + 7x + 2
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
An automobile's radiator has a capacity of fifteen quarts, and it currently contains twelve quarts of a thirty percent antifreeze solution. How many quarts of antifreeze are currently in the radiator?
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Answer:
3.6 quarts.
Step-by-step explanation:
just take 30% of 12 which is 3.6
(I just did the assignment and got 100, so dw.)
Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has
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25 + 2.5d > 50 +
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25 - 2.5d > 50 -
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Answers
Answer: 25 - 2.5d > 50 - 3.25d
Graph (1,1), (1,2), (1,3), (1,4)
Answers
Answer:
There is not a way that I can show you how to graph it, so I will try and explain it.
Step-by-step explanation:
(1,1)
^ ^ y-axis
x-axis
You are just going right however many, and then up however many it says.
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Ralph wants to build a rectangular deck with a predefined area of 66 feet squared. One side of the deck will be 5 feet longer than the other. To find the side lengths, he first writes the equation (x)(x+5)=66 and later simplifies (x-6)(x+11)=0 it to , where x is the length of the shorter side. Which of these are the side lengths, in feet, of the rectangular deck? Select all that apply
Answers
Answer:
The shorter side is 6 ft and the longer side is 11 ftStep-by-step explanation:
The options are not given, but we could solve and arrive at an answer
say the shorter side is x
and the longer side is x+5
we know that the area of a rectangle is given as
x*(x+5)=66
open the bracket
x^2+5x=66
x^2+5x-66=0
Find two factors of -66 whose sum equals the coefficient of the middle term, which is 5 .
the factors are 11 and -6
splitting the middle term using the two factors 11 and -6
x2 +11x - 6x - 66=0
x(x+11)-6(x+11)=0
(x-6)=0
x=6
(x+11)=0
x=-11
The shorter side is 6 ft and the longer side is 11 ft
This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes.
What is the unknown value representing the unit rate?
A. 8
B. 125
C. 140
D. 156
Answers
Have a good day!
Answer:
C
Step-by-step explanation:
