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n200080 [17]
2 years ago
10

Find two acute angles that satisfy the equation sin(2x + 7) = cos(x + 23). Check that your answers make

Mathematics
1 answer:
Vera_Pavlovna [14]2 years ago
3 0

Answer:

The smaller angle is 43 and the larger angle is 47

Step-by-step explanation:

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1. Find the value of x.<br><br> A. 90<br> B. 80<br> C. 60<br> D. 45
tia_tia [17]

Answer:

A 90

Step-by-step explanation:

multiple ways to prove this.

e.g. since the angle between the two lines from the center of the circle to the 2 tangent touching points is 90 degrees (that is the meaning of these 90 degrees here as the angle of the circle segment defined by the 2 tangent touching points and the circle center), the tangents have the same "behavior" as tan and cot = the tangents at the norm circle at 0 and 90 degrees. they hit each other outside of the circle again at 90 degrees.

another way

imagine the two right triangles of the tangents crossing point to the circle center and the tangent/circle touching points.

the Hypotenuse of each triangle is cutting the 90 degree angle of the circle segment exactly in half (due to the symmetry principle). so the angle between radius side and Hypotenuse is 90/2 = 45 degrees.

that means also the angle of such a right triangle at the tangent crossing point is 45 degrees (as the sum of all angles in a triangle must be 180, we have the remainder of 180 - 90 - 45 = 45 degrees).

the angles of both right triangles at that point are the same, and so we can add 45+45 = 90 degrees for the total angle at the tangent crossing point.

8 0
3 years ago
A 12 foot ladder is leaning against the side of a building. The top of the ladder reaches 10 feet up the side of the building. A
Soloha48 [4]
√135=3√15.....................

5 0
3 years ago
What term must be precisely defined before writing a sufficient definition of angle?
madreJ [45]

The answer is C.

Step-by-step explanation:

It's C) Ray

8 0
2 years ago
Is 13 a perfect square
ladessa [460]
1^2=1 \\ 2^2=4 \\ 3^2=9 \\ 4^2=16 \\ 5^2=25 \\ 6^2=36 \\ 7^2=49 \\ 8^2=64 \\ 9^2=81 \\ 10^2=100 \\ 11^2=121 \\ 12^2=144 \\ \boxed{13^2=169} \\  14^2=196 \\ 15^2=225 \\
8 0
4 years ago
A botanist was measuring how tall her plant grew. After two weeks it had grown 12.93 inches.The second week alone it had grown 3
Korolek [52]

Answer:

  9.5 inches

Step-by-step explanation:

The relationship is presumed to be ...

  (first week's growth) + (second week's growth) = (growth in two weeks)

  (first week's growth) + 3.43 inches = 12.93 inches . . . . . fill in the numbers

Subtract 3.43 from both sides of the equation:

  first week's growth = 12.93 inches - 3.43 inches

  first week's growth = 9.50 inches

The plant grew 9.50 inches in the first week.

6 0
3 years ago
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