Let i = sqrt(-1) which is the conventional notation to set up an imaginary number
The idea is to break up the radicand, aka stuff under the square root, to simplify
sqrt(-8) = sqrt(-1*4*2)
sqrt(-8) = sqrt(-1)*sqrt(4)*sqrt(2)
sqrt(-8) = i*2*sqrt(2)
sqrt(-8) = 2i*sqrt(2)
<h3>Answer is choice A</h3>
1. 60,30,90 right triangle. y will be hypotenuse/2, x will be
hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646
y = 16/2 = 8
2. 45,45,90 right triangle (2 legs are equal length and you have a right angle).
X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So
x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8
3. Just a right triangle with both legs of known length. Use the Pythagorean theorem
x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13
4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again.
y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800 5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem. x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374
6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful.
x = y.
12^2 = x^2 + y^2
12^2 = x^2 + x^2
12^2 = 2x^2
144 = 2x^2
72 = x^2
sqrt(72) = x
6*sqrt(2) = x
x is approximately 8.485281374
7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem.
y = 11*2 = 22.
x = sqrt(22^2 - 11^2) = sqrt(484 - 121) = sqrt(363) = sqrt(121 * 3) = 11*sqrt(3). Approximately 19.05255888
8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem.
x = 2y
y^2 = x^2 - (22.5*sqrt(3))^2
y^2 = (2y)^2 - (22.5*sqrt(3))^2
y^2 = 4y^2 - 1518.75
-3y^2 = - 1518.75
y^2 = 506.25 = 2025/4
y = sqrt(2025/4) = sqrt(2025)/sqrt(4) = 45/2
Therefore:
y = 22.5
x = 2*y = 2*22.5 = 45
9. Just a generic right triangle with 2 known legs. Use the Pythagorean theorem.
x = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34
10. Another right triangle, another use of the Pythagorean theorem.
x = sqrt(50^2 - 14^2) = sqrt(2500 - 196) = sqrt(2304) = 48
Answer:
b. 160°
Step-by-step explanation:
angle A = (far arc - near arc)/2
far arc is arc BC and near arc is arc BE. Replacing into the equation:
∠A = (arc BC - arc BE)/2
50 = [4x + 20 - (2x - 10)]/2
50*2 = 2x + 30
x = (100 - 30)/2
x = 35°
Replacing this information into arc BC equation:
arc BC = 4(35) + 20 = 160°
Kimm since the function is g(x) = 3(x-2) and we are given g(x)=6 That means: 6 = 3(x-2) Then we need to know what is x? 6 = 3x - 6 (distribute the 3) 12 = 3x (add 6 to both sides) 4 = x (divide both sides by 3)You can check it this way. Is g(4) = 3(4-2) = 6 ? 3*2 = 6
Answer:
651 i think
Step-by-step explanation:
31/2 =15.5 so 15.5 times 42 = 651
