What is the value of x?
1 answer:
Because the two triangles together create another 90 degree angle on the right-most side, we can tell the triangle is a 45-45-90 triangle
So the base of the height (the given value is 3). Because it is a 45-45-90, the height is also 3.
You can now find x by using Pythagorean theorem OR just the proof of a 45-45-90 triangle.
Pythagorean theorem version:
a^2 + b^2 = c^2
3^2 + 3^2 = x^2
9 + 9 = x^2
18 = x^2
x = 3
45-45-90 proof
The legs of a 45-45-90 triangle are congruent so you just take the value of a leg and place a at the end of it.
Leg length is 3 units. Slap a on the end; answer is 3
So the base of the height (the given value is 3). Because it is a 45-45-90, the height is also 3.
You can now find x by using Pythagorean theorem OR just the proof of a 45-45-90 triangle.
Pythagorean theorem version:
a^2 + b^2 = c^2
3^2 + 3^2 = x^2
9 + 9 = x^2
18 = x^2
x = 3
45-45-90 proof
The legs of a 45-45-90 triangle are congruent so you just take the value of a leg and place a
Leg length is 3 units. Slap a
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Answer:
A. = 8i
B. 8i + 5i = 13i
C. 8i - 5i = 3i
D. 8i x 5i = -40
Step-by-step explanation:
A. The square root of any negative number would lead to a complex number. Complex numbers are number which consist a complex part denoted by i.
-1 =
=
= i
Example: 1. What is the square root of -64?
square root of -64 =
=
= x
= i x 8
= 8i
= 8i
2. find the square root of -25.
=
= 5i
B. To add two complex numbers, they are considered as algebraic expressions.
Example, the sum of 8i and 5i can be determined as;
8i + 5i = 13i
C. To add two complex numbers, they are considered as algebraic expressions.
Example, the subtraction of 8i and 5i can be determined as;
8i - 5i = 3i
D. To multiply two complex numbers, the complex part is considered.
Example, determine the product of 8i and 5i.
8i x 5i = 8 x 5 x i x i
= 40
= -40 (∵ = -1)
8i x 5i = -40