Answer:
x = 10
Step-by-step explanation:
Using the Pythagorean theorem:
8² + 6² = x²
64 + 36 = x²
x² = 100
x = 10
Answer: C
Step-by-step explanation:
Your answer is correct! When you multiply 2 matrices, the inner dimensions have to be equal. If they are equal, the resulting dimensions would be the outer dimentions.
(<u>3</u>×4)(4×<u>5</u>)
Since the inner (bolded) dimensions are the same, in this case 4×4, we know these matrices can be multiplied.
Since these matrices can be multiplied, the product will be 3×5, the underlined outer dimensions.
Answer:
Step-by-step explanation:
1) Use Division Distributive Property: (x/y)^a = x^a/y^a.
2) Multiply both sides by 27^x - 8.
3) Use the product rule: x^a x^b = x^a+b.
4) Simplify 1 + x - 8 to x - 7.
5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.
6) Use Change of Base Rule.
7) Use rule of 1: log 1 = 0.
8) Simplify 0/log_27 to 0.
9) Add 7 to both sides.
10) Switch sides.
<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>
5x - 2y + 1z = 8 ⇒ 5x - 2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9x - 2y - 5z = 4 -4x + 3z = 13
5x - 2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9z - 2y - 5z = 4 ⇒ -9x - 2y - 5z = 4
-18x - 3z = 9
-4x + 3z = 13
-18x - 3z = 9
-22x = 22
-22 -22
x = -1
-18x - 3z = 9
-18(-1) - 3z = 9
18 - 3z = 9
- 18 - 18
-3z = -9
-3 -3
z = 3
5x - 2y + z = 8
5(-1) - 2y + 3 = 8
-5 - 2y + 3 = 8
-2y - 5 + 3 = 8
-2y - 2 = 8
+ 2 + 2
-2y = 10
-2 -2
y = -5
(x, y, z) = (-1, -5, 3)
