Answer:
x=-2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
Answer:
126°
Step-by-step explanation:
The sum of angles in a triangle is 180°. Corresponding angles C and H of the similar triangles have the same measure, so you have ...
... ∠G + ∠H + ∠D = 180°
... ∠G + 31° +23° = 180° . . . . . . . subtract the numbers on the left to find ∠G
... 180° -54° = ∠G = 126°
22a) Matts' weekly fee is $7.50. We know this is by looking at the Y-axis. If he doesn't sell any books at the beginning of the week, his earnings are at -$7.50. We can assume that he pays that much for internet fee.
22b) Matt makes $1.50 for each book he sells. We know this because if you look at (5,0) and then the next one (6, 1.5), we see that his Y-value has increased by $1.50, which is equal to one book because 6 - 5 = 1 book.
22c) y = 1.5x - 7.5
22d) I'm going to assume that question means $30 in profit. Let's plug in the 30 in the equation. 30 = 1.5x - 7.5. Simplify.
Matt has to sell 25 books to make $30
L = -4,4
E = -2, -3
N = 2,1
I = 4,3
E = 1,3
The inequality should read:
Subtract 2 from all the terms:
Divide all the terms by -5 to get x by itself (note that you flip the inequality signs as you divide by a negative):
The inequality is 2 ≤ x < 8.
A closed dot represents ≤, and an open dot represents <. Since x can represent all values between 2 and 8, you will shade in between 2 and 8 on the number line. x is greater than or equal to 2, so there will be a closed dot on 2. x is less than 8, so there will be an open dot on 8.
The answer is 'number line with a closed dot on 2 and an open dot on 8 and shading in between'.
