Answer:
The equivalent expression would be 3^6, and without exponents this would be equal to 729.
Step-by-step explanation:
To get the equivalent expression, you have to know that terms with the same base that are multiplied simply add together exponents.
3^4 * 3^2 = 3^6
Then we can find that by expanding the terms and completing the multiplication.
3 * 3 * 3 * 3 * 3 * 3 = 729
Answer:
(x - 2)² + (y + 7)² = 64
(fourth option listed / option D)
Step-by-step explanation:
as you likely know, the equation of a circle (centered at origin) is x²+y²=r²
now, let's say we want to write this using the center (the origin), it could look like this:
(x - 0)² + (y - 0)² = r²
(the center is 0,0)
[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]
We can use this for any center, and we write our circle equation as:
(x - h)² + (y - k)² = r²
(h, k) is the center
So, let's apply the information we know
our (h, k) is (2, -7)
so let's fill that in:
(x - h)² + (y - k)² = r²
(x - 2)² + (y - -7)² = r² (simplify)
(x - 2)² + (y + 7)² = r²
now, we also know that our "r" <em>(r is the radius)</em> is 8, so let's fill that in too:
(x - 2)² + (y + 7)² = r²
(x - 2)² + (y + 7)² = 8² (simplify)
(x - 2)² + (y + 7)² = 64
So, we have found the equation of our circle to be:
(x - 2)² + (y + 7)² = 64
hope this helps! (and hope this makes sense) have a lovely day :)
3/8 becomes 3/2 and 4/5 becomes 1/5
3/2 x 1/5 =3/10
3/10 is ur answer
Answer:
A) x = 3 or -1
B) x = -7
C)x = -7
Step-by-step explanation:
A) x² + 2x + 1 = 2x² - 2
Rearranging, we have;
2x² - x² - 2x - 2 - 1 = 0
x² - 2x - 3 = 0
Using quadratic formula, we have;
x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)
x = (2 ± √16)/2
x = (2 + 4)/2 or (2 - 4)/2
x = 6/2 or -2/2
x = 3 or -1
B) ((x + 2)/3) - 2/15 = (x - 2)/5
Multiply through by 15 to get;
5(x + 2) - 2 = 3(x - 2)
5x + 10 - 2 = 3x - 6
5x - 3x = -6 - 10 + 2
2x = -14
x = -14/2
x = -7
C) log(2x + 3) = 2log x
From log derivations, 2 log x is same as log x²
Thus;
log(2x + 3) = logx²
Log will cancel out to give;
2x + 3 = x²
x² - 2x - 3 = 0
Using quadratic formula, we have;
x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)
x = (2 ± √16)/2
x = (2 + 4)/2 or (2 - 4)/2
x = 6/2 or -2/2
x = 3 or -1
Answer:
Step-by-step explanation:
x² = 10² - 6² = 100 - 36 = 64
x = √64 = √8*8 = 8
Right angle triangle, use Pythagorean theorem
(hypotenuse)² = (adjacent)² + (opposite)²