Answer:
D 8√(10) ^3x
Step-by-step explanation:
We have
sqrt(10) ^ (3/4x)
We can rewrite the sqrt as ^1/2
10 ^ (1/2) ^ (3/4x)
We know that a^b^c = a^(b*c)
10 ^(1/2 *3/4x)
10 ^(3/8 x)
The numerator is the power
The denominator is the root
8√(10) ^3x
So it wants you to write two equations, one for the number of fruit and another for the money spent. gather your important information first:
20 fruits for $11.50
apples cost $0.50
bananas cost $0.75
let's do the cost equation first. it's $0.50 per apple, so 0.50a, and $0.75 per banana, so 0.75b. the total cost is $11.50. put all of this information together:
0.50a + 0.75b = 11.50 ... so, the cost of apples bought plus the cost of bananas bought equals 11.50
note what your variables stand for. a represents the number of apples, b represents the number of bananas. to write an equation for how many fruits bought, you simply have to add these two and set them equal to 20 (the total number of fruits bought).
a + b = 20
and your other equation
0.50a + 0.75b = 11.50
these are your two equations. to solve the system of equations, you first want to get one variable alone; the first equation will be easier.
a + b = 20
a = 20 - b
now take this equation and plug it into the second equation.
0.50(20 - b) + 0.75b = 11.50 ... you'll notice that you only have one variable left: b. solve for it. the first step is to distribute 0.50 to the parentheses
10 - 0.50b + 0.75b = 11.50 ... combine like terms
10 + 0.25b = 11.50 ... subtract 10
0.25b = 1.5 ... divide by 0.25
b = 6
6 bananas were purchased. plug this back into an equation to find out how many apples were purchased.
a + 6 = 20 ... subtract 6
a = 14
14 apples and 6 bananas were bought.
1. 36 = 6·6 and 42 = 6·7 have a common factor of 6.
... x⁴ and x² have a common factor of x²
The GCF is 6x².
The factorization is 36x⁴ -42x² = 6x²(6x² -7)
2. All coefficients are multiples of 4. All variable factors are multiples of x³.
The GCF is 4x³.
The factorization is 4x⁵ -8x⁴ -4x³ = 4x³(x² -2x -1)
3. The GCF of coefficients 6 and 15 is (15 mod 6) = 3, which is also a factor of the other coefficients. The lowest power of m, which is m² is also a factor of the other terms.
The GCF is 3m².
The factorization is 6m⁵ -15m⁴ -21m³ +27m² = 3m²(2m³ -5m² -7m +9)
Answer:
h = - 
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² + 6x + 11 ( factor out 2 from the first 2 terms )
= 2(x² + 3x) + 11
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 3x
y = 2(x² + 2( )x + 
- ) + 11
= 2(x + )² - 
+ 11
= 2(x + )² + 
← in vertex form
with h = -
An expression because it can not be expressive
