8z = 64
divide both sides with 8
8z ÷8 = 64÷8
therefore,
z = 8.
<h3>
Answer: Choice C) x^4 - 2</h3>
Explanation:
If the exponent is negative, then that means we apply the reciprocal. So something like x^(-2) becomes 1/(x^2). A polynomial cannot have a variable in the denominator like this. So we can rule out choices A, B, and D. Choice C is the only thing left. It is a polynomial because the exponent is a positive whole number.
Answer: ![\sqrt[3]{125x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B125x%5E3%7D)
.
Step-by-step explanation: Given radical expression
![\sqrt[3]{5x} \times \sqrt[3]{25x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5x%7D%20%5Ctimes%20%5Csqrt%5B3%5D%7B25x%5E2%7D)
.
According to the product property of roots.
![\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a \times b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%5Ctimes%20%5Csqrt%5Bn%5D%7Bb%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%20%5Ctimes%20b%7D)
On applying above rule, we get
![\sqrt[3]{5x} \times \sqrt[3]{25x^2} = \sqrt[3]{5x \times 25x^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5x%7D%20%5Ctimes%20%5Csqrt%5B3%5D%7B25x%5E2%7D%20%3D%20%5Csqrt%5B3%5D%7B5x%20%5Ctimes%2025x%5E2%7D)
5 × 25 = 125 and
Therefore,
![\sqrt[3]{5x \times 25x^2}= \sqrt[3]{125x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B5x%20%5Ctimes%2025x%5E2%7D%3D%20%5Csqrt%5B3%5D%7B125x%5E3%7D)
<h3>So, the correct option would be second option
.</h3>
<span>2x - 3y - 3z = 8
We've been given the normal vector to the plane <2, -3, -3> and a point within the plane (1, -5, 3). In general if you've been given both the normal vector <a,b,c> and a point (e,f,g) within the plane, the expression for the plane will be:
ax + by + cz = d
and you can compute d by:
d = ae + bf + cg
So let's calculate d:
d = ae + bf + cg
d = 2*1 + -3*-5 + -3*3
d = 2 + 15 + -9
d = 8
And the equation for the plane is
2x - 3y - 3z = 8</span>
Answer:
The given line segment has a midpoint at (−1, −2).
On a coordinate plane, a line goes through (negative 5, negative 3), (negative 1, negative 2), and (3, negative 1).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
y = −4x − 4
y = −4x − 6
y = One-fourthx – 4
y = One-fourthx – 6
y = Three-halvesx + 1
