The slope is undefined because it is a vertical line on the x axis at 0. Its a straight line going up
Answer:
answer:250 pieces
1 metre=100cm so
10metres =100*10 =1000cm
each piece is 4 CM long, so.,
no. of pieces=1000/4
by dividing by 2....
=500/4
again by dividing by2...
=250/1=250 pieces
so 250 pieces of ribbon can be cuttted from 10 metre long ribbon.
Answer:
8
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial 
being divided by a factor in the form of 
, then the remainder of the polynomial is given by 
.
We have the polynomial:
And it is being divided by:
We can rewrite our factor as:
Therefore:
Then our remainder will be:
Evaluate:
So, our remainder will be 8.
For this case we must simplify the following expression:
![\sqrt [3] {\frac {12x ^ 2} {16y}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B%5Cfrac%20%7B12x%20%5E%202%7D%20%7B16y%7D%7D)
We rewrite the expression as:
![\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\sqrt[3]{\frac{4(3x^2)}{4(4y)}}=\\\frac{\sqrt[3]{3x^2}}{\sqrt[3]{4y}}=](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B4%283x%5E2%29%7D%7B4%284y%29%7D%7D%3D%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B4%283x%5E2%29%7D%7B4%284y%29%7D%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B4y%7D%7D%3D)
We multiply the numerator and denominator by:
![(\sqrt[3]{4y})^2:\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{\sqrt[3]{4y}*(\sqrt[3]{4y})^2}=](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%3A%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B%5Csqrt%5B3%5D%7B4y%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%3D)
We use the rule of power
in the denominator:
![\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{(\sqrt[3]{4y})^3}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{4y})^2}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B%28%5Csqrt%5B3%5D%7B4y%7D%29%5E3%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B4y%7D%29%5E2%7D%7B4y%7D%3D)
Move the exponent within the radical:
![\frac{\sqrt[3]{3x^2}*(\sqrt[3]{16y^2}}{4y}=\\\frac{\sqrt[3]{3x^2}*(\sqrt[3]{2^3*(2y^2)}}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B16y%5E2%7D%7D%7B4y%7D%3D%5C%5C%5Cfrac%7B%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B2%5E3%2A%282y%5E2%29%7D%7D%7B4y%7D%3D)
![\frac{2\sqrt[3]{3x^2}*(\sqrt[3]{(2y^2)}}{4y}=\\\frac{2\sqrt[3]{6x^2*y^2}}{4y}=](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Csqrt%5B3%5D%7B3x%5E2%7D%2A%28%5Csqrt%5B3%5D%7B%282y%5E2%29%7D%7D%7B4y%7D%3D%5C%5C%5Cfrac%7B2%5Csqrt%5B3%5D%7B6x%5E2%2Ay%5E2%7D%7D%7B4y%7D%3D)
![\frac{\sqrt[3]{6x^2*y^2}}{2y}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B6x%5E2%2Ay%5E2%7D%7D%7B2y%7D)
Answer:
Answer: Choice B
y = (x+3)^2 - 1
==================================================
Recall that vertex form is y = a(x-h)^2 + k with the vertex being (h,k)
From the given graph, it shows that (h,k) = (-3,1) is the vertex. So we plug this pair of values into the general function above to get
y = a(x-h)^2 + k
y = 1(x-(-3))^2 + (-1)
y = (x+3)^2 - 1
which is the final answer
note: a = 1 is the case for all four answer choices, so we don't have to worry about the value of 'a'
