Answer:
f(x) = -(x-3)^2 + 4
Step-by-step explanation:
(h; k) are the coordinates of the vertex.
On the graph are (3, 4), therefore we have:
f(x) = a(x-3)^2 + 4
We have the x- intercept (1,0) -> x=1; y=0.
Substitute them into the equation:
0 = a(1 - 3)^2 + 4
0 = a(-2)^2 + 4
4a + 4 = 0 | -4
4a = -4 |-4
a = -1
So, we have the answer:
f(x) = -(x-3)^2 + 4
Given two points A(x₁,y₁) and B(x₂,y₂) the distance betwen these points will be:
dist(A,B)=√[(x₂-x₁)²+(y₂-y₁)²].
We have these points: A(0,0) and B(6,3); its distance will be:
dist(A,B)=√[(6-0)²+(3-0)²]
=√(6²+3²)
=√(36+9)
=√45 ≈ 6.71
Answer: D. 6.71 units.
If we multiply the top equation by -4 we can get rid of the x so:
-4x+20y=-12
4x-4y=12
Add these up
16y=0
Y=0
X=3
Answer:
The question is missing, so I will answer all the solution for each possible system of two equations.
Step-by-step explanation:
The equations
x + 5 y = 10 (red)
3 x - y = 1 (blue)
x - 5 y = 10 (green)
3 x + y = 1 (purple)
are shown in the picture atatched. The intersection between two lines is the solution of their system.
<u>system:</u>
x + 5 y = 10 (red)
3 x - y = 1 (blue)
<u>solution</u>: (0.938, 1.813)
<u>system</u>:
x + 5 y = 10 (red)
x - 5 y = 10 (green)
<u>solution</u>: (10, 0)
<u>system</u>:
x + 5 y = 10 (red)
3 x + y = 1 (purple)
<u>solution</u>: (-0.357, 2.071)
<u>system</u>:
3 x - y = 1 (blue)
x - 5 y = 10 (green)
<u>solution</u>: (-0.357, -2.071)
<u>system</u>:
3 x - y = 1 (blue)
3 x + y = 1 (purple)
<u>solution</u>: (0.333, 0)
<u>system</u>:
x - 5 y = 10 (green)
3 x + y = 1 (purple)
<u>solution</u>: (0.938, -1.813)
Option B) (x + 3)^2 − 5 is the correct answer
Step-by-step explanation:
Given expression is:

We will solve eah expression in the options to chek which is equivalent to given expression
So,
<u>A) (x + 3)^2 + 5</u>

NOT equivalent
<u>B) (x + 3)^2 − 5</u>

Equivalent
Hence,
Option B) (x + 3)^2 − 5 is the correct answer
Keywords: Equivalent expressions, polynomials
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