Answer:
x = - 2
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x² - 2x + 6x + 4
= x² + 4x + 4
Equating to zero
x² + 4x + 4 = 0
(x + 2)² = 0
x + 2 = 0
x = - 2
Answer:
Step-by-step explanation:
Simplify:
Group same factor:
Add :
Apply the distributive law: -(a+b) = -a - b
Group same factor:
Subtract:
Add:
Group same factor:
Hence answer =
<u><em>~lenvy~</em></u>
Answer:
Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
- The vertex is the point at which the graph changes direction as we go from left to right.
- Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.
- Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started rising
- Now the answers:
- Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so <em>minimum</em>
- vertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so <em>minimum</em>
- vertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is <em>maximum</em>
- Vertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is <em>maximum</em>
- vertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is <em>minimum</em>
- vertex is (0.5,5) because it was getting big then changed and started getting smaller so <em>maximum</em>
Answer:
No solution
Step-by-step explanation:
24a-22= -4(1-6a)
24a-22= -4+24a
-24a -24a
0-22= -4
-22= -4
Answer:
A. 5
Step-by-step explanation:
The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.
(x +1)^2 +x^2 = (√61)^2
x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses
2x^2 +2x = 60 . . . . . . .subtract 1, collect terms
x^2 +x -30 = 0 . . . . . divide by 2, subtract 30
(x +6)(x -5) = 0 . . . . factor the quadratic
x = -6 or +5
The solution is x = 5.
_____
Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.
