Answer:
z = 1/2
Step-by-step explanation:
Step 1: Write equation
22z + 6 - 10 = 6z + 4
Step 2: Solve for <em>z</em>
- Combine like terms: 22z - 4 = 6z + 4
- Subtract 6z on both sides: 16z - 4 = 4
- Add 4 to both sides: 16z = 8
- Divide both sides by 16: z = 8/16
- Simplify: z = 1/2
Step 3: Check
<em>Plug in z to verify it's a solution.</em>
22(1/2) + 6 - 10 = 6(1/2) + 4
11 - 4 = 3 + 4
7 = 7
To find the maximum height you need to find the vertex:(h,k)
Your equation is in vertex form a(x-h)+k and the vertex is (h,k) where k is the maximum height and the h is the distance it went to reach the maximum height.
k=6 so the kangaroo's maximum height is 6 feet.
To find how long is the kangaroo's jump, take a look at the graph. You will notice that the parabola ends at the distance the kangaroo jumped. You will also see that it is the one of the x-intercepts.
-.03(x-14)^2+6=0
-.03(x-14)^2+6-6=0-6
-.03(x-14)^2=-6
-.03/-.03(x-14)=-6/-.03
(x-14)^2=200
[(x-14)^2]^.5=200^.5
x-14=(200)^.5
x-14+14=(200)^.5+14
x≈28.14 feet
The kangaroo jumped a distance of 28.14 feet.
You will notice that the square root of a number gives you two solutions a positive and a negative one. The other solution is -.14, which we know distance is not negative so we do not use that solution. Also, I used the ^.5 instead of using the square root. It is the same.
Answer:
The hours times 4 equals the miles. The answer is B.
Step-by-step explanation:
A= 2.5
b= 2
LM/ON= 15
LO/MN= 5
Answer:
5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2)
Step-by-step explanation:
In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:
x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)
x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)
Now that you have factored out the two quadratics, plug them into the equation.
5x - 3
(x+4)(x+2) (x+5)(x+2)
Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.
5x (x+5) - 3(x+4)
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)
Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:
5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2
(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)