Answer:
1. false
2. false
3. true
4. true
5. true
6. false
Step-by-step explanation:
1. The value of the first expression when t = 3 is not equal to the value of the second expression when t = 3.
2. The value of the first expression when t = 7 is not equal to the value of the second expression when t = 7.
3. The value of both expressions when t = 3 is 30.
4. The value of both expressions when t = 7 is 54.
5. The expressions are equivalent.
6. The expressions are not equivalent.
6t + 12 = 6(t + 2)
6(3) + 12 =6((3) + 2)
18 + 12 = 6(5)
30 = 30
6(7) + 12 = 6((7) + 2)
42 + 12 = 6(9)
54 = 54
The quadratic that has the roots x=8 and x=-5 is
x^2-3x-40
Hope this helps you! (:
-Hamilton1757
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
Solution:
Let the length of rectangle=x
Width of rectangle=x/10
Perimeter is 2(Length+Width)
= 2(x+x/10)
Area of Rectangle= Length* Width=x*x/10
As, Perimeter=2(Area)
So,2(x+x/10)=2(x*x/10)
Multiplying the equation with 10, we get,
2(10x+x)=2x²
Adding Like terms, 10x+x=11x
2(11x)=2x^2
22x=2x²
2x²-22x=0
2x(x-11)=0
By Zero Product property, either x=0
or, x-11=0
or, x=11
So, Width=x/10=11/10=1.1
Checking:
So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2
Area=Length*Width=11*1.1=12.1
Hence, Perimeter= 2 Area
As,24.2=2*12.1=24.2
So, Perimeter=2 Area
So, Answer:Length of Rectangle=11 units
Width of Rectangle=1.1 units
Multiply the price by (1 + sales tax).
85 x (1+0.07)
85 x 1.07 = 90.95
He will pay $90.95
Answer:
Step-by-step explanation:
We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...
y = a(x -3)² +b
Filling in the values from the first two table points, we get
For (x, y) = (0, 6):
6 = a(0 -3)² + b ⇒ 9a +b = 6
For (x, y) = (2, 22):
22 = a(2-3)² +b ⇒ a +b = 22
Subtracting the second equation from the first gives ...
(9a +b) -(a +b) = (6) -(22)
8a = -16 . . . . . . collect terms
a = -2 . . . . . . . . divide by 8
The second equation above tells us ...
b = 22 -a = 22 -(-2) = 24
So, our equation for y is ...
y = -2(x -3)² +24
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The value of y for x=5 is ...
y = -2(5 -3)² +24 = 16
The height of the ball after 5 seconds is 16 feet.
