The answers to the question are are the equations
y = 0.08x²-1.6x+13
y = 0.08(x-10)²+5
<h3>How to solve for the system of equations</h3>
David starts at (20, 13) and skates along a path that can be modeled by a quadratic function with a vertex at (10, 5).
Vertex form of quadratic function is
y =
13 = a(x-10)²+5
let x = 20
a(20-10)²+5
13 = 100a + 5
take like terms
13 - 5 = 100a
8 = 100a
divide through by 100
a = 0.08
hence the equation would be
y = 0.08(x-10)²+5
Read more on equations here:
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Answer:
Isosceles triangle
Step-by-step explanation:
Given
Two congruent angles and two congruent sides
Base on the given description, the concept being described is an isosceles triangle, as it has two congruent sides and two congruent angles.
If each angle measures 45 degrees each, then the third angle is 90 degrees.
This is shown below.
--- angles in a triangle
Subtract 90 from both sides
p(x) = 2x3 – x2 + 4x – 7
p(x) = x3 – x2 – x – 3
p(x) = x5 + 4x3 - x2 + 6x
Answer:
Age of Alice = 25, Age of Jane = 20.
Step-by-step explanation:
Let age of Alice = x
Then age of Jane is 80% of the age of Alice
=> Age of Jane = 80% of x = 80/100 * x = 0.8x
Adding the two ages gives 45.
The two ages are x and 0.8x.
The sum of the two ages is x+ 0.8 x = (1+0.8)x = 1.8x.
=> 1.8 x = 45
Dividing both sides by 1.8, x = 45/1.8
=> x= 25
But x represents the age of Alice.
So age of Alice is 25.
Age of Jane = 0.8* 25 = 20
Verification: Adding the two ages gives 45.