Answer:
The percentage rate is 4.5%
Step-by-step explanation:
The simple interest earned in this situation is $1270 - $1000, or $270.
the simple interest formula is i =prt.
Here, i = $270 = ($1000)(r)(6 yr).
$270
Then r = ------------------- = 0.045
$1000(6 yr)
The percentage rate is 4.5%
The correct question is
<span>
Penelope determined the solutions of the quadratic function by completing the square.f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
–1 + 1 = 4(x² + 2x + 1)
0 = 4(x + 2)²
0 = (x + 2)²
0 = x + 2
–2 = x
What error did Penelope make in her work?
we have that
</span>f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
4x² + 8x + 1=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² + 8x)=-1
Factor the
leading coefficient
4*(x² + 2x)=-1
Complete the square Remember to balance the equation
by adding the same constants to each side.
4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)
Rewrite as perfect squares
4*(x+1)²=3
(x+1)²=3/4--------> (+/-)[x+1]=√3/2
(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2
(-)[x+1]=√3/2----> x2=(-2-√3)/2
therefore
the answer is
<span>
Penelope should have added 4 to both sides instead of adding 1.</span>
The standard form of a quadratic equation is

, while the vertex form is:

, where (h, k) is the vertex of the parabola.
What we want is to write

as

First, we note that all the three terms have a factor of 3, so we factorize it and write:

.
Second, we notice that

are the terms produced by

, without the 9. So we can write:

, and substituting in

we have:
![\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20y%3D3%28x%5E2-6x-2%29%3D3%5B%28x-3%29%5E2-9-2%5D%3D3%5B%28x-3%29%5E2-11%5D)
.
Finally, distributing 3 over the two terms in the brackets we have:
![y=3[x-3]^2-33](https://tex.z-dn.net/?f=y%3D3%5Bx-3%5D%5E2-33)
.
Answer:
Answer:
No, you can't form a triangle because angles in a triangle add up to 180 degrees.
Step-by-step explanation:
100+50+50= 200 degrees, which means that you cant form a triangle with these measurements because angles in a triangle have to add up to 180 degrees.
Answer:
Part 1) The number of cups of flour needed to make 4 pizzas is 26
Part 2) The number of pizzas Luigi can make with 13 cups of flour is 2
Step-by-step explanation:
we know that
Luigi uses 39 cups of flour for every 6 pizzas he makes
Let
y ----> the number of cups of flour used
x ---> the number of pizzas he makes
In this problem
The relationship between the variables x, and y, represent a proportional variation
we have the ordered pair (6,39)
so

Part 1) Find out the number of cups of flour needed to make 4 pizzas
using a proportion

Solve for y


Part 2) Find out the number of pizzas Luigi can make with 13 cups of flour
using a proportion

Solve for x

