Find the interest earned in an account with $600 invested at 4.5% annual simple interest for 2 years.

What is 5x^2-7x-3=8 by solving using a graph???

Alinara [238K]

Hello!

Simplifying
5x2 + -7x + -3 = 8

Reorder the terms:
-3 + -7x + 5x2 = 8

Solving
-3 + -7x + 5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8

Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0

Begin completing the square. Divide all terms by
5 the coefficient of the squared term:

Divide each side by '5'.
-2.2 + -1.4x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2

The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49

Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69

Calculate the square root of the right side: 1.640121947

Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.

Subproblem 1
x + -0.7 = 1.640121947

Simplifying
x + -0.7 = 1.640121947

Reorder the terms:
-0.7 + x = 1.640121947

Solving
-0.7 + x = 1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7

Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947

Simplifying
x = 2.340121947

Subproblem 2
x + -0.7 = -1.640121947

Simplifying
x + -0.7 = -1.640121947

Reorder the terms:
-0.7 + x = -1.640121947

Solving
-0.7 + x = -1.640121947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7

Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947

Simplifying
x = -0.940121947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}

3 0

3 years ago

See picture below!! :D

Gnesinka [82]

The angles are congruent and corresponding. You can find the missing angles by subtracting the existing ones from 180.

7 0

3 years ago

Y=2x+1 answers anyone?

laila [671]

Answer: y= 2

Step by step: Multiply 2 and 1 to get 2

6 0

3 years ago

Classify the following triangle. Check all that apply

lubasha [3.4K]

Answer:

A. Acute and B. Equilateral

Step-by-step explanation:

8 0

2 years ago

George observes that for every increase of 1 in the value of x, there is a increase of 60 in the corresponding value of y. He cl

Brums [2.3K]

Hi there!

FACTS :

To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).

STEPS TO ANSWER:

x = 1 ; y = 90 → $\frac{1}{90} =$ 1 ÷ 90 = 0.01111111...

x = 2 ; y = 150 → $\frac{2}{150} =$ 2 ÷ 150 = 0.0133333...

x = 3 ; y = 210 → $\frac{3}{210} =$ 3 ÷ 210 = 0.01428571

x = 4 ; y = 270 → $\frac{4}{270} =$ 4 ÷ 270 = 0.0148148...

x = 5 ; y = 330 → $\frac{5}{330} =$ 5 ÷ 330 = 0.01515152

** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.

⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.

There you go! I really hope this helped, if there's anything just let me know! :)

5 0

3 years ago