Answer:
step 1. Angle bisector theorem.
step 2. 14/6 = 21/ (3x - 12)
step 3. 14(3x - 12) =21(6)
step 4. 6x - 24 = 18
step 5. 6x = 42
step 6. x = 7.
Answer:
x = 4
y = 2
Step-by-step explanation:
x - y = 2
x = 2 + y
2x + 3y = 14
2(2 + y) + 3y = 14
4 + 2y + 3y = 14
4 + 5y = 14
5y = 10
y = 2
x - y = 2
x - 2 = 2
x = 4
Answer:
Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
Both expressions are linear expressions. It takes 2 points to define a line. If the lines defined by each expression go through the same two points, then the expressions are equivalent.
If the expressions have the same value for two different variable values, they are equivalent. (choice D)
_____
<em>Additional comment</em>
One more point is needed than the degree of the polynomial expression. That is, quadratic (degree 2) expressions will be equivalent if they go through the same 2+1 = 3 points.
Answer:
$2000 was invested at 5% and $5000 was invested at 8%.
Step-by-step explanation:
Assuming the interest is simple interest.
<u>Simple Interest Formula</u>
I = Prt
where:
- I = interest earned.
- P = principal invested.
- r = interest rate (in decimal form).
- t = time (in years).
Given:
- Total P = $7000
- P₁ = principal invested at 5%
- P₂ = principal invested at 8%
- Total interest = $500
- r₁ = 5% = 0.05
- r₂ = 8% = 0.08
- t = 1 year
Create two equations from the given information:


Rewrite Equation 1 to make P₁ the subject:

Substitute this into Equation 2 and solve for P₂:





Substitute the found value of P₂ into Equation 1 and solve for P₁:



$2000 was invested at 5% and $5000 was invested at 8%.
Learn more about simple interest here:
brainly.com/question/27743947
brainly.com/question/28350785
Answer:
9, 10
Step-by-step explanation:
9² = 81
10² = 100