According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.
By using this theorem we can set up the system of equations as follows:
x=y+1 ...(1)
2x+3= 3y + 3 ..(2)
By using equation (1) next step is to plug in y+1 for x in equation (2). So,
2 ( y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3 By using distribution property.
2y + 5 = 3y + 3
2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.
2y = 3y - 2
2y - 3y = -2 Subtract 3y from each sides.
-y = -2
So, y=2
Next step is to plug in y=2 in equation (1) to get the value of x. Hence,
x= 2+1
=3
So, x=3 and y=2 make these triangles congruent.
So, the correct choice is 3. x = 3, y = 2.
Answer:
8s
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
10s + -2s
<u>Step 2: Simplify</u>
- Rewrite: 10s - 2s
- Combine like terms: 8s
Answer:
Sierra's profit was $41.
Step-by-step explanation:
Sierra realized she lost two-third of a dollar each hour when the shop was closed.
The expression that models this situation is, ............. (1)
Now, we have to calculate Sierra's profit if the shop was closed for 6 hours.
So, putting h = 6 hours in the equation (1) we get,
dollars.
So, Sierra's profit was $41. (Answer)
Step-by-step explanation:
Step-by-step explanation:
Swap the sides of the equation :
⤑
We want to remove the 17.56 first.
Since the original equation is 17.56 , we are going to use the opposite operation and subtract 17.56 from both sides :
⤑
Simplify. 17.56 - 17.56 = 0 on the left. 30.16 - 17.36 = 12.6 on the right.
⤑
Then, we need to think about how to remove the coefficient 5. Since the opposite of multiplication is division , I am going to divide both sides by 5.
⤑
Simplify. 5/5 = 1 on the left and 12.6/5 = 2.52 on the right. So, Our answer is x = 2.52.
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Answer:
C
Step-by-step explanation: