Similar shapes may or may not be congruent.
The value of x is (a) 9.0
The corresponding sides are:
- AB and DE
- BC and EF
- AC and DF
The side lengths are:
![\mathbf{DE = 41}](https://tex.z-dn.net/?f=%5Cmathbf%7BDE%20%3D%2041%7D)
![\mathbf{EF = 23}](https://tex.z-dn.net/?f=%5Cmathbf%7BEF%20%3D%2023%7D)
![\mathbf{DF = 36}](https://tex.z-dn.net/?f=%5Cmathbf%7BDF%20%3D%2036%7D)
![\mathbf{AC = 5x - 9}](https://tex.z-dn.net/?f=%5Cmathbf%7BAC%20%3D%205x%20-%209%7D)
Because the shapes are congruent, and AC corresponds to DF.
This means that:
![\mathbf{AC = DF}](https://tex.z-dn.net/?f=%5Cmathbf%7BAC%20%3D%20DF%7D)
So, we have:
![\mathbf{5x - 9 = 36}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x%20-%209%20%3D%2036%7D)
Collect like terms
![\mathbf{5x = 9 + 36}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x%20%3D%209%20%2B%2036%7D)
![\mathbf{5x = 45}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x%20%3D%2045%7D)
Divide both sides by 5
![\mathbf{x = 9.0}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%209.0%7D)
<em>Hence, the correct option is (a) 9.0</em>
Read more about congruent triangles at:
brainly.com/question/12413243
Answer:
Step-by-step explanation:
(-3/9 + 4/3)+ a = 0
first solve our terms in the parentheses by adding them
to do this we have to find the lcd ( lowest common denominator)
9 works for both so I multiply both halves of 4/3 by 3 to get my denominator to 9 the other fraction is already at a denominator of 9 so we leave it alone
(-3/9 + 12/9)+ a=0
then add
(9/9)
9/9=1 SO WE SIMPLIFY
1+a=0
now we isolate our variable (a) to do this we subtract 1 from both sides of our equals sign to get the answer
a=-1
hope this helps
Answers on following order: 5, 2, 4, 2, 8, 0
Answer:
hen two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. ... Two angles are said to be supplementary when the sum of the two angles is 180°.
Step-by-step explanation:
Ritin has 21/5 lemonade and he distributed meaning he took away 13/4 liters of lemonade. Find a common denominator between 5 and 4. Since we know 5 times 4 is 20 the smallest common denominator so lets multiply 21/5 by 4 getting 84/20 and multiply 13/4 by 5 getting 65/20. Since both fractions have 20 as the denominator, subtract 84/20 by 65/20 and you get 19/20 liters of lemonade as your answer.
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Answer is 19/20 liters of lemonade Ritin has left