Correct answer would be D. hope this helps :)
Answer:
The perimeter of the rectangle is 2x+ 30
Step-by-step explanation:
Sides of the rectangle are 2/3x+10 and 1/3x+5
Now, Perimeter of the Rectangle = 2(Length + Breadth)
Here, sum of the sides = ![(\frac{2}{3}x + 10 ) + (\frac{1}{3}x + 5 ) = (\frac{2}{3}x +\frac{1}{3}x ) + ( 10+ 5 )](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B3%7Dx%20%2B%2010%20%29%20%20%2B%20%28%5Cfrac%7B1%7D%7B3%7Dx%20%2B%205%20%29%20%20%3D%20%28%5Cfrac%7B2%7D%7B3%7Dx%20%2B%5Cfrac%7B1%7D%7B3%7Dx%20%20%29%20%20%2B%20%28%2010%2B%205%20%29)
adding like terms with like terms, we get
(![\frac{2x + x}{3}) + 15 = \frac{3x}{3} + 15](https://tex.z-dn.net/?f=%5Cfrac%7B2x%20%2B%20x%7D%7B3%7D%29%20%20%2B%2015%20%3D%20%5Cfrac%7B3x%7D%7B3%7D%20%20%2B%2015)
Hence, Sum = (x + 15)
Now, 2(Length + Breadth) = 2(x+15) = 2x + 30
hence, the perimeter of the rectangle = 2x+ 30
Answer:
Point U' (-2, 1)
Step-by-step explanation:
When moving up and down on a graph, this affects the y coordinate only.
Since it is moving up 1 unit, we have to add 1 to the y coordinate. So U' will end up being (-2, 1).
![\boxed{The\:value\:of\:x\:is\:7.375.}](https://tex.z-dn.net/?f=%5Cboxed%7BThe%5C%3Avalue%5C%3Aof%5C%3Ax%5C%3Ais%5C%3A7.375.%7D)
![\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}](https://tex.z-dn.net/?f=%5Clarge%5Cmathfrak%7B%7B%5Cpmb%7B%5Cunderline%7B%5Cred%7BStep-by-step%5C%3Aexplanation%7D%7D%7B%5Corange%7B%3A%7D%7D%7D%7D%7D)
![(4x - 5)2 = 49 \\ ⇢8x - 10 = 49 \\⇢8x = 49 + 10 \\ ⇢8x = 59 \\ ⇢x = \frac{59}{8} \\ ⇢x = 7.375](https://tex.z-dn.net/?f=%284x%20-%205%292%20%3D%2049%20%5C%5C%20%E2%87%A28x%20-%2010%20%3D%2049%20%5C%5C%E2%87%A28x%20%3D%2049%20%2B%2010%20%5C%5C%20%20%E2%87%A28x%20%3D%2059%20%5C%5C%20%E2%87%A2x%20%3D%20%20%5Cfrac%7B59%7D%7B8%7D%20%20%5C%5C%20%E2%87%A2x%20%3D%207.375)
Therefore, the value of x is 7.375.
![{ \bf{ \underbrace{To\:verify :}}}](https://tex.z-dn.net/?f=%7B%20%5Cbf%7B%20%5Cunderbrace%7BTo%5C%3Averify%20%3A%7D%7D%7D)
![(4x - 5)2 = 49 \\ ⇢(4 \times 7.375 - 5)2 = 49 \\ ⇢(29 .5 - 5)2 = 49 \\ ⇢24.5 \times 2 = 49 \\ ⇢49 = 49 \\ ⇢ L.H.S.=R. H. S](https://tex.z-dn.net/?f=%284x%20-%205%292%20%3D%2049%20%5C%5C%20%E2%87%A2%284%20%5Ctimes%207.375%20-%205%292%20%3D%2049%20%5C%5C%20%E2%87%A2%2829%20.5%20-%205%292%20%3D%2049%20%5C%5C%20%E2%87%A224.5%20%5Ctimes%202%20%3D%2049%20%5C%5C%20%E2%87%A249%20%3D%2049%20%5C%5C%20%E2%87%A2%20L.H.S.%3DR.%20H.%20S)
Hence verifed.
![\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}](https://tex.z-dn.net/?f=%5Clarge%5Cmathfrak%7B%7B%5Cpmb%7B%5Cunderline%7B%5Corange%7BHappy%5C%3Alearning%20%7D%7D%7B%5Corange%7B.%7D%7D%7D%7D%7D)
The preimage WXYZ is to undergo a rotation of 90° in the clockwise direction.
A 90° clockwise rotation leads to the following change in the coordinates;
(x,y) -> after rotation (y,-x)
this rule applies for all the vertices in the preimage
W - (3,-5) --> W' (-5,-3)
X - (1,-3) ---> X' (-3,-1)
Y - (-1,-5)---> Y' (-5,1)
Z - (1,-7) ---> Z' (-7,-1)
therefore the new coordinates are W' (-5,-3), X' (-3,-1), Y' (-5,1) and Z' (-7,-1)