Answer:
B. Gaining
Step-by-step explanation:
Answer:
The answer is letter D.
Step-by-step explanation:
320/80
=4
If the polygons are similar then the sides are in proportion.
![\dfrac{32}{24}=\dfrac{32:8}{24:8}=\dfrac{4}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B32%7D%7B24%7D%3D%5Cdfrac%7B32%3A8%7D%7B24%3A8%7D%3D%5Cdfrac%7B4%7D%7B3%7D)
Therefore we have the equations:
![\dfrac{x-1}{6}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(x-1)=(4)(6)\\\\3x-3=24\qquad\text{add 3 to both sides}\\\\3x=27\qquad\text{divide both sides by 3}\\\\\boxed{x=9}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-1%7D%7B6%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28x-1%29%3D%284%29%286%29%5C%5C%5C%5C3x-3%3D24%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C%5C%5C3x%3D27%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D9%7D)
![\dfrac{y+1}{21}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(y+1)=(21)(4)\\\\3y+3=84\qquad\text{subtract 3 from both sides}\\\\3y=81\qquad\text{divide both sides by 3}\\\\\boxed{y=27}](https://tex.z-dn.net/?f=%5Cdfrac%7By%2B1%7D%7B21%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28y%2B1%29%3D%2821%29%284%29%5C%5C%5C%5C3y%2B3%3D84%5Cqquad%5Ctext%7Bsubtract%203%20from%20both%20sides%7D%5C%5C%5C%5C3y%3D81%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7By%3D27%7D)
Answer:
8 cm
Step-by-step explanation:
Squares have equal side lengths so if we call each side x, then x × x gives us the area (32 cm²). This means that x² = 32 and therefore, one side is √32 cm.
Next, to work out the diagonal we can use Pythagoras' theory, since we can form a right-angled triangle. a² + b² = c² (c is the diagonal or the hypotenuse)
(√32)² + (√32)² = c²
(note: the square and the square root cancel out)
32 + 32 = 64
c² = 64 ∴ c = √64 which is 8
Hope this helps!
Answer:
y=9x+75
Step-by-step explanation:
since we know that the slope must be the same for two lines to be proportional, we are gonna start there.
so our equation is: y= 9x + b
we need to find b to complete our equation, so substitute in the points we were given.
3 = 9(-8) + b
so now,
3 = -72 + b
now we have to isolate b to find out what it is,
3 = -72 + b
+72 +72
so now: 75= b
Put that back into the starting equation: y = 9x + 75