Given
GO.o has 3 orange picks for every 2 green
there are 25 picks in all
Find out how many picks are orange.
To proof
As given in question
GO.o has 3 orange picks for every 2 green
i.e the ratio of orange to every green becomes
total number of picks = 25
let the GO.o pick of 3 orange picks for every 2 green =x
than the equation becomes
3x + 2x = 25
5x = 25
x = 5
Than
the number of oranges = 3x
putting the value of x
= 15
the number of green = 2x
= 10
thus the 15 picks are orange.
Hence proved
(ab)² and ab² are not equal. When you have something in parentheses being squared, you have to square everything inside, so in the case of (ab)², you have to "distribute" the ² to both variables inside. That gives you a²b², not just ab².
If the abstract way is kind of confusing for you, just pick two random numbers for a and b and plug them in to test it. Say a = 3 and b = 4. Then
(3*4)² = 3*4²
(12)² = 3*16
144 ≠ 48
Answer:
2:7 = 14:59
Step-by-step explanation:
2 + 7 = 9
63 divided by 9 = 7
Get the 2 from "2:7"
2 x 7 = 14
Get 7 from "2:7"
7 x 7 = 49
First one: x would be equal to 8 because the angles opposite sides 8 and x are congruent (isosceles triangle)
Second one: x is 75° because the sides opposite x and 75° are congruent (isosceles triangle)
Third one: This is an equilateral triangle since all the sides are equal. In equilateral triangles, every angle is 60° because 60*3=180. So both x and y are 60°
Fourth one: We know that all three angles in a triangle add to 180°. And we also know that the last unlabled angle would be equal to x because this is an isosceles triangle. So we can write
x+x+38=180 (combine like terms)
2x+38=180 (subtract 38 from both sides)
2x=142 (divide both sides by 2)
x=71°
Fifth one: This is an equilateral triangle so all the angles are congruent and add to 180. So we can write
3(4x+12)=180 (distribute)
12x+36=180 (subtract 36 from both sides)
12x=144 (divide both sides by 12)
x=12
Last one: Since the two given angles are opposite congruent sides, these angles are equal. Therefore, we can just make each of these angles 3x to solve for x first. And since we know the last angle is 90° we can write
3x+3x+90=180 (combine like terms)
6x+90=180 (subtract 90 from both sides)
6x=90 (divide both sides by 6)
x=15
So the angle 3x would be 3*15 or 45.
So we can set 45 equal to y+7 and solve for y
y+7=45 (subtract 7 from both sides)
y=38
Hope this helps<span />
