Answer:
Step-by-step explanation:
1) To find the cube root of a number prime factorize
46656 = 2*2*2*2*2*2 * 3 * 3 * 3 * 3 * 3 * 3
![\sqrt[3]{46656}=\sqrt[3]{2*2*2*2*2*2*3*3*3*3*3*3} =2*2*3*3 = 36](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B46656%7D%3D%5Csqrt%5B3%5D%7B2%2A2%2A2%2A2%2A2%2A2%2A3%2A3%2A3%2A3%2A3%2A3%7D%20%20%3D2%2A2%2A3%2A3%20%3D%2036)
Length of each side = 36 m
Q) i) -512 = (-8) * (-8)*(-8)
-512 is a cube number
v) -17576 = (-26) * (-26)*(-26)
-17576 is cube number
First find how much you've had. Make the fractions with similar denominaters: 1/3(2)=2/6, 1/2(3)=3/6, 5/6(1)=5/6. Now add the fractions: 2/6+3/6+5/6=10/6 or 1 4/6 or 1 2/3. Then add the whole numbers: 10+15+20+1=46. So you've had 46 2/3 oz now subtract that from how much you need: 64-46 2/3= 63 3/3-46 2/3=17 1/3. You still need 17 1/3 water :)
We know that the angles of a triangle sum to 180°. For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180
Combining like terms,
16x+20=180
Subtracting 20 from both sides:
16x=160
Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.
For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180
Combining like terms,
20x-20=180
Adding 20 to both sides:
20x=200
Dividing both sides by 20:
x=10
This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.
Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.
Step-by-step explanation:
(9x2 - 2x +7) +(4x2+7x +2)
9x2 - 2x +7 +4x2 +7x +2
13x2 +5x +9
