31/8 5/4
=31/40 /4
=31/100
hope this helps :3
Answer:
x=−5+√29 or x=−5−√29
Step
Let's solve your equation step-by-step.
x2+10x+10=14
Step 1: Subtract 14 from both sides.
x2+10x+10−14=14−14
x2+10x−4=0
For this equation: a=1, b=10, c=-4
1x2+10x+−4=0
Step 2: Use quadratic formula with a=1, b=10, c=-4.
x=
−b±√b2−4ac
2a
x=
−(10)±√(10)2−4(1)(−4)
2(1)
x=
−10±√116
2
x=−5+√29 or x=−5−√29
Answer:
the fraction of the sheet of paper does he use is 1 ÷ 12
Step-by-step explanation:
The computation of the fraction of the sheet of paper does he use is shown below:
= Piece of construction paper × piece to make a flower
= 1 ÷2 × 1 ÷ 6
= 1 ÷ 12
hence, the fraction of the sheet of paper does he use is 1 ÷ 12
Answer:
![A_{f}=4\pi (\sqrt[3]{36} r)^{2}\\\\V_{f}=\frac{4}{3} \pi (36r^{3})](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29)
Step-by-step explanation:
In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:
![V_{1}=\frac{4}{3} \pi (r^{3})\\\\V_{2}=\frac{4}{3} \pi (2r)^{3}\\\\V_{3}=\frac{4}{3} \pi (3r)^{3}\\\\V_{f}=\frac{4}{3} \pi (r^{3}+(2r)^{3}+(3r)^{3})\\\\V_{f}=\frac{4}{3} \pi (r^{3}+8r^{3}+27r^{3})\\\\V_{f}=\frac{4}{3} \pi (36r^{3})\\\\V_{f}=\frac{4}{3} \pi R^{3}\\\\R=\sqrt[3]{36} r](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%29%5C%5C%5C%5CV_%7B2%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%282r%29%5E%7B3%7D%5C%5C%5C%5CV_%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%283r%29%5E%7B3%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B%282r%29%5E%7B3%7D%2B%283r%29%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B8r%5E%7B3%7D%2B27r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E%7B3%7D%5C%5C%5C%5CR%3D%5Csqrt%5B3%5D%7B36%7D%20r)
Now that we know the radii of the new sphere, we can calculate the surface area:
![A_{f}=4\pi R^{2}\\\\A_{f}=4\pi (\sqrt[3]{36} r)^{2}](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20R%5E%7B2%7D%5C%5C%5C%5CA_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D)
Answer:
Step-by-step explanation:
(-8 + (-3))/2= -11/2 = -5.5
(-9+(-1))/2= -10/2 = -5
(-5.5, -5): midpoint