Answer:
The correct scientific notation for the number 500.0 is ![500=5.0\times10^2](https://tex.z-dn.net/?f=500%3D5.0%5Ctimes10%5E2)
Step-by-step explanation:
While writing a large number in scientific notation we do below mentioned two things.
- We take any number between 1 and 10
- Then we multiply this number with an exponent of 10.
Hence, any number in scientific notation is in the form ![a\times10^b](https://tex.z-dn.net/?f=a%5Ctimes10%5Eb)
Here a is any number between 1 and 10.
b is exponent of 10.
Now, writing 500 in scientific notation, we take a = 5
Hence, we have to take b = 2, since 5 multiplied by 100 equas 500.
Thus, we have
![500=5.0\times10^2](https://tex.z-dn.net/?f=500%3D5.0%5Ctimes10%5E2)
Answer:
(2x+3) y (3x+5)
Step-by-step explanation:
For this exercise we have that the volume is
V = 6x ^ 3 + 31X ^ 2 + 53x + 30
H = X + 2
The formula for the Volume its
V = H * L * W
for find L and W (width and length) we divide V / H = L * W
So,
![\frac{V}{H} =\frac{6X^{3}+31X^{2}+53X+30 }{X+2}=(2x + 3) * (3x + 5)\\](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7BH%7D%20%3D%5Cfrac%7B6X%5E%7B3%7D%2B31X%5E%7B2%7D%2B53X%2B30%20%7D%7BX%2B2%7D%3D%282x%20%2B%203%29%20%2A%20%283x%20%2B%205%29%5C%5C)
this division is in the attachment
so, L * W = (2x + 3) * (3x + 5)
48 girls are there. Given that there is a ratio of boys to girls of 7:8. Then divide 42 boys by 7 boys which equals 6. After, multiply 6 by 8 girls equals 48 girls.
Answer:
slope = -1/2 and y-intercept = 80
Step-by-step explanation:
A water tank has 80 gallons of water. But the tank has a leak from which water flows at a rate of 1 gallon every 2 minutes
Rate of change is the slope
Given that rate of change is 1 gallon every 2 minutes that is 1/2. The water flows out at the rate of 1/2. since it flows out the slope is negative.
So slope = -1/2
y intercept is the initial amount of water in the tank
A water tank has 80 gallons of water. so y intercept is 80 gallons of water
y intercept = 80
Let:
A(5,-8)=(x1,y1)
B(-2,-10)=(x2,y2)
m1 = slope of the line AB
![m1=\frac{y2-y1}{x2-x1}=\frac{-10-(-8)}{-2-5}=\frac{-2}{-7}=\frac{2}{7}](https://tex.z-dn.net/?f=m1%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D%3D%5Cfrac%7B-10-%28-8%29%7D%7B-2-5%7D%3D%5Cfrac%7B-2%7D%7B-7%7D%3D%5Cfrac%7B2%7D%7B7%7D)
Let:
C(-6, -13)=(x1,y1)
D(-2,1)=(x2,y2)
![m2=\frac{y2-y1}{x2-x1}=\frac{1-(-13)}{-2-6}=\frac{14}{-8}=-\frac{7}{4}](https://tex.z-dn.net/?f=m2%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D%3D%5Cfrac%7B1-%28-13%29%7D%7B-2-6%7D%3D%5Cfrac%7B14%7D%7B-8%7D%3D-%5Cfrac%7B7%7D%7B4%7D)
Now:
![\begin{gathered} \text{Two lines are parallel if:} \\ m1=m2 \\ \text{Two lines are perpendicular if:} \\ m1\cdot m2=-1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BTwo%20lines%20are%20parallel%20if%3A%7D%20%5C%5C%20m1%3Dm2%20%5C%5C%20%5Ctext%7BTwo%20lines%20are%20perpendicular%20if%3A%7D%20%5C%5C%20m1%5Ccdot%20m2%3D-1%20%5Cend%7Bgathered%7D)
So: