Answer:
16
Step-by-step explanation:
3x+8=7x+2
-3x. =-3x
=4x
8. = 4x
x=2
Answer:
(a)81 yards (b)27 seconds
Step-by-step explanation:
Let Shontal distance to the point where he overtakes Diego=x
Since Diego is given a head start of 27 yards, his distance to the point where he is overtaken by Shontal=x-27
Diego hops at a rate of 2 yards per second.
Shontal hops 3 yards per second.
Now, Time Taken=Distance ÷ Average Speed
- For Diego, Time Taken = (x-27) ÷ 2
- For Shontal, Time taken = x ÷ 3
At the point where Shontal overtakes Diego, their time taken are equal.
Therefore:
![\frac{x-27}{2}=\frac{x}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-27%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B3%7D)
Cross multiplying
3(x-27)=2x
3x-81=2x
3x-2x=81
x=81 yards
(a) Therefore, Shontal will have to hop 81 yards
(b)Recall, for Shontal,
Time taken = x ÷ 3 = 81 ÷ 3 =27 seconds
It will take Shontal 27 seconds to overtake Diego.
Answer:
3x + y = 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + y = - 12 ( subtract 3x from both sides )
y = - 3x - 12 ← in slope- intercept form
with slope m = - 3
• Parallel lines have equal slopes , then
y = - 3x + c ← is the partial equation
to find c substitute (- 1, 5 ) into the partial equation
5 = 3 + c ⇒ c = 5 - 3 = 2
y = - 3x + 2 ← equation in slope- intercept form
add 3x to both sides )
3x + y = 2 ← equation in standard form
Answer: ![b=1](https://tex.z-dn.net/?f=b%3D1)
Step-by-step explanation:
Given the equation
you need to solve for the variable "b".
You need to apply Distributive property on both sides of the equation:
![-3(-8b+7)=3(2b-1)\\\\24b-21=6b-3](https://tex.z-dn.net/?f=-3%28-8b%2B7%29%3D3%282b-1%29%5C%5C%5C%5C24b-21%3D6b-3)
Now you need to add 21 to both sides of the equation:
![24b-21+21=6b-3+21\\\\24b=6b+18](https://tex.z-dn.net/?f=24b-21%2B21%3D6b-3%2B21%5C%5C%5C%5C24b%3D6b%2B18)
Subtract
from both sides:
![24b-6b=6b+18-6b\\\\18b=18](https://tex.z-dn.net/?f=24b-6b%3D6b%2B18-6b%5C%5C%5C%5C18b%3D18)
And finally, you can divide both sides of the equation by 18:
![\frac{18b}{18}=\frac{18}{18}\\\\b=1](https://tex.z-dn.net/?f=%5Cfrac%7B18b%7D%7B18%7D%3D%5Cfrac%7B18%7D%7B18%7D%5C%5C%5C%5Cb%3D1)