Answer:
There are 29 chickens and 19 sheep.
Step-by-step explanation:
Samantha has chickens and sheep on her farm.
Let the number of chickens be c.
Let the number of sheep be s.
Each chicken has one head and each sheep has one head.
She looked out one day and counted 48 animal heads. Each chicken has one head and each sheep has one head.
This means that the number of chickens and sheep add up to 48:
c + s = 48 ____________(1)
She also counted 134 legs. Each chicken has one head and each sheep has one head. This means that:
2c + 4s = 134 ________(2)
From (1),
c = 48 - s ____________ (3)
Put (3) in (2):
2(48 - s) + 4s = 134
96 - 2s + 4s = 134
Collecting like terms:
2s = 134 - 96
2s = 38
s = 38 / 2 = 19
Putting this back in (3):
c = 48 - 19
c = 29
There are 29 chickens and 19 sheep.
<span>Simplifying
7(2e + -1) + -3 = 6 + 6e
Reorder the terms:
7(-1 + 2e) + -3 = 6 + 6e
(-1 * 7 + 2e * 7) + -3 = 6 + 6e
(-7 + 14e) + -3 = 6 + 6e
Reorder the terms:
-7 + -3 + 14e = 6 + 6e
Combine like terms: -7 + -3 = -10
-10 + 14e = 6 + 6e
Solving
-10 + 14e = 6 + 6e
Solving for variable 'e'.
Move all terms containing e to the left, all other terms to the right.
Add '-6e' to each side of the equation.
-10 + 14e + -6e = 6 + 6e + -6e
Combine like terms: 14e + -6e = 8e
-10 + 8e = 6 + 6e + -6e
Combine like terms: 6e + -6e = 0
-10 + 8e = 6 + 0
-10 + 8e = 6
Add '10' to each side of the equation.
-10 + 10 + 8e = 6 + 10
Combine like terms: -10 + 10 = 0
0 + 8e = 6 + 10
8e = 6 + 10
Combine like terms: 6 + 10 = 16
8e = 16
Divide each side by '8'.
e = 2
Simplifying
<span>e=2
</span></span>
(sorry, i went into depth)
Answer: B. 4
Step-by-step explanation: Divide 20 by 5 and get 4.
When a line is perpendicular to another line, the gradient becomes the “negative reciprocal” which basically means flip the gradient and change the sign. In this instance the negative reciprocal of 5x has to be -1/5 as it has been flipped and made negative. At this point the answer can only be B or C.
After this you can use the point given to work out the y-intercept:
y-y1 = m(x-x1)
y-3 = -1/5(x+10)
y-3 = -1/5x - 2
y = -1/5x -1
And there’s your answer: C
