Answer:
There are two pairs of solutions: (2,7) and (-1,4)
Step-by-step explanation:
We will use substitution.
y = x^2 + 3
y = x +5
Since the second equation is equal to y, replace y in the first equation with the second equation.
y = x^2 + 3
x + 5 = x^2 + 3
Rearrange so that one side is equal to 0.
5 - 3 = x^2 - x
2 = x^2 - x
0 = x^2 - x - 2
You may use quadratic formula or any form of factoring to find the zeros (x values that make the equation equal to 0).
a = 1, b = -1, c = -2
Zeros = 
and 
Zeros = 2 and -1
Now that you have your x values, plug them into the equations to find their corresponding y values.
y = x^2 + 3
y = (2)^2 + 3
y = 7
Pair #1: (2,7)
y = x^2 + 3
y = (-1)^2 + 3
y = 4
Pair #2: (-1,4)
Therefore, there are two pairs of solutions: (2,7) and (-1,4).
Answer: 4 x 16 = 64
16 + 44 = 60
I think..
Step-by-step explanation:
Answer:
<h2>h = 9, k = 8</h2>
Step-by-step explanation:
Answer:
138 cm.
Step-by-step explanation:
So first, we find the S.A. of the front and back.
The diagram says the side length of the front is 3 cm. and 3 cm.
3x3=9. So then, the back is also 9 cm, 9+9=18.
Now to find the S.A.'s of the four sides, you have to see the side lengths of each of them. The side lengths are 3 and 10.
3x10=30. This means each of them is 30 cm.
30x4=120. 120 is the total surface area of the four sides.
To find the total surface area of the whole rectangle, you add all the surface areas.
120+18=138 cm. (Not squared, since it's surface area and not area.)
Answer:
see explanation
Step-by-step explanation:
Given A is directly proportional to r² then the equation relating them is
A = kr² ← k is the constant of proportion
To find k use the condition when r = 5, A = 75 , then
75 = k × 5² = 25k ( divide both sides by 25 )
3 = k
A = 3r² ← equation of proportion
(a)
when r = 4, then
A = 3 × 4² = 3 × 16 = 48
(b)
when A = 147 , then
147 = 3r² ( divide both sides by 3 )
49 = r² ( take the square root of both sides )
r = 
= 7
