All math problems are solved the same way:
You always use the information you're given
to find the information that's missing.
You didn't give us any information at all, so there's
no way to find the missing information.
We can solve this with the following system
a(2)^2 + b(2) + c = 23
a(4)^2 + b(4) + c = 55
a(10)^2 + b(10) + c = 247 simplifying, we have
4a + 2b + c = 23 (1)
16a + 4b + c = 55 (2)
100a + 10b + c = 247 (3)
Subtract (1) from (2) and (2) from (3) ...and we get the following system
12a + 2b = 32
84a + 6b = 192 these simplify to
6a + b = 16 → b = 16 - 6a (4)
28a + 2b = 64 (5)
Substitute (4) into (5)
28a + 2[16 - 6a] = 64 simplify
28a + 32 - 12a = 64
16a + 32 = 64 subtract 32 from both sides
16a = 32 divide both sides by 16
a = 2
And using (4) .....
b = 16 - 6(2) = 16 - 12 = 4
And using (1) ......
4(2) + 2(4) + c = 23
8 + 8 + c = 23
16 + c = 23
So c = 7
And our cost function is :
c(x) = 2x^2 + 4x + 7 and the cost to produce 8 widgets is
c(8) = 2(8)^2 + 4(8) + 7 = 2*64 + 32 + 7 = 128 + 39 = $ 167
Answer:
x = 0.59 to the nearest hundredth
Step-by-step explanation:
Look at the attached figure
- The equation is 2x + = 3
- The red curve represents the left side of the equation
- The blue line represents the right side of the equation
- The solution of the equation is the point of intersection of the two graphs
∵ There are 5 small squares between every 2 numbers on the x-axis
∴ Each square represents 0.2
∵ There are 5 small squares between every 2 numbers on the y-axis
∴ Each square represents 0.2
∵ The point of intersection between the 2 graphs is nearest to
the 3rd small square after the zero on the x-axis
∵ 0.2 × 3 = 0.6
∴ The x-coordinate of the point is approximately located at 0.59
∴ x = 0.59 to the nearest hundredth