When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89
1)
b: 3.75 since it is half of the segment that measures 7.5, this is proven because the line in the middle is a bisector of the top and bottom line indication that both half measure the same; 3.75
2) 15 not sure why
Answer:
216 cm³
Step-by-step explanation:
1/3x + 63 = 5/8x
subtract 1/3x from each side; (1/3x = 8/24x and 5/8x = 15/24x)
63 = 7/24x
7x = 63(24)
7x = 1512
x = 216
F(x) = x² + x - 20 = x² + 5x - 4x - 20 = x(x + 5) - 4(x + 5) = (x + 5)(x - 4)
f(x) = 0 ⇔ (x + 5)(x - 4) = 0 ⇔ x + 5 = 0 or x - 4 = 0 ⇒ x = -5 or x = 4
Answer: C. x = -5 and x = 4.
