Answer:
Step-by-step explanation:
When you are changing a repeating decimal to a fraction, there is a trick you have to know. 2 actually. Put the decimal right before the repeating starts and right after the repeating starts. This one is a bit tricky since the decimal is after a 1, and 1 is what is repeating. So let's leave that one as is and simply say that
x = -1.11111
Now let's move the decimal right after the second one. To do that you have to multiply by 10. So we then can say that
10x = -11.11111
For this problem, we will disregard the negative til the end because it just makes things confusing.
Subtract the smaller equation from the larger:
10x = 11.111111
- 1x = 1.111111
and get
9x = 10
Divide both sides by 9 to get 10/9 which is 1 1/9 as a mixed fraction. Let's check it first to see if we're correct, then we'll throw the negative sign back on.
10/9 on your calculator gives you 1.111111111 repeating, so now that we know we are correct, the mixed fraction is
-1 1/9
Answer:
117 yards
Step-by-step explanation:
From the diagram here, we can see that we are to calculate the diagonal of the rectangular football field
we can calculate this by the use of Pythagoras’ theorem which posits that the square of the hypotenuse = the sum of the squares of the two other sides
From the diagram, the diagonal is the hypotenuse while the other two sides complete the right triangle
let’s say the diagonal is length d
Mathematically;
d^2 = 100^2 + 60^2
d^2 = 10,000 + 3,600
d^2 = 13,600
d = √13,600
d = 116.62 yards which is approximately 117 yards
Answer:
Step-by-step explanation:
By the Mean Value Theorem, there is at least one number, c, in the interval (1,6) such that
f'(c) = [f(6) - f(1)]/ (6 - 1)
So, f(6) - f(1) = 5f'(c).
Since 2 ≤ f'(c) ≤ 4, 10 ≤ 5f'(c) ≤ 20
So, f(6) - f(1) is between 10 and 20.
If x₁ and x₂ are solutions of the quadratic equation, then we can write it in quadratic factorization:
a(x - x₁)(x - x₂)
We have x₁ = 5 and x₂ = 7
(x - 5)(x - 7) = (x)(x) + (x)(-7) + (-5)(x) + (-5)(-7) = x² - 7x - 5x + 35 = x² - 12x + 35
<h3>Answer: x² - 12x + 35 = 0</h3>