Answer: 0.78 and 39/50
<h3>
Explanation:</h3>
What we know:
- We need to find 78% as a fraction and decimal
How to solve:
The decimal is easy enough, and then the fraction can be found from there. D will represent decimal, p will represent percentage, and F will represent fraction.
<h3>
Process:</h3>
Decimal
Set up equation D = p / 100
Substitute D = 78% / 100
Simplify D = 0.78%
Remove % sign D = 0.78
Fraction
Set up equation F = p / 100
Substitute F = 78% / 100
Remove % sign F = 78 / 100
Simplify if needed F = /2 /2
F = 39 / 50
Solution: 0.78 and 39/50
Check:
Multiply the decimal by 100 to check the decimal
0.78 x 100 = 78; 78%
Divide the fraction to check the fraction
39/50 = 0.78; see above
Distance = rate times time.
Let the first cyclist's rate be r1 and the 2nd cyclist's rate be r2.
Let r2 = r1 + 10 (km per hour).
The total distance between them after 3 hours is 174 km; using the distance= rate times time formula, we also get:
r1(3 hrs) + r2(3 hrs) = 174 km
Then
r1(3 hrs) + (r1+10)(3hrs) = 174 km
Then 3r1 + 3r1 + 30 = 174
6r1 = 144, and r1 = 24 km/hr. Then r2 = (24 + 10) km/hr = 34 km/hr.
9514 1404 393
Answer:
sin -12/13
Step-by-step explanation:
You can use the identity ...
tan = sin/cos
to solve for sine:
sin = cos·tan
sin = (-5/13)(12/5) =
sin -12/13
Answer:
f(x) = x² - 81 = ( x+ 9)(x - 9) Difference of two squares
g(x) = x+9/x-9
g(x) . f(x) = x + 9/ x - 9 × (x+9)(x - 9)
= ( x + 9)(x +9)
= ( x + 9)²
= x² + 18x + 81
Hope this helps.
Factor out the gcf first.
3(4y^2-9)
The binomial inside is a perfect square so keep factoring.
3(2y+3)(2y-3)
The pair of binomials cannot be further factored so stop there.
