They’re equivalent because 3 • 3 is 9 and whatever you do to the top, you do to the bottom, therefore 4 • 3 is 12. That would equal 9/12.
We will expand the factored form of (x − 9)(x − 1) into the same form as x² − 10x + 9 to show they are equal.
Distribute and multipy out:
(x − 9)(x − 1)
x * x = x²
x * -1 = -x
x * -9 = -9x
-9 * -1 = 9
Add together:
x² + -x + -9x + 9
x² − 10x + 9
Use the Reflexive property:
x² − 10x + 9 = x² − 10x + 9 ✓
Hey there!
(f * g)(6) is equal to x(x-1) × 3x.
So, let's plug in 6 for x.
(f * g)(6) = 6(6-1) × 3(6)
Subtract inside parenthesis.
(f * g)(6) = 6(5) × 3(6)
Multiply.
(f * g)(6) = 30 × 18
Multiply again.
(f * g)(6) = 540
Hope this helps!
Answer:
50 violins were sold
Step-by-step explanation:
You can solve this problem using ratios.
6/7 of the fish have a red stripe.
18 fish have a red stripe.
6:7 = 18:x
6/7 is just a simplified fraction of 18/x, both of which are equal.
In these fractions, the numerator represents the fish with red stripes and the denominator represents the total number of fish.
6:7 = 18:x
x = Total fish
The question is asking us to find x.
Since the fractions are equivalent and there is a known numerator in both of them, divide the numerator of 18:x, or 18/x, which is 18, by the numerator of 6:7, or 6/7, which is 6.
18 / 6 = 3
Now multiply 3 by the known denominator, which is 7.
7 • 3 = 21
6/7 = 6:7
18/x = 18:x
6:7 = 18:x
6:7 = 18:21
x = 21
There are 18 fish with red stripes.
There are 21 total fish.
6/7, or about 86%, of the fish have red stripes.
The answer is there is a total of 21 fish in the tank.
Hope this helps!
