Answer:
Step-by-step explanation:
The given functions are:
and
We want to find
Recall that:
This implies that:
We combine similar terms to get:
<h3>
Answer: 60 muffins</h3>
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Explanation:
x = some positive whole number
2x = amount Helen baked initially
5x = amount Rebecca baked initially
Notice that the ratio 2x:5x reduces to 2:5 after dividing both parts by x.
So (2x)/(5x) = 2/5
Helen then bakes another 12 muffins, bumping the 2x up to 2x+12. The ratio is now 1:2, which means,
(amount Helen bakes)/(amount Rebecca bakes) = 1/2
(2x+12)/(5x) = 1/2
2(2x+12) = 5x*1 .... cross multiply
4x+24 = 5x
24 = 5x-4x
24 = x
x = 24
From here, we then can say,
- Helen = 2x+12 = 2*24+12 = 48+12 = 60
- Rebecca = 5x = 5*24 = 120
Helen baked 60 muffins and Rebecca baked 120 muffins. We see that 60:120 reduces to 1:2 after dividing both parts by the GCF 60.
Furthermore, note how
- 2x = 2*24 = 48
- 5x = 5*24 = 120
- 48:120 reduces to 2:5 after dividing both parts by 24
This helps confirm we have the correct answer.
Answer:
h(x)=1/4x
Step-by-step explanation:
Inverse function is when the domain and range of a function are swapped, or in other words the y and x values are swapped.
To do this you simply change x to y, and y to x in the equation
So we have the original equation
y = 4x
swap y and x
x = 4y
now solve for y by dividing by 4
y = x/4
which can also be expressed as h(x)=1/4x
(a^3 - 2a + 5) - (4a^3 - 5a^2 + a - 2)
=a^3 - 2a + 5 - 4a^3 + 5a^2 - a + 2
= -3a^3 + 5a^2 - 3a + 7
The thousands place is <u /><em></em>the 9 in 39<u>9</u>,713. 7 is closer to 10 than to 0, therefore, you roundup, increasing the thousands place by one. Carry the 0 to the next 9 in the ten thousands place, and again to the hundred thousands, adding one to the 3. Therefore the answer is 400,000.<u />
