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aniked [119]
2 years ago
9

Which function is the inverse of f(x) = 2x + 3?

Mathematics
1 answer:
olga_2 [115]2 years ago
8 0

Answer: Option 2

Step-by-step explanation:

Let f(y)=x.

x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}

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Translate the following into verbal phrases. 3x-4
nadezda [96]
Answer:
Three x negative four
7 0
3 years ago
can someone please help me figure this out? this is a summative and I'm failing for the year. it's algebra 1. ​
34kurt

Part (a)

  • x = number of bass caught
  • y = number of trout caught

x and y are nonnegative whole numbers.

3x represents the total weight of all the bass, since one bass weighs 3 pounds. Similarly, 2y is the total weight of the trout with each one being 2 pounds.  Adding up all the weight of all the fish, we get 3x+2y. This is set equal to 34 pounds which is the total stated weight caught.

In short, we end up with the equation 3x+2y = 34

Now onto the second equation. The expression 5x represents how many points Pat gets from catching x bass, because he gets 5 points per bass. Then we subtract off 2y to represent Pat losing 2 points per trout he catches. Overall, his point total is 5x-2y. This is set equal to his point total of 14.

The second equation is 5x-2y = 14

------------

Answer:

3x+2y = 34

5x-2y = 14

Both equations are needed to form this particular system.

===================================================

Part (b)

We could use a number of methods to solve for (x,y). Possibly the most efficient is elimination. Why? Because note how we have 2y up top and -2y down below. They add to 0y which is just 0. The y terms go away, and are eliminated. Afterward, all we're left with is x in which we can solve for just like any other single variable equation. More info is in part (c).

===================================================

Part (c)

Refer to the answer in part (a). We'll add straight down. So that means we have these three sets of addition operations.

  • 3x+5x becomes 8x
  • 2y + (-2y), aka 2y-2y, becomes 0y and the y terms go away
  • 34+14 simplifies to 48

After those three sets of addition operations, we're left with the much simpler equation 8x = 48. To solve this, we divide both sides by 8 and we get x = 6. This says Pat caught 6 bass.

Use this value of x to find y. So we'll plug x = 6 into either equation involving x,y and solve for y

3x+2y = 34

3(6)+2y = 34

18+2y = 34

2y = 34-18

2y = 16

y = 16/2

y = 8

So we can see that Pat caught 8 trout as well.

The check portion is shown in the attached image below. Effectively, all we're doing is replacing x and y with 6 and 8 respectively. Then we're simplifying both sides. Getting the same number on both sides results in a true equation, and therefore verifies we have the correct (x,y) solution.

Solution: (x,y) = (6,8)

Interpretation: Pat caught 6 bass and 8 trout

7 0
3 years ago
I became a tutor and idk how to do this
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Answer:

y = <u>1</u><u> </u>x - <u>9</u><u> </u><u> </u><u>(</u><u> </u><u>L</u><u>.</u><u>C</u><u>.</u><u>M</u><u> </u>= 2 )

2 2

<u>1</u><u>(</u><u>1</u><u>x</u><u>)</u><u>-</u><u>1</u><u>(</u><u>9</u><u>)</u>

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<u>x-9</u>

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<u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u>

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2 years ago
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Answer: then he had $70.80

Step-by-step explanation:

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3 years ago
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45 because it’s an acute angel
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