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serious [3.7K]
2 years ago
14

a dog weighs two pounds less than three times the weight of a cat. The dog also weighs twenty-two more pounds than the cat. writ

e and solve an equation to find the weights of the dog and the cat.
Mathematics
1 answer:
Law Incorporation [45]2 years ago
8 0

Answer:

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Step-by-step explanation:

Let d represent weight of dog and c represent weight of cat.

We have been given that a dog weighs two pounds less than three times the weight of a cat.

3 times weight of cat: 3c

We can represent the given information in an equation as: d=3c -2...1

We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:

d=c+22...(2)

3c-2=c+22--->c=12

Therefore subsitute c=12 in equation 2

d=+22

d=12+22

d=34

Therefore, the weight of dog is 34 pounds.

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8-14 or -6

Step-by-step explanation:


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The graph of g(x) is a transformation of the graph of f(x)=2x. Enter the equation for g(x) in the box. g(x) =
Lunna [17]
<h3>Answer:  g(x) = 2^x - 3</h3>

The -3 is not in the exponent

Explanation:

The parent function is f(x) = 2^x. Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.

g(x) = f(x) - 3\\\\g(x) = 2^x - 3

You could look at other points as well, but I find working with x = 0 is easiest.

As a check, plugging x = 0 into g(x) leads to...

g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2

This confirms our answer.

4 0
3 years ago
Rashida brought three tickets to a concert for $75 at this rate how much would 5 tickets cost
Wittaler [7]

 In order for you to understand this question you have to know what the unit rate is. In order to find it you divide 75 by 3  which is 25 so you know that 1 ticket will cost 25$ so then you multiply that 25 times 5 to get your final answer which is 125.

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3 years ago
The table and the graph each show a different relationship between the same two variables, x and y:
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1. y₁ = 70x
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3 years ago
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
GrogVix [38]

Answer:

  1. D. f^-1(x) = log2(x -6)
  2. 4x^2 -3 . . . . x ≤ 0
  3. B. √(x^5) -3√(x^3) -18√x

Step-by-step explanation:

1. When you replace f(x) by x and x by y, you have

... x = 2^y + 6

The first thing you do is subtract 6; then you take the base-2 logarithm:

... (x -6) = 2^y

... log2(x -6) = y = f^-1(x)

You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.

2. When you swap x and y and solve for y, you have ...

... x = -1/2√(y+3)

... -2x = √(y +3) . . . . . . multiply by -2

... (-2x)^2 = y +3 . . . . . square

... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3

The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.

3. The product of the two functions is ...

... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)

<em>Every term</em> will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.

7 0
2 years ago
Read 2 more answers
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