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2 years ago

21 Linear Functions

Mathematics

1 answer:

WARRIOR [948]2 years ago

5 0

The equation is y = 40x + 125

The slope of this situation is $40 per month while the y-intercept is $125 for adoption.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

Let y represent the total cost of keeping a dog for x months. Hence:

y = 40x + 125

The slope of this situation is $40 per month while the y-intercept is $125 for adoption.

Find out more on equation at: brainly.com/question/2972832

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A shark is swimming 60 feet below the surface of

Charra [1.4K]

Answer:

Step-by-step explanation:

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8 0

3 years ago

which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!

coldgirl [10]

9514 1404 393

Answer:

(a) -(x+7)/y

(b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

$\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}$

Likewise, the expression of (b) with the minus sign factored out is ...

$\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}$

On the other hand, simplifying expression (c) gives something different.

$\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}$

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

Given: (-x-7)/y = (-x/y) +(-7/y)

(a) -(x+7)/y = (-x/y) +(-7/y)

(b) (x+7)/(-y) = (-x/y) +(-7/y)

Of course, you need to know the use of the distributive property and the rules of signs.

a(b+c) = ab +ac

-a/b = a/(-b) = -(a/b)

-a/(-b) = a/b

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

$\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0$

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

3 0

3 years ago

65 people took a clarinet exam. Before the exam, 23 people predicted that they would pass, and the rest predicted they would fai

kakasveta [241]

Answer:

The answer is 29/42

Step-by-step explanation:

First, let's calculate how many people predicted they would fail. The question states that 65 people took the exam and 23 predicted they would pass, so we can find the number of people that predicted they would fail by the following calculation:

Let FP be the people who predicted they'd fail

65 = 23 + FP

65 - 23 = FP

42 = FP

Now, let's move on to the next part. The question states that a total of 31 people passed the test, from those 18 being the people who predicted they would pass and the rest are people who had predicted they would fail but ended up passing.

Let's set x as the number of people who predicted they would fail but have passed.

31 = 18 + x

31 - 18 = x

13 = x

Since 13 of the 42 FP have passed, we can calculate how many of them failed. Let y be the number of people that predicted to fail and ended up failing:

13 + y = 42

y = 42 - 13

y = 29

Finally, now we have the fraction of those who predicted that they would fail actually did fail and that's 29/42

3 0

2 years ago

Which pairs of rational numbers are equivalent? Select all that apply.

Airida [17]

Answer:

-0.5 and negative one-half

-1/50 and -0.02

Step-by-step explanation:

-0.5 can be rewritten as -5/10. This can be simplified to -1/2 which is the same as negative one-half.

7/10 isn't equivalent to 11/20. If you multiply 7/10 by 2/2 to get the denominator of 20, it will become 14/20 not 11/20.

-1/50 in decimal form is -0.02 so -1/50 and -0.02 are equivalent.

0.15 and 1/5 aren't equivalent because 1/5 in decimal form is is 0.2, not 0.15.

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3 years ago

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I have made it bigger.

Ilya [14]

Answer:

u got the right answer in I was just doing this

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3 years ago

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