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2 years ago

Solve for g: 5=5g+5h Show all your work please.

Mathematics

1 answer:

natka813 [3]2 years ago

5 0

5 = 5 (g + h)
1 = g + h
1 - h = g
g = 1 - h

Answer: g = 1 - h.

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One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This likely means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,

Since $s$ is not positive in this case, $l = 10$ is not a solution.

Thus, $l = 28$ is our only solution. In this case,

$s = 28 - 14 = 14$ ,

which means that the smaller number is 14 and the larger number is 28.

5 0

2 years ago

Which of the following is the simplest form of this expression?

Softa [21]

Step-by-step explanation:

which expression there is no expression here

4 0

2 years ago

A movie rental website charges $5.00 per month for membership and $1.25 per movie.How many movies did Andrew rent this month if

Oksanka [162]

So to start subtract $5 from $16.25 for the monthly membership
That gives you $11.25
So then you Just divide...
$11.25 divided by $1.25
which gives you 9
So bill rented 9 movies for the month

Hope this helped! :)

6 0

2 years ago

One number exceeds another by 24. The sum of the numbers is 58. What are the numbers?

Anna35 [415]

X + x + 24 = 58
x = (58-24)/2=17
the first number is 17 and the second number is the sum of 17 and 28. Finding it has been left as an exercise for the reader.

3 0

2 years ago

So, I undestood slope right. But, I get confused with the other points that intersect there is multiple of them. How do i look f

ivanzaharov [21]

Answer:

slope = 2

Step-by-step explanation:

Find 2 points on the line that land perfectly on the grid. I'll choose these 2 here:

(-2, -1) and (0, 3)

Rise is the change in the y value from one point to the other, and run is the change in the x. Looking at these 2 points, y went from -1 to 3. That is a rise of 4. The x went from -2 to 0, so that is a run of 2. "rise over run" means rise literally over run in a fraction like this:

$m=\frac{rise}{run}$

The more proper way to calculate slope looks like this, but it's really the same thing in the end:

$m=\frac{y2-y1}{x2-x1}$

where (x1, y1) and (x2, y2) are your 2 points.

Finally, the slope of this line is:

$m=\frac{3--1}{0--2}\\\\m=\frac{4}{2}\\\\m=2$

That's a rise of 4 over a run of 2, and that simplifies to just a slope of 2.

8 0

2 years ago