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Reptile [31]
3 years ago
5

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

reciprocal of the larger​ number, the sum is one fourth. Find the two numbers.
Mathematics
1 answer:
Kipish [7]3 years ago
5 0

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 <em>likely </em>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.

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NemiM [27]

Answer: The answer is x = 19.

Step-by-step explanation:  Given that a flower pot has a base with six equal sides of measurement (x - 6) units. We are to find the value of the unknown quantity 'x' if the perimeter of the base is 78 units.

We know that the perimeter of a polygon is given by the sum of the lengths of all the sides of the polygon.

Since each side of the six-sided base is (x - 6) units, so its perimeter will be

6\times(x-6)~\textup{units}.

According to the question, we have

6(x-6)=78\\\\\Rightarrow x-6=13\\\\\Rightarrow x=19.

Thus, the value of 'x' is 19 units.

6 0
3 years ago
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A​ self-tanning lotion advertises that a 4 ​-oz bottle will provide seven applications. Jen found a great deal on a 13 ​-oz bott
Rainbow [258]

Answer:

22.75 applications

Step-by-step explanation:

From the above question, we understand that:

4 ​-oz bottle = 7 applications

13 ​-oz bottle = x applications

Cross Multiply

4 -oz bottle × x applications = 13 -oz bottle × 7 applications

x applications = 13 -oz bottle × 7 applications/4 -oz bottle

x applications = 22.75 applications

Therefore, the number of applications of the 13 -oz bottle​ self-tanner that should Jen​ expect is 22.75 applications.

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3 years ago
A circle is centered at the point (5,-4) &amp; passes through the point (-3,2).
maxonik [38]

Equation of the circle:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

The equation of a circle is given by

(x-x_0)^2+(y-y_0)^2=r^2

where

(x_0,y_0) are the coordinates of the center of the circle

r is the radius of the circle

For the circle in this problem, we know that:

(5,4) are the coordinates of the center

We also know that the circle passes through the point (-3,2), therefore we can calculate the radius as the distance between the point on the circle and the center of the circle:

r=\sqrt{(-3-(5))^2+(2-(-4))^2}=\sqrt{(-8)^2+(6)^2}=\sqrt{64+36}=10

Therefore, the equation of the circle is:

(x-5)^2+(y-(-4))^2=10^2\\(x-5)^2+(y+4)^2=100

Learn more about circles:

brainly.com/question/4713715

brainly.com/question/3456442

brainly.com/question/3333996

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5 0
3 years ago
A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all arou
Arisa [49]

Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

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Marie saved $3,000 dollars last year. She saved $600 in the month of January. What percent of the money she saved last year was
Archy [21]

Answer:

20% of the money was saved from January.

Here is the way to find percentage.

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then:  divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

<u>Step-by-step explanation:</u>


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