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Mazyrski [523]
3 years ago
7

James recorded his reading times over the course of 5 days. ​

Mathematics
1 answer:
amid [387]3 years ago
8 0

ohhhhhhhhhhhhhhh did he

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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 <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.

5 0
3 years ago
Can any experts help me??<br> Solve for x° and y°.<br> Easy for anyone.
Annette [7]

Answer:

<u>X=46</u>

<u>Y=130</u>

<u>reflective angles</u>

Step-by-step explanation:

4 0
3 years ago
A student was given two data sets, Set A and Set B. Which of the following
Elden [556K]

Answer:

I don't know were the statement are but here are the specs of each set

Step-by-step explanation:

Set A

mean; 83.83333

median; 87.5

mode; it has no mode

range; 147

Set B

mean; 67.08571

median; 3

mode; no mode

range; 376

hope this helps sorry for late answer :)

5 0
3 years ago
What is the theoretical probability of picking a diamond, not replacing it, and then picking another diamond? Write your answer
BARSIC [14]
You start with a 1/4 chance of picking a diamond.
you remove it from the deck you now have a 12/51 chance of picking a diamond
1/17 is your answer!



Like my answer? Make it a Brainliest! Thanks!
3 0
3 years ago
A table top in the shape of a trapezoid has an area of 2250 square centimeters and the shorter base is 80 centimeters. The longe
Citrus2011 [14]
The area of a trapezoid has a formula of:
Area = (a + b) h / 2

Using the formula, we can easily find the height of the trapezoid.
<span>Area = (a + b) h / 2
</span>2250 = (80 + 100) h / 2
2250 = 180h / 2
2250 = 90h
h = 25 centimeters

So the height of the trapezoid is 25 centimeters.
3 0
3 years ago
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