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Dovator [93]
2 years ago
15

Only questions 5 and 6 pls.

Mathematics
1 answer:
lesantik [10]2 years ago
4 0

theres no pic so how do we answer

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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
Someone help me please please someone help
Hoochie [10]
I Believe that it's -120
7 0
3 years ago
Read 2 more answers
Liz polishes rings for a jeweler. She can polish 9 rings per hour. How many rhours will it take her to polish 315 rings?
Annette [7]
315 divided by 9 = 35 hours
3 0
3 years ago
Read 2 more answers
A student rolls a standard number cube. What is the probability the student rolled a 4. given that the number rolled was
Debora [2.8K]

Answer:

A

Step-by-step explanation:

Because on a dice there are only 6 sides meaning there is a 1/6 chance of you to role a 4

3 0
3 years ago
100 POINT QUESTION<br> Which postulate or theorem can be used to prove △ABC ≅ △KLM?
Solnce55 [7]

Answer:

ASA congruence theorem

Step-by-step explanation:

Given two triangles ABC and KLM.

In ΔABC and ΔKLM,

m∠CBA = m∠MLK (given angle)

BC = LM (given side)

m∠CAB = m∠MKL (given angle)

Therefore, ΔABC ≅ ΔKLM (by ASA congruence theorem)

Hence by ASA congruence theorem ΔABC ≅ ΔKLM.

5 0
3 years ago
Read 2 more answers
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