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postnew [5]
3 years ago
7

Find two consecutive integers whose product is 50

Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

n, n+1 - two consecutive integers

n(n + 1) = 50     <em>use distributive property</em>

n² + n = 50     <em>subtract 50 from both sides</em>

n² + n - 50 = 0

-----------------------------------------------------

ax² + bx + c =0

if b² - 4ac > 0 then we have two solutions:

[-b - √(b² - 4ac)]/2a and [-b - √(b² + 4ac)]/2a

if b² - 4ac = 0 then we have one solution -b/2a

if  b² - 4ac < 0 then no real solution

----------------------------------------------------------

n² + n - 50 = 0

a = 1, b = 1, c = -50

b² - 4ac = 1² - 4(1)(-50) = 1 + 200 = 201 > 0 → two solutions

√(b² - 4ac) = √(201) - it's the irrational number

Answer: There are no two consecutive integers whose product is 50.

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A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2
Yuliya22 [10]

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.

Answer: The correct option is B) about 34%

Proof:

We have to find P(4.2

To find P(4.2, we need to use z score formula:

When x = 4.2, we have:

z = \frac{x-\mu}{\sigma}

          =\frac{4.2-5.1}{0.9}=\frac{-0.9}{0.9}=-1

When x = 5.1, we have:

z = \frac{x-\mu}{\sigma}

          =\frac{5.1-5.1}{0.9}=0

Therefore, we have to find P(-1

Using the standard normal table, we have:

P(-1= P(z

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                               =0.3413 or 34.13%

                               = 34% approximately

Therefore, the percent of data between 4.2 and 5.1 is about 34%

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The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in ast
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You have an account with a principal of $200. it pays 8% at the end of every year. calculate the principal at the end of 3 years
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Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The principal at the end of 3 years is $248.

<h3>What is simple interest?</h3>

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = (P × R × T)/100

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The principal at the end of 3 years is,

Principal after 3 years = P + (P × R × T)

= $200 + ($200 × 0.08 × 3)

= $200 + $48

= $248

Hence, the principal at the end of 3 years is $248.

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1 year ago
Find the length of the hypotenuse of a right triangle whose legs are 3 and square root of 2.
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