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3 years ago

Two numbers have a sum of 1212 and a difference of 518 what are are the two numbers

2 answers:

7 0

This question involves systems of equations. You can use matrices on a graphing calculator or solve by elimination. Set this up as x+y=1212 and x-y=518. If you solve on a graphing calculator, click 2nd matrix then edit. Change the matrix to a two by three and input on the first line horizontally 1, 1, 1212 and on the second line 1, -1, 518. Then hit the quit button and go to the home screen. Click 2nd matrix again and hit rref and quit again and click on the name of the matrix. If you solve by elimination multiply the first one by -1 so your ys can cancel and then find x and plug in. So your two numbers are 865 and 347.

-Trust me, learn how to do these on your calculator, it will minus the tricky solving of systems.

Mila [183]3 years ago

6 0

So write down your 2 equations:
x + y = 1212
x - y = 518

If you add them together, the y's will cancel out, leaving you to solve for you x
2x = 1730
x = 865

then substitute x back into one of your equations to find y
ex: 865 + y = 1212, y = 347
ex: 865 - y = 518, -y = -347, y = 347

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A firm has the marginal-demand function where D(x)=-1400x÷√25-x² is the number of units sold at x dollars per unit. Find the dem

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The equation of the demand function is D(x) = 1400√(25-x²) + 11400

<h3>How to determine the demand function?</h3>

From the question, we have the following parameters that can be used in our computation:

Marginal demand function, D'(x) = -1400x÷√25-x²

Also, we have

D = 17000, when the value of x = 3

To start with, we need to integrate the marginal demand function, D'(x)

So, we have the following representation

D(x) = 1400√(25-x²) + C

Recall that

D = 17000 at x = 3

So, we have

17000 = 1400√(25-3²) + C

Evaluate

17000 = 5600 + C

Solve for C

C = 17000 - 5600

So, we have

C = 11400

Substitute C = 11400 in D(x) = 1400√(25-x²) + C

D(x) = 1400√(25-x²) + 11400

Hence, the function is D(x) = 1400√(25-x²) + 11400

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1 year ago

In which of the following quadrilaterals are consecutive and opposite angles always congruent?

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Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi

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Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$s = \sqrt{\dfrac{875.5}{7}} = 11.18$

$\text{ Sample variance} = s^2 = 125.07$

Population:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46$

$\text{ Population variance} = \sigma^2 = 109.44$

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