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3 years ago

Find the value of two numbers if their sum is 23 and their difference is 3.

Mathematics

1 answer:

Yakvenalex [24]3 years ago

3 0

x+y=23

x-y=5

First, add the equations.

2x=28

x=14

Then...

14+y=23

y=9

Therefore the answer is...

x=14 y=9

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Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

Last step: substitute the slope and y intercept into y=mx+b.

$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

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3 years ago

A. How many centimeters across a handprint

vladimir2022 [97]

Answer:7.87402

Step-by-step explanation: please leave a thx! :)

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3 years ago

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Eva took a taxi from her house to the airport. The taxi company charged a pic of feet of 3 dollars and 20 cents, plus 3 dollars

svetoff [14.1K]

Answer:

3x + 3.20 =33.20

Step-by-step explanation:

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2 years ago

W hich of the following are you not likely to see on a graph? dependent variable, units, independent variable, prediction ...?

nekit [7.7K]

"Prediction" is the one among the following choices given in the question that you are not l<span>ikely to see on a graph. The correct option among all the options that are given in the question is the fourth option or the last option. I hope that this is the answer that has actually come to your desired help.</span>

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3 years ago

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8. In right triangle LMN shown below, altitude MK is drawn to LN from M. IF LM = 12 and LK =10, then

Elena-2011 [213]

The length of the KN is 4.4

Step-by-step explanation:

We know from Pythagoras theorem

In a right angle ΔLMN

Base² + perpendicular² = hypotenuse ²

From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.

Hence ∠LKM = ∠NKM = 90 °

Given values-

LM=12

LK=10

Let KN be “s”

⇒LN= LK + KN

⇒LN= 10+x eq 1

Coming to the Δ LKM

⇒LK²+MK²= LM²

⇒MK²= 12²-10²

⇒MK²= 44 eq 2

Now in Δ MKN

⇒MK²+ KN²= MN²

⇒44+s²= MN² eq 3

In Δ LMN

⇒LM²+MN²= LN²

Using the values of MN² and LN² from the previous equations

⇒12² + 44+s²= (10+s) ²

⇒144+44+s²= 100+s²+20s

⇒188+s²= 100+s²+20s cancelling the common term “s²”

⇒20s= 188-100

∴ s= 4.4

Hence the value of KN is 4.4

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3 years ago