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3 years ago

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The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the fi

rst number and y for the second number what are the two numbers

1 answer:

notsponge [240]3 years ago

6 0

<h2>Steps:</h2>

So for this, we will be setting up a system of equations with the information we have:

$x+y=13\ \textsf{"The sum of two numbers is 13."}\\2x-3y=1\ \textsf{"Two times the first number minus three times the second number is 1."}$

Now we have our system of equations set up. Next, I will be using the substitution method to solve this system. So firstly, subtract y on both sides of the first equation:

$x=13-y\\2x-3y=1$

Now, substitute x for (13 - y) in the second equation and solve for y as such:

$2(13-y)-3y=1\\26-2y-3y=1\\26-5y=1\\-5y=-25\\y=5$

Now that we have the value of y, substitute it into either equation to solve for x:

$x+5=13\\x=8\\\\2x-3(5)=1\\2x-15=1\\2x=16\\x=8$

<h2>Answer:</h2>

<u>In short, the first number (x) is 8 and the second number (y) is 5.</u>

You might be interested in

Y-8= - * - 4<br> y=-*<br> 4<br> (3,-5)<br> no solution<br> an infinite number of solutions

muminat

Given:

The system of equation is

$y-8=-\dfrac{1}{3}x-4$

$y=-\dfrac{1}{3}x-4$

To find:

The solution of given system of equations.

Solution:

The slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

Write the given equation in slope intercept form.

The first equation is

$y-8=-\dfrac{1}{3}x-4$

$y=-\dfrac{1}{3}x-4+8$

$y=-\dfrac{1}{3}x+4$ ...(i)

Here, slope is $-\dfrac{1}{3}$ and y-intercept is 4.

The second equation is

$y=-\dfrac{1}{3}x-4$ ...(i)

Here, slope is $-\dfrac{1}{3}$ and y-intercept is -4.

Since the slopes of both lines are same but the y-intercepts are different, therefore the given equations represent parallel lines.

Parallel lines never intersect each other. So, the given system of equation has no solution.

Hence, the correct option is B.

3 0

3 years ago

What is the value of x in the triangle?

Maksim231197 [3]

Answer:

5.619

Step-by-step explanation:

SOH 22 =x/15

cross multiply

X =SOH 22 *15

X =0.3746*15

X =5.619

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3 years ago

Convert 125 km to miles

makkiz [27]

(125 km) x (1mile / 1.609344 km) = <em>77.6714 miles</em> (rounded)

7 0

3 years ago

Read 2 more answers

A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. What is the volume of the roof to the ne

Lubov Fominskaja [6]

The volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

<h3>How to find the volume of the composite figures?</h3>

To find the volume of the composite figures, follow the steps listed below:,

Separate the figure.
Calculate the volume of each figure by which the composite figure is made of.
Add the volume of all the individual figures to get the total volume of composite figures.

A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. The volume of the roof is:

$V=\dfrac{1}{3}(\text{length x width x height})\\V=\dfrac{1}{3}40\times40\times20\\V\approx10667\rm\; ft^3$

The volume of the room is:

V=length x width x height

V=40 x 40 x 30

V=48000 ft³

The volume of the entire house, including the roof, is,

V=10667+48000

V=58667 ft³

Thus, the volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

Learn more about the volume of composite figures here;

brainly.com/question/1205683

#SPJ1

7 0

2 years ago

The weights of soy patties sold by a diner are normally distributed. A random sample of 25 patties yields a mean weight of 4.2 o

just olya [345]

Answer:

$t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2$

The degrees of freedom are given by:

$df =n-1=25-1=24$

And the p value would be given by:

$p_v = P(t_{24}>2) =0.0285$

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate

Step-by-step explanation:

Data provided

$\bar X=4.2$ represent the sample mean for the weigths

$s=0.5$ represent the sample standard deviation

$n=25$ sample size

$\mu_o =4$ represent the value that we want to analyze

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:

Null hypothesis: $\mu \leq 4$

Alternative hypothesis: $\mu > 4$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2$

The degrees of freedom are given by:

$df =n-1=25-1=24$

And the p value would be given by:

$p_v = P(t_{24}>2) =0.0285$

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate

5 0

3 years ago