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tino4ka555 [31]
3 years ago
14

The sum of two numbers is 15. three times one of the numbers is 11 less than five times the other. find the numbers. write your

solution in a complete sentence.
Mathematics
1 answer:
lions [1.4K]3 years ago
6 0
Translating that problem with x being our variable you get 3x + 5x-11 = 15. Combine like terms to get 8x-11 = 15. Add 11 to both sides to get 8x = 26. Divide by 8 on both sides to get x = 26/8. This can be reduced to 13/4 or 3 and 1/4. 

Now we plug in. Our first number was represented by 3x. So 3*(13/4) = 39/4 or 9 and 3/4. The second number was represented by 5x-11. 5*(13/4) = 65/4 or 16 and 1/4. 16 and 1/4 minus 11 is 5 and 1/4.

To check our answer 9 + 5 = 14. 3/4 + 1/4 = 4/4 or 1. 14+1 = 15. Another way to check is adding (39+21)/4.

So your complete sentence should read: The two numbers whose sum equal 15 in this equation are 5 and 1/4 (or 21/4) and 9 and 3/4 (or 39/4).
You might be interested in
the case of napkins contained 45 packs with a total of 10,125 napkins. each napkin contained the same number of napkins. write a
Pavlova-9 [17]
You would need to do 10,125/45 = n, and in which case we just solve. 
10,215/45=227, so there are 227 napkins in each box.


Hope this helps and have a nice day:)
7 0
2 years ago
In the solution of the equation 5 + 3x = -2x + 9, 2 x is added to the equation first. which of the following should be done next
wariber [46]

Hi!

<h3>Let's do the first step (add 2x). </h3>

5 + 3x + 2x = -2x + 2x + 9

<em>5 + 5x = 9</em>

<h3>Our goal is to isolate x on one side, so the next step would be to subtract 5 (or add -5).</h3>

5 + -5 + 5x = 9 + -5

<u><em>5x = 4</em></u>

<h2>The answer is B. add -5</h2><h3><em>And if you want to finish solving, you would divide by 5 on both sides.</em></h3>

5x/5 = 4/5

x = 0.8

Hope this helps! :)

-Peredhel

4 0
2 years ago
D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
MA_775_DIABLO [31]
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

r^2-16k=0\implies r=\pm4\sqrt k

which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
b(1-16k)=30\implies b=\dfrac{30}{1-16k}

and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
8 0
2 years ago
If tanisha has $100 to invest at 8% annum compounded monthly, how long will it be before she has $150?
marissa [1.9K]

An exponential behavior can be observed.

Let x be the number of years she has to wait.

100((1+0.08/12)^12x) = 150

Now solve for x.

log base 1.08/12 of 1.5 = 61.02 approx

12x=61.02

x=5.09 years

4 0
3 years ago
What is the answer for this
KonstantinChe [14]

Answer:  y=\frac{1}{30}x+1

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

You need to find slope of the line with the formula:

m=\frac{y_2-y_1}{x_2-x_1}

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula:

 m=\frac{2-3}{30-60}=\frac{1}{30}

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

b=1

Substituting the slope and the y-intercept found into  y=mx+b, you get the equation of this line:

 y=\frac{1}{30}x+1

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

3 0
3 years ago
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