The height of a box is 7 inches the length is 3 inches more then the width find the width if the volume is 126

1 answer:

8 0

It looks like we have two unknowns here and two possible equations so to solve this we will need to utilize our systems of equations, I will be using the substitution method.
We know that all of the parts multiplied together is equal to the volume.
We know that the volume is 126 square inches
The height is seven inches
The width is unknown, let w be the width
The length is unknown, let l be the length
We know that the length is three inches more than the width (l=w+3)
We know that the height times the length times the width is equal to the volume (7lw=126)
Since we know that l=w+3, we can substitute w+3 in for l,
7(w+3)(w)=126
Now we can solve our equation
7(w+3)(w)=126
(7w+21)(w)
7w^2+21w=126
Now we will complete the square to solve for w
7w^2+21w=126
w^2+3w=18
w^2+3w+2.25=20.25
(w+1.5)^2=20.25
w+1.5=4.5
w=3
We have now found out using our knowledge of systems of equations that the width of this prism is 3 inches.

You might be interested in

How do you factor m^2=2m?<br><img src="https://tex.z-dn.net/?f=m%20%5E%7B2%7D%20%20%3D%202m" id="TexFormula1" title="m ^{2} = 2

Sonbull [250]

First move all terms to one side:

$m^2=2m\implies m^2-2m=0$

Then all terms on the left side share a common factor of $m$ :

$m(m-2)=0$

The zero product product property says that if $ab=0$ , then $a=0$ or $b=0$ . So either $m=0$ or $m-2=0\implies m=2$ .

5 0

3 years ago

A line passes through (2, −1) and (4, 5).

mash [69]

The answer to the first problem is the top left corner because it is the only one with a -3 y-intercept and that's in the problem

To find the answer of the second problem you find the slope of the two points with the formula y2-y1 divided by x2-x1 and you just plug it in so 5+1 (the minus signs cancel out and turn into positives) divided by 4-2 and which is 6/2 which is 3 is your slope. then you could plug this information into a point slope form using either point I'm just going to choose the one with no negatives so plugging this in would be y-5=3(x-4) then you distribute the 3 and that gives you y-5=3x-12 then
+5 +5 add five to both sides of the equation and get
y=3x-7 and then you can put that into standard form which would be -3x+y=-7 and your answer would be the second one.

6 0

3 years ago

An item is priced at $14.92. If the sales tax is 7%, what does the item cost including sales tax?

exis [7]

Answer: 15.96$

Step-by-step explanation:

(14.92 x .07) + 14.92 =15.9644$ simplified is 15.96$

3 0

3 years ago

SOMEONE PLEASE HELP ME WITH THIS!!! I really need help I try doing it but I just end up getting lost, please help me, I give out

gavmur [86]

X=36.2 feet. See picture