Draw a rectangle 37 cm by 42 cm and then count how many 1cm by 1cm squares are inside it.
Answer:
Step-by-step explanation:
x² - 24x + 5 = 0
x² - 24x = -5
Now divide the co efficient of x by 2 and square the quotient and add to both sides
24/2 = 12
12² = 144. Now add 144 to both sides of the equation.
x² - 24x + 144 = 5 + 144
x² - 24x + 144 = 149
x² - 2*12*x + 12² = 149
(x - 12)² = 149
Both sides take square root
x - 12 = ±√149
x = 12 ± √149
First set up the equation based on the description.
![\frac{1}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20)
x + 16 = 3x
Use subtraction to get the "x"s on one side of the equation. You can next subtract <span>
![\frac{1}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20)
x from both sides.
16 = </span>
![\frac{8}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B3%7D%20)
<span> x
Now you can multiply both sides of the equation by </span>
![\frac{3}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B8%7D%20)
<span> to solve for x
x = 6</span>
Answer:
345
Step-by-step explanation:
We can solve this problem by two equations. Our variables will be the following:
is the amount to be multiplied
and
is the amount that should be obtained by multiplying by 43
Thus our <u>first equation</u> is:
![43x=y](https://tex.z-dn.net/?f=43x%3Dy)
But the problem tells us that there was an error and the number
was multiplied by 34, so the result failed by 3105, thus the <u>second equation</u> is as follows:
![34x=y-3105](https://tex.z-dn.net/?f=34x%3Dy-3105)
By multiplying the quantity by 34, an amount is obtained that differs from 3105 from what it would have been obtained if multiplied by 43.
Now we are going to <u>replace the first equation in the second one </u>(
):
![34x=43x-3105](https://tex.z-dn.net/?f=34x%3D43x-3105)
And clear to find x:
![3105=43x-34x\\3105=9x\\\frac{3105}{9}=x\\345=x](https://tex.z-dn.net/?f=3105%3D43x-34x%5C%5C3105%3D9x%5C%5C%5Cfrac%7B3105%7D%7B9%7D%3Dx%5C%5C345%3Dx)
The number that jimmy was supposed to multiply by 43 is 345.