Answer:
![(2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14](https://tex.z-dn.net/?f=%282x%5E2%2B2x%2B1%29-%287x%5E2%2B2x%2B15%29%3D-5x%5E2-14)
Step-by-step explanation:
To explain how to approach this question, I am going to place letters in the blank spaces:
![(ax^2+bx+c)-(dx^2+ex+f)=-5x^2-14](https://tex.z-dn.net/?f=%28ax%5E2%2Bbx%2Bc%29-%28dx%5E2%2Bex%2Bf%29%3D-5x%5E2-14)
First, compare the <u>coefficients</u> of the x² terms on both sides of the equation: ![a - d = -5](https://tex.z-dn.net/?f=a%20-%20d%20%3D%20-5)
Therefore, we need to choose any two numbers in place of a and d whose difference is -5:
⇒ a = 2 and d = 7 as 2 - 7 = -5.
Similarly, upon comparing the <u>coefficients</u> of the x terms, we can see that there is no x term on the right side of the equation. Therefore, we need to choose numbers in place of b and e for which the difference is zero. So b and e should be the <u>same number</u>:
⇒ b = 2 and e = 2 as 2 - 2 = 0.
Finally, compare the constant term on both sides of the equation: ![c - f = -14](https://tex.z-dn.net/?f=c%20-%20f%20%3D%20-14)
Therefore, we need to choose any two numbers in place of c and f whose difference is -14:
⇒ c = 1 and f = 15 as 1 - 15 = -14.
Plug in the numbers in place of the letters on the left side of the equation:
![(2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14](https://tex.z-dn.net/?f=%282x%5E2%2B2x%2B1%29-%287x%5E2%2B2x%2B15%29%3D-5x%5E2-14)
<u>Check</u>
Remove the brackets:
![2x^2+2x+1-7x^2-2x-15=-5x^2-14](https://tex.z-dn.net/?f=2x%5E2%2B2x%2B1-7x%5E2-2x-15%3D-5x%5E2-14)
Collect like terms:
![2x^2-7x^2+2x-2x+1-15=-5x^2-14](https://tex.z-dn.net/?f=2x%5E2-7x%5E2%2B2x-2x%2B1-15%3D-5x%5E2-14)
Combine like terms:
![-5x^2-14=-5x^2-14](https://tex.z-dn.net/?f=-5x%5E2-14%3D-5x%5E2-14)
Hence proving that the left and right sides of the equation are the same.
Answer:
-37
Step-by-step explanation:
1) to find the equation of the given line (its slop-interception form is y=mx+i, where m - slop, i - interception):
a) y=2x+i, where m=2;
b) it is possible to calculate the value of 'i' after the substitution the point (5;-3) into the equation y=2x+i:
-3=2*5+i; ⇒ i= -13;
c) the equation of the given line is y=2x-13.
2) to calculate the value of 'R':
if to substitute the point (-12;R) into the equation y=2x-13, then
R=2*(-12)-13; ⇒ R= -37.
Answer:
y=1/2x-7
Step-by-step explanation:
Well first you must find what 71/2 is equal to:
71 / 2 = 35.5
Now you should convert this to a decimal instead of a percent. All you have to do is move the decimal two places to the left when going from percent to decimal:
35.5% = .355
Now that you know the decimal value, you want to know what number is 12 35.5% of. To do this, think, if you were wondering what is 10% of 100, you would multiply 100 by .10 so in this case since you are going the opposite way, you would divide 12 by .335, which gives you:
35.8208955224
This can be approximated to:
≈35.82
Answer:
Torus
Step-by-step explanation:
This particular solid is called a torus, and looks like a dough-nut. Note: The 2-D figure may appear on coordinate axes, from which you can obtain measurement information about the figure.