A rational number can be written as two integers. Ex: .6 or 6/10 or 3/5.
An irrational number can’t be expressed as two integers such as pie or 3.14
Answer:
<h2>Perimeter: 16x + 16</h2><h2>Area: 40x + 15</h2>
Step-by-step explanation:
![l-\text{length}\\\\w-\text{width}\\\\\text{The formula of a perimeter of a rectangle:}\ P=2(l+w)\\\text{The formula of an area of a rectangle:}\ A=lw\\\\\text{We have}\ l=8x+3\ \text{and}\ w=5.\\\text{Substitute:}\\\\P=2(8x+3+5)\\P=2(8x+8)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\P=(2)(8x)+(2)(8)\\\boxed{P=16x+16}\\\\A=(8x+3)(5)\qquad\text{use the distributive property}\\A=(8x)(5)+(3)(5)\\\boxed{A=40x+15}](https://tex.z-dn.net/?f=l-%5Ctext%7Blength%7D%5C%5C%5C%5Cw-%5Ctext%7Bwidth%7D%5C%5C%5C%5C%5Ctext%7BThe%20formula%20of%20a%20perimeter%20of%20a%20rectangle%3A%7D%5C%20P%3D2%28l%2Bw%29%5C%5C%5Ctext%7BThe%20formula%20of%20an%20area%20of%20a%20rectangle%3A%7D%5C%20A%3Dlw%5C%5C%5C%5C%5Ctext%7BWe%20have%7D%5C%20l%3D8x%2B3%5C%20%5Ctext%7Band%7D%5C%20w%3D5.%5C%5C%5Ctext%7BSubstitute%3A%7D%5C%5C%5C%5CP%3D2%288x%2B3%2B5%29%5C%5CP%3D2%288x%2B8%29%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%3A%7D%5C%20a%28b%2Bc%29%3Dab%2Bac%5C%5CP%3D%282%29%288x%29%2B%282%29%288%29%5C%5C%5Cboxed%7BP%3D16x%2B16%7D%5C%5C%5C%5CA%3D%288x%2B3%29%285%29%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5CA%3D%288x%29%285%29%2B%283%29%285%29%5C%5C%5Cboxed%7BA%3D40x%2B15%7D)
Answer: y= -3/2x
Explanation:
3x+ 2y- 6
→ 2y= -3x+ 6
→ y= -3/2x+ 3
Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.
For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).
![D=b^2-4ac\\D=4^2-4(4)(1)\\D=16-16\\D=0](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%5C%5CD%3D4%5E2-4%284%29%281%29%5C%5CD%3D16-16%5C%5CD%3D0)
Meaning there's only 1 real root, complete the square and you get the answer.
![(x+y)^2=x^2+2xy+y^2](https://tex.z-dn.net/?f=%28x%2By%29%5E2%3Dx%5E2%2B2xy%2By%5E2)
We're going to use this formula, so if x² = 4x² then x = 2x
and if y² = 1 then y = 1
Straight to formula
![(2x+1)^2=0\\x=-\frac{1}{2}](https://tex.z-dn.net/?f=%282x%2B1%29%5E2%3D0%5C%5Cx%3D-%5Cfrac%7B1%7D%7B2%7D)
Because (2x+1)² is basically (2x+1)(2x+1), we get the same value of x.
So the answer is x = -1/2
(When D>0, there are 2 real roots.)
(When D=0, there are only 1 real root.)
(When D<0, there are no real roots, but 2 complex roots.)
Best Answer:
<span>
to multiply fractions you simply take the denominator of both fractions
and multiply them, do the same to the numerator, and you have your
answer.
ex.
2 5 10
-- * -- = ----
4 8 32
then, of course, you would need to simplify.
so the answer is
10(/2) 5
-------- = -----
32(/2) 16
To multiply mixed numbers, you need to convert them to improper
fractions, multiply and then convert them back to a mixed number. For
example:
2 1/2 x 5 1/3 = 5/2 x 16 /3
numerator 5 x 16 = 80 denominator 2 x 3 = 6
so now you convert 80/6 into a mixed number
80 / 6 = 13 and 2/6 or, reduced, 13 1/3. </span>