Answer:
Step-by-step explanation:
P = 4x(x - 3) + 4y(y - 3) + 8xy
= 4x² - 12x + 4y² - 12y + 8xy
= (4x² + 8xy + 4y²) - (12x + 12y)
= 4(x² + 2xy + y²) - 12(x + y)
= 4(x + y)² - 12(x + y)
x+y =2 ⇒ P = 4.2² - 12.2 = 16 - 24 = -8
What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)
Three consecutive integers are . . . x, x+1, and x+2
The smallest two are . . . x and x+1
Their product is . . . . . x(x+1)
5 times the largest one is . . . 5(x+2)
5 less than that is . . . . . . 5(x+2)-5
Now, the conditions of the problem say that <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .
Eliminate parentheses: x² + x = 5x + 10 - 5
Combine like terms: x² + x = 5x + 5
Subtract 5x from each side: x² - 4x = 5
Subtract 5 from each side: <u>x² - 4x - 5 = 0</u>
You could solve that by factoring it, or use the quadratic equation.
Factored, it says that (x + 1) (x - 5) = 0
From which <em>x = -1</em>
and <em>x = +5</em>
We only want the positive results, so our three consecutive integers are
5, 6, and 7 .
To answer the question, the smallest one is <em><u>5 </u></em>.
<u>Check</u>:
5 x 6 ? = ? (7 x 5) - 5
30 ? = ? (35) - 5
30 = 30
yay !
Answer:
coefficient is 128 and exponent is 8
Step-by-step explanation:
1. This shape is called a parallelogram and it’s area formula is A=W*H, so you would plug in 12 1/3 for H and 17 1/5 for W. The answer would be 215yd.
2. This is a triangle and it’s area formula is A=1/2bh. Plug in 14 as H and 17 for b. The answer would be 119ft.
Im not sure if you wrote this wrong because (x+y)2 does equal x2+y2. An example would be if x equals 3 and y equals 4 (3+4)2=(3)2+(4)2 (7)2=6+8 14=14.
