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:what’s the lowest value?
what’s the highest value?
there is your range
Step-by-step explanation:
Let’s take the number .666666 repeating
If we turn it into a fraction it’s 2/3.
It doesn’t matter how many numbers repeat to write a fraction.
Hope this helps.
Answer:
20 inches
Step-by-step explanation:
Since the cape is trapezoid shaped and has an area of 600 in², the area of a trapezoid is given by
A =1/2(a + b)h where a = length along the top of the cape = 24 in, b = length along the bottom of the cape = 36 in and h = height of the cape
So, h = 2A/(a + b)
= 2 × 600 in²/(24 in + 36 in)
= 1200 in²/60 in
= 20 in
So, the height of the cape is 20 inches
