The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Answer:
Step-by-step explanation:
To calculate a+1/a, we first need to calculate for a.
a = 7 - 4 * ![\sqrt[2]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B2%5D%7B3%7D)
square root of 3 = 1.73
a = 7 - 4 * 1.73
a = 7 - 6.9
a = 0.1
0.1 + 1 / 0.1 = 0.1 + 10 = 10.1
Now, in case 4 wasn't being multiplied with the square root of 3, and instead, it was four root of 3, I am gonna do the calculations again:
a = 7 - ![\sqrt[4]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B3%7D)
a = 7 - 1.31
a = 5.69
5.69 + 1 / 5.69 = 5.69 + 0.17 = 5.86
Hope I Helped!
Answer
Good question!
A. false. Even though 5 is usually greater than 2, in this case it is less because it is negative and positives are always greater than negatives.
B. true. Just like the last question, positives are always greater than negatives and even though 8 is usually greater than 3, in this case the 3 is a negative so it is less.
C. true. Think about which number is closer to the number line. When we are talking about negative numbers, the number closer to the number line is greater.
D. false. Same concept as the last question where -12 is closer to the number line than -12.5 so -12 is actually greater.
If you have any additional questions feel free to ask me or your teacher so you can really master what you're learning. :)
<span>1.66666666667 is the answer I swear man</span>
