Answer:
63 Full loads of laundry
Step-by-step explanation:
We have been told in the question that 1 3/5 oz or 8/5 oz of detergent is used for a full load of laundry.
So,
1 full load of laundry requires 8/5 oz of detergent
Then,
x full loads of laundry require 100 oz of detergent
100 = 8/5x
x = 100 * 5/8
x = 63 Full loads of laundry (to the nearest whole number)
Answer:
um I did the math and I got 5, so i dont really understand
The number of partial products Alan will have when he multiplies a 4-digit number by 36 is; 8 partial products.
First, we must establish that a 4-digit number will have 4 place values namely;
- Thousands
- Hundreds
- Tens
- Ones.
And since, 36 has 2 place values;
We can conclude that the number of partial products that Alan wil have is; 2× 4 = 8.
Read more on partial products;
brainly.com/question/705781
Answer:
30
Step-by-step explanation:
triangle ABC is proportional to triangle BCD so
hypothenuse of ABC/ ajdacent of ABC = hypotrnus BCD/ ajdacent of BCD
in short
AC/BC = BC/DC
10/x = x/3
10 . 3 = x²
x² = 30
x = √30
so the question mark is 30
Answer:
<em>a) </em>
<em />
<em />
<em>b) p is in the interval (-4,4)</em>
Step-by-step explanation:
<u>Quadratic Equation</u>
It's given the following quadratic equation:
![x^2+px+4=0](https://tex.z-dn.net/?f=x%5E2%2Bpx%2B4%3D0)
a)
It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:
![a^2+2ab+b^2=(a+b)^2](https://tex.z-dn.net/?f=a%5E2%2B2ab%2Bb%5E2%3D%28a%2Bb%29%5E2)
We already have the first term squared, and we need to find the second term. Rewriting the equation:
![\displaystyle x^2+2(\frac{1}{2}px)+4=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2%2B2%28%5Cfrac%7B1%7D%7B2%7Dpx%29%2B4%3D0)
The second term of the binomial is 1/2p, thus completing the squares with
:
![\displaystyle x^2+2(\frac{1}{2}px)+\left(\frac{1}{2}p\right)^2+4-\left(\frac{1}{2}p\right)^2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2%2B2%28%5Cfrac%7B1%7D%7B2%7Dpx%29%2B%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp%5Cright%29%5E2%2B4-%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp%5Cright%29%5E2%3D0)
Factoring:
![\displaystyle \left(x+\frac{1}{2}p\right)^2+4-\frac{1}{4}p^2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28x%2B%5Cfrac%7B1%7D%7B2%7Dp%5Cright%29%5E2%2B4-%5Cfrac%7B1%7D%7B4%7Dp%5E2%3D0)
Moving the independent term to the right side:
![\displaystyle \left(x+\frac{1}{2}p\right)^2=\frac{1}{4}p^2-4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28x%2B%5Cfrac%7B1%7D%7B2%7Dp%5Cright%29%5E2%3D%5Cfrac%7B1%7D%7B4%7Dp%5E2-4)
Taking the square root:
![\displaystyle x+\frac{1}{2}p=\pm\sqrt{\frac{1}{4}p^2-4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%2B%5Cfrac%7B1%7D%7B2%7Dp%3D%5Cpm%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7Dp%5E2-4%7D)
Solving for x:
![\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D-%5Cfrac%7B1%7D%7B2%7Dp%5Cpm%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7Dp%5E2-4%7D)
b) If the equation won't have real roots, then the radicand should be negative:
![\displaystyle \frac{1}{4}p^2-4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B4%7Dp%5E2-4%3C0)
Factoring:
![\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp-2%5Cright%29%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp%2B2%5Cright%29%3C0)
The zeros of the left-side polynomial are:
![\displaystyle \frac{1}{2}p-2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7Dp-2%3D0)
![\displaystyle \frac{1}{2}p=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7Dp%3D2)
p = 4
![\displaystyle \frac{1}{2}p+2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7Dp%2B2%3D0)
![\displaystyle \frac{1}{2}p=-2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7Dp%3D-2)
p = -4
The inequality:
![\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp-2%5Cright%29%5Cleft%28%5Cfrac%7B1%7D%7B2%7Dp%2B2%5Cright%29%3C0)
Is satisfied for values of p in the interval (-4,4)