Answer:
<em>120 minutes or 2 hours</em>
Step-by-step explanation:
<u>Proportions</u>
The method to solve the problem is to compute how many cans produce each machine per minute, then add them to obtain the total cans produced by both. Finally, we compute the time to produce 4200 cans at that level of production.
The newer machine produces 4200 cans in 210 minutes, it means it produces
![\displaystyle \frac{4200}{210}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4200%7D%7B210%7D)
=20 cans per minute
The older machine needs 280 minutes to produce the same 4200 cans, to it produces
![\displaystyle \frac{4200}{280}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4200%7D%7B280%7D)
= 15 cans per minute
Together, they produce 20+15=35 cans per minute. Thus, to produce 4200 cans, they need
![\displaystyle \frac{4200}{35}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4200%7D%7B35%7D)
= 120 minutes or 2 hours
Answer:
7
Step-by-step explanation:
|24| - |-17|
The absolute value of 24 is 24 so,
24 - |- 17|
and the absolute value of -17 is 17 so all you have to solve for is
24 - 17
which is 7
hope this helps :)
Answer: The length of the base is 10.
Step-by-step explanation:
You can draw an isosceles triangle like the one shown attached.
An isosceles triangle has two equal sides. Then, you can divide it into two right triangles, where the base of each one of them will be:
![b'=\frac{2x}{2}=x](https://tex.z-dn.net/?f=b%27%3D%5Cfrac%7B2x%7D%7B2%7D%3Dx)
The hypotenuse of each right triangle shown is 13 and the other legs are (x+7) and x, therefore you can apply the Pythagorean Theorem:
![13^2=x^2+(x+7)^2](https://tex.z-dn.net/?f=13%5E2%3Dx%5E2%2B%28x%2B7%29%5E2)
Simplify the expression:
![169=x^2+(x^{2}+2(x)(7)+7^2)\\169=x^{2}+x^{2}+14x+49\\0=2x^{2}+14x-120](https://tex.z-dn.net/?f=169%3Dx%5E2%2B%28x%5E%7B2%7D%2B2%28x%29%287%29%2B7%5E2%29%5C%5C169%3Dx%5E%7B2%7D%2Bx%5E%7B2%7D%2B14x%2B49%5C%5C0%3D2x%5E%7B2%7D%2B14x-120)
Use the quadratic formula, where:
![a=2\\b=14\\c=-120](https://tex.z-dn.net/?f=a%3D2%5C%5Cb%3D14%5C%5Cc%3D-120)
![x=\frac{-b\±\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Then:
![x=\frac{-14\±\sqrt{14^2-4(2)(-120)}}{2+2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5C%C2%B1%5Csqrt%7B14%5E2-4%282%29%28-120%29%7D%7D%7B2%2B2%7D)
![x_1=5\\x_2=-12](https://tex.z-dn.net/?f=x_1%3D5%5C%5Cx_2%3D-12)
Choose the positive value, because lengths are not negative.
Substitute the value of x into the base 2x. Therefore, the answer is:
![b=2x=2(5)=10](https://tex.z-dn.net/?f=b%3D2x%3D2%285%29%3D10)
Answer:
m = 8.2 × 10³ grams
Step-by-step explanation:
Given that,
The weight of a monkey = 8.2 kilograms.
We need to convert its mass from kilograms to grams.
We know that,
1 kg = 1000 grams
or
1 kg = 10³ grams
In 8.2 kg,
8.2 kg = 8.2 × 10³ grams
Hence, the weight of the monkey is equal to 8.2 × 10³ grams.