Answer:
A + B = 24
16A + 20B = 434
Step-by-step explanation:
To write a system of equations for this scenario, let's say that A represents the number of hours machine A ran, and B represents the number of hours machine B ran.
The first equation will be:
A + B = 24
because the total number of hours ran is 24.
The second equation will be:
16A + 20B = 434
because the total number of items made is 434.
A + B = 24
16A + 20B = 434
First solve for one variable, and let's just do A.
Using the first equation, A + B = 24, A is equal to 24 - B.
Substitute this value to the second equation.
16 (24 - B) + 20B = 434
384 - 16B + 20B = 434
4B = 50
B = 12.5
Now use this value of B to find the value of A.
A + 12.5 = 24
A = 11.5
Machine A ran for 11.5 hours, and Machine B ran for 12 hours.
Answer:
The answer is 38 red marbles are in the bin.
Step-by-step explanation:
Divide 76 by 2 to get your answer.
Answer:
![m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right]](https://tex.z-dn.net/?f=m%20%5Ctimes%20H%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D%5Cboxed%7B-9%7D%20%26%20%5Cboxed%7B36%7D%20%26%20%5Cboxed%7B-%5Cdfrac%7B9%7D%7B2%7D%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
<u>Calculate the value of m</u>
Given:
![3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]](https://tex.z-dn.net/?f=3%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%7D-1%20%26%202%20%5C%5C4%20%26%208%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B2%7D%7B3%7Dm%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%7D-1%20%26%202%20%5C%5C4%20%26%208%5Cend%7Barray%7D%5Cright%5D)
Therefore:
<u>Calculate the value of H</u>
Given:
![\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)](https://tex.z-dn.net/?f=%5Cleft%28H%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D1%20%26%204%20%26%20-2%5Cend%7Barray%7D%5Cright%5D%5Cright%29%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D3%20%26%202%20%26%20-6%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D-2%20%26%208%20%26%20-1%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D1%20%26%204%20%26%20-2%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D3%20%26%202%20%26%20-6%5Cend%7Barray%7D%5Cright%5D%5Cright%29)
Therefore:
![\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]](https://tex.z-dn.net/?f=%5Cimplies%20H%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D-2%20%26%208%20%26%20-1%5Cend%7Barray%7D%5Cright%5D)
<u />
<u>Calculating m × H</u>
<u />
<u />![\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Ctimes%20H%3D%5Cdfrac%7B9%7D%7B2%7D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D-2%20%26%208%20%26%20-1%5Cend%7Barray%7D%5Cright%5D)
<u />![\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right]](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Ctimes%20H%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D%5Cdfrac%7B9%7D%7B2%7D%28-2%29%20%26%20%5Cdfrac%7B9%7D%7B2%7D%288%29%20%26%20%5Cdfrac%7B9%7D%7B2%7D%28-1%29%5Cend%7Barray%7D%5Cright%5D)
![\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Ctimes%20H%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%20c%20c%7D-9%20%26%2036%20%26%20-%5Cdfrac%7B9%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
<u />
Answer:
x = 10
Step-by-step explanation:
Form the information given, we can deduce that:
m<OPQ is an exterior angle of ∆NOP = (6x - 15)°
m<PNO = (2x + 18)° and m<NOP = (2x - 13)° are both interior angles that are opposite to the exterior angle.
Therefore, based on the exterior angle theorem:
m<OPQ = m<PNO + m<NOP
(6x - 15)° = (2x + 18)° + (2x - 13)°
Solve for x
6x - 15 = 2x + 18 + 2x - 13
6x - 15 = 4x + 5
6x - 15 - 4x = 4x + 5 - 4x (Subtraction property of equality)
2x - 15 = 5
2x - 15 + 15 = 5 + 15 (addition property of equality)
2x = 20
2x/2 = 20/2 (division property of equality)
x = 10
Answer:
-19
Step-by-step explanation:
-3+10- (-4) × (-5)+(-6)
-3+10+4 × (-5)-6
4×(-5) = -20 -3+10-20-6 = -19
♡ There's this app called Photomath. It will help you with problems like these. I hope this helps. Please mark me as BRAINLINESS....
