Answer:
3x+24 more widgets
Step-by-step explanation:
A company owns two manufacturing plants:
- 1st plant: 8x+17 widgets;
- 2nd plant: 5x-7 widgets.
To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,
![(8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24](https://tex.z-dn.net/?f=%288x%2B17%29-%285x-7%29%5C%5C%20%5C%5C%3D8x%2B17-5x%2B7%5C%20%5B%5Ctext%7BEliminate%20brackets%7D%5D%5C%5C%20%5C%5C%3D%288x-5x%29%2B%2817%2B7%29%5C%20%5B%5Ctext%7BCombine%20the%20like%20terms%7D%5D%5C%5C%20%5C%5C%3D3x%2B24)
First simplify the square roots.
√25 is 5 and √16 is 4
so the equation is 3x5 + 4x4
15+16
31
The matrix equation that represents this situation is
![\left[\begin{array}{ccc}3&2&0\\1&0&4\\3&1&1\end{array}\right]*\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}13.50\\16.50\\14.00\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%262%260%5C%5C1%260%264%5C%5C3%261%261%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13.50%5C%5C16.50%5C%5C14.00%5Cend%7Barray%7D%5Cright%5D%20)
Use technology to find the inverse of matrix A:
![A^{-1}= \left[\begin{array}{ccc}-\frac{2}{5}&-\frac{1}{5}&\frac{4}{5}\\ \frac{11}{10}&\frac{3}{10}&-\frac{6}{5}\\\frac{1}{10}&\frac{3}{10}&-\frac{1}{5}\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2%7D%7B5%7D%26-%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B4%7D%7B5%7D%5C%5C%0A%5Cfrac%7B11%7D%7B10%7D%26%5Cfrac%7B3%7D%7B10%7D%26-%5Cfrac%7B6%7D%7B5%7D%5C%5C%5Cfrac%7B1%7D%7B10%7D%26%5Cfrac%7B3%7D%7B10%7D%26-%5Cfrac%7B1%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D%20)
Multiplying A inverse by B, we get the solution matrix
[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]
Answer:
Compare your work to ours, especially if your answer is different than our ... Build a different number that is between 300 and 500. ... I can represent addition and subtraction word problems using objects, ... She bought a pack of 36 hair clips to add to her collection. ... Write a number sentence below to solve the problem.
Step-by-step explanation:
Compare your work to ours, especially if your answer is different than our ... Build a different number that is between 300 and 500. ... I can represent addition and subtraction word problems using objects, ... She bought a pack of 36 hair clips to add to her collection. ... Write a number sentence below to solve the problem.
Given:
Height of Isabelle = 62 inches
Shadow of Isabelle = 93 inches
Shadow of tree = 279 inches
To find:
The height of the tree.
Solution:
Let height of tree be x.
Ratio of height to shadow for Isabelle and tree are
The shadow of Isabelle and tree are proportional to their shadows. So, both ratios must be equal.
Multiply both sides by 279.
Therefore, the height of tree is 186 inches.
