Answer:
14x
Step-by-step explanation:
Step 1: Collect like terms by adding their coefficients
(11+3)x
Step 2: Add the numbers
14x
Could be y=8x + 16?
The gradient is 8 bcause each time x increases by one y increases by 8
1-2 is right
3 you have to draw a shape and then put 3 lines then shade in one
number 4 you have to draw a shape again but put 8 lines through then shade 1
5 your answer is 1/8
6 your answer is 1/4
7 you have to draw a shape again draw 3 line in the shape then shade 1 and your fraction is 1/3
Answer:
The height of the triangle could be found by the <u>Pythagoras theorem</u>, where the result is, with the data of the exercise:
- <u>Height of the triangle = 10.392</u>
And the area of the triangle is:
- <u>Area of the triangle = 31.176 units^2</u>
Step-by-step explanation:
When you have two measurements of a triangle, as the case in the picture, you can find the third with the <em>Pythagoras theorem</em>, which is:
- <u>(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2</u>
As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:
- (opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2
- (adjacent leg)^2 = hypotenuse^2 - (opposite leg)^2
Now, we can replace the values in the formula obtained:
- (adjacent leg)^2 = hypotenuse^2 - (opposite leg)^2
- (adjacent leg)^2 = 12^2 - 6^2
- (adjacent leg)^2 = 144 - 36
- (adjacent leg)^2 = 108
Now, as we just need the adjacent leg, we take the square root of both sides:
- adjacent leg =
![\sqrt{108}](https://tex.z-dn.net/?f=%5Csqrt%7B108%7D)
- <u>adjacent leg = 10.392 approximately</u>.
Now, with these data, we can find the area of the triangle with the next formula:
- Area of a triangle = (base * height) / 2
- And we replace the measurements:
- Area of a triangle = (6 * 10.392) / 2
- <u>Area of a triangle = 31.176</u>
As the image does not contain units, it would be simply this number, however, <em>you should know that the area units are usually given squared, for example: in^2 or ft^2</em>.
Answer:
![\:c_{11}=-2,\:\:\:c_{12}=-2](https://tex.z-dn.net/?f=%5C%3Ac_%7B11%7D%3D-2%2C%5C%3A%5C%3A%5C%3Ac_%7B12%7D%3D-2)
![\:c_{21}=5,\:\:\:c_{22}=8](https://tex.z-dn.net/?f=%5C%3Ac_%7B21%7D%3D5%2C%5C%3A%5C%3A%5C%3Ac_%7B22%7D%3D8)
Step-by-step explanation:
Given the matrices
![A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bpmatrix%7D1%26-1%5C%5C%202%261%5Cend%7Bpmatrix%7D)
![B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}](https://tex.z-dn.net/?f=B%3D%5Cbegin%7Bpmatrix%7D1%262%5C%5C%20%5C%3A3%264%5Cend%7Bpmatrix%7D)
Calculating AB:
![\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D1%26-1%5C%5C%20%5C%3A%5C%3A2%261%5Cend%7Bpmatrix%7D%5Ctimes%20%5C%3A%5Cbegin%7Bpmatrix%7D1%262%5C%5C%20%5C%3A%5C%3A3%264%5Cend%7Bpmatrix%7D%3D%5Cbegin%7Bpmatrix%7Dc_%7B11%7D%26c_%7B12%7D%5C%5C%20%5C%3A%5C%3A%5C%3Ac_%7B21%7D%26c_%7B22%7D%5Cend%7Bpmatrix%7D)
Multiply the rows of the first matrix by the columns of the second matrix
![=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D1%5Ccdot%20%5C%3A1%2B%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A3%261%5Ccdot%20%5C%3A2%2B%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A4%5C%5C%202%5Ccdot%20%5C%3A1%2B1%5Ccdot%20%5C%3A3%262%5Ccdot%20%5C%3A2%2B1%5Ccdot%20%5C%3A4%5Cend%7Bpmatrix%7D)
![=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D-2%26-2%5C%5C%205%268%5Cend%7Bpmatrix%7D)
Hence,
![\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7Dc_%7B11%7D%26c_%7B12%7D%5C%5C%20%5C%3A%5C%3A%5C%3Ac_%7B21%7D%26c_%7B22%7D%5Cend%7Bpmatrix%7D%3D%5Cbegin%7Bpmatrix%7D-2%26-2%5C%5C%20%5C%3A5%268%5Cend%7Bpmatrix%7D)
Therefore,
![\:c_{11}=-2,\:\:\:c_{12}=-2](https://tex.z-dn.net/?f=%5C%3Ac_%7B11%7D%3D-2%2C%5C%3A%5C%3A%5C%3Ac_%7B12%7D%3D-2)
![\:c_{21}=5,\:\:\:c_{22}=8](https://tex.z-dn.net/?f=%5C%3Ac_%7B21%7D%3D5%2C%5C%3A%5C%3A%5C%3Ac_%7B22%7D%3D8)