Answer:
75
Step-by-step explanation:
The measure of two supplementary angles = 15:21
The angles are 15x , 21x
15x + 21x = 180 {Supplementary}
36x = 180
x = 180/36
x = 5
Smallest angle = 15 * 5 = 75
A parabola is the locus of points equidistant from the focus and directrix. This means the distance from the green point is the same to the focus as it is to the directrix. The appropriate choice is ...
... B. 7
Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
Answer:
Step-by-step explanation:
To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:
![A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%262%262%5C%5C-7%26-3%265%26-8%5C%5C4%261%261%261%5C%5C3%267%26-1%261%5Cend%7Barray%7D%5Cright%5D)
And the vector B is formed with the solution of each equation of the system:![b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-3%5C%5C6%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called 
.
![A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]](https://tex.z-dn.net/?f=A_%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%263%262%262%5C%5C-7%26-3%265%26-8%5C%5C4%266%261%261%5C%5C3%261%26-1%261%5Cend%7Barray%7D%5Cright%5D)
The value of y using Cramer's rule is:
Find the value of the determinant of each matrix, and divide:
Answer:
30
Step-by-step explanation:
