D^2 - 4d = 3d
d^2 - 7d = 0
d(d - 7) = 0
d = 0 or d - 7 = 0
d = 0 or d = 7
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 4)² + (y + 6)² = 16 is in this form
with r² = 16 ⇒ r =
= 4
---------------------------------------------------------------
given (h, k) = (5, 2) and r = 20, then
(x - 5)² + (y - 2)² = 400 ← represents the delivery area
Answer:
Step-by-step explanation:
By triangle sum theorem,
Sum of interior angles of a triangle is 180°.
Therefore, measure of third angle in the larger triangle = 180° - (35° + 120°) = 25°
Similarly, measure of third angle in the smaller triangle = 180° - (25° + 120°)
= 35°
Since, measure of interior angles of larger triangle is equal to the measure of smaller triangle,
Both the triangles will be similar by AA property of similarity.
Answer:
x=6
b= 126
Step-by-step explanation:
8x+78 = 2x+114
8x-2x = 114-78
6x=36
x=6
--------
b=2x6+114
b= 126
Answer:
n times 5
Step-by-step explanation:
A matrix Anxn of this way is called an upper triangular matrix. It can be proved that the determinant of this kind of matrix is

In this case, it would be 5+5+...+5 (n times) = n times 5
We are going to develop each determinant by the first column taking as pivot points the elements of the diagonal
![det\left[\begin{array}{cccc}5&a_{12}&a_{13}...&a_{1n}\\0&5&a_{23}...&a_{2n}\\...&...&...&...\\0&0&0&5\end{array}\right] =5+det\left[\begin{array}{ccc}5&a_{23}...&a_{2n}\\0&5&a_{3n}\\...&...&...\\0&0&5\end{array}\right]=5+5+...+det\left[\begin{array}{cc}5&a_{n-1,n}\\0&5\end{array}\right]=5+5+...+5+5\;(n\;times)](https://tex.z-dn.net/?f=det%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%26a_%7B12%7D%26a_%7B13%7D...%26a_%7B1n%7D%5C%5C0%265%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C...%26...%26...%26...%5C%5C0%260%260%265%5Cend%7Barray%7D%5Cright%5D%20%3D5%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C0%265%26a_%7B3n%7D%5C%5C...%26...%26...%5C%5C0%260%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26a_%7Bn-1%2Cn%7D%5C%5C0%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2B5%2B5%5C%3B%28n%5C%3Btimes%29)