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aniked [119]
3 years ago
15

Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -5x2 + 7x + 6.

Mathematics
1 answer:
scoray [572]3 years ago
4 0
7/10

f (x)=-5x^2+7x+6

df(x)/dx=-10x+7

set df(x)/dx=0 to find vertex

10x=7

x=7/10
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Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
The equation of s circle is x2+y2+6x+4y+10=1. What is this equation written in standard form?
Andreas93 [3]

Answer:

i think it would be x two+ y two + six x + four y+ ten= one is that one the answers if so i hope this helps if not just give me the answers and i will try to help you as much as i can thanks

Step-by-step explanation:


4 0
3 years ago
Yuri purchased 8 trees to have planted at his house. The store charged a delivery fee of $5 per tree.
cestrela7 [59]

Answer:

$16.

Step-by-step explanation:

Let t represent the cost of each tree.

We have been given that Yuri purchased 8 trees to have planted at his house. So the cost of 8 trees will be 8t.

We are also told that the store charged a delivery fee of $5 per tree. So the delivery charges of 8 trees will be 8\times \$5=\$40

The total cost of purchasing 8 trees will be 8t+40.  

Since the total cost of the trees including the delivery was $168, so we can get an equation as:

8t+40=168

8t+40-40=168-40

8t=128

Upon dividing both sides of our given equation by 8, we will get:

\frac{8t}{8}=\frac{128}{8}  

t=16  

Therefore, the cost of each tree is $16.

5 0
3 years ago
Please help ASAP
babymother [125]
(-6, 4), (-3, -8), and( 1, -1)
3 0
3 years ago
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Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription fr
frozen [14]

Answer:

the first one is B and the second one is A

Step-by-step explanation:

I guessed and I got it right

5 0
3 years ago
Read 2 more answers
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