Compute the inverse of the following matrix with steps.

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4

Dmitry [639]

Answer:

$\boxed{\sf Standard-form :x + 4y -17=0 }\\$

$\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

$\longrightarrow x + 4y = 7\\$

Firstly convert it into slope intercept form of the line which is y = mx + x , as ;

$\longrightarrow 4y = -x + 7 \\$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\$

On comparing it to y = mx + c , we have ,

$\longrightarrow m =\dfrac{-1}{4}\\$

$\longrightarrow c =\dfrac{7}{4}\\$

Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}\\$

Now we may use point slope form of the line as ,

$\longrightarrow y - y_1 = m(x-x_1) \\$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\$

$\longrightarrow 4(y -5 ) =-1(x +3) \\$

$\longrightarrow 4y -20 = - x -3 \\$

$\longrightarrow x + 4y -20+3=0\\$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\$

6 0

2 years ago

To how many decimal places are you supposed to 'estimate' the answer to?

padilas [110]

Answer:

79.2135

Step-by-step explanation:

5.34 - 2.52 = 2.82

2.82 divided by 0.0356 = 79.2135

6 0

2 years ago

The Math Club is renting a banquet room for a party with door prizes. The banquet room costs

juin [17]

Answer:

14

Step-by-step explanation:

8 0

3 years ago

The length of a rectangle is three more than twice the width. The perimeter is 96. What are the dimensions?

SIZIF [17.4K]

Answer:

Width =15

Length =33

Step-by-step explanation:

Take width as x

And length as 2x+3

Perimeter as 96

Formula of the perimeter of a rectangle is 2l+2w

X+×+2×+3+2×+3=96

6x+6=96

6x=96-6

6×=90

X=15

Width =x and x =15 so width =15 while length =33

7 0

3 years ago

A cereal box has dimensions of 10 1/2 inches by 7 1/2 inches by 2 1/2 inches. What is the volume of the cereal box? 19 1/2 in³ 2

Temka [501]

196 3/8 in^3. To get this, multiply all the numbers together. To find volume, the equation is length x width x height.

5 0

3 years ago