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3 years ago

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The point slope form of an equation of the line that passes through (-4, -3) and (12, 1) is y -1 =1/4(x-12). What is the standar

d form of the equation for this line?

1 answer:

luda_lava [24]3 years ago

6 0

The standard form: Ax + By = C.

We have:

$y-1=\dfrac{1}{4}(x-12)\qquad|\text{multiply both sides by 4}\\\\4y-4=x-12\qquad|\text{add 12 to both sides}\\\\4y+8=x\qquad|\text{subtract 4y from both sides}\\\\8=x-4y$

<h3>Answer: x - 4y = 8</h3>

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f(x)= 1 / x-3 g(x)= 3x + 1/x A. Use composition to prove whether or not the functions are inverses of each other. B. Express the

Alisiya [41]

Step-by-step explanation:

(A) To find inverse of f(x) = y = 1 / x - 3 :

<u>Transform in terms of x</u>

y = 1 / x - 3

x - 3 = 1 / y

x = 3 + 1 / y

<u>Exchange x with y</u> :

${f}^{ - 1} (x) = 3 + \frac{1}{x}$

Therefore, g(x) is not inverse of f(x) and vice versa.

(B)

Domain of f(x) = R - {3}

Domain of g(x) = R - {0}

7 0

3 years ago

Two collinear points on a line are given in the table below:

katrin [286]

Answer:

$(4,3)$ and $(7,2)$ do not lie on the line

Step-by-step explanation:

Given

$(0,0)\ and\ (2,1)$

Required

Determine which points that are not on the line

First, we need to determine the slope (m) of the line:

$m = \frac{y_2 - y_1}{x_2- x_1}$

Where

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (2,1)$

So;

$m = \frac{y_2 - y_1}{x_2- x_1}$

$m = \frac{1 - 0}{2-0}$

$m = \frac{1}{2}$

Next, we determine the line equation using:

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

Where

$m = \frac{1}{2}$

$(x_1,y_1) = (0,0)$

$y - y_1 = m(x -x_1)$ becomes

$y - 0 = \frac{1}{2}(x - 0)$

$y = \frac{1}{2}x$

To determine which point is on the line, we simply plug in the values of x to in the equation check.

For $(4,2)$

$x = 4$ and $y =2$

Substitute 4 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 4$

$2 = \frac{4}{2}$

$2=2$

<em>This point is on the graph</em>

<em></em>

For $(4,3)$

$x = 4$ and $y = 3$

Substitute 4 for x and 3 for y in $y = \frac{1}{2}x$

$3 = \frac{1}{2} * 4$

$3 = \frac{4}{2}$

$3 \neq 2$

<em>This point is not on the graph</em>

<em></em>

For $(7,2)$

$x = 7$ and $y = 2$

Substitute 7 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 7$

$2 = \frac{7}{2}$

$2 \neq 3.5$

<em></em>

<em>This point is not on the graph</em>

<em></em>

<em></em> $(\frac{4}{8},\frac{2}{8})$ <em></em>

<em></em> $x = \frac{4}{8}$ and<em> </em> $y = \frac{2}{8}$ <em></em>

<em>Substitute </em> $\frac{4}{8}$ <em> for x and </em> $\frac{2}{8}$ <em> for y in </em> $y = \frac{1}{2}x$ <em></em>

<em></em> $\frac{2}{8} = \frac{1}{2} * \frac{4}{8}$ <em></em>

<em></em> $\frac{2}{8} = \frac{1 * 4}{8 * 2}$ <em></em>

<em></em> $\frac{2}{8} = \frac{4}{16}$ <em></em>

<em></em> $\frac{1}{4} = \frac{1}{4}$ <em></em>

<em></em>

<em>This point is on the graph</em>

3 0

3 years ago

An mp3 player is on sale for 25% off. The original price is $52.60. What is the sale price?

Paha777 [63]

First, you need to find 25% of 52.60

Convert 25% to decimal:
25% = .25

Find 25% by multiplying its decimal equivalent by the sales price.

.25 x 52.60 = 13.15

Next, subtract that amount from 52.60 to find the new sale price.

52.60 - 13.15 = 39.45

The final price is $39.45

4 0

3 years ago

Mr. Sarpy went to shoot some hoops on the basketball court. For every shot that he made within the three-point line he earned 2

Lostsunrise [7]

Answer:

x + y = 50 (1) and 2x + 3y = 115 (2); x = 35, y = 15

Step-by-step explanation:

Since x represents the number of 2 point shots and y represents the number of 3 point shots. If the total number of shots is 50, then x + y = 50 (1)

Also, the total 2 point shots is number of 2 point shots × points per shot = 2x and the total 3 point shots is number of 3 point shots × points per shot = 3y. Since the total number of points is 115, then

2x + 3y = 115 (2)

So, the system of equations are

x + y = 50 (1) and 2x + 3y = 115 (2)

We can solve for x and y by substituting x = 50 - y into (2)

So, 2(50 - y) + 3y = 115

100 - 2y + 3y = 115

100 + y = 115

y = 115 - 100

y = 15

So, x = 50 - y

= 50 - 15

= 35

6 0

2 years ago

8x - 9 - 5x = 3x - 36 - 18x

makkiz [27]

Answer:

$8x - 9 - 5x = 3x - 36 - 18x \\ 8x - 5x - 9 = 3x - 18x - 36 \\ 3x - 9 = - 15x - 36 \\ 3x = - 15x - 36 + 9 \\ 3x = - 15x - 27 \\ 3x + - 15x = - 27 \\ - 12x = - 27 \\ x = \frac{ 27}{12}$

8 0

2 years ago