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3 years ago

Simplify the problem

Mathematics

1 answer:

Natasha2012 [34]3 years ago

5 0

$\frac{6}{10x^2} \div \frac{6}{10x^3-60x^2} = \frac{6}{10x^2} \cdot \frac{10x^3-60x^2}{6} =\frac{1}{10x^2} \cdot \frac{10x^2(x-6)}{1} =x-6$

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Slope intercept form of a line that has a slope of -3/4 and passes through (4, 3)

tia_tia [17]

<h3>Explanation</h3>

First Method

We have the given slope value and the coordinate point that the graph passes through.

$y = mx + b$

where m = slope and b = y-intercept. Substitute the value of slope in the equation.

$y = - \frac{3}{4} x + b$

We have the given coordinate point as well. After we substitute the slope, we substitute the coordinate point value in the equation.

$3 = - \frac{3}{4} (4) + b \\$

Solve the equation for b-term

$3 = - 3 + b \\ 3 + 3 = b \\ 6 = b$

The value of b is 6. We substitute the value of b in the equation.

$y = - \frac{3}{4} x + 6$

Second Method

We can also use the Point-Slope form to solve the question.

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

Given the y1 and x1 = the coordinate point value.

Substitute the slope and coordinate point value in the point slope form.

$y - 3 = - \frac{3}{4} (x - 4)$

Simplify/Convert into Slope-intercept

$y = - \frac{3}{4} (x - 4) + 3 \\ y = - \frac{3}{4} x + \frac{12}{4} + 3 \\ y = - \frac{3}{4} x + 3 + 3 \\y = - \frac{3}{4} x + 6$

<h3>Answer</h3>

 $\large \boxed {y = - \frac{3}{4} x + 6}$ 

6 0

3 years ago

I need to answer and explain

nignag [31]

Answer:

parallel

Step-by-step explanation:

Solve both equations for y to make it easier to compare them.

2x - 5y = 0 ↔ 5y = 2x, or y = (5/2)x.

y = (5/2)x - 3

Since the slopes are the same, the two lines are parallel.

8 0

3 years ago

Your family has a cable television package that costs $40.99 per month. Pay-per-view movies cost $3.95 each. Your family budgets

ELEN [110]

Answer:

3 movies

Step-by-step explanation:

55$-40.99$= 14.01$ left to spend on movies

$14.01/$3.95=3.54

Which means you can buy 3 movies.

5 0

3 years ago

-4x + 8 > 12 inequality solution ?

BARSIC [14]

Answer:

x<-1

Step-by-step explanation:

-4x+8>12

-4x>12-8

-4x>4

x>4/-4

x>-1

x<-1

6 0

3 years ago

F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the coordinates of F?

Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

The ratio by which the point F divides the line = 3:1

The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) = (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

$l_{HF} = \sqrt{\left (4-7 \right )^{2}+\left (1-(-11) \right )^{2}} = \sqrt{\left (-3 \right )^{2}+\left (12 \right )^{2}} = 3\cdot \sqrt{17}$

Similarly, we check the length of HJ, to get;

$l_{HF} = \sqrt{\left (3-7 \right )^{2}+\left (5-(-11) \right )^{2}} = \sqrt{\left (-4 \right )^{2}+\left (16 \right )^{2}} = 4\cdot \sqrt{17}$

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

7 0

3 years ago