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3 years ago

Find the slope of the lines that passes though the points (2,5) and (4,1)

Mathematics

1 answer:

Gnoma [55]3 years ago

4 0

Answer:

2)-2

Step-by-step explanation:

The slope of a line is given

m = (y2-y1)/ (x2-x1)

= (1-5)/(4-2)

= -4/2

=-2

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Look at the following graph of the given equation. Determine whether the equation is a function. Explain why or why not.

Vadim26 [7]

The equation $y=2x+2$ is a function

Explanation:

Given that the graph contains the coordinates $(-1,0)$ , $(0,2)$ , $(1,4)$ and $(2,6)$

We need to determine whether the equation $y=2x+2$ is a function.

To determine the equation is a function, let us substitute the coordinates in the equation and check whether it satisfies the equation.

Let us substitute the coordinate $(-1,0)$ in the equation $y=2x+2$

Thus, we have,

$0=2(-1)+2$

$0=-2+2$

$0=0$

Thus, the coordinate $(-1,0)$ satisfies the equation $y=2x+2$

Substituting the coordinate $(0,2)$ in the equation, we have,

$2=2(0)+2$

$2=2$

Thus, the coordinate $(0,2)$ satisfies the equation $y=2x+2$

Substituting the coordinate $(1,4)$ in the equation $y=2x+2$

$4=2(1)+2$

$4=4$

Thus, the coordinate $(1,4)$ satisfies the equation $y=2x+2$

Substituting the coordinate $(2,6)$ in the equation, we get,

$6=2(2)+2$

$6=6$

Thus, the coordinate $(2,6)$ satisfies the equation $y=2x+2$

Hence, the coordinates $(-1,0)$ , $(0,2)$ , $(1,4)$ and $(2,6)$ satisfies the equation $y=2x+2$

Thus, the equation $y=2x+2$ is a function.

6 0

3 years ago

5) Your stock investments went from $450 in 2013 to $350 ir

Hatshy [7]

The most appropriate choice for percentage will be given by Percentage decrease in the investment is 22.22%

<h3>What Does Percent Mean?</h3>

Using a percentage of 100, we may express a ratio as a %.

Stock investments in this case decreased from $450 in 2013 to $350 in 2014.

Decrease in stock equals $100 ($450 - $355)

Decrease in percentage: 100/450 100 = 22.22%

<h3>What format does a percentage use?</h3>

The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals. A total is considered to be made up of 100 equal parts when expressed as a percentage. The symbol % or, less commonly, the abbreviation 'pct' can be used to represent a percentage.

To learn more about percentage, refer to the link : brainly.com/question/24304697

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3 0

1 year ago

The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart

azamat

Answer:

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio $\big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)}$ to create an equation with the two angles.

$\displaystyle \text{tan(45)} = \frac{h}{x}$
$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Let's take these two equations and solve for x in both of them.

<h2> $\textbf{Equation I}$ </h2>

$\displaystyle \text{tan(45)} = \frac{h}{x}$

tan(45) = 1, so we can rewrite this equation.

$\displaystyle 1=\frac{h}{x}$

Multiply x to both sides of the equation.

$\displaystyle x = h$

<h2> $\textbf{Equation II}$ </h2>

$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Multiply x + 200 to both sides and divide h by tan(30).

$\displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}$

Subtract 200 from both sides of the equation.

$\displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200$

Simplify h/tan(30).

$x=\sqrt{3}h - 200$

<h2> $\textbf{Equation I = Equation II}$ </h2>

Take Equation I and Equation II and set them equal to each other.

$h=\sqrt{3}h-200$

Subtract √3 h from both sides of the equation.

$h-\sqrt{3}h=-200$

Factor h from the left side of the equation.

$h(1-\sqrt{3}) =-200$

Divide both sides of the equation by 1 - √3.

$\displaystyle h=\frac{-200}{1-\sqrt{3} }$

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

$\displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}$
$\displaystyle h=\frac{-200+200\sqrt{3} }{1-3}$
$\displaystyle h =\frac{-200+200\sqrt{3} }{-2}$