4) A triangle has a base length of 2.5 cm and corresponding height 4.5 cm,

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murzikaleks [220]

Answer:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$\boxed{y=mx+b}$

where:

m is the slope.
b is the y-intercept (where the line crosses the y-axis).

Slope formula

$\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}$

Equation 1

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(-1, 6)$

$\textsf{Let }(x_2,y_2)=(0, 1)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5$

From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=-5x+1$

Equation 2

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(1, 1)$

$\textsf{Let }(x_2,y_2)=(0, -4)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5$

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=5x-4$

Conclusion

Therefore, the system of linear equations shown by the graph is:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Learn more about systems of linear equations here:

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5 0

1 year ago

Read 2 more answers

Drag each number to the correct location on the equations. Each number can be used more than once, but not all numbers will be u

7nadin3 [17]

The system of equations to find the cost of one adult ticket, a, and the cost of one child ticket, c are Roy's; 6a+2c=66 Elisa's 5a+4c=62.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let's consider adults tickets be a and child tickets be c

so

Roy's purchase

6a+2c=66------1

Elisa's purchase

5a+4c=62-------2

Hence, the system of equations

6a+2c=66------1

5a+4c=62-------2

solving simultaneously

6a+2c=66

5a+4c=62

Also,

12a+4c=132

-5a+4c=62

7a=70

a=$10

put a=70 in 1

6(10)+2c=66

60+2c=66

2c=66-60

2c=6

c=$3

Learn more about equations here;

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4 0

1 year ago

<img src="https://tex.z-dn.net/?f=%5Ctext%7BSolve%20for%20x%3A%7D%5C%5C%5C%5C3x%20%2B%2054%20%3D%20180" id="TexFormula1" title="

vagabundo [1.1K]

Hi there!

»»————-　★　————-««

I believe your answer is:

$x = 42$

»»————-　★　————-««

Here’s why:

We will use inverse operations to solve for 'x'.

⸻⸻⸻⸻

$\boxed{\text{Calculating the Answer....}}\\\\3x+54=180\\----------\\\rightarrow 3x + 54 - 54 = 180-54\\\\\rightarrow 3x = 126\\\\\rightarrow\frac{3x=126}{3}\\\\\rightarrow\boxed{x=42}$