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3 years ago

−5y+8x=−18 5y+2x=58 Solve the system of equations.

Mathematics

1 answer:

kvasek [131]3 years ago

8 0

Answer:

1: −5y+8x=−18

Slope = 3.200/2.000 = 1.600

x-intercept = -18/8 = -9/4 = -2.25000

y-intercept = 18/5 = 3.60000

2: Slope = -0.800/2.000 = -0.400

x-intercept = 58/2 = 29

y-intercept = 58/5 = 11.60000

Step-by-step explanation:

1: Step 1 :

Equation of a Straight Line

1.1 Solve -5y+8x+18 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -5y+8x+18 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 18/5 so this line "cuts" the y axis at y= 3.60000

y-intercept = 18/5 = 3.60000

Calculate the X-Intercept :

When y = 0 the value of x is -9/4 Our line therefore "cuts" the x axis at x=-2.25000

x-intercept = -18/8 = -9/4 = -2.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 3.600 and for x=2.000, the value of y is 6.800. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 6.800 - 3.600 = 3.200 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

2: Same thing

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The true statement is:

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<h3>Which statements are true?</h3>

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1 year ago

Brady made a scale drawing of a rectangular swimming pool on a coordinate grid. The points (-20, 25), (30, 25), (30, -10) and (-

djverab [1.8K]

Answer:

Length = 50 units

width = 35 units

Step-by-step explanation:

Let A, B, C and D be the corner of the pools.

Given:

The points of the corners are.

$A(x_{1}, y_{1}})=(-20, 25)$

$B(x_{2}, y_{2}})=(30, 25)$

$C(x_{3}, y_{3}})=(30, -10)$

$D(x_{4}, y_{4}})=(-20, -10)$

We need to find the dimension of the pools.

Solution:

Using distance formula of the two points.

$d(A,B)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ ----------(1)

For point AB

Substitute points A(30, 25) and B(30, 25) in above equation.

$AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}$

$AB=\sqrt{(30+20)^{2}}$

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Similarly for point BC

Substitute points B(-20, 25) and C(30, -10) in equation 1.

$d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}$

$BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}$

$BC=\sqrt{(-35)^{2}}$

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Similarly for point DC

Substitute points D(-20, -10) and C(30, -10) in equation 1.

$d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}$

$DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}$

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DC = 50 units

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Substitute points A(-20, 25) and D(-20, -10) in equation 1.

$d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}$

$AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}$

$AD=\sqrt{(-20+20)^{2}+(-35)^{2}}$

$AD=\sqrt{(-35)^{2}}$

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Therefore, the dimension of the rectangular swimming pool are.

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Answer:

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−5y+8x=−18 5y+2x=58 Solve the system of equations. ​

−5y+8x=−18 5y+2x=58 Solve the system of equations.