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Artemon [7]
2 years ago
9

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, o

r neither.
3x=4y-5 and 2/3 y=x/2+8

Mathematics
1 answer:
ss7ja [257]2 years ago
4 0

Answer:

The lines are parallel

The graph in the attached figure

Step-by-step explanation:

we have

3x=4y-5 ---> equation A

\frac{2}{3}y=\frac{x}{2}+8 -----> equation B

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Find the slope of the line A

3x=4y-5

Isolate the variable y

Adds 5 both sides

4y=3x+5

Divide by 4 both sides

y=\frac{3}{4}x+\frac{5}{4}

The slope is

m_A=\frac{3}{4}

step 2

Find the slope of line B

\frac{2}{3}y=\frac{x}{2}+8

Multiply by 6 both sides to remove the fractions

4y=3x+48

Divide by 4 both sides

y=\frac{3}{4}x+\frac{48}{4}

Simplify

y=\frac{3}{4}x+12

The slope is

m_B=\frac{3}{4}

step 3

Compare the slopes

we have

m_A=\frac{3}{4}

m_B=\frac{3}{4}

so

m_A=m_B

therefore

The lines are parallel

see the attached figure to better understand the problem

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2 years ago
Whats the volume of the cylinder? Round your answer to the nearest hundred the top is B the left side of the cylinder is 13cm th
Wittaler [7]

Answer:

The volume of the cylinder is 163.3 m³.

Step-by-step explanation:

Given that,

Height = 13 cm

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Using formula of cylinder

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Put the value into the formula

V=\pi\times(2)^2\times13

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6 0
2 years ago
-3x minus 2 minus -6x = -4 minus -4x plus 12
DochEvi [55]

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6 0
2 years ago
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What
krok68 [10]

The area of the required triangle is <u>9/π²(3  + √3)</u> sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

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or, Area = 9/π²(3  + √3).

Thus, the area of the required triangle is <u>9/π²(3  + √3)</u> sq. units.

Learn more about a triangle at

brainly.com/question/13734546

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5 0
1 year ago
Jake and Erica were solving a system of equations. They both noticed that the two lines had the same slope. Jake said that becau
cluponka [151]
The correct answer is option A. Erica is correct in saying that the two lines are not necessarily the same and we should also look at the y-intercepts before determining how many solutions there were. <span>Two lines with equal slopes could be the same line, but only if they have the same y-intercept.</span>
3 0
2 years ago
Read 2 more answers
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