Parallel to y= -2x + 3 passes through the point (-2, -1)

Mathematics

1 answer:

elena55 [62]3 years ago

6 0

Answer:

y = -2x - 5

Step-by-step explanation:

An equation of a line in slope-intercept is y=mx + b.

x and y are points on the line.

m is the slope.

b is the y-intercept.

To find this equation, we will need to find m and b.

When lines are parallel, they have the same slope.

A line parallel to y = -2x + 3 has a slope of -2.

m = -2

To find b, substitute into the equation a point on the line (-2, -1) and m = -2.

A point is in the form (x, y). So x = -2, y = -1.

y = mx + b

-1 = (-2)(-2) + b Simplify by multiplying the (-2)(-2)

-1 = 4 + b Subtract 4 from both sides to isolate b

-5 = b

b = -5 Writing the variable on the left side is standard formatting

Since we now know the y-intercept, b= -5, and the slope, m = -2, substitute them into y=mx + b to get the equation of the line.

y = -2x - 5

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a room in a form of a cuboid has a length of 5cm, height 8cm and breadth 0.07m. if one person can occupy a volume of 14cm3(cube)

Over [174]

Answer:

20 people

Step-by-step explanation:

The volume of a cuboid is equal to length * breadth * height.

First, we want to figure out the values relative to each other. Everything is in centimeters except the breadth, which is 0.07m. To convert meters to centimeters, we can multiply by 100: 0.07 * 100 = 7, so the breadth is 7cm.

Next, the volume is length * breadth * height = 5cm * 7cm * 8cm = 280cm³. Each person occupies 14cm³. To find how many people can occupy the cube, we can divide the volume by the space each person takes, so

280cm³/14cm³ = 20 people

Note that we can divide because each person takes x amount of space, and the total space, z, can be represented by x * y = z, with y representing the amount of people, because we add x space for each person. Dividing both sides by x, we get y = z/x

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3 years ago

How many different pairs of parallel edges are there on a rectangular solid?

Monica [59]

Answer:

Step-by-step explanation:

A rectangular prism has four parallel edges along its length, four parallel edges along its width, and four parallel edges along its height.

We want to know how many different pairs of parallel edges there are. Starting with the length, the number of unique pairs is:

₄C₂ = 6

The same is true for the width and height. So the total number of different pairs of parallel edges is:

3 × 6 = 18

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