Two sides of a triangle are 5 and 10. Which is a<br> possible length for the third side?

Consider the graph of the line y = x – 4 and the point (−4, 2).

Hitman42 [59]

Answer:

a. The slope of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

a. For the line $y = x - 4$

You can identify that:

$m=1$

By definition, two lines are parallel if they have the same slope. Then, the slope of a line parallel to the given line is:

$m=1$

b. The equation of the line in Point-slope form is:

$y -y_1 = m(x - x_1)$

Where m is the slope and ( $x_1,y_1$ ) is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

$y -2 = (x +4)$

Give a value to "x", substitute it into this equation and solve for "y":

For $x=1$ :

$y -2 = (1 +4)$

$y= 5+2$

$y= 7$

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the slope of a line perpendicular to the given line is:

$m=-\frac{1}{1}\\\\m=-1$

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

$y -2 = -1(x +4)$

$y -2 = -(x +4)$

Give a value to "x", substitute it into this equation and solve for "y":

For $x=3$ :

$y -2 = -(3 +4)$

$y= -7+2$

$y= -5$

Then, you get the point (3,-5)

8 0

3 years ago

Complete the following statements.

stiv31 [10]

Answer:

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains 67.62 fluid ounces of liquid.

The soda bottle contains 0.525 gallons of liquid.

2) A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains 8 quarts of milk.

The milk jug contains 7.6 liters of milk.

Step-by-step explanation:

We need to complete the statements.

1)

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains ------- fluid ounces of liquid.

Converting Liters to fluid ounces

We know that 1 liter = 33.81 fluid ounces

So, 2 liter = 2 x 33.81 = 67.62 fluid ounces

The soda bottle contains 67.62 fluid ounces of liquid.

The soda bottle contains gallons of liquid.

Converting liters to gallons

As, we are not given direct conversion from liters to gallons, first we convert liter to quarts and then convert quarts to gallons

We know that

1 liter = 1.05 quarts

2 liters = 2 x 1.05 = 2.1 quarts

4 quarts = 1 gallon

1 quarts = 1/4 gallon

2.1 quarts = 1/4 * 2.1 = 0.525 gallon

The soda bottle contains 0.525 gallons of liquid.

2)

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains -------- quarts of milk.

Converting gallons to quarts

We know:

1 gallon = 4 quarts

2 gallons = 2 x 4 = 8 quarts

The milk jug contains 8 quarts of milk.

The milk jug contains ------ liters of milk.

Converting gallons to liters

We know:

1 gallon = 4 quarts

2 gallon = 8 quarts

1.05 quarts = 1 liter

1 quarts = 1/1.05 liter

8 quarts = 1/1.05 * 8 = 7.6 liter

The milk jug contains 7.6 liters of milk.

6 0

2 years ago

If the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle???? First corre

kogti [31]

The supplement of 30° is the angle that when added to 30° forms a straight angle (180° ).

8 0

2 years ago

2(y-4)+5=3(y+2) for y

brilliants [131]

2(y-4)+5=3(y+2)

multiply the first bracket by 2

(2)(y)=2y

(2)(-4)=-8

multiply the second bracket by 3

(3)(y)=3y

(3)(2)=6

2y-8+5=3y+6

2y-3=3y+6

move 3y to the other side

sign changes from +3y to -3y

2y-3y-3=3y-3y+6

-y-3=6

move -3 to the other side

-y-3+3=6+3

-y=9

multiply both sides by -1 to get +y

(-1)(-y)=9(-1)

Answer:

y=-9

3 0

3 years ago

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grandymaker [24]

Answer:

Step-by-step explanation:

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5 0

3 years ago

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Two sides of a triangle are 5 and 10. Which is a possible length for the third side?