All categories

4 years ago

If line t is a transversal of lines l and m, name the angle relationship of the given angle pairs.

Mathematics

1 answer:

Ghella [55]4 years ago

8 0

Answer:

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and they are supplementary(sum=180°).

Step-by-step explanation:

Given:

Line $l\parallel m$

Line $t$ is traversal.

By angle properties we can name the angle relationship of given angle pairs.

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and thus they are supplementary.

You might be interested in

Kevin and is father have collected 1,456 different coins over the years. They have a coin album that holds 3 coins on a page. If

quester [9]

Answer:

486 pages

Step-by-step explanation:

1456/3 = 485.33333333, but you have to round up so 486

3 0

3 years ago

A 10-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

Alex777 [14]

Answer:

The area is changing at 15.75 square feet per second.

Step-by-step explanation:

The triangle between the wall, the ground, and the ladder has the following dimensions:

H: is the length of the ladder (hypotenuse) = 10 ft

B: is the distance between the wall and the ladder (base) = 6 ft

L: the length of the wall (height of the triangle) =?

dB/dt = is the variation of the base of the triangle = 9 ft/s

First, we need to find the other side of the triangle:

$H^{2} = B^{2} + L^{2}$

$L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}}$

Now, the area (A) of the triangle is:

$A = \frac{BL}{2}$

Hence, the rate of change of the area is given by:

$\frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}]$

$\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}]$

$\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}]$

$\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9]$

$\frac{dA}{dt} = 15.75 ft^{2}/s$

Therefore, the area is changing at 15.75 square feet per second.

I hope it helps you!

5 0

3 years ago

A car travels 17 miles on one gallon of gas.

ehidna [41]

Answer:

$y$ ranges from 2890 miles to 5780 miles.

Step-by-step explanation:

Let us call $y$ the number of miles the car travels, and $x$ the number of gallons of gas that are used, then we have the relationship

$y=17x$ <em>(this says the car travels 17 miles for each gallon of gas).</em>

Now, when $x=170$ , we have

$y=17(170)$

$y=2890\: miles$

and when $x=340$ , we have

$y=17(340)$

$y=5780\:miles$

So, when $x$ goes from 170 to 340, $y$ goes from $2890$ to $5780$ .

Therefore, when $x$ ranges from 170 to 340 gallons, the distance traveled ranges from 2890 to 5780 miles.

5 0

3 years ago

A line is parallel to y = 3x - 12 and

olya-2409 [2.1K]

Answer:

y = 3x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 12 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (1, - 2 ) into the partial equation

- 2 = 3 + c ⇒ c = - 2 - 3 = - 5

y = 3x - 5 ← equation of parallel line

3 0

2 years ago

I NEED HELP ASAP BEFORE MARCH 26th <br> Find the Value of X

leva [86]

Answer:

Step-by-step explanation:

90+45=135 180-135 is 45

7 0

3 years ago