I need to simplify #4

The figure below shows segments PQ and RS which intersect at point t. Segment PR is parallel to segment SQ.

professor190 [17]

Answer:

C

Step-by-step explanation:

Anything that says congruent line segments using this figure is incorrect. There are no givens that indicate any congruency of segments. So both A and B are incorrect.

PRT and QTS are vertically opposite and are equal. All vertically opposite angles are equal to the angle across from them. C must be your answer.

PRT might Be equal to QTS. Most of the time this will not be true. D is not universally the answer.

4 0

3 years ago

The following week the company was hired for a 225 mile move. If each truck traveled at hte same speed it has the previous week

iogann1982 [59]

I added a screenshot of the original question.

Now, first we will need to calculate the speed of each truck and then get the time that each of them will take to travel the 225 miles.
The basic rule that we will use for this question is:
velocity = distance / time

Part (a): getting the velocity of each truck:
For the large truck:
We are given that the truck took 4 hours to travel 180 miles. Therefore:
velocity of large truck = 180 / 4 = 45 miles/hour

For the small truck:
We are given that the truck took 3 hours to travel the same 180 miles. Therefore:
velocity of small truck = 180 / 3 = 60 miles/hour

Part (b): getting the time required for each truck to travel 225 miles:
For the large truck:
We have the distance = 225 miles and the velocity = 45 miles/hour. Therefore:
velocity = distance / time
time = distance / velocity = 225 / 45 = 5 hours

For the small truck:
We have the distance = 225 miles and the velocity = 60 miles/hour. Therefore:
velocity = distance / time
time = distance / velocity = 225 / 60 = 3.75 hours

8 0

3 years ago

Mr. Bernstein owns 11 paintings, but has only enough wall space in his home to display five of

SpyIntel [72]

Answer:

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?

Step-by-step explanation:

4 0

3 years ago

Find an equation of the circle that has center (-4,3) and passes through (6,-4).

kumpel [21]

Answer:

$(x+4)^2+(y-3)^2=149$

Step-by-step explanation:

The equation of a circle is $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center of the circle and $r$ is the radius of the circle.

Given that $(h,k)\rightarrow(-4,3)$ and it passes $(6,-4)$ , their distance between each other must the radius of the circle, so we can use the distance formula to find the radius:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(-4-3)^2+(6-(-4))^2}\\\\d=\sqrt{(-7)^2+10^2}\\\\d=\sqrt{49+100}\\\\d=\sqrt{149}$

Therefore, if the length of the radius is $r=\sqrt{149}$ units, then $r^2=149$ , making the final equation of the circle $(x+4)^2+(y-3)^2=149$

5 0

3 years ago

Use the graph of y = csc x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true. (Enter your answers as a comma-

Zina [86]

Cosecant (csc) is defined as the reciprocal of sine, therefore:
$y = cscx \\
y = \frac{1}{sinx}$ .

1/sinx will be undefined when the denominator sinx = 0.

Recalling the unit circle, sinx = 0 at x = 0 ± πn, where n is an integer.

Since the domain x is restricted from (0, 2π), we only consider the values x = 0, x = π, and x = 2π.

Therefore in the domain 0 ≤ x ≤ 2π, y = csc(x) will be undefined at x = 0, x = π, and x = 2π.

3 0

4 years ago