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2 years ago

Which pairs of angles in the figure below are vertical angles?

Mathematics

1 answer:

ch4aika [34]2 years ago

6 0

Answer: Option A and Option C.

Step-by-step explanation:

For this exercise it is important to know the definition of "Vertical Angles".

When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".

By definition, Vertical angles are congruent, which means that the have the equal measure.

In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.

You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:

$\angle ISN$ and $\angle TSW$

$\angle TSN$ and $\angle ISW$

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Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

$P(t) = 0.8t^{2} + 6t + 19000$

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

$P(t) = 0.8t^{2} + 6t + 19000$

$0.8t^{2} + 6t + 19000 = 34200$

$0.8t^{2} + 6t - 15200 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$0.8t^{2} + 6t - 15200 = 0$

So $a = 0.8, b = 6, c = -15200$

Then

$\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356$

$t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14$

$t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64$

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

6 0

2 years ago

What is the value of z in the equation 3z - 7 = 14

Arte-miy333 [17]

This is simply solving an equation...

You do this...

3x-7=14
+7 +7
---------------
3z=21
--- ----
3 3

z=7
hope this helped! Give me a 5-rate and a thanks if so!

6 0

2 years ago

On a map, Cary drew a set of coordinate axes. He noticed that the town of Coyner is located at the point (3, 1) and Woottonville

sp2606 [1]

Answer:

The coordinates of the school should be at (10.5 , 4.25)

Step-by-step explanation:

We are dealing with two points here on a plane. These are:

Town of Coyner, Point A(3,1)

town of Coyner, Point B (18, 7.5)

in coordinate geometry, to get the mid point of two points we simply use the formula:

$(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})$

where x and y are the first and second points respectively

applying this formula, we have that

the mid point of the two towns is

$(\frac{3+18}{2}, \frac{1+7.5}{2})=(10.5 , 4.25)$

Hence the coordinates of the school should be at (10.5 , 4.25)

4 0

2 years ago

Marika is training for a race track. she starts by sprinting 100 yards. she gradually increases her distance, adding 4 yards a d

iren2701 [21]

Answer: the correct answer is D.

Step-by-step explanation:

4 0

2 years ago

In a production process, the diameter measures of manufactured o-ring gaskets are known to be normally distributed with a mean d

Art [367]

Answer:

DIRECT WAY EXCEL

"=NORM.DIST(75,80,3,TRUE)"

And we got: $P(X\leq 75)= 0.04779$

OTHER WAY

$P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z$

And we can find this probability using the normal standard table or excel:

$P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

$X \sim N(80,3)$

Where $\mu=80$ and $\sigma=3$

And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:

$P(X\leq 75)$

One way to do this in excel is with the following formula:

"=NORM.DIST(75,80,3,TRUE)"

And we got: $P(X\leq 75)= 0.04779$

And the other way is use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z$

And we can find this probability using the normal standard table or excel:

$P(Z$

3 0

2 years ago