All categories

1 year ago

Which of

Mathematics

1 answer:

Kobotan [32]1 year ago

6 0

Answer:

Step-by-step explanation:

The mean of a data set is described as the sum of the data values divided by the total number of data values.

You might be interested in

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Suppose y = 2x +10. Find y if x = -2.

liubo4ka [24]

If x = -2, y = 6.

To solve this quesiton, we need to find the value of y if x is equal to -2. We can do this by substiuting the value of x and then solving.

y = 2 (-2) + 10

y = -4 + 10

y = 6

5 0

3 years ago

Read 2 more answers

Using the Laws of exponents, simplify the following problem.

den301095 [7]

$\frac{4 {}^{4} }{ {4}^{ - 8} ({4}^{ - 14}) } = \frac{4 {}^{4} }{ {4}^{ - 22 } }$

(4^4)/(4^-22)
4^(4-(-22))
4^26

Follow my Account.

7 0

3 years ago

PLS I NEED HELP I NEED DEM SMART PEOPLE. A sweater is on sale for 65% of the original price of $35. Calculate the sale price

zheka24 [161]

Answer:

your answer is 100 <3 have a nice day

Step-by-step explanation:

7 0

3 years ago

What is the slope of the line represented by the equation 6y-14x=5

ioda

Answer:

slope = $\frac{7}{3}$

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 )

rearrange 6y - 14x = 5 into this form

add 14x to both sides

6y = 14x + 5 ( divide all terms by 6 )

y = $\frac{14}{6}$ x + $\frac{5}{6}$ ← in slope- intercept form

with slope m = $\frac{7}{3}$ ← in simplest form

7 0

2 years ago