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3 years ago

How many people in the survey worked on Election Day?

Mathematics

1 answer:

Lelechka [254]3 years ago

8 0

69 I’m pretty sure don’t get me wrong

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Solve for x. x= In e x=

IgorLugansk [536]

Good morning ☕️

Answer:

x = 1

Step-by-step explanation:

since the function ln is the inverse of the function exponential then :

$ln(e )=lne^{1} = 1$

3 0

3 years ago

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

A cone has a slant height of 17cm and a base radius of 8cm. How high is the cone?

Orlov [11]

Answer:disuxysidux

Step-by-step explanation:suussususu

7 0

2 years ago

Circle theorem - easy work

makvit [3.9K]

Angle in a semi circle is 90°
<a = 180-90-<b = 90-28 = 62°

opposite angles of a cyclic quadrilateral sums up to 180°
<b + <a = 180
<b = 180-62
<b = 118°

8 0

3 years ago

G(x) = 4x + 2

mojhsa [17]

Answer:

$4x \times 2x + 4x \times 5 + 2 \times 2x + 2 \times 5 = 8x {}^{2} + 24x + 10$

6 0

3 years ago