In the middle of a test <br> Please answer!

Find the value of x that makes the equation true:

vazorg [7]

16 - x = 4
16 - 12 = 4
x = 12

5 0

2 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

2 years ago

Read 2 more answers

Which equation has solution x = -3? *

Alex73 [517]

Answer:

1/2(2x-6)= -6

Step-by-step explanation:

Multiply the two sides by the equation 2

2x-6=12

move the constant to the right hand side change sign

2x = -12 + 6

calculate the sum

2x= -6

Divide the 2 sides by 2

x= -3

8 0

2 years ago

THE SHINKANSEN PASSENGER TRAIN OF JAPAN TRAVELS AT A RATE

OlgaM077 [116]

Answer:

srry need points

Step-by-step explanation:

r u sure thats college work

8 0

3 years ago

F(x) = 2x^2 − 3x − 5 Part

riadik2000 [5.3K]

Answer: Answer is in the steps..

Step-by-step explanation:

f(x)= $2x^{2}$ - 3x -5

A) To find the x intercepts of a parabola we have to set the whole equation equal zero because the x intercept is when y equal zero in other words where f(x) equal zero.

$2x^{2}$ - 3x - 5 = 0 Now solve using quadratic formula.

x = -b± $\frac{\sqrt{b^2 -4ac } }{2a}$

x = 3 ± $\sqrt{9+40} /2a$

x = 3 ± $\sqrt{49}$ / 2a

x= 3 ± 7 /4

x= -1 or x = 5/2

The x intercepts are (5/2,0) and (-1,0)

B) The graph vertex of the graph of f(x) is going to be at a minimum because the leading coefficient of the function has a positive integer which means the parabola will open up and its vertex will be at the minimum point.

Using the x coordinates we could find their average and find the x coordinate of the vertex.

$\frac{5}{2} + -\frac{1}{1}$ = $\frac{3}{2} / \frac{2}{1}$ = 3/4

The x coordinate of the vertex is 3/4 so we will input that into the equation and solve for the y coordinate

$2(\frac{3}{4})^2 - 3 (\frac{3}{4}) - 5$ = 18/16 - 9/4 -5 = -49/8

The y coordinate of the vertex is -49/8

So the vertex is (3/4, -49/8)

C) First I will graph the vertex and then graph he two x intercepts and connect then like a U shape.

5 0

3 years ago

In the middle of a test Please answer!