How do I solve this problem?

Answer:

[tex]A = 74.7^\circ[/tex]

[tex]B = 42.5^\circ[/tex]

[tex]C = 62.8^\circ[/tex]

Step-by-step explanation:

Given

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]

For AB

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]d = \sqrt{(-1 - 2)^2 + (2 - 8)^2[/tex]

[tex]d = \sqrt{(-3)^2 + (-6)^2[/tex]

[tex]d = \sqrt{45[/tex]

So:

[tex]AB = \sqrt{45[/tex]

For BC

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]BC = \sqrt{(2 - 4)^2 + (8 - 1)^2[/tex]

[tex]BC = \sqrt{(-2)^2 + (7)^2[/tex]

[tex]BC = \sqrt{53[/tex]

For AC

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2[/tex]

[tex]AC = \sqrt{(-5)^2 + (1)^2[/tex]

[tex]AC = \sqrt{26[/tex]

So, we have:

[tex]AB = \sqrt{45[/tex]

[tex]BC = \sqrt{53[/tex]

[tex]AC = \sqrt{26[/tex]

By representation

[tex]AB \to c[/tex]

[tex]BC \to a[/tex]

[tex]AC \to b[/tex]

So, we have:

[tex]a = \sqrt{53[/tex]

[tex]b = \sqrt{26[/tex]

[tex]c = \sqrt{45[/tex]

By cosine laws, the angles are calculated using:

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex]c^2 = a^2 + b^2 -2ab\ cos C[/tex]

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex](\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A[/tex]

[tex]53 = 26 +45 - 2 * 34.21 * \cos A[/tex]

[tex]53 = 26 +45 - 68.42 * \cos A[/tex]

Collect like terms

[tex]53 - 26 -45 = - 68.42 * \cos A[/tex]

[tex]-18 = - 68.42 * \cos A[/tex]

Solve for [tex]\cos A[/tex]

[tex]\cos A =\frac{-18}{-68.42}[/tex]

[tex]\cos A =0.2631[/tex]

Take arc cos of both sides

[tex]A =\cos^{-1}(0.2631)[/tex]

[tex]A = 74.7^\circ[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex](\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B[/tex]

[tex]26 = 53 +45 -97.67 * \cos B[/tex]

Collect like terms

[tex]26 - 53 -45= -97.67 * \cos B[/tex]

[tex]-72= -97.67 * \cos B[/tex]

Solve for [tex]\cos B[/tex]

[tex]\cos B = \frac{-72}{-97.67}[/tex]

[tex]\cos B = 0.7372[/tex]

Take arc cos of both sides

[tex]B = \cos^{-1}(0.7372)[/tex]

[tex]B = 42.5^\circ[/tex]

For the third angle, we use:

[tex]A + B + C = 180[/tex] --- angles in a triangle

Make C the subject

[tex]C = 180 - A -B[/tex]

[tex]C = 180 - 74.7 -42.5[/tex]

[tex]C = 62.8^\circ[/tex]

Answer:

75

Step-by-step explanation:

Answer:

75,000,000

Step-by-step explanation:

first what we do is we do 10^5 which could also be seen as

10*10*10*10*10=100,000

now we times that by 3

100,000*3=300,000

and now divide by 4

300,000÷4=75,000

now times 75,000 by 10^3 (10*10*10=1,000)

75,000*1,000=

75,000,000

75,000,000 is your answer

Answer:

please dont use the r slur :)) and if you care so much about your grades, heres an idea!! study on your OWN and dont rely on others

Step-by-step explanation:

Answer:

A cylinder

Step-by-step explanation:

When you rotate the rectangle you are make a circle but since its volume the original height of the rectangle is the height of the circle which would mean a cylinder.

Answer:

CYLINDER

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

hope this helps with the problem

Answer:

3

Step-by-step explanation:

Answer:

2 tickets

Step-by-step explanation:

a + c = 5

9a + 4c = 30

let a = 5-c

substitute:

9(5-c) + 4c = 30

45 - 9c + 4c = 30

45 - 5c = 30

-5c = -15

c = 3

a = 2

Answer:

x = 2

4 x 4 = 16

25% of 16 = 4

2 x 2 = 4

i chose 2 bc i said it x -= 25% of the larger squares area meaning it would be 2

Step-by-step explanation:

Answer:

960 cm³ I think it may be correct

Answer:

C

Step-by-step explanation:

I believe the answer would be C because its the only actual line on a graph.

A Is a line segment

D is a ray

(I'm not sure what the exact name for the one on graph B is.)

Answer:

the answer ic C!

Step-by-step explanation:

AP EX

Answer:

The probability of choosing 3 kings and 4 queens out of the 8 (4+4) kings and queens is given by 0.42857

Step-by-step explanation:

There are 4 queens and 4 kings in a deck of 52 cards. So we have to choose 5 cards having 3 queens and 2 kings out of the 52

Therefore the combinations can be written like this 8C5= 56 ways

And the probability this can be chosen is  given by

4C3*4C2/8C5

=4*6/56

=24/56

=0.42857

The probability of choosing 2 kings and 3 queens out of the 8 (4+4) kings and queens is given by 0.42857 or 24/56

Complete question :

One gallon of gasoline in buffalo, New York costs $2.29. In Toronto, Canada, one liter of gas costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto?

Answer:

$3.458

Step-by-step explanation:

Given that :

Cost per gallon in Buffalo, New York = $2.29

Cost per Litre in Toronto, Canada = $0.91

Number of litres in 1 gallon = 3.8

The cost per gallon in Toronto, Canada will be :

3.8 * cost of a Litre

3.8 * $0.91 = $3.458

Hence, cost of a gallon in Toronto, Canada = $2.73

Answer:

4. H0: u1= u2    Ha; u1≠ u2

5. The smaller value of p supports the null hypothesis.

Step-by-step explanation:

4. The null and alternate hypotheses are

H0: u1= u2   i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

Ha; u1≠ u2   i.e there a difference between the mean pinch strengthof the two surgeries

It can be written like this as well

H0: u1 -u2= 0   i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

Ha; u1 -u2≠ 0   i.e there a difference between the mean pinch strengthof the two surgeries

Part 5. The test having a p- value less than 0.05  tells that the null hypothesis cannot be rejected. Theres no evidence to reject the null hypothesis.

The smaller value of p supports the null hypothesis.

Answer:

-6 2/3

Step-by-step explanation:

Answer:

I belive the answer for the first box is 9.67

I belive the answer for the second box is 71.

I hope I helped

Answer:

30

Step-by-step explanation:

First, you have to convert 20% into a decimal.

Explanation:

20 ÷ 100 = 0.2

Now multiply 0.2 by 150

Explanation:

0.2 × 150 = 30.

Therefore, 20% of 150 is 30.

Answer:

-7 and - 9

Step-by-step explanation:

Area of rectangule is length *width

==========================================================

Explanation:

Pick any term that isn't the first term. Then subtract off the previous term. If we get the same result each time, then the sequence is arithmetic, and that result is the common difference.

We get -8 each time, so the sequence is arithmetic with common difference d = -8. It says to add -8 to each term to get the next term. This is the same as subtracting 8 from each term to get the next term.

Note how:

Answer:(1,2)

Step-by-step explanation:

The image of point P = (2, -1) is (1, 2)

For given question,

We have been given a point P = (2, -1)

We know that if point (x, y) is rotated 90 degrees counterclockwise about the origin then the coordinates of image is (-y, x)

So, when point P is rotated 90 degrees counterclockwise about the origin then the coordinates of the image would be (-(-1), 2) = (1, 2)

Therefore, the image of point P is (1, 2)

Learn more about the rotation transformation here:

https://brainly.com/question/12865301

#SPJ2

Answer:

72 and -2

Step-by-step explanation:

x - y = 74

2x + 3y = 138

x - y = 74

y = x - 74

2x + 3(x - 74) = 138

2x + 3x - 222 = 138

5x = 360

x = 72

x - y = 74

72 - y = 74

-y = 2

y = -2

Answer:

a. 4.00

b. 3.00

I hope this helps

Answer:

Amaya is wrong.

Step-by-step explanation:

The perimeter of the square is 20 inches, which means each side of the square needs to add up to 20 inches. If the side length of that side Amaya pointed out is 4 inches, then the total perimeter would only be 18 inches, in another case, if they were talking about the area of the square/rectangle (now), it would be 20 inches. So, Amaya is wrong.

Not sure if I'm right but I think it's 3(x - 6) (x^2 + 5x)

Step-by-step explanation:

3x^3 - 3x^2 - 90x

Apply GCF: 3 (x^3 - x^2 - 30)

Split 30 into -6 and 5

(x^3 - 6x^2) (5x^2 - 30x)

GCF of both: x^2 (x - 6) and 5x (x - 6)

DON'T FORGET TO CARRY THE 3

And your answer is 3 (x - 6) (x^2 + 5x)

Answer:

x = 4/5

FILLER FILLER FILLER

Answer:

z = 20 , x = 5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

hi

Equation which describe relationship between total cost and number of t-shirt is    [tex]c(t)=75.93e^{0.06t}[/tex].

Data given are ,

Number of t-shirt (t)                  total cost c(t)

12                                            156

17                                             211

22                                            266

According to above table, exponential function best describes the relationship between the total cost, c(t), and the number of T-shirts, t.

Let,        [tex]c(t)=Ae^{kt}[/tex]

Substitute ,   t=12  and c(t) = 156

We get,     [tex]156=Ae^{12k}.......(1)[/tex]

Substitute ,  t=17 and c(t) = 211

We get,     [tex]211=Ae^{17k} ........(2)[/tex]

After solving above equations.

We get,    A = 75.93  and  k = 0.06

Thus,     [tex]c(t)=75.93e^{0.06t}[/tex]

Learn more:

https://brainly.com/question/12626186

Answer:

[tex]x = \frac{50 + 92}{2} = 71[/tex]

Answer:

Step-by-step explanation:

c circle