Triangle ABC has vertices of A(-6, 7), B(4, -1), and C(-2, -9). Find the length of the median from
A. 4
B. Square Root of 18
C. 8
D. Square Root of 68

Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

99°  is the measure of angle 1 by vertically opposite angles.

What is Vertically opposite angle?

Angles that cross two straight lines at a certain vertex and are vertically opposing to one another are known as vertically opposite angles. Angles that are perpendicular to one other vertically are equal. Vertical angles are another name for them.

                            On the vertical plane*, or between a low point and two higher points, a vertical angle is the angle created by two linked lines. The lines that make these angles are often lines of sight since they are located in the vertical plane.

2x + 91 = 3x + 87   (Adjacent angle )

     3x - 2x =  91 - 87

         x =  4

∠1 = 2x + 91  (vertical opposite angle )

    = 2 * 4 + 91

      = 8 + 91

       = 99°

Learn more about vertically opposite angle

brainly.com/question/18045519

#SPJ1

The correct option is A) 20.2.

What is triangle sum?

The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.

Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:

Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:

K = 180 - A - B

= 180 - 84 - 65

= 31 degrees

Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:

sin(A)/x = sin(K)/17

Substitute the values we know into the equation and solve for x:

sin(84)/x = sin(31)/17

x = sin(84)*17/sin(31)

Using a calculator, we get:

x ≈ 20.2

Therefore, the value of x in the triangle is approximately 20.2.

So, the correct option is A) 20.2.

To know more about triangle sum visit:

https://brainly.in/question/28314721

#SPJ9

Answer:

P(A) * P(B)

.25*.55

.1375

Step-by-step explanation:

P(A) * P(B)

.25*.55

Answer:

13

Step-by-step explanation:

u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .

Let the total amount of money in the account before withdrawal or deposit of funds be x

so that for every withdrawal we subtract from x and add for a deposit and equate this to the balance after withdrawal and deposits

x + 100 -125 + 24 = 27.28

x = 27.28+125-24-100

x= $28.28

Balance before deposits or withdrawal = $28.28

The volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis is 2π[e - e^1 + 1]   and the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis is πtan^2(1).

1) To find the volume of the solid generated by rotating the region bounded by the curve y = x(e^x), x = 0, x = 1, and y = 0 about the y-axis, we can use the method of cylindrical shells.

First, let's express the equation in terms of x: x = ln(y)/y. Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πx(e^x) dx.

Using integration by parts, we can evaluate this integral as follows:

V = 2π ∫[0,1] x(e^x) dx

 = 2π [x(e^x) - ∫[0,1] e^x dx]

 = 2π [x(e^x) - e^x] | [0,1]

 = 2π[(1(e^1) - e^1) - (0(e^0) - e^0)]

 = 2π[e - e^1 + 1].

2) To find the volume of the solid generated by rotating the region bounded by the curve y = arctan(x), x = 0, x = 1, and y = 0 about the y-axis, we can again use the method of cylindrical shells.

Let's express the equation in terms of x: x = tan(y). Now we can set up the integral to calculate the volume. The volume can be obtained by integrating the product of the circumference of each cylindrical shell and its height over the interval [0, 1]:

V = ∫[0,1] 2πtan(y) dy.

Using the substitution method, we can evaluate this integral as follows:

Let u = tan(y), then du = sec^2(y) dy.

When y = 0, x = tan(0) = 0, and when y = 1, x = tan(1).

Now, the integral becomes:

V = 2π ∫[0,1] u du

 = 2π [u^2/2] | [0,1]

 = 2π[(tan(1))^2/2 - 0]

 = πtan^2(1).

For more such questions on volume,click on

https://brainly.com/question/463363

#SPJ8

Answer:

The radical cannot be simplified, but it can be approximated.

Exact Form:

24

√

30

Decimal Form:

131.45341380

Step-by-step explanation:

cannot show steps right now

Answer: 45

Step-by-step explanation: the fub

Answer:

x=7 and y=3

Step-by-step explanation:

Step: Solve x−3y=−2 for x:

x−3y=−2

x−3y+3y=−2+3y(Add 3y to both sides)

x=3y−2

Step: Substitute3y−2for x in x+3y=16:

x+3y=16

3y−2+3y=16

6y−2=16(Simplify both sides of the equation)

6y−2+2=16+2(Add 2 to both sides)

6y=18

6y

6

=

18

6

(Divide both sides by 6)

y=3

Step: Substitute3foryinx=3y−2:

x=3y−2

x=(3)(3)−2

x=7(Simplify both sides of the equation)

Answer:

x=7 and y=3

Answer:

Step-by-step explanation:

2x = 14

x = 7

7 + 3y = 16

3y = 9

y = 3

(7, 3)

answer is A

Answer:

207+ 364 = 571

Step-by-step explanation:

i guess?._.

Hey there!

The answer is 72 - 2n.

"twice a number" represents a number multiplied by 2. So we have "2n"

"decreased by twice a number" would mean subtracting twice a number, or subtracting "2n".

"72 decreased by" means that we are subtracting the number FROM 72, so we get "72 - 2n".

Have a super awesome day! :)

Answer:

19.4 units

Step-by-step explanation:

The hypotenuse length (c) of the given right triangle, ∆ABC, can be calculated using the Pythagorean Theorem, \( a^2 + b^2 = c^2 \),

Where,

c is the longest/hypotenuse, a and b are the length of the other two legs.

Therefore,

\( c^2 = (16)^2 + (11)^2 \)

\( c^2 = 256 + 121 = 377 \)

\( c = \sqrt{377} = 19.4 \) (nearest tenth)

If we have to find the total number of coins then we can use the following rule:

Thus,

︎⠀⠀ ⠀⠀ ⠀⠀ ⠀︎⠀⠀ ⠀⠀ ⠀8×Total Number of Purse.

The expression for the magical coin for d days will be \(C = (3)^d\).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that A magical $1 coin that triples every day. The coin turns into three coins on the first day. The three coins turn into nine coins on the second day. The nine coins tripled to 27 coins on the third day. This doubling will continue for 28 days.

The equation can be written as,

\(C = (3)^d\)

At d = 28, the value of the coin will be,

C = (3)²⁸

C = $2.28 x 10¹³

To know more about an expression follow

https://brainly.com/question/29189142

#SPJ1

Answer:

133 m^2

Step-by-step explanation:

to find are of a circle it’s r^2 times pi

6^2 x pi

36 pi

113 m^2

Hopes this helps please mark brainliest

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 6m

Let us find the area of the circle.

A = πr²

A = 3.14 × 6 × 6

A = 113.04 m²

Approx. = 113m²

Answer:

False. The product of two negative integers is a positive integer.

Answer:

1078

Step-by-step explanation:

22 x 49 = 1078

Answer:

1,078

Step-by-step explanation:

Anytime that the word "product" is used in math, it means that you are multiplying numbers together to get your answer out of the two numbers being multiplied. For example:

"Factor x Factor = Product."

So we have: "22 x 49 = __"

Now we need to cross-multiply.

  22

x 49

  198

+ 880

1078

So, the answer is: "22 x 49 = 1,078."

I hope that this helps.

Answer:

It would be 27.328  but since it is money, we have to leave the 8 out.

So the answer is 27.32

Step-by-step explanation:

Answer:

$27.33

Step-by-step explanation:

You multiply 12.2 and 2.24 and the answer is 27.328. You then round it to the nearest tenth which is 27.33.

Answer:

13

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

So, in order to find the range, you first order the data from least to greatest. Which it is already.

3, 7, 11, 14, 16

Then subtract the smallest value from the largest value in the set.

16 - 3 = 13

Hope this helps you out! : )

Answer:

$0.25

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

For more such questions on annuity

https://brainly.com/question/25792915

#SPJ8

The volume of the composite figure is 228 ft³.

To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.

From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.

First prism:

Length = 8 ft, Width = 4 ft, Height = 6 ft

Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³

Second prism:

Length = 3 ft, Width = 2 ft, Height = 6 ft

Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³

Now, let's add the volumes of both prisms:

192 ft³ + 36 ft³ = 228 ft³

Therefore, the volume of the composite figure is 228 ft³.

for similar questions on volume.

https://brainly.com/question/463363

#SPJ8

What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft

Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³ ​

Using the z-distribution, we have that:

a)

b) Since the p-value of the test is of 0.0668 > 0.05, there is not enough evidence to conclude that the manufacturer's advertising campaign is legitimate.

Item a:

At the null hypothesis, it is tested if the mean is still of 50 miles per gallon, that is:

\(H_0: \mu = 50\)

At the alternative hypothesis, it is tested if the mean has increased, that is:

\(H_1: \mu > 50\)

Item b:

We have the standard deviation for the population, hence, the z-distribution is used to solve this question.

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

Hence, the values of the parameters are:

\(\overline{x} = 51.5, \mu = 50, \sigma = 6, n = 36\)

Hence, the value of the test statistic is:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{51.5 - 50}{\frac{6}{\sqrt{36}}}\)

\(z = 1.5\)

Using a z-distribution calculator, with a right-tailed test, as we are testing if the mean is greater than a value, with z = 1.5, the p-value is of 0.0668.

Since the p-value of the test is of 0.0668 > 0.05, there is not enough evidence to conclude that the manufacturer's advertising campaign is legitimate.

You can learn more about the use of the z-distribution to test an hypothesis at https://brainly.com/question/16313918

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Answer:

B

Step-by-step explanation:

Because all of these letters are distinct, the total number of ways to draw them is 4!, or 24.

Another way you can do this is by discerning the number of ways the individual numbers can be drawn. In the beginning, there are 4 letters to pick. If you pick a letter out, you now have 3 letters to pick. If you pick a letter out, you now have 2 letters to pick. After, you only have 1 letter to pick. 4 * 3 * 2 * 1 = 24.

Answer:

C

Step-by-step explanation:

I think it's C, 4 * 3 * 2 * 1 = 24

Answer:quadratic parent function

Step-by-step explanation: