Find x the missing side length of the triangle

Answer:

[tex]Q = 96.4^\circ[/tex]

[tex]R = 58.4[/tex]

[tex]P =25.2[/tex]

Step-by-step explanation:

Given

See attachment for PQR

Required

Solve the triangle

From the attached triangle, all sidea of the triangle are known.

i.e.

[tex]PQ = 6\\QR=3\\PR=7[/tex]

So, we are to solve for [tex]\angle P, Q \& R[/tex]

Using cosine rule:

[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]

To solve for Q, we have:

[tex]PR^2 = PQ^2 + QR^2 - 2 * PQ * QR Cos(Q)[/tex]

[tex]7^2 = 6^2 + 3^2 - 2 * 6 * 3 * \cos(Q)[/tex]

[tex]49 = 36 + 9 - 36 * \cos(Q)[/tex]

Collect like terms

[tex]49 - 36 - 9 = - 36 * \cos(Q)[/tex]

[tex]4 = - 36 * \cos(Q)[/tex]

Divide both sides by -36

[tex]\cos(Q) = \frac{-4}{36}[/tex]

[tex]\cos(Q) = -0.1111[/tex]

Take arc cos of both sides

[tex]Q = cos^{-1}(0.1111)[/tex]

[tex]Q = 96.4^\circ[/tex]

To solve for R, we make use of sine rule;

[tex]\frac{a}{\sin A} = \frac{b}{\sin B}[/tex]

So, we have:

[tex]\frac{PQ}{\sin R} = \frac{PR}{\sin Q}[/tex]

[tex]\frac{6}{\sin R} = \frac{7}{\sin 96.4}[/tex]

Cross multiply

[tex]\sin R * 7 = 6 * \sin 96.4[/tex]

Solve for sin R

[tex]\sin R = \frac{6 * \sin 96.4}{7}[/tex]

[tex]\sin R = \frac{6 * \0.9938}{7}[/tex]

[tex]\sin R = 0.8518[/tex]

Take arc sin of both sides

[tex]R = sin^{-1}(0.8518)[/tex]

[tex]R = 58.4[/tex]

Solving P:

[tex]P+ Q + R = 180[/tex] --- angles in a triangle

Solve for P

[tex]P =180-Q-R[/tex]

[tex]P =180-96.4-58.4[/tex]

[tex]P =25.2[/tex]

r = 1/15

a branliest from the answer will be appreciated

Step-by-step explanation:

1/x-9= 6

cross multiply

1= 6×{x-9}

1= 6x - 54

collect like terms

1+54= 6x

55= 6x

x= 55/6 or 9.1667

Answer:

I think it's mean, range, median, and outlier

Answer:

range,mode and median I think hehehe

Answer:

I graphed it for you in the image below.

Step-by-step explanation:

Graph the logarithmic function f(x) = log2(x - 1) + 2 is attached below.

The function is referred to as a particular kind of relationship, every value in the domain is associated with exactly one value in the range. They have a set perimeter and territory.

It is given that the logarithmic function is, f(x) = log2(x - 1) + 2.

The first step in graphing a logarithmic function is to locate some points on the exponential f. (x). The graph will look better as we plot more points, and we can flip the x and y values to get points on the opposite axis. locate the asymptote. The following logarithmic functions can be graphed. Specify the domain and the range.

Thus, the graph is attached below.

Learn more about the function here:

brainly.com/question/5245372

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Answer:

C

Step-by-step explanation:

hope this helps

Answer:

The radius is 6

[tex] \sqrt{v \div \pi \times h =} [/tex]

=791.28/3.14×7.0

=

[tex] \sqrt{36} [/tex]

=6

The radius of cylinder is 3.764 cm.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us determine how much material is needed to fill it, such as how much water is needed to fill a bottle, aquarium, or water tank.

Given volume of cylinder = 791.28 cm³

height  = 7.0 inches

so, 1 inch  = 2.54 cm

7 inch  = 2.54 x 7 = 17.78 cm

height  = h = 17.78 cm

volume of cylinder = πr²h

where r = radius

V = πr²h

791.28 = 3.14(17.78)r²

r² = 791.28/55.8292

r² = 14.1732

r = √14.17732

r  = 3.764 cm

Hence the radius  is 3.764 cm.

Learn more about volume;

https://brainly.com/question/1578538

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Answer:

48

Step-by-step explanation:

by parallel laws

132 + x = 180

x = 48

so x must be 48

Answer:The mean absolute deviation (MAD) of the number of pages in the 5 books Rori read =24

Step-by-step explanation:

To find the the mean absolute deviation (MAD,we start firt by

Getting  the mean of all values

Mean =120, 106, 94, 100, 180/5  =600/5=120

Next we subtract the mean value  from each value which is called distance

120 -120  = 0

106 -120 = -14

94 -120=  -26

100 -120=-20

180 -120=60

Thirldly, we find the mean of the distances  ignoring the negative signs

0+14+26+20+60 / 5 = 120/5=24

Answer:

2: 45     3: 45   4: 135    5: 135   6: 45   7: 45

Step-by-step explanation:

they are vertical angles meaning they will mirror each other, subract 135 from 180 and you will get the other angle

Answer:

3x-2

Step-by-step explanation:

12x-8/4 = 3x-2 is one side length of a square

Answer:

3, 4, 5

5, 12, 13

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

[tex]\cos x + \sqrt{3} = -\cos x\\2\cos x = -\sqrt{3}\\\cos x =-\frac{\sqrt{3}}{2}\\x=\frac{\pi}{6}[/tex]

(the other solutions can be obtained by adding 2pi as many times as you want)

Answer:

9.1m

Step-by-step explanation:

h = V ÷ l w = 819 ÷ (10 × 9) = 9.1m

Have a good day

Answer:

It would be B. 3.5 Pints.

Step-by-step explanation:

x, x+10

5(x+10)=40+6x

5x+50=40+6x

x=10

and the other number is x+10

Hence teh numbers are 10,20

Step-by-step explanation:

The measures of variability is blank, the number that best summarizes the data is blank, and the number that best describes how the data varies is blank

Please send the box plot, I can solve it then but there is not enough info right here. Sorry!

Answer:

549.5

Step-by-step explanation:

For a estimate of pi we use 3.14. So 3.14x5x5x7=549.5

For a realistic answer its 549.778714378.....

Answer:

x = 2 and -4

Step-by-step explanation:

(x + 1)² = 9

First, take the square root of both sides. This will eliminate the square on the left side.

(x + 1) = √9

Note that √9 can be 3 or -3.

Let's write out both possibilities.

(x + 1) = 3

(x + 1) = -3

Solve.

(x + 1) = 3

[subtract 1 from both sides]

x = 2

--

(x + 1) = -3

[subtract 1 from both sides]

x = -4

Your answers are 2 and -4.

Let's check our answers by plugging in the values back into the original equation.

(x + 1)² = 9

(2 + 1)² = 9

(3)² = 9

9 = 9

That solution is correct.

(x + 1)² = 9

(-4 + 1)² = 9

(-3)² = 9

9 = 9

That solution is also correct.

Your answer is correct.

Hope this helps!

Answer:

Exponential decay

Step-by-step explanation:

Because the values are exponentially decreasing.

Answer:

Steps:

600 - 480 = 120

100(120/480) = 25

Answer:

increase in percentage = 25%

Step-by-step explanation:

here's your solution

==> Total number of students last year = 480

==> Number of students this year = 600

==> Number of increased students = 600 - 480

= 120 students

==> now , in percentage = (120/480)*100

==> percentage increase = 25%

hope it helps

Answer:

son consonantes

guíate por esto.

La rima asonante se caracteriza porque solo coinciden los sonidos vocálicos en la última sílaba de cada verso, mientras que la rima consonante es aquella donde coinciden tanto vocales como consonante.

Answer:

The vertex angle is 94 degrees

Step-by-step explanation:

Let the vertex angle be x

Mathematically, the base angles of an isosceles triangle are the same

So if one of the base angles is 43 degrees, then the other base angle would be 43 degrees too

Mathematically, the sum of angles in a triangle is 180 degrees

Thus;

43 + 43 + x = 180

x = 180-86

x = 94 degrees

Answer:

Each Interior Polygon angle = 180 - [ 360 / number of sides]

Each Angle = 180 - [ 360 / 10]

Each Angle = 180 - 36

Each Angle = 144 degrees  

Source http://www.1728.org/polygon.htm

Step-by-step explanation:

Answer:

408.3%

Step-by-step explanation:

the answer is  224 im pretty sure hope this helps

9514 1404 393

Explanation:

(a) Keep in mind the meaning of the variables:

With these definitions in mind, we can examine the constraints.

  x ≥ 0 . . . . . we cannot sell a negative number of PS4 units

  y ≥ 0 . . . . . we cannot sell a negative number of X.box 1 units

  y ≥ 5 . . . . . we intend to sell at least 5 X.box 1 units

  y ≤ 10 . . . . we cannot sell more than 10 X.box 1 units

  x + y ≤ 10 . . . . . we can sell at most 10 units total

(Please note that the constraints y ≥ 0 and y ≤ 10 are redundant to other more restrictive conditions.)

__

(b) The objective function tells us the total profit:

  P(x, y) = 100x + 80y

__

(c) Juan's goal: P(2, 7) = 100(2) +80(7) = 200 +560 = 760

  Justin's goal: P(4, 5) = 100(4) +80(5) = 400 +400 = 800

Meeting Justin's goal would result in more profit.

__

(d) It is not possible to sell a negative number of units*, so negative values for the variables do not make any sense. (This is consistent with the x≥0, y≥0 constraints above.)

_____

* Some linear programming problems plan for a certain number of returned items. Those could be considered to be negative sales.