what is the angle of x

Answer: The value of [tex]\angle B[/tex] is [tex]30^o[/tex], the length of BC and AC is 28 units and 25 units respectively.

Step-by-step explanation:

To calculate the value of each part of the triangle, we use:

1) Angle sum property

2) Law of sines

Starting with 1:

Calculating [tex]\angle B[/tex] by angle sum property:

[tex]\angle A+\angle B+\angle C=180^o\\\\34^o+\angle B+116^o=180^o\\\\\angle B=(180^o-116^o-34^o)=30^o[/tex]

Applying 2:

The Law of sines relates the length of the side with the sines of the angle opposite to it.

[tex]\frac{\sin 34^o}{BC}=\frac{\sin 116^o}{45}\\\\BC=\frac{\sin 34^o\times 45}{\sin 116^o}\\\\BC=28units[/tex]

Similarly,

[tex]\frac{\sin 30^o}{AC}=\frac{\sin 116^o}{45}\\\\AC=\frac{\sin 30^o\times 45}{\sin 116^o}\\\\AC=25units[/tex]

Hence, the value of [tex]\angle B[/tex] is [tex]30^o[/tex], the length of BC and AC is 28 units and 25 units respectively.

Answer:

C

Step-by-step explanation:

In quadrilateral PQRS, ∠P and ∠S are opposite angles is false statement. Option c is correct.

False statement to be determine.

Quadrilateral is geometric shape encloses by 4 lines.

For A. The diagonals of a rhombus are perpendicular and bisect each other. This statement is true.
B. A quadrilateral is a polygon with four angles. Its also true.

C. In quadrilateral PQRS, ∠P and ∠S are opposite angles. Its false because ∠P is opposite to ∠R.

D. A rhombus is a quadrilateral. It is also true

Thus, In quadrilateral PQRS, ∠P and ∠S are opposite angles is false statement.

Learn more about quadrilateral here:
https://brainly.com/question/13805601

#SPJ5

Answer:  56 degrees approximately

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

Work Shown:

tan(angle) = opposite/adjacent

tan(x) = 15/10

tan(x) = 1.5

x = arctan(1.5)

x = 56.3099 approximately

x = 56 degrees

Note: arctan is the same as inverse tangent

Answer:

See below and attached

Step-by-step explanation:

Let the number of paintings is x and the number of mugs is y.

We have following inequalities:

The graphical solution is attached.

The solution is:

Answer:

72-57-24=-9

Step-by-step explanation:

simple subtraction

Answer:12 - 5y

Step-by-step explanation:

The quantity five times a number y decreased by twelve means that  5 multiplied by a number is subtracted from 12, it also means that 12 minus 5 times a number y and can be written mathematically as

12 - 5y

Answer:

i think its 5.7

Step-by-step explanation:

Answer:

4 1/10

Step-by-step explanation:

Answer:

y = 2x + 5

Step-by-step explanation:

Step 1 :  Find slope:

          [tex]slope , m = \frac{y_B - y_A}{x_B - x_A}[/tex]

                       [tex]=\frac{-1 - 7}{-3-1} \\\\= \frac{-8}{-4}\\\\ = 2[/tex]

Step 2 : Find the equation of the line :

[tex](y - y_A) = m(x - x_A) \ or \ (y - y_B) = m(x - x_B)\\\\we \ will \ consider \ points \ of \ A :\\\\[/tex]

                                          [tex](y - 7) = 2(x -1)\\\\y - 7 = 2x - 2\\\\y = 2x - 2 + 7\\\\y = 2x + 5[/tex]

9514 1404 393

Answer:

  B.  y < -x +1

Step-by-step explanation:

The boundary line has a y-intercept of +1, eliminating choices A and C.

The boundary line has a negative slope, eliminating choices C and D.

The only viable choice is B: y < -x +1.

Answer:

to blury

Step-by-step explanation:

Answer:

subtract 5 , m=(-15)

Step-by-step explanation:

15-5

=10

n:

5-10

=(-5)

m:

(-5)-10

=(-15)

hope it help

Answer:

The answer would be 25.

4x4=16

16+9=25

Step-by-step explanation:

I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.

Answer:

25

Step-by-step explanation:

rewrite the equation

(4x4)+9

do the equation

16+9=25

Answer:

Sorry I had to go to dinner here you go hope this helps! :D

Step-by-step explanation:

So, before we start, there are two things we have to go over.

First off, we have "or"

When using or between two probabilitess, you are basically adding them together.

For instance, you first question asks what the probability is of rolling a 5 or a number greater than 3(assuming this is a 6 sided dice).

So, rolling a 5 is a change of 1/6. Since 1 of the 6 dice iwll be 5. The other probability is a 1/2, since 3 of the 6 dice are over 3.

Now lets add these two together because of the "or":

1/2+1/6=3/6+1/6=4/6

So the probabily of rolling a 5 OR rolling a number greater than 3 is 4/6.

This is inclusive, since rolling a 5 is possible and greater than 3.

Now "and" is a bit different and more complex than or is.

Here is an example:

What is the change of rolling a even number or rolling a number above 4?

Well, rolling a even number has a probability of 1/2. Rolling a number above 4 is 1/3.

To find the "and", we multiply the two probabilities.

So 1/3*1/2=1/6

So the probability of rolling a even number and a number above 4 is 1/6.

Now, lets get back to the answers.

So what is the probability of rolling a 2 or a 6?

There is a 1/6 probability to get a 2, and a 1/6 probability to get a 6.

Add it together since they use or:

1/6+1/6=2/6

So the probability of rolling a 2 or a 6 is 2/6, or 1/3.

This is exlusive since you cant roll both a 6 and a 2 at the same time.

Next we have what the probability is of drawing a 6 or a king.

There are 13 different cards in a deck.

There is a 4/52 chance of drawing a 6(spade/heart/etc), and a 4/52 chance of drawing a king. This simplyfies to 1/13 for each.

This is:

1/13+1/13=2/13

So the probability of drawing a 6 or a king is 2/13

This is a exclusive event since a king and 6 cant be drawn at the same time.

Finally, we have:

What is the probability of drawing a queen or a spade?

Again, there is a 4/52 chance of drawing a queen. A spade, however, is different.

13 of the 52 cards can be spades, which simplies to 1/4.

So we have 1/13+1/4=4/52+13/52=17/52

So there is a 17/52 probability of drawing a queen or spade.

This is a inclusive event since it is possible to draw both a spade and queen at the same time.

Hope this answers all your questions and helps you understand what "and" "or" are in probability.

Answer:

B

Step-by-step explanation:

His friends snack was 6 dollars.

15.25+1.25= 16

16+1.25= 17.25

17.25+1.25= 19

1/6 of 30 is 5 because 5x6=30.

30-19=11

He has to have 5 left over so the snack was 6 dollars.

Answer:

no

Step-by-step explanation:

because it's unequal

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x

Answer:

Median = 44

Step-by-step explanation:

Arrange the data in ascending order:

36, 37, 40, 43, 44, 49, 50 , 51, 56.

Choose the number in the middle.

Median = 44

Answer and Step-by-step explanation:

Solve for the middle side, then  for x using Pythagorean Theorem.

[tex]A^2 + B^2 = C^2\\\\\\6^2 + 8^2 = C^2\\\\100 = C^2\\\\C = 10\\\\\\\\A^2 + 10^2 = 12^2\\\\A^2 + 100 = 144\\\\A^2 = 44\\\\A^2 = 2\sqrt{11} <-Answer[/tex]

#teamtrees #PAW (Plant And Water)

Answer:

the answer is $1.32×7.5=$9.9

Answer:

£9.90

Step-by-step explanation:

There are 2 ways you can do this. Both are similar.

For the first method it's much quicker but you might need a calculator.

You would simply do 7.5 × 1.32 = £9.90 that should give you the answer.

If you were to do it with out a calculator then what you need to do is 7 × 1.32 = 9.24

Because there is still 0.5 (or 1/2) left from the 7 that you multiplied, you do 1.32 ÷ 2 = 0.66.

Add the 2 numbers together

0.66 + 9.24 = £9.90

Answer:

gd

Step-by-step explanation:

line gd is congruent to kh

Answer:

d. x9 + x3 – 10 = 0

Answer:

Option C is correct

Step-by-step explanation:

[tex]8 + 8 + 8 + 8 + 8 + 8 = 48[/tex]

[tex]6 \times 8 = 48[/tex]

Answer:

2cm

Step-by-step explanation:

First, it is important to define both the radius and diameter. A diameter is the length of a line through the center of a circle that touches two points on the edge.

In the semicircle on the top, if we can imagine it making up a full circle, we can note that the bottom center of the semicircle is the center of the full circle, with the line of length 4cm going right through it. Similarly, for the bottom semicircle, as the line between the semicircles is straight, the diameter for that one is 4cm as well.

The radius is equal to half of the diameter. The diameter is 4cm, so the radius is 4cm/2 = 2cm

Answer:

6 x 8 = 48 yd2 (square yards)

Step-by-step explanation:

Answer:

Area of triangle is 23 yd².

Step-by-step explanation:

Given :-

Base of triangle = 8 yd

Height of triangle = 6 yd

To find

Area of triangle

Solution :-

we know that,

Area of triangle = 1 / 2 × base × height

substitute the values

Area of triangle = 1/2 × 8 yd × 6 yd

multiplying the values

Area of triangle = 1/2 × 46 yd²

divide the values

Area of triangle = 46 yd ² /2 = 23 yd².

Therefore, Area of triangle is 23 yd ².

Answer:

576 FT^3

243 m^3

95 cm^3

400 cm^3

150 m^3

Step-by-step explanation:

Volume of a pyramid = 1/3 x ( length base x height)

Volume of a prism= ( length base x height)

1. prism = 192 x 3 = 576 FT^3

2. prism = 729 / 3 = 243 ft^3

volume of a cylinder = nr^2h

Volume of a cone =  1/3(nr^2h)

3. cone = 285/3 = 95

5. cylinder = 50 x 3 = 150

4. sphere = 600 / 1.5 = 400

Answer:

R = 13%

Step-by-step explanation:

P = $4000

I = $780

T = 18 months = 18/12 years

[tex]I = \frac{PRT}{100} \\\\780 = \frac{ 4000 \times R \times \frac{18}{12}}{100}\\\\780 = \frac{6000 \times R }{100}\\\\780 = 60R\\\\R = \frac{780}{60} = 13 \%[/tex]