2sin² theta = sin theta for - 270° ≤ 0 ≤180°

The exact length of a which is equivalent to BC is 7units

A triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule

c² = a² + b² - 2abcosC

Given the following parameters

b = 2

c = 5√3

theta = 30 degrees

Substitute

c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2

c² = 79 - 30
c² = 49
c = 7 units

Hence the exact length of a which is equivalent to BC is 7units

Learn more on triangles here: https://brainly.com/question/17335144

#SPJ1

Answer: 32

Step-by-step explanation: this is arithmetic sequence

general formula = a+(n-1)d

nth term = 5+(n-1)3

=5+3n-3

=2+3n

10th term = 2+3(10)

=32

It will take 32 minutes for the population to grow from 1,000 to 32,000.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If the population of an alien race doubles every two minutes,

1,000 x 32 = 32,000

Hence, It would take 32 minutes.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

Answer:

Step-by-step explanation:

1/2 chance for 1

1/4 for 2

1/8 for 3

1/16 for 4

1/32 for 5

1/64 for 6

1/128 for 7

1/256 for 8

1/512 for 9

1/1024 for 10

Answer:

223

Step-by-step explanation:

find the area for each side.

The value of x must be 25.0. The correct option is the second option-  25.0

From the question, we are to determine the value of x

From the given diagram, we can write that

m ∠SOR + m ∠UOR + m ∠TOU = 180° (Sum of angles on a straight line)

∴ (2x +8)° + (3x - 14)° + (3x -14)° = 180°

2x° + 8° + 3x° -14° + 3x° -14° = 180°

Collect like terms

2x° + 3x° + 3x° + 8° - 14° -14° = 180°

8x° -20° = 180°

8x° = 180° + 20°

8x° = 200°

x = 200/8

x = 25.0

Hence, the value of x must be 25.0. The correct option is the second option-  25.0

Learn more Solving linear equations here: https://brainly.com/question/1413277

#SPJ1

Answer:

25.0

Step-by-step explanation:

just took it

\

Since it is said to be a hollow rectangular prism,  she will fill it with sand to weigh it about (573 + 9/2) cubic inches.

What is the prism about?

Note that the volume is said to be:

V = L x B x H

316 in = 6 √2 x 2 √3

The answer is 573 while the other part of the prison is 9√2 cubic inches.

Therefore, option A is correct.

See full question below

Chandra is constructing a weighted bookend for her shelf. It is a hollow rectangular prism, as shown, and she will fill it with sand to weigh it

down

6 √(2  in

316 in

2 √3 in

What is the volume of the bookend?

(Hint: The volume of a rectangular prism is the product of its length width and height.)

OA (573 + 9/2) cubic inches

B. 36/12 cubic inches

C 108 cubic inches

D. 216 cubic inches

Learn more about prism from

https://brainly.com/question/23963432

#SPJ1

Answer:

A=πr^2

Step-by-step explanation:

A=π*r^2

Where, A is area of circle

r is radius of circle

π is constant

.

Hope it's help and I think I have give brainleist answer

Answer:

πr^2

Step-by-step explanation:

it's just πr^2.

easy

Answer:

Pretty certain it's 100



Answer:

V =512 m^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = 8^3

V =512 m^3

Answer:

C

Step-by-step explanation:

14 + w is the same as w + 14

Answer:

C.  w + 14.

Step-by-step explanation:

The order does not matter when you are adding terms.

this is called the Commutative Property of Addition.

[tex]Prove\ that\ the\ assumption \is \true for\ n=1\\1^3=\frac{1^2(1+1)^2}{4}\\ 1=\frac{4}{4}=1\\[/tex]

Formula works when n=1

Assume the formula also works, when n=k.

Prove that the formula works, when n=k+1

[tex]1^3+2^3+3^3...+k^3+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k+1)^2}{4}+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k^2+2k+1)}{4}+(k+1)^3=\frac{(k^2+2k+1)(k^2+4k+4)}{4} \\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+4k^3+4k^2+2k^3+8k^2+8k+k^2+4k+4}{4}\\\\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+2k^3+k^2}{4}+\frac{4k^3+12k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+6k^3+13k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\[/tex]

Since the formula has been proven with n=1 and n=k+1, it is true. [tex]\square[/tex]

y = (1/3)x+10

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

Explanation:

x = number of minutes of the original flight

Because the pilot travels 3 times faster than before, it means she travels 1/3 of the original time. If she took x minutes on the original flight, then she will take (1/3)x minutes for the new faster flight.

Then add on the 10 minute delay to end up with (1/3)x+10

Answer:

alternate exterior angles

Step-by-step explanation:

<3 i hope this helps! sorry if it doesnt :)

[tex]~~~-\dfrac 12 + c = \dfrac{31}4\\\\\\\implies c = \dfrac{31}{4}+\dfrac 12\\\\\\\implies c = \dfrac{31}{4}+ \dfrac 24\\\\\\\implies c = \dfrac{31+2}{4}\\\\\\\implies c = \dfrac{33}4[/tex]

Answer:

i think its point D. So that means the answer is B. I think so because if the middle like going side to side is marked first then it must mean the positive is first and so it's point D

To identify the value that goes in each box, we must perform the corresponding operation and calculate the final result.

In mathematics there are procedures such as addition (+), subtraction (-), division (÷), and multiplication (×) to solve problems. These operations are the four basic operations of mathematics.

According to the above, what we must do is identify what operation we must perform with the given numbers and then identify the result and put it in the corresponding box.

Note: This question is missing because there is some information missing. Howeve i can answer it based on my general knowledge.

Learn more about numbers in: https://brainly.com/question/17429689

#SPJ1

I think the incorrect data is the second x to the left.

The ratio of the area of sector abc to the area of sector dbe is 4/3

For sector abc, we have:

Angle = x

Radius  = 2r

For sector dbe, we have:

Angle = 3x

Radius = r

The area of a sector is:

[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]

So, we have:

[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]

Evaluate

[tex]ABC =\frac{x* \pi r^2}{90}[/tex]

For DBE, we have:

[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]

Evaluate

[tex]DBE =\frac{x}{120}* \pi r^2[/tex]

The ratio of both areas is:

[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]

Cancel out the common factors

[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]

Express as fraction

[tex]Ratio = \frac{120}{90}[/tex]

Divide

[tex]Ratio = \frac{4}{3}[/tex]

Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3

Read more about sector areas at:

https://brainly.com/question/1582027

#SPJ4

4/3

its the answer edmentum

Answer:

y=2x+4

Step-by-step explanation:

From(0,4)

Equation in slope intercept form

[tex]\text{For angle N,}\\\\PQ= \text{Perpendicular.}\\\\QN = \text{Hypotenuse.}\\\\\text{Now,}\\\\\sin N = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\~~~~~~~=\dfrac{QP}{QN}[/tex]

Answer:

7x <5x-16

Step-by-step explanation:

7x-5x < 5x -16 -5x

Answer:

by solving the divisions

Step-by-step explanation:

8/9 ÷ 3/10 = 8/9 × 10/3 = 80/27 = 2.96.

now from the solutions you can get the least to greatest

1.40 , 2.96, 5.28 and 23.75

After getting answer in decimal form change it to fraction like how they set the question

The amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.

x grams of 20% and 20-x grams of 35%

Hence:

0.20x+0.35(20-x)=0.26×20

0.20x-0.35x+7=5.2

Collect like terms

-0.15x=-1.80

Divide both side by -0.15x

x=-1.80/-0.15

x=12 grams of 20% or 2.4 grams pure

20-x= (20-12) =8 grams of 35% or 2.8 grams pure

Therefore the amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.

Learn more about amount of grams here:https://brainly.com/question/1107267

#SPJ1

The statistic that is most affected by the lowest score is A. the mean

The stem and leaf plot is missing from the question;

However, the question can be solved without it.

The lowest score on the stem and leaf plot is an outlier of the plot.

In statistics, outliers have huge effect on the mean of the dataset and they have little or no effect on the median and mode

This means that, the statistic that is most affected by the lowest score is A. the mean

Read more about stem and leaf plot at:

https://brainly.com/question/12276901

#SPJ1

Answer: -6.5

Step-by-step explanation:

First, you take the values on both sides to the power of 2 to get:

-x = x + 13

Subtract x on both sides.

-2x = 13

Divide both sides by -2.

x = -6.5

Answer:

[tex]x=-\dfrac{13}2[/tex]

Step-by-step explanation:

[tex]~~~~~\sqrt{-x} = \sqrt{x+13}\\\\\implies -x= x+13~~~~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\implies -x -x = 13\\\\\implies -2x = 13\\\\\implies x = -\dfrac{13}2\\\\\text{Verify solution:}\\\\~~~~~~~\sqrt{-\left(- \dfrac{13} 2 \right)} = \sqrt{-\dfrac{13}2 +13}\\\\\\\implies \sqrt{\dfrac{13}2} = \sqrt{\dfrac{13}2}\\\\\text{Hence, the solution is}~ x=-\dfrac{13}2[/tex]