Express sin O as a fraction in simplest form

Answer:

[tex]24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]

Step-by-step explanation:

[tex]2\sqrt{8x^{3} } (3\sqrt{10x^{4} } -x\sqrt{5x^{2} } )[/tex]

[tex]=2.2x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]

[tex]=4x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]

[tex]=12x^{3} \sqrt{2xx10} -4x^{3} \sqrt{2xx5}[/tex]

[tex]=24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]

OAmalOHopeO

Answer:    [tex]\fbox{C} \: \: \: \dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]

Step-by-step explanation:

36,070 = 3.607 · 10⁴ ≈ 4 · 10⁴

29,029 = 2.9029 · 10⁴ ≈ 3 · 10⁴

Let's how manytimes greater the distance to the bottom of Challenger Deep is than the distance to the top of Mount Everest:

[tex]\dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]

Answer:

C

Step-by-step explanation:

First, the question is asking how many times greater the distance to the Challenger Deep is compared to Mount Everest. This means that the Challenger Deep will be on top, with the distance to Mount Everest on the bottom.

Next, we can see that in our answers, we are only given one significant digit. This means that we have to round our original numbers to the nearest significant digit and work from there. For Challenger Deep, 36,070 must be rounded to the nearest ten thousandth as it is in the ten thousands. Therefore, it must be rounded to 40,000 or 30,000. As 36,070 is closer to 40,000 than 30,000 (we can tell this because the second number, 6, is greater than 5, so we round up), we can represent this as 40,000. For Mount Everest, we can round 29,029 to either 20,000 or 30,000. 30,000 is the appropriate choice here because 9, the second number, is greater than 5.

Therefore, our ratio is now 40,000 / 30,000 . Our answers are written in scientific notation, so we must convert our numbers to those values.

Let's start with 40,000 . Our one significant digit is 4, so we can write this as 4 * something. For each number in 10 to the power of x (x is a placeholder value), we add x amount of zeros. For example, for 4 * 10², we add 2 zeros, making it 400. There are 4 zeros here, so to write this in scientific notation, we have 4 * 10^4

Similarly, for 30,000 , we can write this as 3 * 10^4 as there are 4 zeros.

Our ratio is thus 40,000 = 4*10^4 , which is the Challenger Deep value rounded, over 30,000 = 3 * 10^4, which is the Mount Everest value rounded. We can write this as [tex]\frac{4*10^{4}}{3*10^{4}}[/tex], or C

Answer:

5/12

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Answer:

geometric

x=number of terms

∑ 2(-5)^(k-1)

k=1

Step-by-step explanation:

the sequence has a ratio of -5 (2*-5=-10, -10*-5=50)

x=number of terms

∑ 2(-5)^(k-1)

k=1

for this i don't know what the last term is since it doesn't show in the question but just find 2(-5)^x and x will be the top term

Step-by-step explanation:

here's the answer to your question

Answer:

х=6

Step-by-step explanation:

[tex]7 + 5(x -3 ) = 22 \\ 7 + 5x - 15 = 22 \\ 5x = 22 - 7 + 15 \\ 5x = 30 \\ x = 6[/tex]

Answer:

C

x=6

Step-by-step explanation:

8.18

Step-by-step explanation:

8.18

pow pom wyh oqhw uwhwn 8.18 ge wk

Answer:

37 Dimes, 29 Nickels

Step-by-step explanation:

x= dimes

66-x = nickels

.1 (x) = dimes

.05 (66-x) = nickels

Solve

3.3 + 0.5x = 5.15

Solve again then you come out with

x= 37

66 - 37 = 29

Answer:

The volume of the irregular figure would be 102 [tex]cm^3[/tex].

Step-by-step explanation:

If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be [tex]6*3*5=30*3=90 cm^3[/tex], and the volume of the smaller rectangular prism would be [tex]3*2*2=6*2=12 cm^3[/tex]. So the volume of the entire irregular figure would be [tex]90+12=102 cm^3[/tex].

Answer:

102

Step-by-step explanation:

Large rectangle:

6 × 3 × 5 = 18 × 5 = 90

Small rectangle:

7 - 5 = 2

3 × 2 × 2 = 6 × 2 = 12

90 + 12 = 102

Hope this helped.

Answer: A, C, D

Step-by-step explanation:

To find which logarith simplifies to 2, we first need to know how they work.

We now know that [tex]log_a(a^x)=x[/tex].

This tells us that only A, C, D would work.

[tex]8^2=64\\ \\6^2=36\\\\10^2=100[/tex]

Note: whenever you have a log that doesn;t specify the base, it is always 10, as shown in D.

Answer:

A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.

Answer:

The average value of the Function f(x) by squeeze theorem states that no extreme or greater value will exist within the designated area for f(x)

Answer:

considering it was simple interest,

We have the formula:

I = PRT ÷ 100

where,

for the first part of the question,

Thus, I = (2160 × 20 × 4)÷ 100

I = Rs. 1728

Now, for the second part,

T = 100×I÷PR

T = 100 × 1728÷(1800 × 12)

T = 8 Years

9514 1404 393

Answer:

Step-by-step explanation:

The reflections are illustrated in the attached.

  A1, A1' are opposite vertices of the reflected original triangle. They are part of a kite figure.

  A2, A2' are opposite vertices of a reflected isosceles triangle, where BA=BC. Figure A2BA2'C is a kite.

  A2a, A2a' are opposite vertices of a reflected isosceles triangle with AB=AC. Figure A2aBA2a'C is a rhombus.

  A3, A3' are opposite vertices of a right triangle with the right angle at A3. Figure A3BA3'C is a kite figure.

  A4, A4' are opposite vertices of a reflected right isosceles triangle with AB=AC and the right angle at A4. Figure A4BA4'C is a square.

Cot A=1/tan A=12/5

cos A= 12/13

sin A=5/13

Draw a right angled triangle

the hypotenuse is the longest side which is 13 using Pythagoras theorem

the side opposite the angle A is 5

the side closest to the angle A which is called the adjacent is 12

sinA =opp/hyp

cos A= adj/hyp

cotA =1/tanA=cos A/sinA

Note: Pythagoras theorem is

hyp²=opp²+adj²

Answer:

Step-by-step explanation:

[tex]tan \ A = \frac{5}{12}=\frac{opposite \ site}{adjacent \ side}[/tex]

hypotenuse² = (opposite side)² + (adjacent side)²

                      =  5² + 12²

                      = 25 + 144

                      = 169

hypotenuse = √169 = √13*13 = 13

[tex]Cot \ A = \frac{adjacent \ side}{opposite \ side}=\frac{12}{5}\\\\Cos \ A = \frac{adjacent \ side}{hypotenuse}=\frac{12}{13}\\\\Sin \ A = \frac{opposite \ side}{hypotenuse}=\frac{5}{13}[/tex]

Answer:

8/12 or 2/3

Where the first number is on the top and vice versa.

Step-by-step explanation:

Answer:

(base x height x length)/2 = volume

6x8x8 = 384/2 = 192in^3

hope that answers your question

When the Center of dilation is inside the figure

When the Center of dilation is outside the figure

    3. The original figure is closer to the the center of dilation

    4. The dilated figure is closer to the center of dilation

The center of dilation is the fixed point from which the distances in a dilation are measured

The scale factor is ratio of the side lengths of an original figure or preimage to  the side lengths of the newly formed image

Center of dilation is inside the figure

The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation

Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure

     2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;

The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation

Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure

Center of dilation outside the figure

     3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;

The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure

     4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1

The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation

Learn more about scale factors and center of dilation here;

https://brainly.com/question/12162455

Answer:

G

Step-by-step explanation:

you know its G just by the way it is

Answer:

y = | x-5|

Step-by-step explanation:

y = |x-h| +k  where (h,k) is the center of the "v"

The "v" is located at (5,) so h=5 and k = 0

y = | x-5| +0

Answer:

max: -4

Step-by-step explanation:

(x+3)^2 》0 mọi x

<=> -(x+3)^2 《0

<=> -(x+3)^2 -4 《 -4

Answer:

3a^2 + 20a + 34

Step-by-step explanation:

(2a + 5)^2 = 4a^2 + 20a + 25

(a +3)(a - 3) = a^2 - 9

Put these two partial answers together.

4a^2 + 20a + 25 -(a^2 -9 )                 Remove the brackets.

4a^2 + 20a + 25 -  a^2 + 9

4a^2 + 20a + 25 - a^2 + 9

3a^2 + 20a + 34

Answer: 3a² + 20a + 34

Concept:

When doing simplifying expressions, following the PEMDAS method would be easier.

When expanding parentheses, following the FOIL method would be easier.

Solve:

Given expression

(2a + 5)² - (a + 3) (a - 3)

Simplify exponenets

= (2a + 5) (2a + 5) - (a + 3) (a - 3)

Expand parentheses

= 4a² + 10a + 10a + 25 - (a² - 3a + 3a - 9)

= 4a² + 10a + 10a + 25 - a² + 3a - 3a + 9

Combine like terms

= 4a² - a² + 10a + 10a + 3a - 3a + 25 + 9

= 3a² + 20a + 34

Hope this helps!! :)

Please let me know if you have any questions

Answer:

45 / 27 = 30 / 18 = x / 24

x = 40

Step-by-step explanation:

Hi there!

The question here states that the two polygons are similar

Polygons that are similar have similar side length ratios.

If we want to find a side length we must create a proportional relationship

We are already given a partial proportional relationship.

Which is...

45 / __ = __ / 18 = x / __

First let's fill in the blanks

The side that is corresponding to the side with a length of 45 has a length of 27. So it would be 45/27

The side that is corresponding to the side with a length of 18 has a length of 30. So it would be 30/18

The side corresponding to side labeled "x" has a length of 24. so it would be x/24

So we would have

45 / 27 = 30 / 18 = x / 24

Now let's find x

We only need 2 ratios ( the one including x of course, and the other one can either be 30/18 or 45/27)

30 / 18 = x / 24

Now let's solve for x

Cross multiply

30*24=720

18*x=18x

We now have 18x = 720

Divide both sides by 18

18x / 18 = x

720 / 18 = 40

x = 40

To check our answers we can see if the ratios are similar

If they are then we are correct

45/27 = 1.66

30/18 =1.66

40/24 = 1.66

They are all equivalent meaning that our answers are correct

Answer:

The polygons are NOT similar. The ratio of 12 to 18 equals 2 to 3, and the ratio of 26 to 32 equals 13 to 16. They're not the same, thus not similar.

Answer:

They are not similar, and the instructions says to put "None" otherwise, so...

Step-by-step explanation:

You can find this by dividing 32 by 16 to get something like 1.7777....

and dividing 26 by 12 should give the same ratio if they are similar, but it gives something like 2.1666...

Therefore they are not similar.

Congruent means two or more shapes are the same size and are similar, but for some things to be similar means that they have the same ratio, but not necessarily the same dimensions.

Hey there!

We know that Danielle earns $10 per hour, so muliply that by 3 and get 30.

Because Danielle works an extra half an hour, divide 10 by 2 and get 5.

Danielle earns $35 in 3 hours and a half.

Hope this helps! Please mark me as brainliest!

Have a wonderful day :)