In a 30-60-90 triangle, the length of the long leg is 8. Find the length of the hypotenuse.

Hey there!

Let’s turn everything into yards (instead of feet) so we can determine which is greater

To do this, all we have to do is divide 3 (that’s how many feet are in a yard) by 429 & 460 (these are the 2 lengths that are represented by feet)

429 ÷ 3 = 143

460 ÷ 3 = 153.333... (let’s round to 153)

Now, we determine which is greater:

150 yards > 143 yards

So, 150 yards is greater than 143 yards (or 429 feet)

130 yards < 153 yards

So, 130 yards is less than 153 yards (or 460 feet)

Hope this helps you!

God bless ❤️

Brainliest would be appreciated

xXxGolferGirlxXx

Answer:

Ivan has 20 more miles to walk.

Step-by-step explanation:

If the hike is 60 miles long and he has already walked 15 miles the first day and 25 miles the next we can do this equation :

60 - 15 - 25 = 20.

Which means the third day he has to walk 20 whole miles! Good luck Ivan :D

Hope this helps,

Davinia.

Answer:

Ivan have left to walk  = 20 miles .

Step-by-step explanation:

Given:Ivan is on a three-day hike. The hike is 60 miles long. If he walked 15 miles on the first day and 25 miles on the second day.

To find: How many miles does he have left to walk.

Solution: We have given that

Total length of hike = 60 miles .

Ivan walked  on the first day = 15 miles .

Ivan walked  on the second day = 25 miles .

Ivan walked in 2 days = 15 + 25 = 40 miles .

So, Ivan have left to walk  = 60 -40 = 20 miles .

Therefore , Ivan have left to walk  = 20 miles .

Answer: The answer is 2160

Answer:

2160

Step-by-step explanation:

all the numbers are small so instead of rounding up you round dow to zero for the forth.

Answer:

Yes, because 3^2 + 4^2 = 5^2

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

it doesn't have the same length so one sides gonna be longer

Answer:

a) The volume of the dunking booth = 98 feet³

b) They will need 84 feet³ of water to fill 6/7 of dunking booth

Step-by-step explanation:

* Lets talk about the rectangular prism

- It has 6 rectangular faces each two opposite faces are congruent

- It has three dimensions Length, Width and Height

- Its volume = Length × Width × height

* In our problem the dunking booth is a rectangular prism

 with dimensions:

- Width = 3.5 ft

- Length = 3.5 ft

- Height = 8 ft

∴ Its volume = 3.5 × 3.5 × 8 = 98 feet³

a) The volume of the dunking booth = 98 feet³

* They want to fill 6/7 of the dunking booth with water

∴ The volume of the water will be 6/7 from the volume

   of the dunking booth

∵ The volume of the dunking booth = 98 feet³

∴ The volume of the water = 6/7 × 98 = 84 feet³

b) * They will need 84 feet³ of water

a) 98

b) 84

hope this helps!

-4 < -12 would be my answer, just from looking at it. If you write it out on a number line, the number -4 is higher than -12. The higher the negative number, the lower it is on the line. So, -4 is greater than -12, not lower than.

The comparison which is not correct is Option (D) -4<-12

The inequality, greater than or lesser than between two numbers indicate that whether one number is greater than the other number or less than the other number. The inequality is represented by ">" and "<".

In number system, when comparing two numbers less than zero then the magnitude of smaller negative number is always greater than the magnitude of bigger negative number. Or in other words it is opposite to the positive number system .

For example,  -10<-4  or  -2<-1

Thus the comparison which is incorrect is Option (D)  -4 < -12.

To learn more about comparison between two numbers, refer -

https://brainly.com/question/2954013

#SPJ2

The given equation is :

[tex]24x^{3}y^{2} -4x^{2}y +84x^{4}[/tex]

Now taking [tex]4x^{2}[/tex] common from all the terms, we get

[tex]4x^{2} (6xy^{2} -y+21x^{2} )=0[/tex]

Writing the equation in standard form we get:

[tex]21x^{2} +6xy^{2} -y=0[/tex]

Now we will use the formula of quadratic equations to solve this,

[tex]x1,2 = \frac{-b+\sqrt{b^{2}-4ac }} {2a}[/tex] and

[tex]x1,2 = \frac{-b-\sqrt{b^{2}-4ac }} {2a}[/tex]

Now putting a = 21, b = 6y² and c = -y and solving the equations, we get

[tex]x=\frac{-6y^{2}+\sqrt{36y^{4}+84y }}{42}[/tex] and

[tex]x=\frac{-6y^{2}-\sqrt{36y^{4}+84y }}{42}[/tex]

Answer:

3 m^2

Step-by-step explanation:

The shaded area = Area of Sector - Area of Triangle

First we find area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]

We know the angle is 60° (vertical angles are equal) and the radius is 6, so we find the area of sector to be:

[tex]\frac{\theta}{360}*\pi r^2\\\frac{60}{360}*\pi (6)^2\\=18.85[/tex]

Secondly, we find area of triangle (isosceles) = [tex]\frac{1}{2}abSinC[/tex]

where

a and b are the two sides bordering the known angle, so a=b=6, and

C is the angle which is 60°

Now we find the area to be:

[tex]\frac{1}{2}(6)(6)Sin(60)\\=15.59[/tex]

Hence, area of shaded = [tex]18.85 - 15.59=3.26[/tex]

Rounding to nearest whole number, area of shaded region = 3m^2

Answer:

15

Step-by-step explanation:

we need to write the equation. I came up with....

3(5 - x) = 30

so take the 3 away from the 30. I think your not supose to do the 3 because it out of the ( ). the opppisite of multiplication is division. so...

3 divided by 30 =10

rewrite

(5 - x) = 10

take the 5 away. the oppisite of subbtraction is addition.

5 + 10 = 15

check your; plug in x

3(5 - 15) = 30  This equation looks true!

Hope this helped! Please mark as brainliest! Thanks

Answer:

The expression would be = to 0.

Step-by-step explanation:

Starting with -4(3s) + 2(-t), substitute (1/2) for s and (-3) for t:

                    -4(3/2) + 2(+3)

This gives us:

                       -12/2 + 6 = 0              

Answer:

-12

Step-by-step explanation:

3 times 1/2 is 1 1/2. 1 1/2 times -4 is -6. Then, -3 times 2 equals to -6. lastly -6 plus -6 equals to -12

Answer:

3/10. 1/2 and 7/10

Step-by-step explanation:

For P(x) = x/10

When x = 3;

Then;

P(3) = 3/10

When x = 5

Then;

P(5) = 5/10

       = 1/2

When, x = 7

Then;

P(7) = 7/10

Answer:

[tex]P(3)=\frac{3}{10}=0.3\\\\P(5)=\frac{5}{10}=0.5\\\\P(7)=\frac{7}{10}=0.7[/tex]

Step-by-step explanation:

Probability is the possibility of happening of some event .

Probability = [tex]\frac{No.\,\,of\,\,outcomes}{Total\,\,no.\,\,of\,\,outcomes}[/tex]

Probability distribution links each outcome of an experiment with it's probability of occurrence .

Given: [tex]P(x)=\frac{x}{10}[/tex]

To find: Probability  distribution for the given function for x = 3 , 5 and 7

Solution:

For x = 3 :

On putting x = 3 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(3)=\frac{3}{10}=0.3[/tex]

For x = 5 :

On putting x = 5 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(5)=\frac{5}{10}=0.5[/tex]

For x = 7 :

On putting x = 7 in function [tex]P(x)=\frac{x}{10}[/tex] , we get

[tex]P(7)=\frac{7}{10}=0.7[/tex]

Answer: [tex]\frac{5}{8}[/tex] yard.

Step-by-step explanation:

You have the following information given in the problem:

- You have 3/4 yard of felt.

- You used 1/8 yard,

Therefore, to find the fraction of a yard of felt that you have left over (which you can call x), you only need to subtract 3/4yard and 1/8 yard, as you can see below:

[tex]x=\frac{3}{4}yard-\frac{1}{8}yard\\\\x=\frac{5}{8}yard[/tex]

Answer: OPTION A

Step-by-step explanation:

To simplify the expression you must multiply the numerator and the denominator of the expression by √3.

As all the square roots have equal index, you can multiply the radicands, which are the numbers inside of the sqaures roots.

You also must keep on mind that:

[tex](\sqrt[n]{a})^n=a[/tex]

Therefore, you obtain:

[tex]\frac{6\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{6\sqrt[]{6}}{3}=\frac{2\sqrt[]{6}}{3}[/tex]

Answer:

The correct answer is option B.  2√6

Step-by-step explanation:

It is given that an expression, 6√2/√3

To simplify the expression

6√2/√3

Multiplying numerator and denominator with √3

6√2/√3 = (6√2 x √3)/(√3 x √3)

  = [ 6 x √(2x3)]/3)                    (√2 x √3 = √(2 x 3)

  = 6√6/3  

  = 2√6

Therefore the simplified form of given expression 6√2/√3 is 2√6.

The correct answer is option B. 2√6

[tex]\huge\text{B. $\boxed{x+(y-z)}$}[/tex]

First, let's take a look at the terms in the original expression. Since its just addition and subtraction, we can get rid of the parentheses, leaving behind just [tex]x+y-z[/tex].

As long as an answer is made up of a positive [tex]x[/tex], a positive [tex]y[/tex], and a negative [tex]z[/tex], its correct!

Removing the parentheses in choice A leaves us with [tex]z+x+y[/tex], which has a positive [tex]z[/tex] rather than a negative [tex]z[/tex], so it's incorrect.

Removing the parentheses in choice B on the other hand gives us [tex]x+y-z[/tex], which means it's the correct answer! This is a good example of the associative property of addition in action.

The correct expression that is equivalent is option B.  x +(y − z)

Let's simplify each expression to see if they are equivalent to (x + y) - z:

A. ( z + (x + y))

We can rearrange the terms:

z + (x + y) = (x + y) + z

This is not equivalent to (x + y) - z  because the terms are added in a different order.

B. (x + (y - z))

We can expand the expression:

[tex]\[ x + (y - z) = x + y - z \][/tex]

This expression is indeed equivalent to (x + y) - z because the terms are arranged in the same order and operations are consistent.

So, the correct answer is:

[tex]\[ \text{B. } x + (y - z) \][/tex]

Answer:

Step-by-step explanation:

Any one color would be 1/4 of the total. So the number of times you should get red is 1/4 of 160 = 40

Notice that this very odd problem does not depend on what the total is. It only depends on the number of times you make the draw. Unusual question.

Answer:

[tex]Area = (30 + x)(20 + x)[/tex]

Step-by-step explanation:

By definition, the area of a rectangle is the product of its length multiplied by its width.

Initially the dog run has a length of 30 ft long and 20 ft wide.

If you want to expand the track, increase the length of each side by a factor x. So, the dimensions of the expanded dog run will be:

[tex]Length = 30 + x\\Width = 20 + x[/tex]

Then, the area is:

[tex]Area = Length * Width[/tex]

[tex]Area = (30 + x)(20 + x)[/tex]

The total area of an expanded rectangular dog run, after increasing each side by the same amount x, is calculated using the formula A = (l + 2x)(w + 2x), where l is the original length and w is the original width. The new area after expansion is 4x^2 + 100x + 600 square feet.

The student is asking how to calculate the total area of an expanded rectangular dog run after increasing each side by the same amount, x. To solve this, we can use the formula A = lw, where A is the area, l is the length, and w is the width of the rectangle. In the original dimensions, the dog run has a length of 30 ft and a width of 20 ft. After expanding, the new dimensions will be (30 + 2x) ft for the length and (20 + 2x) ft for the width, since each side is increased by x on each end.

Expanded Dog Run Area Calculation:

First, we write out the new dimensions:

Then, we calculate the new area:

A = (30 + 2x)(20 + 2x)

A = 600 + 60x + 40x + 4x^2

A = 4x^2 + 100x + 600

The expanded area of the dog run will be 4x^2 + 100x + 600 square feet.

Answer:

2.1

Step-by-step explanation:

There were a total of 435 people in the House. 9 were neither Republican nor Democratic. Divide 9/435. multiply that by 100

Answer:

The answer is C.

Step-by-step explanation:

In 1997 U.S. House of Representatives there were 222 Republicans, 204 Democrats, 2 Independents, and 7 undecided.

So total number in the House = 222 + 204 + 2 + 7

= 435

Total number who is neither Republican nor Democrat = 2 + 7

= 9

Percentage of the total is neither Republican nor Democrat

= 9 / 435 * 100%

= 2.1%

Answer:

[tex]\large\boxed{21845}[/tex]

Step-by-step explanation:

The formula of a sum of terms of a geometric sequence:

[tex]S_n=a_1\cdot\dfrac{1-r^n}{1-r}[/tex]

We have:

[tex]a_1=1,\ a_2=4,\ a_3=16\ and\ n=8[/tex]

Calculate the common ratio:

[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_{n+1}}{a_n}\\\\r=\dfrac{4}{1}=4\\\\r=\dfrac{16}{4}=4[/tex]

CORRECT :)

Substitue:

[tex]S_8=1\cdot\dfrac{1-4^8}{1-4}=\dfrac{1-65536}{-3}=\dfrac{-65535}{-3}=21845[/tex]

Answer:

V = 240 in ^3

SA = 2(lw+lh+wh)

SA = 236 in^2

Step-by-step explanation:

Volume = l*w*h where l=length, w= width and h =height

We know l=6, w=5 and h =8

V = 6*5*8

V = 240 in ^3

The formula for surface area of a rectangular prism is

SA = 2(lw+lh+wh)  where l=length, w= width and h =height

We know l=6, w=5 and h =8

Substituting into the equation

SA = 2(6*5+6*8+5*8)

     = 2 (30+48+40)

     =2(118)

     = 236 in ^2

Final answer:

The surface area covered by the banner is 27,000 square meters. The side length of a square with the same area would be approximately 164.3 meters.

Explanation:

The office building is a right rectangular prism with a height of 200m, a length of 60m, and a width of 40m. The upper quarter of each vertical face needs to be covered with a large banner.

To find the surface area covered by the banner, we need to calculate the surface area of each vertical face. The surface area of a rectangular prism is given by the formula 2lw + 2lh + 2wh. Since we need to cover the upper quarter of each face, we can consider only three quarters of the height, resulting in a formula of 2lw + (3/4)lh + 2wh.

Plugging in the given values, we get:

Surface area = 2(60)(40) + (3/4)(200)(60) + 2(40)(200)

Simplifying the expression, we get the surface area covered by the banner to be 27,000 square meters.

If we want to represent the area as a square with the same area, we can take the square root of the surface area. In this case, the side length of the square representing the area would be approximately 164.3 meters.

Answer:

10^5

Step-by-step explanation:

100,000

= 10 x 10 x 10 x 10 x 10

= 10^5

Answer:

36.952

Step-by-step explanation:

22+14=36

.12+.83= .95

36+.95=36.95

Answer:

36.952

Step-by-step explanation:

Step 1. First think of regular addition add all of your number together.

Step 2. Once you've added all your numbers, place the decimal point. This can be done by counting the number of numbers behind the decimal point.

Step 3. Once you've added and placed your decimal point you should have gotten 36.952. Hope this helped you! <3

Answer:

multiplication

Step-by-step explanation:

See what is happening to the expression x - 4 and choose the opposite operation.

x - 4 is being divided by 5.

The opposite operation to division is multiplication, so you need to use multiplication to get x - 4 alone on the left side.

the answer to the question is multiplication

Answer:

400

Step-by-step explanation:

scale factor is 2

so you cube the 2 to get 8

50 times 8 = 400

Oh that question

Parallel sides

Opposite sides are congruent

And diagonals bisect each other

A rectangle is a four-sided quadrilateral with four right angles, opposite sides are parallel and of equal length, and the area is the product of its base and height. Rectangles typically have a larger perimeter than a square with the same area and can form larger rectangles when equal rectangles are combined. The golden rectangle has sides in the golden ratio, considered aesthetically pleasing.

A rectangle is a geometrical figure with some specific properties. First, it is a quadrilateral, meaning it has four sides. A defining characteristic of a rectangle is that it has four right angles (90°). Due to this property, opposite sides of a rectangle are parallel and equal in length. The area of a rectangle can be calculated by multiplying its base (length) by its altitude (height). A square is a special type of rectangle where all four sides are of equal length.

In terms of perimeter, a rectangle has a larger perimeter compared to a square of the same area, because it will have two longer sides and two shorter sides, whereas a square has four sides of equal length. This also means that in geographic terms, a rectangle would represent a larger coastline if used to approximate a peninsula. When constructing a golden rectangle, which is a rectangle with aesthetically pleasing proportions found in nature and art, the ratio of the longer side to the shorter side is known as the golden ratio.

Another important fact about rectangles is that by placing equal rectangles together, we can form a larger rectangle with sides that simply are multiples of the corresponding sides of the original rectangles. This principle is used in various mathematical proofs and constructions.

Answer: 94

Step-by-step explanation:

Answer:

Yes, it does.

Step-by-step explanation:

Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.

To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »

So, a square has rotational symmetry, but not a rectangle.

A equilateral triangle has rotational symmetry, but not any other type of triangle.

Answer:

  yes, -6

Step-by-step explanation:

6/-1 = -36/6 = 216/-36 = -6

Adjacent terms have a common ratio of -6, so they comprise a geometric sequence.