Find the exact length of the midsegment of the trapezoid with the vertices A(2,0), B(8,-4), C(12, 2), D(0, 10)

The length of the midsegment is

Answer:

x = 20

Step-by-Step Explanation:

The two angles are supplementary, which means that when you add them together, they equal 180 degrees. So this is the equation to solve for x: 180 = (3x+10) + (6x-10). When it is solved, you find that x = 20.

Answer:

predator killed animals to eat and prey is described as organism that predator kill for food.

Answer:

She will get back $4.21

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

Learn more on a Ferris wheel here;

https://brainly.com/question/30524034

#SPJ1

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Answer:

5 calories

Step-by-step explanation:

So, Raquel will burn 5 calories in 1 minute.

I hope this helps!

Answer:find the distance between the co ordinate of the points A(2,3) and B(10,-3)

Distance formula,

━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore the distance is 10 units

Step-by-step explanation:

The sum of angles at a point is equal 360 degrees and using that, the value of x is 261 degrees.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360°.

In this question, when we sum all angles up, it will give us the sum of 360 degrees.

20 + 40 + 39 + x = 360

x + 99 = 360

x = 360 - 99

x = 261

x has a value of 261 degrees.

Learn more on angle at a point here;

https://brainly.com/question/24375372
#SPJ1

Salad was left (A) Five and three-sixteenths pounds.

Fraction is the comparison between numbers or mathematical quantities.

Given that, Juan bought pineapple of = (3 + 3/4) pounds = 15/4 pounds

Juan bought strawberries of = (3 + 3/8) pounds = 27/8 pounds

So now the amount total fruit salad = 15/4 + 27/8 = (30+27)/8 = 57/8 pounds

Juan eats = (1+15/16) = 31/16 pounds

Now salad left = 57/8 - 31/16 = (114-31)/16 = 83/16 = (5+3/16) pounds

Hence the correct option is (A).

To know more about Fraction refer to:

https://brainly.com/question/78672

#SPJ1

Answer:

x= 14

Step-by-step explanation:

First (and only) we subtract 17 from both sides :

17 + x - 17 = 31 - 17

x = 31 - 17

x = 14

Hope this helped and have a good day

The answer is 14.

To solve this, only one step is required, which is : Subtract 17 from each side.

Answer:3 yards

Step-by-step explanation:

36 inches equals a yard so 36 Multiplied by 3 is 108 Therefore 3 yards

The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer:

Step-by-step explanation:

You want to identify the given shapes as a regular or irregular polygon, or neither.

A regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.

Polygon E is a regular polygon.

A polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.

Any simple polygon that is not a regular polygon is an irregular polygon.

Polygons A, B, D are irregular polygons.

A circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.

<95141404393>

Th equation is \(3v=54\\\).

Given,

product of 3 and vidya's height is 54

v is represented as vidya's height.

Representation of equation is as follows:

The product of 3 and vidya's height can be written as \(3*v=3v\)

and their product is 54,

\(3v=54\).

Thus, the equation is \(3v=54\\\).

To learn more about representation of equation refer here

brainly.com/question/22157922

#SPJ9

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

Given :-

Two legs of a rt. triangle : 8 and 10 respectively.

To find :-

Length of the hypotenuse

Solution :-

Using Pythagorean Theorem;

(hypotenuse)² = (8)² + (10)²

= 64 + 100

hypotenuse = √164

= 12.8 units

Answer:

12.80

Step-by-step explanation:

We have to use the Pythagoras theorem to find the value of the hypotenuse.

Let the value of the hypotenuse be c.

Let us use the below formula to find the length of the hypotenuse.

First, let us replace a and b with 8 and 10 ( the lengths of the legs of the right triangle) with a and b.

a² + b² = c²

8² + 10² = c²

64 + 100 = c²

And now let us solve the above and find the value of c.

164 = c²

√164 = c

12.80 = c

Therefore, the length of the hypotenuse is:

12.80 units

Answer

x=52/5

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators next

Cancel multiplied terms that are in the denominator after that you

Multiply the numbers

Answer:

a = {-5/6 , 1}

Step-by-step explanation:

6a² - a -5 = 0

Factor

(6a + 5)(a - 1) = 0

Root 1

6a + 5 = 0

6a = -5

a = -5/6

Root 2

a - 1 = 0

a = 1

Solution set

a = {-5/6 , 1)

Step-by-step explanation:

the volume of the cylinder is

pi×r²×height = base area × height = 42×13 = 546 in³

the volume of a cone is

pi×r²×height/3 = base area × height / 3

so, the volume of the cone with the same basic sizes as the cylinder is the volume of the cylinder / 3 =

= 546 / 3 = 182 in³

Answer:

Step-by-step explanation:

Regs.

Spinner A and Spinner B below are each to be spun once.

0 18

O 12

6

Spinner A

5

2

4

00

The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

For more such question on probability

https://brainly.com/question/251701

#SPJ8

Answer:

its c and thats on purrrr

Step-by-step explanation:

Answer:

x = 21.19

Step-by-step explanation:

For this problem, we can apply the pythagorean theorem for right triangles.  That equation is:

a^2 + b^2 = c^2

Where side a is 7 and side b is 20 and the hypotenuse c is x.

(7)^2 + (20)^2 = c^2

49 + 400 = c^2

449 = c^2

21.19 = c

Hence, the value of the hypotenuse x is 21.19.

Cheers.

Answer:

B is the correct answer--each x-value corresponds to exactly one y-value.

The answer is 10.67. It can be calculated by integrating and then applying the limits.

What is the integration of \(x^n\)?

The integration of power of a variable is given by the following formula:

\(\int x^ndx=\frac{x^{n+1}}{n+1}\)

If limits are there then limits can be applied after integration.

Consider the given function.

\(\int^3_1(x^2-4x+9)dx\)

Now, apply integration on each term as follows:

\(\int^3_1x^2dx-4\int^3_1xdx+9\int^3_1dx\)

Now, use the following formula to integrate:

\(\int x^ndx=\frac{x^{n+1}}{n+1}\)

Now, the integration will look like as follows:

\([x^3/3]^3_1-4[x^2/2]^3_1+9[x/1]^3_1\)

Now, apply limits to find the answer as follows:

\([3^3/3-1^3/3]-4[3^2/2-1^2/2]+9[3-1]\\\)

\([9-\frac{1}{3}]-4[9/2-1/2]+18\\10.67\)

Hence, the answer is 10.67. It can be calculated by integrating and then applying the limits.

Learn more about integration from the following link:

https://brainly.com/question/22008756

#SPJ1

Trigonometric identity is tanθ ≅ 0.4364

\($\sin A=\frac{2}{5}$\)

\($\cos ^2 A=1-\sin ^2 A=\frac{21}{25}$\)

\($\cos A=\frac{\sqrt{21}}{5}$\)

\($\tan A=\frac{\sin A}{\cos A}=\frac{\left(\frac{2}{5}\right)}{\left(\frac{\sqrt{21}}{5}\right)}=\frac{2}{\sqrt{21}} \cong 0.4364$\)

Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.

The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. tan ( − θ ) = − tan θ tan ( − θ ) = − tan θ cot ( − θ ) = − cot θ cot ( − θ ) = − cot θ sin ( − θ ) = − sin θ sin ( − θ ) = − sin θ csc ( − θ ) = − csc θ csc ( − θ ) = − csc θ

To learn more about Trigonometric identity visit:https://brainly.com/question/24377281

#SPJ9

Answer:

no

Step-by-step explanation: