Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel. please Show All Work! Thanks!!

Answer:

The ordered pair (e₁, e₂) is (6, 8).

Step-by-step explanation:

Consider the pathway attached below.

It is provided that Fred moves to either 0 or 2 with equal probability, i.e. 0.50.

    e₁ :    1              3             5              7        ...

P (e₁) : 0.50       0.50²      0.50³       0.50⁴   ...

The expected number of steps Fred takes to get to 0 if he is at 1 is:

[tex]e_{1}=(1\times 0.50)+(3\times 0.50^{2})+(5\times 0.50^{3})+(7\times 0.50^{4})+...\\\\[/tex]

The sum series e₁ is an AGP.

The sum of infinite AGP is:[tex]\frac{a}{1-r}+\frac{dr}{(1-r)^{2}}[/tex]

Then the value of e₁ is:

[tex]e_{1}=\frac{1}{(1-0.50)}+\frac{2\times 0.50}{(1-0.50)^{2}}\\\\=2+4\\\\=6[/tex]

It is provided that Fred always moves to 1 if he at step 2.

    e₂ :    2             4             6              8        ...

P (e₂) : 0.50       0.50²      0.50³       0.50⁴   ...

The expected number of steps Fred takes to get to 0 if he is at 2 is:

[tex]e_{2}=(2\times 0.50)+(4\times 0.50^{2})+(6\times 0.50^{3})+(8\times 0.50^{4})+...\\\\[/tex]

The sum series e₂ is an AGP.

The sum of infinite AGP is:[tex]\frac{a}{1-r}+\frac{dr}{(1-r)^{2}}[/tex]

Then the value of e₂ is:

[tex]e_{1}=\frac{2}{(1-0.50)}+\frac{2\times 0.50}{(1-0.50)^{2}}\\\\=4+4\\\\=8[/tex]

Thus, the ordered pair (e₁, e₂) is (6, 8).

Answer:

(3, 4)

Step-by-step explanation:

For e_1, there is first a 1/2 chance that Fred will go to point 0 on the first move, giving us an expected value of 1/2. Similarily, there is 1/4 chance that Fred will go to point 0 on the 3rd move, giving us an expected value of 3/4th moves. We continue, and we see that the expected value for the number of moves is this.

[tex]1/2 + 3/4 + 5/8 + 7/16 + 9/32 + 11/64 ...[/tex]

This equation eventually equals to 3, so e_1 is equal to 3.

For e_2, it's just e_1 + 1, because Fred has to move to point 1 in the first place.  

Answer:

2x+y -3 =0

Step-by-step explanation:

0 = Ax + By + C is the general form of a line

2x+4y +2 = 3y +5

Subtract 3y from each side

2x+4y-3y +2 =3y+5-2y

2x+y +2 = 5

Subtract 5 from each side

2x+y +2-5 = 5-5

2x+y -3 =0

Answer:

≈ 12.05

Step-by-step explanation:

Pythagora

x = √(9² + 8²)

= √(81 + 64)

= √145

≈ 12.05

Answer:

D. Yes The Triangles ARE ≅

Step-by-step explanation:

By definition equilateral triangles have all equal angles and sides. Since they share a side that means one of each triangle's sides are congruent. Using the transitive property (if side a ≅ side b and side b ≅ side c, then side a ≅ side c), you can prove that all other sides are congruent or equal in measure, no matter how you pair them.

Answer:

a) How much water was released during the flood?

14878080000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

0.78%

Step-by-step explanation:

a) How much water was released during the flood?

The first step would be to find out how many seconds are in a week

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

Hence, the number of seconds in a week =

1 week × (7 days/1 week)× (24 hours/1 day )×( 60 minutes/1 hour) ×( 60 seconds/1 minute)

= 604800 seconds

Therefore, the quantity of water released per week =

604800 seconds × 24,600 cubic feet per second

= 14,878,080,000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

This is calculated as quantity released during the week ÷ Quantity of water in the dam × 100%

Quantity of water released during the flood in a week = 14,878,080,000 cubic feet

Quantity of water in the dam= 1,900,000,000,000 cubic feet of water

Percentage of the dam released during the flood =

14,878,080,000 cubic feet ÷ 1,900,000,000,000 × 100

= 0.7830568421%

Approximately = 0.78%

Answer:

40.

Step-by-step explanation:

That is 5 * 4 * 2

= 40 combinations of a set of bowl, cup and spoon.

Answer:

4 seconds.

Step-by-step explanation:

The given equation is

[tex]h=-16t^2+64t[/tex]

where, h is height in feet of a golf ball above the ground after being hit into the air and t is the number of seconds elapsed since the ball was hit.

We need to find the time for the ball to hit the ground.

At ground level the height of ball is 0, i.e., h=0.

[tex]-16t^2+64t=0[/tex]

[tex]-16t(t-4)=0[/tex]

Using zero product property, we get

[tex]-16t=0\Rightarrow t=0[/tex]

[tex]t-4=0\Rightarrow t=4[/tex]

Therefore, it will take 4 seconds for the ball to hit the ground.

Answer:

4 seconds

That's your answer!!

Answer:

Equation of a line is y = mx + c

where m is the gradient

c is the y intercept

y = 4x - 1

Comparing with y = mx + c

The gradient = 4

y intercept = - 1

[tex]y = \frac{1}{3} x + 3[/tex]

Comparing with y = mx + c

The gradient is 1/3

The y intercept is 3

Hope this helps you

Answer:

4 and  -1

1/3 and 3

Step-by-step explanation:

for y=4x-1

y intercepts where  x=0 so f(0)=4*0-1=-1

y intecepts = -  1

the gradient is y2-y1/x2-x1 where y2=f(x2)=4x2-1 and y1=f(x1)=4x1-1

the gradient is 4x2-1-4x1+1/x2-x1=4 ( the coeficient of x)

for y=1/3x+3

the gradient is 1/3

y intercepts is f(0)=3

Answer:

The length of the side PC is 34 cm.

Step-by-step explanation:

We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.

Suppose BP = 16 cm and AD = 90 cm.

As, it is given that AD = 90 cm and the three sides AB = BC = CD.

From the figure it is clear that AD = AB + BC + CD

So, AB = [tex]\frac{90}{3}[/tex] = 30 cm

BC = [tex]\frac{90}{3}[/tex] = 30 cm

CD = [tex]\frac{90}{3}[/tex] = 30 cm

Since the triangle, BPC is a right-angled triangle as [tex]\angle[/tex]PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.

Now, the Pythagoras theorem states that;

[tex]\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}[/tex]

[tex]\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}[/tex]

[tex]\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}[/tex]

[tex]\text{PC}^{2} = 256+900[/tex] = 1156

[tex]\text{PC}=\sqrt{1156}[/tex]

PC = 34 cm

Hence, the length of the side PC is 34 cm.

Answer:

752x·39·2z·34y

Step-by-step explanation:

add like terms then put it all into multiplication

Answer:

c on edge

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it's a half circle , rectangle and triangle that can exactly be carved out of the figure

Answer:

C

Step-by-step explanation:

half-circle ; rectangle ; triangle

we also need the vertical distance between the original spot and the ground to solve this,

Answer:

tan 35° = \frac{4m}{r}

Step-by-step explanation:

Tan is the length of the opposite leg over the length of the adjacent length and for angle 35 4 was the length of the opposite leg and r was the length of the adjacent leg

Answer:

x = 65

Step-by-step explanation:

interior angles = 180°

45° + (2x - 5)° = 180°

(2x - 5)° = 180° - 45°

(2x - 5)° = 135°

2x° = 135° - 5°

2x° = 130°

x° = 130° ÷ 2

x° = 65°

x = 65

Answer:

About 137 tigers.

Step-by-step explanation:

You can solve this by using a proportion...

If 54 tigers out of 1234 were marked, then 6 out of x were marked in the second time.

54 / 1234 = 6 / x

54x = 1234 * 6

54x = 7404

x = 7404 / 54

x = 137.11111111, which can be rounded to about 137.

To check the work, 54 / 1234 is about 0.0438. 6 / 137 is about 0.0438. That means that about 4.38% of the tigers in each batch were marked.

Answer:

s = t - m

Step-by-step explanation:

Assuming s equals the amount of time it would take Sam, subtracting the amount of time it takes Mark from the time it takes them together would give you the time Sam would take since with Sam's help, the time would equal t hours. Then without Mark's help is how long it would take him.

Answer:

4

Step-by-step explanation:

(3^8 x 2^-5 x 9^0)^-2 x (2^-2/3^3)^4 x 3^28 =

= 3^-16 x 2^10 x 1 x 2^-8 x 3^-12 x 3^28

= 3^0 x 2^2

= 4

Answer: 35/16

Step-by-step explanation:

Answer:

20 cookies

Step-by-step explanation:

Change from minutes and seconds to seconds

1 minute 30 seconds = 90 seconds

3 minutes 45 seconds = 3 *60 +45 = 180+45 = 225 seconds

Now we can use ratios to solve

8 cookies          x cookies

-------------   = -----------------

90 seconds         225 seconds

Using cross products

8 * 225 = 90x

Divide each side by 90

1800/90 = 90x/90

20 =x

Answer:

80

Step-by-step explanation:

720/P = 9/1

Cross multiply.

9P = 720

P = 720/9

P = 80

Answer:

solution,

Area of trapezoid:

[tex] = \frac{a + b}{2} \times h \\ = \frac{3 + 7}{2} \times h \\ = \frac{10}{2} \times 3 \\ = 15 \: {units}^{2} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

The area below has an Area of 15 (meters?) squared.

Step-by-step explanation:

[( 7 + 3 ) x 3] / 2 = [ 10 x 3 ] / 2

= 30 / 2

= 15

Answer:

Dependent = cost

independent = number of DVDs

Discrete

Function :f(x) = 16 x  = 16 (6)

Solution = $96

Step-by-step explanation:

Hi, to answer this question we have to write a function:

The cost (f(x)) must be equal to the price per DVD (16) multiplied by the number of DVDs (x)

Function: f(x) = 16 x  

Dependent = f (x) =(cost)

Independent = x (number of DVDs)

Solution for x=6

f(6) = 16 (6)

Cost = $96

Since the number of DVDs can't be fractional it's a Discrete function.

Answer:

u have insta

Step-by-step explanation:

Answer:

17. (B)

18. both opposite sides are equal in length and height.

Step-by-step explanation:

Answer:

q = 18 ?

Step-by-step explanation:

This is not a complete question but ill give it a shot!

If we are following a pattern then we see q is 11 more than r.

So we do 11 + r (7) to get 18!

mark as brainliest

Answer:

13 inches

Step-by-step explanation:

Use the formula P = 2l + 2w to find width.

80 = 2(27) + 2w

80 = 54 + 2w

80 - 54= 2w

26 = 2w

w = 26/2

w = 13

The width of the rectangle is 13 inches.

Answer:

She spent $70.65.

Step-by-step explanation:

Represent the amount spent by x.

Then $22.50 - x = -$48.15.

Combining like terms, we get:

$22.50 + $48.15 = x, or

x = $70.65

She spent $70.65.

Answer:

[tex]\frac{r^{15}}{512}[/tex]

Step-by-step explanation:

Given

[tex](8r^{-5})^{-3}[/tex]

Required

Simplify

This can be simplified using the following law of indices;

[tex](ab)^n = a^{n}b^{n}[/tex]

The equation becomes

[tex](8^{-3})(r^{-5})^{-3}[/tex]

Express [tex]8^{-3}[/tex] as a fraction

[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]

Simplify [tex]8^3[/tex]

[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]

The expression can further be simplified using the following law of indices;

[tex](a^m)^n = a^{mn}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes

[tex](\frac{1}{512})(r^{-5*-3})[/tex]

[tex](\frac{1}{512})(r^{15})[/tex]

[tex]\frac{r^{15}}{512}[/tex]

Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

19 units

Step-by-step explanation:

In a parallelogram, opposite sides are congruent. So, we can set up a formula that looks like this: 3x - 8 = x + 10. When you solve for x, you'll get 9. 9 + 10 = 19 units

The length of the side TU of the parallelogram is 19 units long.

A parallelogram is a quadrilateral with opposite pair of sides parallel and equal.

In the question, we are given a parallelogram STUV.

The length of the side TU is given as x + 10.

The length of the side VS is given as 3x - 8.

As the sides, TU and VS are opposite to each other, and the quadrilateral STUV is a parallelogram, so they are equal.

∴ TU = SV

or, x + 10 = 3x - 8

or, x + 10 - 3x = 3x - 8 - 3x (Subtracting 3x from both the sides)

or, -2x + 10 = -8 (Simplifying)

or, -2x + 10 - 10 = -8 - 10 (Subtracting 10 from both sides)

or, -2x = -18 (Simplifying)

or, -2x/(-2) = -18/(-2) (Dividing both sides by -2)

or, x = 9 (Simplifying).

Now, TU = x + 10 = 9 + 10 = 19.

∴ The length of the side TU of the parallelogram is 19 units long.

Learn more about parallelograms at

https://brainly.com/question/24056495

#SPJ2

Answer:

(-2,3)

Step-by-step explanation:

When you reflect a point over the x axis, the y value is changed to the opposite value (positive)

So (2,-3) reflected across the x axis is (2,3)

Next, we need to reflect this across the y axis

When you reflect a point over the y axis, the x value is changed to the opposite value (negative)

(2,3) reflected across the y axis is (-2,3)

Answer:

24 different ways

Step-by-step explanation:

( 1 ) We can apply factorial in this case. We have 4 elements, melon, apple, orange, and peach. The number of ways with which we have to arrange these fruits should be 4! ( again, there are 4 elements ).

4! = 4 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1

4 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1 = 12 [tex]*[/tex] 2 [tex]*[/tex] 1

12 [tex]*[/tex] 2 = 24 different ways

( 2 ) The first method was the simpler approach. You can confirm this answer through another method...simply list out the different possibilities, altering their order in a specified manner.

{ melon, apple, orange, peach }

{ melon, apple, peach, orange }

{ melon, peach, apple, orange }...and keep on trying different combinations!