A cylindrical rain barrel with a diameter of 3 feet and a height of 4.5 feet is filled to a height of 2.5 feet. How many more gallons of water can the barrel hold? Round your answer to the nearest whole number ( 1 ft ^3 ≈ 7.5 gal)

Let's call one triangle ABC, and M the midpoint of AB.

Let's call the other triangle DEF, and midpoint N of DE.

We have a congruent side, AB=DE, congruent medians CM=FN, and congruent angles, ∠AMC=∠DNF

AB ≅ DE  Given

AM ≅ BM and DN ≅ EN    Def median/midpoint

AM+BM=AB  and DN+EN=DE     Segment addition theorem

2AM=2BM=AB and 2DN=2EN=DE   Substitution (eg BM for AM)

AM ≅ BM ≅ DN ≅ EN        Transitivity, algebra

CM ≅ FN   Given

∠AMC ≅ ∠DNF   Given

ΔAMC ≅ ΔDNF     Side Angle Side

AC ≅  DF   CPCTC

∠BMC ≅ ∠ENF   Supplements of congruent angles are congruent

ΔBMC ≅ ΔENF     Side Angle Side

BC ≅  EF      CPCTC

Δ ABC ≅ Δ DEF   Side Side Side

Answer:

see explanation

Step-by-step explanation:

Verifying that the left side equals the right side

left side = sin2x = 2sinxcosx

Consider the right side

2cotxsin²x

= 2 × [tex]\frac{cosx}{sinx}[/tex] × sin²x ← cancel sinx on numerator/ denominator

= 2cosxsinx = left side ⇒ verified

Answer:

4 x minus 3 y = 16. 8 x minus 6 y = 34

Step-by-step explanation:

2 x + 8 y = 15. 4 x + 16 y = 30.

Multiply the first equation by 2

4x +16y = 30

They are identical so they are the same line so there are infinite solutions

2 x - y = 18. 4 x + 2 y = 38.

Multiply the first equation by 2

4x -2y = 36

Add to the first equation

4x -2y = 36

4 x + 2 y = 38.

-----------------------

8x =74

This has a solution

4 x + 7 y = 17. 8 x - 14 y = 36.

Multiply the first equation by 2

8x +14y = 34  add to the second equation

8x +14y = 34

8 x - 14 y = 36.

------------------------

16x = 70

This has a solution

4 x - 3 y = 16. 8 x - 6 y = 34.

Multiply the first equation by -2

-8x + 6y = -32

Add to the second

-8x + 6y = -32

8x - 6y = 34

---------------------------

  0 = 2

This is never true so there is no solution

Answer:

Last one:

4x minus 3y = 16

8x minus 6y = 34

Step-by-step explanation:

4x - 3y = 16

y =(4x - 16)/3

y = (4/3)x - 16/3

8x - 6y = 34

y =(8x - 34)/6

y = (4/3)x - 17/3

These are two distinct parallel lines, hence will never meet

Therefore no solutions

Answer:

upper:65 lower:44

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

In order to find the area you have to complete a formula for triangles going Area =  1/2 bh ( bh means base time the height height is the 13 and the base is the 10 in the photo.)

Answer:

First, the girl walked to the tree. Next, she placed a towel underneath the tree. The, she sat down and took out her book. Finally, the girl took out her food and ate it while reading.

Step-by-step explanation:

It's simple, but it's in a sequence. I dont know if this was related to a passage, if so, could i see it?

Answer:

1. Arc angle

2. Angle at circumference

3. Base angle of an isosceles triangle

4. Sum interior of angles in a triangle

5. Sum interior of angles in a triangle

6. The sum of angles on a straight line

7. Sum interior of angles in a triangle

8. Sum interior of angles in a triangle

9. Angle from a tangent to the radius of a circle

10. Alternate angles of line crossing two parallel lines

Step-by-step explanation:

Here, we note that, the angles where derived as follows;

1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°

2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference

∴ The angle at the circumference, angle 2 = 180°/2 = 90°

3.  Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°

4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)

∴ 25° + 90° + ∡C = 180°

Hence ∡C = 180° - (90° + 25°) = 65°

5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius

Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives

∡8 + 90° + 30° = 180°, hence;

∡8 = 180° - (90° + 30°) = 60°

∡8 = opposite ∡8 = 60°

Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)

Therefore ∡5  = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°

6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)

Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°

7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)

∡E + ∡2 = 180° (The sum of angles on a straight line)

∴ ∡E = 180° - ∡2 = 180° - 90° = 90°

Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°

∴ ∡7 = 35°

8. ∡8 = 60° as found above

9. ∡9 = 90° (Angle from a tangent to the radius of a circle)

10. ∡10 = ∡8 = 60° (Alternate angles).

Answer:6/11

Step-by-step explanation:

The probability of spinning a 1 and flipping a heads is given by the equation A = 1/10

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of spinning a 1 and flipping a heads be A

Now , the equation will be

The total number of values in the spinner = { 1 , 2 , 3 , 4 , 5 }

So , the number of possible outcomes = 5

The probability of spinning a 1 = 1 / number of possible outcomes

Substituting the values in the equation , we get

The probability of spinning a 1 = 1/5

The number of outcomes for flipping a coin = { heads , tails }

Now , the probability of flipping a head = 1/2

So , the probability of spinning a 1 and flipping a heads A = probability of spinning a 1 x probability of flipping a head

Substituting the values in the equation , we get

The probability of spinning a 1 and flipping a heads A = ( 1/5 ) ( 1/2 )

On simplifying the equation , we get

The probability of spinning a 1 and flipping a heads A = 1/10

The probability of spinning a 1 and flipping a heads A = 0.1

Hence , the probability is 1/10

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Answer:

Domain: [0, 6]

Step-by-step explanation:

There's a rising slope between 0 and 6 and then it's decreasing for the rest.

I hope this helped and have a good rest of your day!

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

a^2 + b^2 = c^2

a = side of right triangle

b = side of right triangle

c = hypotenuse

*can only be used for a RIGHT triangle*

( hope i was able to help)

Answer: 4x + 6

Step-by-step explanation:

Answer: 4x + 6

Step-by-step explanation:

Answer: The lower quartile is 10, the upper quartile is 21, and the median is 17.

Step-by-step explanation:

Answer:

It sould be 5,10,26

Step-by-step explanation:

Answer:

the numbers in Set A would round to 0

Step-by-step explanation:

Answer: 118 feet

Step-by-step explanation:

For a rectangular shape: Area = W × L

450 = 9 × L

450 ÷ 9

L = 50

Perimeter of a rectangular shape = 2L + 2W

Perimeter = (2 × 50) + (2 × 9)

= 100 + 18 = 118 feet

Answer:

15

Step-by-step explanation:

800/8 = 100

sooo.......

120/8 = 15

15/100

hope this helps ! :)

Answer:

my answer was B.

Step-by-step explanation:

I chose C and i got it wrong

Answer:

If a bag contains 4 red marbles, 3 blue marbles, and 7 green marbles and a marble is randomly selected from the bag, what is the probability that it is blue? P=3/(3+4+7)=3/14 because each of 14 marbles is equally likely to be drawn.

Step-by-step explanation:

Y is equal to -50. (y= -50)

Step-by-step explanation: Solve for y

by simplifying both sides of the equation, then isolating the variable.y=−50

Answer:

to cover this cube she needs at least 1,176 square inches of protective covering.

Step-by-step explanation:

The surface area of a cube is given by the following formula:

surface area cube = 6*l²

While the perimeter of each face of the cube is:

perimeter face = 4*l

Where l is the length of each side of the cube. Applying the data from the problem we have:

56 = 4*l

l = 56/4= 14 inches

surface area cube = 6*(14)²

surface area cube = 6*(196)

surface area cube = 1,176 square inches.

Therefore to cover this cube she needs at least 1,176 square inches of protective covering.

Answer: 292

Step-by-step explanation:

The formula is: [tex]a_n=a_1+(n-1)d[/tex]

Where;

[tex]a_n=[/tex] [tex]n^t^h[/tex] term or the term we're trying to find.

[tex]a_1=[/tex] First term

[tex]d=[/tex] Common difference.

To find the common difference, take [tex]a_2-a_1[/tex], or [tex]a_3-a_2[/tex] or [tex]a_4-a_3[/tex]

4-(-2)=?

4+2=?

6 -> this is our common difference

---------------------------------

10-4=?

6 -> this is our common difference

--------------------------------

16-10=?

6 -> this is our common difference

------------------------------------------------------------

Knowing this, we plug into the formula the number we're trying to find.

[tex]a_n=a_1+(n-1)d\\a_5_0=-2+(50-1)6\\a_5_0=-2+(49)6\\a_5_0=-2+294\\a_5_0=292[/tex]

Answer:

C. 292

Step-by-step explanation:

Answer:

The answer should be C. 0.29563

Step-by-step explanation:

Answer:

B. 1/2

It will always be a 50/50 probability cause there are only 2 sides

Answer:

Step-by-step explanation:

the first one is D

Answer:

first one is 180

Step-by-step explanation:

526.36 rounded will be =

= 530

Answer:

2(1x1-16)

Step-by-step explanation:

1. Find the gcf (greatest common factor) which is 2

2. Divide by each of the factors and put it inside of the parentheses

Answer:

Answer is option b)

Step-by-step explanation:

[tex]sum \: of \: opposite \: angles \: of \: a \: \\ cyclic \: quadrilateral \: is \: 180 \: degrees \\ from \: the \: diagram \\ 2x + 2x - 12 = 180 \\ 4x - 12 = 180 \\ 4x = 180 + 12 \\ 4x = 192 \\ x = \frac{192}{4} \\ x = 48 \\ angle \: P \: = 2x \\ \: \: \: = 2(48) \\ \: \: \: = 96 \: degrees \\ angle \: N \: = 2x - 12 \\ \: \: \: \: = 96 - 12 \\ \: \: \: = 84 \: degrees[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer:

the answer is (-1, -9)

that is the axis of symmetry

This is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.

Let the point be (x,y)

Case 1: Symmetry with respect to the x-axis

The point becomes (x, -y) as the point flips itself up or down which changes its y coordinate to the negative of whatever it was previously. And no motion is done horizontally so no change in x coordinate.

Case 2: Symmetry with respect to y-axis

The point becomes (-x, y) as the point flips itself left or right which changes its x coordinate to negative of whatever it was previously. And no motion is done vertically so no change in y coordinate.

Case 3: Symmetry with respect to origin

Origin is point at (0,0)

Symmetry with this is a bit ill defined. We use a slant line as if its a diagonal of a square.

The point is reflected to its diagonally opposite quadrant to whatever coordinate it belongs to.

Since diagonally opposite reflection causes both x and y axis to become negative of what it was before, thus,

The point becomes (-x,-y)

The axis of symmetry is where the left side is the mirror image of the right side.

Since this is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.

It will be the x coordinate of the vertex

x = 1

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