A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides. The exterior surface area of the trough is ________. The volume of the trough is _____. If a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be ______ cubic feet of water left in the trough.

Answer:

y = 5x

Step-by-step explanation:

20 = 5(4)

20 = 20

Since they directly vary, this is a linear equation, and the slope is 5.

y = mx + b

y = 5x + b

20 = 20 + b

b = 0

So the equation is

y = 5x

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have:

[tex](x-2)^2+(y+3)^2=9\\\\(x-2)^2+(y-(-3))^2=3^2[/tex]

a) center (2, -3)

b) radius r = 3

c) in the attachment

The answers are:

The equation of a circle centered in the point (a, b) of radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

Then for the equation:

(x-2)^2+(y+3)^2 = 9 = 3^2

We can see that:

a) The center is the point (2, -3)

b) The radius is R = 3, and the diameter is twice the radius, so it is equal to 6.

c) The graph can be seen below:

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Answer:

F

Step-by-step explanation:

Each vertex of ABCD corresponds to the vertex of EFGH in the same position.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex A corresponds to vertex E.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex B corresponds to vertex F.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex C corresponds to vertex G.

Parallelogram ABCD is similar to parallelogram EFGH.

Vertex D corresponds to vertex H.

Answer:

-10416.

Step-by-step explanation:

This is a Geometric Series with first term 4 and common ratio -5.

Sum of 6 terms = a1 .  (r^6  - 1 )/ ( r - 1)

= 4 *( (-5)^6 - 1) / (-5-1)

= -10416  (answer).

Answer:

-10416

Step-by-step explanation:

The correct option is B.

The exact circumference of a circle with radius X/2 miles is Xπ miles.

To find the circumference of a circle, we use the formula: Circumference (C) = 2πr, where r is the radius of the circle. Given that the radius is X/2 miles, we substitute this value into the formula:

C = 2π × (X/2)

  = Xπ miles

Therefore, the exact circumference of the circle with radius X/2 miles is Xπ miles.

The correct answer is B) xπ miles.

In summary, to find the circumference, we simply multiply the radius (X/2) by 2π, which gives us Xπ miles. This answer aligns with option B) xπ miles.

The complete question is here:

Find the exact circumference of a circle with the given radius.

X/2 miles

C = _____

A) ¼xπ miles

B) xπ miles

C) 2xπ miles

Answer:

20

Step-by-step explanation:

So to get 20 all you had todo was multiply 20,000 by 0.001, because milliliters converted into liters is 1 milliliter= 0.001 liters.

Answer:

20 Liters

Step-by-step explanation:

One way to look at it is that there are 1000 mL in one L.  But I think a better way in general for  unti conversions is to do it like this.

20000 ml * [tex]\frac{1L}{1000 mL}[/tex] Where you can just cancel out the units.  Hopefully it made sense.  If you were converting from L to ml you would use [tex]\frac{1000 mL}{1 L}[/tex]

Answer:

(1, 5)

Step-by-step explanation:

You need a point in the shaded region that is not on the line of the graph.

The points can't be on the line because the line is a dotted line, which means there is either a < or > sign in the inequality, so the solutions are strictly less than or greater than the values on the line.

 Points A and B are on line so they aren't solutions.

Point (5, -5) is below the line, so that isn't a solution for this equation either

Point (1, 5) is in the shaded region, so it's a solution

Answer:

The distance between Saugerties and Kingston is 10 miles.

Step-by-step explanation:

4*2.5 = 10.

Answer:

x³+y³=4697

Step-by-step explanation:

x+y=11

y=11-x

325=x²+y²

=x²+(11-x)(11-x)

=x²+121-11x-11x+x²

325=2x²-22x+121

0=2x²-22x-204

=(2x+12)(x-17)

0=2x+12 or 0=x-17

-12=2x 17=x

-6=x

y=11-x

y=17 or -6

(-6,17) or (17,-6)

=x³+y³

=(-6)³+(17)³

=4697

Answer:

for 5 hours: b is 6

for 5 minutes: b is 4

60 times more skin in 5 hours than 5 minutes

Step-by-step explanation:

I think it should be written as a x 10^b, so I'm going to answer it that way.  

3 x 10^6 = 5 times 10^6

   10^6 = 1,000,000, so we have 3 x 1,000,000 = 3,000, 000

5 x 10^4 = 5 times 10^4

   10^4 = 10,000, so we have 5 x 10,000 = 50, 000

For part 3, divide 3 million by 50 thousand to find the scalar multiple

   3,000,000/50,000 = 300/5 = 60

Answer:

The approximate number of particles of skin a human can shed in five hours can be written in the form a × 10b, where a is 3 and b is 6.

The approximate number of particles of skin a human can shed in five minutes can be written in the form a × 10b, where a is 5 and b is 4.

Humans shed approximately 60 times more particles of skin in five hours than in five minutes.

Step-by-step explanation:

In scientific notation, a number can be written in the form, a × 10b, where a is a number that must be greater than or equal to 1, but less than 10, and b is any integer.

First, write the approximate number of particles of skin a human can shed in five hours in scientific notation. This number is three million which can be written in the form a × 10b, where a is 3 and b is 6.

Next, write the approximate number of particles of skin a human can shed in five minutes in scientific notation. This number is fifty thousand which can be written in the form a × 10b, where a is 5 and b is 4.

Then, divide the approximate number of particles a human can shed in five hours by the approximate number of particles a human can shed in five minutes to find out how many times more skin is shed in five hours than in 5 minutes.

Therefore, humans shed approximately 60 times more particles of skin in five hours than in five minutes.

The scale factor is 1/3

The correct answer is 1/3

:))

The scale factor of the given dilation is 1/3

To change the size of a figure without changing the figure's shape, we use a exact number or factor which is called scale factor.

Dilated figure = Original figure × Scale factor

In the diagram,

Co-ordinate of the point V in original triangle is (3, - 6)

Co-ordinate of the point V' in dilated triangle is (1, -2)

We know that, if we multiply scale factor to the original co-ordinate then we get dilated co-ordinate.

Here, if we multiply 1/3 to the original co-ordinate V(3, - 6) then we get the dilated co-ordinate V' (3/3, -6/3) , i.e. V'(1, -2)

So, the scale factor is 1/3.

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Answer:

See below. An example is C = 0.2s.

Step-by-step explanation:

You can write an expression to represent any situation. Harlan makes a commission which is usually a percentage of the price. For example, if Harlan earns 20% on each purchase then when he sells a $100 he earns $20 of commission. For any price or cost on shoes s, this would be 0.2s. His commission C = 0.2s.

Answer:

84

Step-by-step explanation:

3 times 4= 12

12 times 7= 84

Answer:

1000 units wide, 300 units is the height

Step-by-step explan

you do 500-(-500) for the wideness, 1000 and for height, 0-(-300) is 300

Answer:  320

Step-by-step explanation:

Coterminal means it is in the same place on the Unit Circle but with one or more rotations clockwise or counterclockwise.

Note: one rotation is 360°

-760 + 360 = -400

                     -400 + 360 = -40

                                           -40 + 360 = 320  

320 is between 0 and 360 so this is the angle we are looking for!

5×4 is 20. So I figure 9×4 is 36. 36 minutea

Answer: 20 minutes

Step-by-step explanation:

Imagine that each person is assigned one wall, and all 5 people begin painting at the same time.

Since everyone will finish painting their assigned wall after 20 minutes, it takes one person 20 minutes to paint one wall.

If we have 9 people and 9 walls, we can again assign one wall to each person.

Everyone will take 20 minutes to paint their assigned wall.

In other words, it takes 20 minutes for 9 people to paint 9 walls.

Answer:

D 13

Step-by-step explanation:

(b^4)^4         b^5 * b^x

-------------- = ----------------

b^2                 b^4

We know that a^c^d = a^ (c*d)

b^(4*4)         b^5 * b^x

-------------- = ----------------

b^2                 b^4

b^16         b^5 * b^x

-------------- = ----------------

b^2                 b^4

We know that a^ c * a^d = a^ (c+d)

b^16              b^(5+x)

-------------- = ----------------

b^2                 b^4

We know that a^c / a^d = a^ (c-d)

b^(16-2) = b^(5+x-4)

b^14 = b^(1+x)

Since the base is the same, the exponent must be the same

14=1+x

Subtract 1 from each side

14-1 = 1+x-1

13 =x

Answer:

Period, but I have to add more characters so it'll let me post this answer.

Period gives the horizontal length of one cycle of a periodic function as 2π.

Given that,
To determine which term gives the horizontal length of one cycle of a periodic function.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the periodic function 1 period is consist of 2π on the horizontal axis, so, the period represents the horizontal length of the periodic function.

Thus, Period gives the horizontal length of one cycle of a periodic function as 2π.

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Answer:

=[{(x+4)*5} + 4] * 5

Step-by-step explanation:

If x is input

Adding 4

=x+4

then multiplying by 5

=(x+4)*5

Giving the result of first run in second will give

=[{(x+4)*5} + 4] * 5

Answer: 15 Inches

Step-by-step explanation:Remember that the Perimeter of a rectangle is the distance around it.

So,

    Perimeter = Length + Width + Length + Width

or

     P = 2L + 2W

If P=42 inches and W = 6 inches,

    42 = 2L + 2(6)

    42 = 2L + 12

    30 = 2L              [subtract 12 from both sides]

    15 = L               [divide both sides by 2]

The length (L) is 15 inches.

The length (L) is 15 inches. so the correct option is B.

Its the sum of length of the sides used to made the given figure.

It is given that the Perimeter of a rectangle is the distance around it.

Given that the perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches then we need to find the length.

So,

The Perimeter = Length + Width + Length + Width

Let the length of the rectangle = l

the width of the rectangle = w

or P = 2L + 2W

If P=42 inches and W = 6 inches,

42 = 2L + 2(6)

42 = 2L + 12

30 = 2L            

L = 15

Hence, The length (L) is 15 inches.

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Answer:

57 in²

Step-by-step explanation:

S=1/2*8*3=12

4s+9=4*12+9=57

Tim is 9 years old, and Amy is 18 years old. We found this by dividing 54 by 6 and 3 respectively, based on the given equations 6T = 54 and 3A = 54.

To solve the problem involving Tim and his sister Amy's ages, we need to set up equations based on the information given. The problem states that six times Tim's age is 54 and that three times Amy's age is also 54.

Let's let T represent Tim's age and A represent Amy's age. We can set up the following two equations based on the problem:

To find Tim's age, we divide both sides of the first equation by 6:

T = 54 / 6

T = 9

So, Tim is 9 years old.

To find Amy's age, we divide both sides of the second equation by 3:

A = 54 / 3

A = 18

So, Amy is 18 years old.

Answer:

$618.80

Step-by-step explanation:

If the tablet is on sale for 15% off, you pay 85% of the original price.

85% of $700 is

700(0.85) = $595

You pay 4% sales tax on $595, which is

$595(0.04) = $23.80

The total cost you pay is $595 + $23.80 = $618.80

Final answer:

To find out how many hours Jorge volunteers on Saturday, we multiply his Wednesday volunteer hours of 2/3 hour by 5, which gives us 10/3 hours or 3 1/3 hours.

Explanation:

If Jorge volunteers for 2/3 hour at the animal shelter on a Wednesday and volunteers 5 times as many hours on Saturday, we can calculate the hours he volunteers on Saturday. First, multiply the time he volunteers on Wednesday by 5:

2/3 hour × 5 = 10/3 hours, which is equivalent to 3 1/3 hours or simply 3.33 hours when converted to decimal form.

Therefore, Jorge volunteers 3 1/3 hours or 3.33 hours on Saturday at the animal shelter.

Answer:

The final price is $34.83

Step-by-step explanation:

we know that

1) The original price is $64.50

2) Is now on sale for 1/10 off

so

the new price is

$64.50(1-0.10)=$58.05

3) Get an additional 40%

$58.05(1-0.40)=$34.83

[tex]OA=OD=AD=R\Rightarrow \bigtriangleup OAD\: is\: an\: equilateral\: triangle \\ \Rightarrow \widehat{AOD}=\widehat{OAD}=\widehat{ODA}=60° \\ \widehat{ABD}= \frac{\widehat{AOD}}{2} = \frac{60°}{2} = 30°[/tex]

Answer:

Step-by-step explanation:

Given: AD≅AO

To find: m∠OAD and m∠DBA.

Solution: It is given that AD≅AO, and also OA≅OD (Radius of circle), therefore ΔAOD is an equilateral triangle.

Hence, m∠OAD=m∠ODA=m∠AOD=60°.

Now, we know that the intercepted angle is half of the central angle, thus

[tex]m{\angle}DBA=\frac{m{\angle}AOD}{2}[/tex]

⇒[tex]m{\angle}DBA=\frac{60^{\circ}}{2}[/tex]

⇒[tex]m{\angle}DBA=30^{\circ}[/tex]

Hence, the measures of [tex]{\angle}OAD[/tex] and [tex]{\angle}DBA[/tex] are [tex]60^{\circ}[/tex] and  [tex]30^{\circ}[/tex] respectively.

Answer:

[tex]x^{2}-\frac{5\sqrt{3}}{2}x+3[/tex]

Step-by-step explanation:

we know that

The quadratic equation is equal to

[tex](1)(x-\frac{\sqrt{3}}{2})(x-2\sqrt{3})\\ \\=x^{2} -2\sqrt{3}x-\frac{\sqrt{3}}{2}x+3\\ \\=x^{2}-\frac{5\sqrt{3}}{2}x+3[/tex]      

Answer:

x < -1.8

Step-by-step explanation:

First, subtract 2.4 from each side, you will get 3x > -5.4

Second, divide by 3 on both sides, this will make the > turn into <.

Finally you will end up with x < -1.8.

Mark brainliest plz!

Answer:

The answer to 3x+2.4 > 3.0 is x > 0.2

Step-by-step explanation:

6.75 feet is the actual height of the horse