Stephan has a box in the shape of a hexagonal prism where the hexagonal bases are regular. A net of the box is below.

In the hexagon diagram, all the sides are drawn with a rectangle on every side and each is added and another hexagon is added to a rectangle.

Note: Figure is not drawn to scale.

He measured the height of the box to be 7 in. Then, Stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 9 in and a base of 10 in.

The geometry of the hexagon is equally divided into six parts of the triangles are shaded inside. The top side is marked as 10 inches, and the length of the triangle is 9 inches.

Note: Figure is not drawn to scale.

What is the surface area of the hexagonal prism?
A.
750 sq in
B.
690 sq in
C.
960 sq in
D.
1,380 sq in

4/5 is a real number.

A real number is a value in mathematics that expresses a quantity along a continuous line. Real numbers can be expressed as fractions or decimals and can be positive, negative, or zero.

4/5 is a rational number in this situation, which is a form of real number that may be written as a ratio of two integers. A real number can also be irrational, which means that it cannot be stated as a ratio of two integers and that its decimal representation goes on indefinitely without repeating.

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The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

From the question, we have the following parameters that can be used in our computation:

5y+4= (x+3)²+12

Swap x and y in the equation

So, we have

5x + 4= (y + 3)² + 12

When we make the vairiable y the subject, we have

y = -3 ± √(5x - 8)

Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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The rate of the speeding car is 0.493.

We have,

The police car is at 80 mph and it is 44 yards from the intersection, is increasing at 45 mph, while the other car is 117 yards away from the intersection.

So, Rate of speeding car

= (45- 80)/ (117- 44)

= -35/(-73)

= 35/73

= 0.493

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Answer: correct answer is A 2/3x^2

Step-by-step explanation:Multiply each side of the equation by 2cos2θ to get 2rcos2θ=3sinθ.

Multiply each side of the equation by r to get 2r2cos2θ=3rsinθ. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 2x2=3y.

Divide each side of the equation by 3 and reverse the order of the equation to find that y=2/3x^2

Answer:

Therefore, the fully factorised form is 5a(1 + 3b).

Step-by-step explanation:

5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.

The composition of functions is solved and gof ( -7 ) = 1,286

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 13 - 2x

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = 2x² - 6x - 10

Now , g o f ( x ) = 2 ( 13 - 2x )² - 6 ( 13 - 2x ) - 10

On simplifying , we get

g o f ( x ) = 2 ( 169 + 4x² - 52x ) - 78 + 12x - 10

g o f ( x ) = 250 + 8x² - 92x

Now , the composition of function is

g o f ( -7 ) = 8 ( -7 )² - 92 ( -7 ) + 250

g o f ( -7 ) = 392 + 894

g o f ( -7 ) = 1,286

Hence , the function is g o f ( -7 ) = 1,286

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Answer:

An inequality that represents this situation is:

x + 5 ≤ 11

where x is the number of outfits you can pack in addition to the 5 you already have.

Step-by-step explanation:

i got a what if If you have 6 outfits packed already, then the inequality becomes:

x + 6 ≤ 11

where x is the number of outfits you can pack in addition to the 6 you already have. happy to help

The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

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Answer:(4,5π/4)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).

11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

The relationship between the distance that birds fly in relation to the time they do so, is positive.

There are about 3 outliers but for the most part, the relationship is positive.

The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.

There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.

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Marcus jogged [tex]2\frac{1}{2}[/tex] miles over the weekend.

Marcus jogged [tex]1\frac{2}{5}[/tex] miles on Saturday and 9/10 miles on Sunday.

we first need to find a common denominator:

[tex]1\frac{2}{5}[/tex]  = 7/5

9/10 = 0.9 miles

Now, we can round each of these to the nearest 1/2:

7/5 is closer to [tex]1\frac{1}{2}[/tex] than 1, so we round to [tex]1\frac{1}{2}[/tex]

0.9 is closer to 1 than 1/2, so we round to 1

Adding these rounded values, we get:

[tex]1\frac{1}{2}[/tex] + 1 =[tex]2\frac{1}{2}[/tex]

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Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

[tex] - 16 = a - 19[/tex]

[tex]a = - 16 + 19[/tex]

[tex]a = 3[/tex]

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

Step-by-step explanation:

well, the combination of all set elements.

FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).

the combination of both sets is then

{b, c, d, e, g, h}

The solution of the equation x - √x + 4 - 2√(x+3) =0 is given by x ≈ 0.449 or x = 2.

The expression is equal to,

x - √x + 4 - 2√(x+3) =0

By rearranging the terms and simplifying the expression as follows,

x - √x + 4 - 2√(x+3) = 0

⇒x + 4 = √x + 2√(x+3)

Square both sides to eliminate the square root,

⇒ (x + 4)² = (√x + 2√(x+3))²

⇒ x² + 8x + 16 = x + 4(x+3) + 4√x√x+3

⇒x² + 8x + 16 -x -4x -12 = 4√x√x+3

⇒ x² + 3x + 4 = 4√x√x+3

⇒x² + 3x + 4 = 4√x√(x+3)

⇒ x² + 3x + 4 = 4√(x²+3x)

Squaring both sides again gives,

⇒ (x² + 3x + 4)² = 16(x²+3x)

Expanding the left side gives,

x⁴ + 6x³ + 17x² + 24x + 16 = 16x² + 48x

Simplifying and rearranging the terms,

x⁴ + 6x³ + x² - 24x + 16 = 0

Factor this equation as follows,

(x² + 4x - 2)(x² + 2x - 8) = 0

The solutions are,

x²+ 4x - 2 = 0 or x² + 2x - 8 = 0

Solve each quadratic equation using the quadratic formula,

For x² + 4x - 2 = 0

x = (-4 ± √(4² - 4(1)(-2))) / (2(1))

⇒ x = (-4 ± √24) / 2

Simplifying the expression under the square root gives,

⇒ x = (-4 ± 2√6) / 2

⇒ x = -2 ± √6

For x² + 2x - 8 = 0

x = (-2 ± √(2² - 4(1)(-8))) / (2(1))

⇒x = (-2 ± √36) / 2

Simplifying the expression under the square root gives,

⇒ x = (-2 ± 6) / 2

⇒ x = -4 or x = 2

Discard the negative solution -2-√6 and -4

As it would lead to a negative value under the square root.

The final solutions are,

x ≈ 0.449 or x = 2

Therefore, the solution of the given equation is equal to x ≈ 0.449 or x = 2.

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The above question is incomplete , the complete question is:

Solve for x.

x - √x + 4 - 2√(x+3) =0

The pairs of supplementary angles are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.

Thus, the pair of supplementary angles in the given diagram are;

B. <SQT and <SQR

C. <TQP and <RQP

D. <SQR and <RQP

F. <SQT and <TQP

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If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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The trio of sides that will make a right triangle are the ones in the first option:

5, 12, and 13.

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.

So for example, for the first option we would have:

5^2 + 12^2 = 13^2

25 + 144 = 169

169 = 169

The equation is true, thus, these sides make a right triangle.

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Answer:

12 • (17 • 23) = (12 • 17) • 23

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

We have,

The formula given is incorrect.

The correct formula for Pythagorean triples with a given integer z is:

(z² - 1², 2z, z² + 1²)

Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:

z² + 1² = 29²

z² + 1 = 29²

z² = 29² - 1

z² = 840

z = √840

z = 28.98

Since z must be an integer, we can try integer values close to 28.98 to find one that works.

Trying z = 29,

a = z² - 1² = 840 - 1 = 839

b = 2z = 58

c = z² + 1² = 840 + 1 = 841

Therefore,

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

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The values of the trigonometric functions are

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A = 5/12

5. cosec A = 13/12

6. sec A = 13/5

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Examples of these functions are; sin, cos , tan cot, cosec , sec e.t.c

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

here the opposite side to angle A is 12 and the adjascent is 5 while the hypotenuse is 13.

Therefore,

1. sin A = 12/13

2. cos A = 5/13

3. Tan A = 12/5

4. cot A =1/tan A = 5/12

5. cosec A = 1/sin = 13/12

6. sec A = 1/cos = 13/5

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Answer:

The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.

Step-by-step explanation:

The entrepreneur's revenue is  $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is  $625x - $33,750

The entrepreneur's revenue from x sold-out performances is given by the formula:

Revenue = (Price per Performance) x (Number of Performances)

Revenue = $2325 x x

Revenue = $2325x

The entrepreneur's cost from x sold-out performances is given by the formula:

Cost = Overhead + (Production Cost per Performance) x (Number of Performances)

Cost = $33,750 + $1700x

The entrepreneur's profit from x sold-out performances is the revenue minus the cost:

Profit = Revenue - Cost

Profit = $2325x - ($33,750 + $1700x)

Profit = $625x - $33,750

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Answer:

(5,5π/4)

(5,−3π/4)

(−5,π/4)

(−5,−7π/4)

Step-by-step explanation:The correct answer is:

r = 5 units (distance from the pole)

θ = 5π/4 radians (angle measured counterclockwise from the ray θ = 0)

Note: The polar coordinates for point A on the given graph are r = 5 and θ = 5π/4. The r-value represents the distance from the pole to the point, and the θ-value represents the angle measured counterclockwise from the reference ray θ = 0.

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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To produce 60 liters of a 55% acid solution, we need 18 liters of a 50% acid solution and 42 liters of a 60% acid solution.

Let x be the number of liters of the 50% acid solution needed, and y be the number of liters of the 60% acid solution needed.

We can set up two equations based on the amount of acid and the total volume:

0.50x + 0.60y = 0.55(60)

x + y = 60

Simplifying the first equation:

0.50x + 0.60y = 33

5x + 6y = 330 (multiplying both sides by 10)

We can solve for one variable in terms of the other in the second equation, and substitute into the first equation:

y = 60 - x

5x + 6(60 - x) = 330

Simplifying:

x = 18

So we need 18 liters of the 50% acid solution, and:

y = 60 - x = 42

So we need 42 liters of the 60% acid solution.

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Without more information or a diagram, it's not possible to definitively determine which side-angle relationship (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of sides and angles known in a triangle.

Given the question, it's clear that we are discussing a concept in Geometry - the side-angle relationships in a triangle. However, without more information or an accompanying diagram, it isn't possible to definitively determine which of the side-angle relationships (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of side and angle information known about a triangle. For example, ASA means that we know two Angles and the Side between them. SAS relates to knowledge of two Sides and the Angle between them, and so forth. More information or a visual representation would allow a more conclusive answer.

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time tables on the map mannnnn

The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.

Given that,

Last year, they sold 1,080 pounds of cookie dough to 360 people.

This means that they sold an average of 3 pounds of cookie dough per person.

Number of pounds of cookie dough = 3 pounds/person × Number of people

Here, 3×460=1,380

3×500=1500

To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.

Therefore, option B is the correct answer.

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