Describe the end behaviour you would expect to see for a polynomial used to make a road over a hill and the end behaviour you would expect to see used to make a road through a valley.

let's call that point C, thus we get the splits of AC and CB

\(\textit{internal division of a line segment using ratios} \\\\\\ A(0,0)\qquad B(6,9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{1}\implies \cfrac{A}{B} = \cfrac{2}{1}\implies 1A=2B\implies 1(0,0)=2(6,9)\)

\((\stackrel{x}{0}~~,~~ \stackrel{y}{0})=(\stackrel{x}{12}~~,~~ \stackrel{y}{18}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{0 +12}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{0 +18}}{2+1} \right)} \\\\\\ C=\left( \cfrac{ 12 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies C=(4~~,~~6)\)

Answer:

30 cubes are added

Step-by-step explanation:

The image of the solid shape is attached.

From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.

30 cubes are added

The number of cubes that are added is 30.

What is Cube?

A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.

From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid

= 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added

= 48 cubes - 18 cubes

= 30 cubes.

30 cubes are added.

Hence, The number of cubes that are added is 30.

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The trinomial for the rectangular rug is 3x² + 5x - 2

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.

A trinomial is a polynomial with three terms.

The area of a rectangle = length * width

Area of rectangle = (x + 2) * (3x - 1) = 3x² + 6x - x - 2

Area of rectangle = 3x² + 5x - 2

The trinomial for the rectangular rug is 3x² + 5x - 2

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Answer:

x = 1/5 ,  and   x = - 1/5

Step-by-step explanation:

25x² – 1 = 0

5²x² - 1² = 0

(5x - 1)(5x + 1) = 0

5x -1 = 0,  5x + 1 = 0

x = 1/5 ,     x = - 1/5

Answer:

yes

Step-by-step explanation:

l,l,;,;,;,;l,;,;

It will take approximately 427 months or 35 years and 7 months for a sum of Rs. 9400 to become Rs. 10951.8 at the rate of 3 2/3% per annum.

Let the principal amount be Rs. 9400, rate of interest be 3 2/3 % per annum and the final amount be Rs. 10951.8

To find: The time required to become Rs. 10951.8

Step 1: Calculation of Interest:

Earned interest = Final amount - Principal amount = Rs. 10951.8 - Rs. 9400 = Rs. 1551.8

Step 2: Calculation of Time:

Time = (100 * Earned interest) / (Principal * Rate * 12/100)

Here, Principal = Rs. 9400,Rate = 3 ,2/3% per annum = (11/3)% per annum,

Time = (100 * 1551.8) / (9400 * (11/3) * 12/100)

= 100 * 1551.8 / 9400 * 11/3 * 12/100

= 15518 / 3636

= 15518/3636*100/100

= 426.906 or 426.91

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The dominant strategy of Farmer Jones is to buy 10 cows.

To determine the dominant strategy of Farmer Jones, we need to compare the outcomes of his two options:

buying either 10 cows or 20 cows.

Let's analyze the potential outcomes for each case:

Buying 10 cows:

If Farmer Smith buys 10 cows:  

The total number of cows in the field would be 30, resulting in each cow producing $3000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

Buying 20 cows:

If Farmer Smith buys 10 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 50, resulting in each cow producing less than $2000 of milk (exact value unknown).

From the given information, we can observe that regardless of the strategy chosen by Farmer Smith, Farmer Jones is better off buying 10 cows.

In all scenarios, the milk production per cow is higher when Farmer Jones buys 10 cows compared to buying 20 cows.

Therefore, the dominant strategy for Farmer Jones is to buy 10 cows.

Formally, we can express this as follows:

For Farmer Jones, no matter the strategy chosen by Farmer Smith, buying 10 cows yields a higher milk production per cow compared to buying 20 cows.

Hence, Farmer Jones' dominant strategy is to buy 10 cows.

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Answer:

Dr. Maette

Step-by-step explanation:

I'm not sure I've never read this :/

Answer:

98 m long

Step-by-step explanation:

588/6 = 98 m long

The populations of Beibertown and Elisville will be equal after approximately 25.61 years.

We have,

To find out when the populations of Beibertown and Ellisville are equal, we need to solve the equation:

B(t) = E(t)

Substituting the given expressions for B(t) and E(t).

18.4e^0.03t = 24.6e^0.02t

Dividing both sides by 18.4e^0.02t.

e^0.01t = 24.6/18.4

Simplifying the right-hand side.

e^0.01t = 1.33696

Taking the natural logarithm of both sides.

0.01t = ln(1.33696)

Solving for t.

t = ln(1.33696)/0.01

t ≈ 25.61

Therefore,

The populations of Beibertown and Elisville will be equal after approximately 25.61 years.

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The length of the diagonal of this square is 11 and option 4 is the correct answer.

A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.

Given that, x is the length of the diagonal of the square.

Also, x² = 132

The value of x is:

x = √132

x = 11.48

Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.

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3 Answers: x = 0, x = 1, or x = 2

==================================================

Explanation:

The relation

{(0, 5) (1, 5) (2, 6) (x, 7)}

has points with x coordinates of: 0, 1, 2, and x.

If we repeated any of the x values listed so far, then we will not have a function.

So if we had the points (0,5) and (0,7), then the input x = 0 leads to multiple outputs. A function is only possible when any input x leads to exactly one output y.

This means that if x = 0, 1, or 2, then we won't have a function.

Side note: The y values can repeat, but if they do, then we won't have a one-to-one function. In this case, y = 5 repeats, so this function is not one-to-one (assuming x is not 0, not 1, and not 2).

Answer:

25

Step-by-step explanation:

4x8=32

32-7=27

Answer: 71 dogs ==> 1st option

Step-by-step explanation:

c=cats. d=dogs.

2d-3=c

d+c=210

d+2d-3=210

3d-3=210

3d=213

d=71 dogs ==> 1st option

We've multiple  styles to find area of triangle. But the formula used is area = 1/2 ×( base × length).    

To  decide formula of area = 1/2 ×( base × length) we can consider the area of a rectangle. Area of a rectangle is =  length × breadth. A triangle is half of a rectangle.  

So, thus we can divide the area of cube by 2 to get the asked area of triangle. Also, area = ( length × breadth)/ 2. In triangle the base is the vertical side of the triangle and the vertical is the distance from the base to the contrary point.  

Now, after multiplying the base with height and dividing it by 2 will give us the formula of area of triangle. Area = 1/2 ×( base × height).

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The question is: Derive the area formula for a triangle.

Part A: From the given triangle, what is Sin C?

Part B: Using your answer from Part A, solve for the height, h.

Part C: Using the area formula = 1/2 bh and your answer form part B, plug in and simplify. Write the simplified equation.

Part D: Using your own words, what formula did you derive?

The value of x in the given 45-45-90 triangle is 9.89.

The given triangle is a right-angled triangle which can be solved using the Pythagoras theorem. The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular. This theorem can be applied to all right-angled triangles.

In the given triangle, we have been told that the length of both legs is 7. Now, after applying the theorem -

= 7²+7² = H²

= 49 + 49 = H²

= 98 = H²

= √98 = H

= 9.89 = H

Hence, this is the value of x.

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Answer:

unlikely

Step-by-step explanation:

it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Based on the given dot plot, we can say that statement a) is true, statement b) is false, and statement c) may or may not be true. Based on the dot plot provided, we can make the following statement about the number of appointments per week at the hair salon.

The median number of appointments is 50 per week. This means that half of the weeks had fewer than 50 appointments and the other half had more. The interquartile range (IQR) can be determined from the dot plot, which is the difference between the upper quartile and lower quartile. The lower quartile is around 38 and the upper quartile is around 57, so the IQR is approximately 19. Therefore, statement a) is true.

The range is the difference between the highest and lowest values. From the dot plot, we can see that the highest value is around 90 and the lowest is around 20. Therefore, statement b) is false. We cannot determine from the dot plot whether more than half of the weeks had more than 50 appointments per week. Therefore, statement c) may or may not be true.

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Answer:

1/5 + 1/3 = 8/15

3/4 - 1/8 = 5/8

Answer:

37.9 liters

Step-by-step explanation:

Multiply the number of gallons by 3.785 to convert to liters

Multiplying by ten moves the decimal point over to the right

3.785 * 10 = 37.85

The tenths place is where the 8 is, and since 5 is \(\geq\) (greater than or equal to) 5 that makes the 8 round up to a 9

resulting in...

10 gallons = 37.9 liters

hope this helps:)

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Answer:

y = - 140

Step-by-step explanation:

Given that y varies jointly as x and z then the equation relating them is

y = kxz ← k is the constant of variation

To find k use the condition y = - 180 when z = 15 and x = - 3, thus

- 180 = k × - 3 × 15 = - 45k ( divide both sides by - 45 )

4 = k

y = 4xz ← equation of variation

When x = 7 and z = - 5, then

y = 4 × 7 × - 5 = - 140

Answer:

120/100

Step-by-step explanation:

120÷20= 6

100÷20=5

6/5 = 1⅕

Answer:

here,

2x=76 (because of adjacent angle)

76/2=x

x=38

again,

x+y=180(because of straight angle)

y=180-38

y=142

The correct option is B. The trips will each bus has to make to get everyone to the stadium is 40 trips.

The number of fans who will need to use satellite parking is:

150,000 x 0.52 = 78,000

Each bus can carry 65 fans, so the total number of trips required is:

78,000 / 65 = 1200

Therefore, each bus will need to make 1200/30 = 40 trips

Satellite parking typically offers lower rates than the central parking area and provides a shuttle service to transport passengers to and from the main terminal. This type of parking is a popular option for travelers who need to park their car for an extended period of time, such as those going on vacation or business trips.

Satellite parking can be located either on-site or off-site, depending on the transportation hub. Some airports have several satellite parking lots located at various distances from the main terminal, while others have a single satellite parking area. Overall, satellite parking is an important component of transportation infrastructure, as it provides a convenient and affordable parking solution for travelers while also helping to alleviate congestion in the main parking area.

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Answer:

88

Step-by-step explanation: