The position of a ball after it is thrown is modeled with the
function f(x) = -2(x - 1)² + 7 in vertex form, where y is
the height, in feet, above the ground and x is the horizontal
distance, in feet, of the ball from where it is thrown.


A. Write the function in standard form.

B. What is the height of the ball when it is thrown?

C. What is the horizontal distance from the point where the ball is thrown to the highest point that the ball reaches?

(a)The value of g(3) = 13/2 + π,  g(-2) = 5 - π

(b) The graph of y g(x) has points of inflection at x = 0, x = 2 and x = 3

This problem described a function g that is defined and differentiable on [-7, 5]  and with g(0) = 5. The graph of y = g′(x) on [ -7, 5] was given, consisting of three line segments and a semicircle.

[tex]g(3) = 5 + \int\limits^3_0 {g'(x)} \, dx \\g(3) = 5 + \frac{\pi.2^{2}}{4} + \frac{3}{2}[/tex]

g(3) = 13/2 + π

[tex]g(-2) = 5 + \int\limits^ 2_0 {g'(x)} \, dx \\[/tex]

g(2) = 5 - π

(b) x-coordinates of points of inflection for the graph of y  = g(x) on the interval [-7 5].

The graph of y = g(x) has points of inflection at x = 0, x = 2 and x = 3 because g′ changes from increasing to decreasing at x = 0 and 3, x = and g′ changes from decreasing to increasing at x = 2.

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The image of this question is probably this

The requried number that consists of the line of symmetry is 3. Option B is correct.

A line of symmetry is defined as the line that bisects the entity in two equal symmetrical halves.

here,
Given numbers,
2, 3,  7.8, 4, 9 since the line of symmetry for the given number would be that line that bisects the shapes of the given number in a mirror-like symmetry so, the only number given the mirror-like symmetry when a line passes through its center is 3.

Thus, the requried number that consists of the line of symmetry is 3. Option B is correct.

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Other things constant, how will an increase in the wage of teenagers affect the market for fast food hamburgers will cause the supply of fast food hamburgers will increase, leading to an increase in price of hamburgers. Option A

supply is the amount of a resource that firms, producers, laborer, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual.

The law of supply in economics states that supply will increase as price increases, due to the fact that producers want to maximize profits. In this instance, the law assumes that all other factors are equal and price is the only independent element, meaning supply is completely dependent on the price.

Hence, an increase in the wages of teenager will lead to an increase in the quantity of hamburgers demanded, which will also leads to an increase in supply.

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The price after the discount but before tax, to the nearest dollar and cent is $24.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. "Off",

Discount is equal to List Price – Selling Price.

Given that, the store was offering a 40% discount.

The discount on the price tag of $40 is:

Discount = 40 (40/100) = $16.

The new price after the discount but before tax is:

New price = 40 - 16

New price = $24.

Hence, the price after the discount but before tax, to the nearest dollar and cent is $24.

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In this using the knowledge of computational language in python, we have that this code will be written as:

Here's an algorithm in pseudocode that you can use to find all the common elements in two sorted lists of numbers:

Input: two sorted lists A and B of size N and M respectively.

Output: a list C of all common elements in A and B.

C = [ ]

i = j = 0

while i < N and j < M:

   if A[i] == B[j]:

       C.append(A[i])

       i += 1

       j += 1

   else if A[i] < B[j]:

       i += 1

   else:

       j += 1

return C

In this algorithm, two pointers i and j are used to traverse both lists A and B. At each step, the algorithm compares the elements at the current positions of i and j in A and B respectively. If they are equal, it means the element is common to both lists, so it is added to the result list C. If the element in list A is less than the element in list B, i is incremented to move to the next element in list A. Similarly, if the element in list B is less, j is incremented to move to the next element in list B.

The algorithm continues this process until either one of the lists is fully traversed.

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Answer:

To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to use optimization. Let's call the length of each square x cm.

To form the box, we will cut out squares of side length x from each corner of the rectangular cardboard sheet, and then fold up the sides to form the box. The dimensions of the base of the box will be (10-2x) cm by (16-2x) cm, and the height of the box will be x cm.

Therefore, the volume of the box will be:

V = (10-2x) * (16-2x) * x

V = 4x^3 - 52x^2 + 160x

To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to find the value of x that maximizes V. To do this, we can take the derivative of V with respect to x, and set it equal to 0:

dV/dx = 12x^2 - 104x + 160 = 0

We can solve for x by factoring the quadratic expression:

3x^2 - 26x + 40 = 0

(3x - 10)(x - 4) = 0

So the critical points are x = 10/3 and x = 4. Since we're looking for a maximum, we need to find which of these critical points gives the highest value of V. We can do this by evaluating V at both points:

V(10/3) ≈ 51.85

V(4) = 128

Therefore, the value of x that gives the maximum volume is x = 4 cm.

So we should cut out squares of side length 4 cm from each corner of the cardboard sheet to make a box of maximum volume.

The requried maximum height of the box should be 2 for the maximum volume.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Let the side measure of the square cut b x,
Now,

The length of the box will be = 16 - 2x
width of the box will be  = 10 - 2x
The height of the box will be  = x

The volume of the box is given as,
V = (16-2x)(10-2x)(x)
V = 4x³ - 52x² + 160x

Differentiate the above equation with respect to x,, and equate it to zero to get the maximum value of x for the maxium volume,
12x² - 104x + 160 = 0
x = 2 and 6.667

We can neglect x = 6.667 because at 6.667 the volume has a negative magnitude.

Thus, the requried maximum height of the box should be 2 for the maximum volume.

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The total surface area of the cylinder is S = 45π units²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the surface area of the cylinder be represented as S

Now , the equation will be

The height of the cylinder h = 4.5 units

The radius of the cylinder r = 3 units

So , Surface area of cylinder = 2πr ( r + h )

Substituting the values in the equation , we get

Surface area of cylinder S = 2π ( 3 ) ( 3 + 4.5 )

On simplifying the equation , we get

Surface area of cylinder S = 2π ( 3 ) ( 7.5 )

Surface area of cylinder S = 45π units²

Hence , the surface area of cylinder is 45π units²

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Answer: 1m/s

Step-by-step explanation: Accleration = Speed/Time

10/10 = 1

The graph of the system is added as an attachment

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

f(x) = 2x + 8 for x < -1

      -2x + 7 for x > 3

The above system is a piece wise fucntion that include

Two linear equations

Next, we plot the graph

See attachment for the graph of the equation

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The value of the expression is [tex]\frac{63}{20}[/tex].

An expression contains more than two variables or numbers with the mathematical operation.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]\frac{1}{4}[/tex] and [tex]\frac{4}{5}[/tex]

Now,

Simplify.

= 7 x [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{5}[/tex]

= 7 x [tex]\frac{5+4}{20}[/tex]

= 7 x [tex]\frac{9}{20}[/tex]

= [tex]\frac{63}{20}[/tex]

Thus,

[tex]\frac{63}{20}[/tex] is the expression.

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Answer:

Maths

Step-by-step explanation:

We find the percent equivalent of each test.

Maths: 14 out of 17

percent = part/whole × 100%

percent = 14/17 × 100%

percent = 82.35%

English: 31 out of 39

percent = part/whole × 100%

percent = 31/39 × 100%

percent = 79.49%

Since 82.35% > 79.49%, she did better in Maths.

Answer: Maths

Reason:

-2 * 2 = -4

-2 + 2 = 0

These values are found through trial and error. The order of -2 and 2 doesn't matter.

a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.

b) At 0 and 40 length the area is zero.

c) At length interval (20, 40), the area is decreasing.

d) At the area 600 the length is 30.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure.

Hence, By the figure we have;

a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.

b) At 0 and 40 length the area is zero.

c) At length interval (20, 40), the area is decreasing.

d) At the area 600 the length is 30.

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The height of flagpole C is approximately 6.1 feet.

Distance is a numerical measurement of how far apart or how far away objects or locations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it only has magnitude and no direction.

The distance between two points is typically calculated using a formula, such as the distance formula in Euclidean geometry, which involves taking the square root of the sum of the squares of the differences in the coordinates of the two points.

Let's start by drawing a diagram of the situation:

          A

          |

          |

          |

          |

          |

          |

          |

-----------S-----------C

We can see that the triangles ASC and ABC are similar, since they have the same angles (90 degrees at S and a common angle at A). Therefore, we can use proportions to find the height of flagpole C:

AC   SC

-- = --

AB   AS

Substituting the given values, we get:

AC   10

-- = --

AB   AB + 12

We can solve for AB by noting that the height of flagpole A is the sum of the heights of AB and BC:

13.2 = AB + BC

Solving for BC, we get:

BC = 13.2 - AB

Substituting this into the first equation, we get:

AC   10

-- = --

AB   AB + 12

AC = 10(AB)/(AB + 12)

Now we can substitute the value we found for AB:

AC = 10(13.2 - BC)/(13.2 - BC + 12)

AC = 10(13.2 - BC)/25.2

We still need to find BC, which we can do by using the fact that the triangles ABC and ASC are similar:

BC/AB = SC/AS

Substituting the given values, we get:

BC/AB = 10/22

BC = 10AB/22

Substituting this into the equation for AC, we get:

AC = 10(13.2 - 10AB/22)/25.2

Now we can solve for AB:

13.2 = AB + 10AB/22

AB = 7.92

Finally, we can substitute this into the equation for AC:

AC = 10(13.2 - 10(7.92)/22)/25.2

AC = 6.1

Therefore, the height of flagpole C is approximately 6.1 feet.

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Answer:

y=1/3x+4

Step-by-step explanation:

Yep

Answer:

A=a+b/2 x h

Step-by-step explanation:

The area for a trapezoid is a+b divided by 2, multiplied by the height.

Since there are no lengths given, I cannot be solved.

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The perimeter of the figure is 68+24=92 cm.

The area of Rectangle is length times of width.

In the given figure there is a rectangle and right angle triangle.

The length of rectangle is 16 cm and width is 18 cm

Perimeter=2(length+Breadth)

=2(16+18)

=68 cm

Now let us find perimeter of triangle

Base of height is 6cm and base is 8

P=a+b+√a²+b²

=6+8+√6²+8²

=24

Hence, the perimeter of the figure is 68+24=92 cm.

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Answer: 5/8

Step-by-step explanation:

We can make the fractions easier to read by changing 1/4 to 2/8, simply by multiplying the fraction by 2/2.

2/8 : 7/8

now you can see how much more George ate.

7/8 - 2/8 = 5/8

George ate 5/8 more than Grace.

use pythagorean theorem : a²+b²=c²

Answer:

(f,g)=(1,-2)

Step-by-step explanation:

72f-12g=96, 6f-2g=10

72f-12g=96

f=5/3+1/3g

72(5/3+1/3g)-12g=96

g=-2

f=5/3+1/3x(-2)

f=1

(f,g)=(1,2)

Since Hong made 162 dollars for 9 hours of work, we can set up the proportion:

162 dollars / 9 hours = x dollars / 13 hours

where x is the amount of money Hong would make for 13 hours of work.

To solve for x, we can cross-multiply and simplify:

162 dollars × 13 hours = 9 hours × x dollars

2106 = 9x

x = 234

Therefore, at the same rate, Hong would make 234 dollars for 13 hours of work.

a. The type of figure shown is a triangular prism.

b. The surface area of the figure is 118.5 sq. in.

A triangular prism is a 3 dimensional shape which has 2 triangular surfaces and a rectangular base. It has 5 surfaces in total.

Considering the given figure in the question, we have;

a. The type of figure shown is a triangular prism.

b. The surface area of the prism can be deduced as follows;

area of one of its triangular surfaces = 1/2*base*height

                                       = 1/2*5*1.7

                                       = 4.25 sq. in.

area of its base = length x width

                   = 10x 5

                   = 50 sq. in.

area of one of its slant sides = length x width

                      = 10 x 3

                      = 30 sq. in.

Therefore, the surface area of the figure = (2*4.25) + 50 + (2*30)

                                    = 8.5 + 50 + 60

                                     = 118.5 sq. in.

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So the solution of the given question is,  the correct answer is D) Both data sets represent multiplicative relationships. from the given conditions.

In mathematics, a multiplicative relationship between two variables means that the ratio of their values remains constant as the values of the variables change. In other words, the product of the two variables is a constant. For example, if we have two variables x and y such that xy = k, where k is a constant, then x and y have a multiplicative relationship. If we increase the value of one variable, we must decrease the value of the other variable proportion in order to maintain the constant product. This type of relationship is often seen in situations involving rates, ratios, and proportions, such as in growth or decay processes, population dynamics, and financial calculations.

In Table A, y is 2.5 times x, and in Table B, y is 3 times x. In both tables, the relationship between x and y is a constant ratio, which is a characteristic of multiplicative relationships. In Table A, the ratio of y to x is always 2.5, meaning that y is always 2.5 times greater than x. In Table B, the ratio of y to x is always 3, meaning that y is always 3 times greater than x. Therefore, both tables represent multiplicative relationships between x and y.

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The measure of ∠A is 37.6°. Angle is a geometric figure that can be described as the amount of rotation.

A figure produced by two rays, line segments, or lines that have a same endpoint is called an angle. It is measured in degrees, with a complete 360-degree angle. The Greek letter theta is commonly used to represent it. An angle can be acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), or reflex (more than 180 degrees).

∠A is an angle measure and is commonly represented by the symbol "∠A".  calculate the measure of ∠A, an angle must be given in degrees. The answer is then rounded to the nearest hundredth. For example, if the angle measure of ∠A is 37.58°, then the answer would be 37.6°.

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The constant 0.9965 is the rate of change per hour. Specifically, it represents the factor by which the quantity changes every hour. In this case, the factor is less than 1, indicating that the quantity is decreasing over time.

To see how this rate of change works, consider an example:

If the initial quantity is 930, after one hour the quantity will be:

f(1) = 930(0.9965) ≈ 926.20

That is, the quantity has decreased by a factor of 0.9965, or about 0.35%.

After two hours, the quantity will be:

f(2) = 930(0.9965)^2 ≈ 922.42

That is, the quantity has decreased by a factor of 0.9965 twice, or about 0.70%.

So the constant 0.9965 reveals the rate of change of the quantity, which is a decrease of about 0.35% per hour.

Answer

4x6=24

24x1 ml=24ml

Answer:

 the answer to your question is 24 milliliters!

Step-by-step explanation:

good luck!

Answer:

they are both circles

Step-by-step explanation:

The perimeter of the triangle is 36√2

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

height = 12

Also, we understand that the triangle is an equilateral triangle

This means that the other sides are

Sides = 12√2

The perimeter is then calculated as

Perumeter =3 * Sides

So, we have

Perimeter =3 * 12√2

Evaluate

Perimeter = 36√2

Hence, the perimeter is 36√2

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Answer: 3 + 3 adds up to 6, which is less than 10.

Step-by-step explanation:

Answer: 3

Step-by-step explanation: Someone is 15 steps behind in a race, then that is sectioned into a fifth. How many steps behind are they?