10. Jade accidentally dropped a candy wrapper from the top of a building that was 600 feet tall.
The height of the wrapper in feet, f(x), can be represented using f(x)=-16x² - 2x + 600 where x
is the time in seconds.
a. If the candy wrapper is now 450 feet in the air, set up an equation that could be used to find
the amount of time since dropping the wrapper.
b. Solve the equation using the quadratic formula.
c. Which solution makes the most sense in the context of the situation? Explain.

The approximate height of the cylindrical barrel is 23 inches.

What is volume of cylinder ?
The volume of a cylinder is the amount of space inside the cylinder. It is given by the formula:

[tex]V = \pi r^2h[/tex]

where V is the volume, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

The formula tells us that the volume of a cylinder is proportional to the square of the radius and the height. This means that if we double the radius or the height, the volume of the cylinder will be multiplied by a factor of 4.

According to the question:

Let's start with the formula for the volume of a cylinder:

[tex]V = \pi r^2h[/tex]

where V is the volume, r is the radius, and h is the height.

We know that the barrel holds 10,164 cubic inches of oil, which is equal to 44 gallons. Since 1 gallon is equal to 231 cubic inches, we can convert the volume to cubic inches:

10,164 cubic inches = 44 * 231 cubic inches/gallon = 10,164 cubic inches.

So, we have:

V = 10,164 cubic inches

r = unknown

h = 23 inches

We can solve for the radius by rearranging the formula:

r = sqrt(V / (πh))

Substituting the values we have:

r = sqrt(10,164 / (π * 23))

r ≈ 8.25 inches

Therefore, the approximate height of the barrel is 23 inches.

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In response to the given question, we can state that As a result, graphs f(-1) = 2 and f(1) = -3.

Mathematicians use graphs to visually express or chart facts or values. A graph point will often represent a relationship between two or more objects. A graph, a non-linear data structure, is made up of nodes, or vertices, and edges. Glue the nodes (also known as vertices) together. This graph includes vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, and so on) are graphical representations of exponential growth. a triangle-shaped logarithmic graph.

We may evaluate the function for the provided input values using the graph as follows:

f(-1) = 2. The y-coordinate of the spot on the graph where the vertical line x = -1 crosses the function represents the function's value when x = -1. We can see from the graph that this point is (x=-1, y=2), hence f(-1) = 2.

f(1) = -3. The y-coordinate of the spot on the graph where the vertical line x = 1 crosses the function represents the value of the function when x = 1. We can see from the graph that this point is (x=1, y=-3), hence f(1) = -3.

As a result, f(-1) = 2 and f(1) = -3.

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-8 -12

Step-by-step explanation:

trust me

The required number of posts Patrick needs to paint 32 fence posts.

A closed route that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's diameter is referred to as its perimeter. There are numerous uses in real life for circle calculations.

The perimeter of the corral is the sum of the lengths of its sides:

P = 2L + 2W = 2(50ft) + 2(30ft) = 100ft + 60ft = 160ft

Since the fence posts are spaced 5 feet apart, we can divide the perimeter by 5 to find the number of posts:

160ft ÷ 5ft/post = 32 posts

Therefore, Patrick needs to paint 32 fence posts.

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Answer:

A = 3 , B = 4

Step-by-step explanation:

given (2, - 4 ) is a solution , then x = 2 and y = - 4 make the system true

substitute x = 2 , y = - 4 into the equations and solve for A and B

2A + 2(- 4) = - 2

2A - 8 = - 2 ( add 8 to both sides )

2A = 6 ( divide both sides by 2 )

A = 3

and

5(2) - B(- 4) = 26

10 + 4B = 26 ( subtract 10 from both sides )

4B = 16 ( divide both sides by 4 )

B = 4

Answer:

A - acute

Step-by-step explanation:

All the sides are equal and all angles are acute, meaning less than 90 degrees.

From the given information provided, the inequality that is correct is 1.29p + 2.25c ≤ 10. Hence, option b is correct.

The inequality that represents this situation is:

1.29p + 2.25c ≤ 10

An inequality is a mathematical statement that compares two values, expressing that one value is less than, greater than, less than or equal to, greater than or equal to, or not equal to another value.

This inequality states that the cost of p packages of paper plates at $1.29 per package plus the cost of c packages of plastic cups at $2.25 per package must be less than or equal to $10.

So, if Roger wants to spend less than $10 on the paper plates and plastic cups, he must satisfy this inequality.

Question - Rodger is going to the store to buy paper plates and plastic cups for a party the store sells paper plates for $1.29 each package and plastic cups for $2.25 each package. if p represents the number of packages of paper plates and c the number of packages of plastic cups rodger buys. He wants to spend less than $10. Which of these inequalities represent this situation?

2.25p+1.29c≤10

1.29p+2.25c≤10

2.25p+1.29c<10

1.29p+2.25c<10

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Answer:

1. 4 zoos

2. option B

Step-by-step explanation:

1. There are 10 zoos. one axis shows no of penguins and the other shows no of visitors. Just count the crossing between 800 and 1000.

2. The highest number of height here is 48cm. so the axis should be between 0 and 50 to avoid unnecessary mistakes

We can use the formula for the area of a rectangle, which is:

Area = length x width

We know that the area of Mr. Baker's yard is 1,472 square feet, and the width is 32 feet. So we can substitute these values into the formula and solve for the length:

1,472 = length x 32

Dividing both sides by 32, we get:

length = 1,472 / 32 = 46

Therefore, the length of Mr. Baker's yard is 46 feet.

Answer:

B. 100^6/7

Step-by-step explanation:

7th root is 1/7

(100^6)^1/7

multiply the exponents

6 * 1/7 = 6/7

The equation that is equivalent to P = B + Brz is:

r = (P - B) / Bz

To see why, we can rearrange the original equation as follows:

P = B + Brz

P - B = Brz

(P - B) / Bz = r

Therefore, r = (P - B) / Bz is equivalent to P = B + Brz.

Now let's check the given options:

x = P/Br + 1/r

This equation is not equivalent to P = B + Brz.

r = (P - B) / Bz

This is the correct equation that is equivalent to P = B + Brz.

r = Bz / (P - B)

This equation is not equivalent to P = B + Brz.

B = P / (rz + 1)

This equation is not equivalent to P = B + Brz.

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From the fraction given, we found that the total length of Jane's drive is 9 miles.

What is a fraction?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be whole. Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. It can be a fraction or a segment of any amount out of a whole, where the entire can be any quantity, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Let the total distance be x.

Given the fraction of distance covered = 2/3 of x

This is given as 6 miles.

So equating,

2/3 * x = 6

x = 6* 3/2 = 3 * 3 = 9 miles.

Therefore from the fraction given, we found that the total length of Jane's drive is 9 miles.

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Since the circle is abοve the x-axis (as it passes thrοugh (4,0) and (20,0)), we have k = 6.

In mathematics, geοmetry is the branch οf mathematics cοncerned with the study οf shapes, sizes, relative pοsitiοns οf οbjects, and the prοperties οf space. It includes tοpics such as pοints, lines, angles, planes, curves, and surfaces, amοng οthers.

Since the circle has center (h,k) and radius 10, we can write its equatiοn as: (x - h)² + (y - k)² = 10²

We are alsο given that the circle passes thrοugh the pοints (4,0) and (20,0). We can use this infοrmatiοn tο set up a system οf equatiοns:

(4 - h)² + (0 - k)² = 10²

(20 - h)² + (0 - k)² = 10²

Expanding the squares and simplifying, we get:

(h - 4)² + k² = 100

(h - 20)² + k² = 100

Subtracting the first equatiοn frοm the secοnd equatiοn, we get:

(h - 20)² - (h - 4)² = 0

Expanding the squares and simplifying, we get:

h² - 40h + 400 - h² + 8h - 16 = 0

Simplifying further, we get: -32h + 384 = 0

Sοlving fοr h, we get: h = 12

Substituting h = 12 intο either οf the twο equatiοns abοve, we can sοlve fοr k:

(h - 4)² + k² = 100

(12 - 4)² + k² = 100

8² + k² = 100

k² = 36

k = ±6

Since the circle is abοve the x-axis (as it passes thrοugh (4,0) and (20,0)), we have k = 6.

Therefοre, the value οf k is 6.

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The domain of f(x) is all real numbers, or (-∞, ∞). and the domain of f⁻¹(x) is all real numbers less than 2, or (-∞, 2).

The collection of all potential input values (also known as the independent variable) for which the function is defined and yields an acceptable output value is known as the domain of a function (also called the dependent variable). Depending on the situation and the type of function—such as intervals, sets, or inequalities—the domain can be expressed in a variety of ways.

The collection of all potential input values—also known as the independent variable—for which a function may be defined is known as the domain of the function.

f(x) = 2 - eˣ, the function is defined for all real numbers.

Therefore, the domain of f(x) is all real numbers, or (-∞, ∞).

To find the domain of the inverse function:

Substitute f(x) = y and rewrite the function:

y = 2 - eˣ

Subtracting 2 from both sides:

y - 2 = -eˣ

Multiplying by -1 and taking the natural logarithm of both sides:

ln(2 - y) = x

f⁻¹(x) = ln(2 - x)

The natural logarithm function is defined only for positive input values, we must have:

2 - x > 0

x < 2

Therefore, the domain of f⁻¹(x) is all real numbers less than 2, or (-∞, 2).

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So the area of the circle, A, is a function of the number of hours elapsed, h, and is given by A(h) = π(12.25 + 87.5h + 156.25h²).

In mathematics, a function is a rule that assigns to each input value (of a certain type) exactly one output value (of a certain type). The input values are often called the domain, and the output values are often called the range. Functions are used to model relationships between variables, and they are an important concept in many areas of mathematics, science, and engineering.

Here,

The formula for the area of a circle is A = πr², where r is the radius. Since the radius is changing at a rate of 12.5 inches per hour, we can express the radius as a function of time, h, using the formula:

r(h) = 3.5 + 12.5h

Substituting this into the formula for the area of a circle, we get:

A(h) = π(3.5 + 12.5h)²

Simplifying this expression, we get:

A(h) = π(12.25 + 87.5h + 156.25h²)

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Answer:Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.

Step-by-step explanation:

Mrs. Roger's class sold 21 soda bottles, and Mrs. Magoo's class sold 42 candy bars ,Mrs. Roger's class earned more money. Mrs. Roger's class earned $52.50, while Mrs. Magoo's class earned $50.40. Therefore, Mrs. Roger's class earned $2.10 more than Mrs. Magoo's class.

(a) Let x be the number of soda bottles sold by Mrs. Roger's class, and y be the number of candy bars sold by Mrs. Magoo's class. We can create a system of equations based on the information given:

Equation 1: 2.5x + 1.2y = 102.9 (the total amount earned by both classes)

Equation 2: x + y = 63 (the total number of items sold by both classes)

To solve for x and y, we can use substitution or elimination method. Using substitution, we can solve for x in Equation 2: x = 63 - y. Then we substitute this value of x in Equation 1:

2.5(63-y) + 1.2y = 102.9

Simplifying and solving for y, we get:

157.5 - 2.5y + 1.2y = 102.9

-1.3y = -54.6

y = 42

Substituting y=42 in Equation 2, we get:

x = 63 - y = 63 - 42 = 21

Therefore, Mrs. Roger's class sold 21 soda bottles, and Mrs. Magoo's class sold 42 candy bars.

(b) To find out which class earned more money, we can calculate the total earnings for each class:

Mrs. Roger's class: 2.5(21) = $52.50

Mrs. Magoo's class: 1.2(42) = $50.40

Mrs. Roger's class earned more money.

(c) Mrs. Roger's class earned $52.50, while Mrs. Magoo's class earned $50.40. Therefore, Mrs. Roger's class earned $2.10 more than Mrs. Magoo's class. This could be because the price per item for soda bottles was higher than for candy bars. Additionally, it's possible that the students in Mrs. Roger's class were more motivated to sell their items or had a larger network of potential buyers. The $2.10 difference may seem small, but it can add up over time and can make a difference in achieving the fundraising goals for the school.

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Answer:

answer: c

this are not polynomials

Answer:

a) x=45°

b) yes because both ∠DAB and ∠ABC are perpendicular to the same line segment, they most be parallel.

Step-by-step explanation:

a) all quadrilaterals have internal angels that add up to 360°

So ∠DAB + ∠ABC + ∠BCD + ∠CDA = 360°. Substituting each ∠ with its given value gives:

2x°+90°+x°+3x°=360°

Simplifying:

-> 90°+6x=360°

Subtracting 90°:

-> 6x=270°

Dividing by 6:

-> x=45°

Substituing back:

∠DAB=2x=2*45°=90°

∠ABC=90°

∠BCD=x=45°

∠CDA=3x=3(45)=135°

b) Yes because both ∠DAB and ∠ABC intersect the line segment AB at 90° angles/both ∠DAB and ∠ABC are perpendicular to the line segment AB. Because both ∠DAB and ∠ABC are perpendicular to the same line segment, they most be parallel.

Answer:

14

Step-by-step explanation:

Answer:14

Step-by-step explanation:

1) brackets (5+4)=9

2)division: 9/3=3

3)multiplications: 6*3=18

4)sum:18+3=21

5)substraction 21-7=14

the car is approximately [tex]23.9[/tex] Meters away from the tower.

The angle of depression is the angle formed when an object is observed from a horizontal line and the horizontal line.

We can solve this problem using trigonometry. Let's start by drawing a diagram:

C

|\

| \

|  \   32m

|   \

|    \

|     \

|      \

|-------T

  x

In the diagram, T represents the top of the tower, C represents the car, and x represents the distance from the tower to the car that we want to find. The angle of depression from the top of the tower to the car is 55 degrees.

We can use the tangent function to solve for x:

[tex]tan(55) = 32 / x[/tex]

To solve for x, we can rearrange this equation as follows:

[tex]x = 32 / tan(55)[/tex]

We can calculate this expression's value by using a calculator to obtain:

[tex]x =23.9[/tex] meters

Therefore, the car is approximately [tex]23.9[/tex] Meters away from the tower.

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The image was made by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the chart.

The first polygon, ABCD, has vertices at (1,- 1), (3,- 5), (7,- 5), and (8,- 5). (5,- 1). The vertices of the second polygon, A'B'C'D', are situated at (1,- 6), (3,- 10), (7,- 10), and (8,- 10). (5,- 6).

Vertices are points in a geometric figure that characterize its shape. A vertex is characterized numerically as the intersection of at least two lines, edges, or curves.

We can look at the coordinates of the two polygons to decide the translation that was used to make the image. The first coordinate of the two polygons is (1,- 1) and the second coordinate is (1,- 1). (1,- 6). The y-coordinate contrast is 5 units, so the translation is 5 units down. The two polygons' second coordinate is (3,- 5) and (3,- 10). The y-coordinate contrast is 5 units, so the translation is 5 units down.

The second polygon's third coordinate is (7,- 5) and (7,- 10). The y-coordinate distinction is 5 units, so the translation is 5 units down. (5,- 1) is the fourth coordinate of the two polygons (5,- 6). The y-coordinate contrast is 5 units, so the translation is 5 units down.

The image was translated as 5 units down, 5 units up, 1 unit down, and 1 unit up.

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After answering the given query, we can state that  Cοnsequently, the area mοsaic has a surface size οf 1176cm².

An area is a measure οf a regiοn's extent οn a surface. The term "surface area" refers tο the area οf an οpen surface οr the perimeter οf a three-dimensiοnal οbject, whereas "planar regiοn" οr "planar regiοn" refers tο the area οf a shape οr planar layer.

The area οf an οbject is the entire vοlume οccupied by its planar (2-D) surface οr shape. On a sheet οf paper, make a square with a pencil. a twο-dimensiοnal figure. On paper, a shape's area is the amοunt οf rοοm it οccupies. Cοnsider that the square is made up οf smaller unit squares.

Since each tile is a right triangle, its area can be calculated by multiplying its limb lengths by twο and dividing by three:

Each blοck has an area οf (7 x 4 cm)/2, οr 14 cm2.

The mοsaic's οverall surface area is because there are 84 pieces in it:

(Area οf each piece) x = tοtal mοsaic area (Number οf tiles)

The mοsaic's tοtal size is 14 cm² times 84, οr 1176 cm².

Cοnsequently, the mοsaic has a surface size οf  1176 cm²

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The transformation or dilation of  y = |x - 2| is right 2 units i.e. B.

What exactly is dilation in mathematics?

In mathematics, dilation refers to a transformation in which an object is uniformly scaled or stretched without changing its shape. Specifically, dilation is a type of transformation in which the size of an object is changed by a scale factor. The scale factor is a positive number that represents the ratio of the lengths of the corresponding sides of the original object and its image.

Now,

The equation y = |x - 2| represents the absolute value function with a vertex at (2, 0).

The transformation involved in this equation is a horizontal translation of 2 units to the right. This means that the graph of the function is shifted 2 units to the right from the origin. The vertex of the absolute value function moves from (0, 0) to (2, 0) as a result of this transformation.

The absolute value function has a "V" shape with the vertex as the point of symmetry. In this case, the vertex is at (2, 0), and the function has a "V" shape opening upwards.

Overall, the transformation in y = |x - 2| is a horizontal translation of 2 units to the right from the parent function y = |x|.

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To find the angle of an arc, you need two pieces of information: the length of the arc and the radius of the circle. The formula to calculate the angle of an arc is:angle (in radians) = arc length / radius.

To convert degrees to radians, we need to multiply the value in degrees by the conversion factor, which is π/180. So, to convert 165 degrees to radians, we would multiply 165 by π/180:

[tex]165[/tex]  degrees * ( [tex]\frac{\pi }{180}[/tex] radians/degree) = ([tex]\frac{165\pi }{180}[/tex]) radians

In this case, the radius is  [tex]11[/tex] in and the central angle is = [tex]165[/tex] degrees counterclockwise. However, we need to convert this angle to radians before using the formula.

Therefore, simplifying the expression, we can see that (165π/180) radians can be further reduced to ([tex]\frac{11\pi }{12}[/tex]) radians. Therefore,  [tex]165[/tex] degrees is equivalent to ([tex]\frac{11\pi }{12}[/tex]) radians.

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The volume of a sphere is given by the formula V = 4/3πr³.This means that the volume of the sphere with a radius of 6 inches and a height of 12 inches is 288π cubic inches.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. In this case, we are given that the radius of all three shapes (sphere, cylinder, and cone) is 6 inches, and the height of all three shapes is 12 inches. We also know that the volume of the cone is 144π cubic inches, and the volume of the cylinder is 432π cubic inches. Therefore, we can solve for the volume of the sphere by subtracting the volume of the cone and the cylinder from each other: V = 432π - 144π = 288π cubic inches. This means that the volume of the sphere with a radius of 6 inches and a height of 12 inches is 288π cubic inches.

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No, he is not correct.

$103.55 is the minimum, not maximum, amount that he should save. If he adds the $103.55 to his current total, he can only by the least expensive model. However, he may want to buy more than that model.

Therefore, Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.

the car is approximately 22.4 meters away from the tower.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

we can write:

tan(55 degrees) = 32 / d

To solve for "d", we can rearrange the equation:

d = 32 / tan(55 degrees)

Using a calculator, we can evaluate the tangent of 55 degrees:

tan(55 degrees) = 1.428

d = 22.4 meters

Therefore, the car is approximately 22.4 meters away from the tower.

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Answer:

P:192

A:2048

B. Area

C. Perimeter

Step-by-step explanation:

Answer:

Step-by-step explanation:

bts v i love them

The graphs of function f(x) and g(x) will intersect at x ≈ 3.8631.

A function with the formula f(x) = aeˣ, where a is a constant and x is a variable, is an exponential function. The base an is normally a positive real number, however in other cases it can also be a negative or complex number. Calculus, probability theory, and physics are just a few of the areas where the exponential function is a basic mathematical idea.

The given functions are:

f(x) = 100 • 2ˣ

g(x) = 50 • (1.5)ˣ

To see if the two functions meet we equate the two as follows:

50 • (1.5)ˣ = 100 • 2ˣ

(1.5)ˣ = 2ˣ / 2

Taking the natural logarithm of both sides, we get:

x ln(1.5) = ln(2) - ln(2)

x ln(1.5) = ln(2)

x = ln(2) / ln(1.5) ≈ 3.8631

Therefore, the graphs of f(x) and g(x) will intersect at x ≈ 3.8631.

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