from the top of a building, a man observes a car moving toward him. as the car moves 100 ft closer, the angle of depression changes from 15 to 33 o o . find the height of the building.

the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.

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Answer: y= 116x

Step-by-step explanation:

The value of x is 30 degrees.

A right-angled triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of the two sides of the triangle that are perpendicular to each other, which are called the legs or the adjacent and opposite sides. The side opposite the right angle is called the hypotenuse, and it is always the longest side in the triangle. The other two sides are usually labeled as a and b, and are called the legs or the adjacent and opposite sides depending on which angle is being considered. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is one of the fundamental properties of right-angled triangles. Right-angled triangles have numerous practical applications in geometry, trigonometry, physics, and engineering.

We can use the trigonometric ratio of sine to find the angle x.

sin(x) = opposite/hypotenuse = PQ/PR = 48/96 = 1/2

Taking the inverse sine of both sides, we get:

x = sin^(-1)(1/2)

Using a calculator, we get:

x ≈ 30 degrees

Therefore, the value of x is 30 degrees.

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Answer:

Ratio of 2/5 can be added like 2+5=7

And then

154÷7=22

22×2=44

22×5=110

They lost 110 games

Answer:

(5+1)^2 = 6^2 = 36

3^2 = 9

Next, we can substitute these values into the expression:

(5+1)^2 - (11+3^2) = 36 - (11+9) = 16

Finally, we can divide by 4:

16/4 = 4

Therefore, the simplified expression is 4.

Step-by-step explanation:

To reach the goal he student council needs to sell a minimum number of 107 tickets.

Sell means to gave someone something we take money from him. It is a transaction in which product is exchange with product or money. In ancient time we use barter system for transaction.

For raising $400 the student council have to sold each ticket at $4. So the number of ticket sold = $400 / $4 = 100.

They also spent $25 on decorations, so they need to recover that cost too. So, they need to sell an additional tickets = $25 / $4 = 6.25

Since we can not sell 0.25 of a ticket, So we can round the answer to 7.

So that overall total number of tickets that must be sold as 107.

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Complete question:

The student council at Deer Creek Middle School is organizing a dance to raise money for their end-of-year trip. They want to raise at least $400. Tickets are priced at $4 each and they already spent $25 on decorations. What is the minimum number of tickets they have to sell to reach their goal?

Answer:

  f(-3) = 6

Step-by-step explanation:

You want the value of f(-3) given a graph of f(x).

To find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.

The attachment shows this process, and that the value of f(-3) is 6.

__

Additional comment

Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.

The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.

The simplest form of the ratio 2m : 8cm : 40mm is

50mm : 2mm : 1mm

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter

2m = 2× 1000mm = 2000mm

8cm = 8 × 10 = 80mm

40mm = 40mm

therefore the ratio will be in form of

2000mm : 80mm ; 40mm

divide through by 10

200mm : 8mm : 4mm

divide through by 4

50mm : 2mm : 1mm

therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm

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Answer:

43

Step-by-step explanation:

We can simplify the expression:

[tex]4^2 + 3^3[/tex]

by rewriting exponents as multiplication of their base.

[tex]4^2 + 3^3[/tex]

[tex]= (4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]

Then, we can simplify using the order of operations (PEMDAS).

[tex](4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]

[tex]= 16 + (9 \cdot 3)[/tex]

[tex]= 16 + 27[/tex]

[tex]\boxed{= 43}[/tex]

Answer:

Step-by-step explanation:

Let us first make the denominators equal, so

600 x 700 = 420000

[tex]\frac{480}{600} * \frac{700}{700} \\\\= \frac{336000}{420000}[/tex]

Similarly,

[tex]\frac{560}{700} * \frac{600}{600} = \frac{336000}{420000}[/tex]

By comparison, both of them are equal.

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The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.

The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.

Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

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The grocer should combine 3 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.

Let x be the number of pounds of $2.4/lb trail mix to be added to 5 pounds of $1.5/lb trail mix.

The total amount of trail mix after combining can be expressed as:

x + 5

The total cost of the combined trail mix can be expressed as:

2.4x + 1.5(5) = 1.9(x + 5)

Solving for x, we get:

2.4x + 7.5 = 1.9x + 9.5

0.5x = 2

x = 4

Therefore, the grocer should combine 4 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.

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The area of the triangular section is 12 square units and the area of the entire figure is 60 square units.

We know that the Area of triangle is defined as the product of its height to its base.

Area of triangle =  height × base

From the figure, we can see that Height is = 4 units and the base is = 6 units,

So, the area of the triangular section is = 1/2 × base × height,

⇒ (1/2) × 6 × 4

⇒ 12 square units

The entire figure consists of two figure , one is a rectangle and the other part is a triangle,

So, the area of the entire figure is = Area of rectangle + area of triangle

⇒ 4×12 + 12

⇒ 48 + 12

⇒ 60 square units

Therefore, the area of the entire figure is 60 square units.

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The given question is incomplete, the complete question is

The area  of the triangular section is ___ square units, and the area of the entire figure is ___ square units. Refer to the figure given below.

The total mass of the apples Alex picked is 25 2/5 kilograms.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants

To find the total mass of the apples Alex picked, we need to add the mass of the red apples and the mass of the green apples.

First, let's convert the mixed numbers to improper fractions to make the addition easier:

15 ⅘ = 15 + 8/10 = 15 + 4/5 = 75/5 + 4/5 = 79/5

9 ⅗ = 9 + 6/10 = 9 + 3/5 = 45/5 + 3/5 = 48/5

Now we can add the fractions:

79/5 + 48/5 = (79 + 48)/5 = 127/5

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case:

127/5 = 25 2/5

Therefore, the total mass of the apples Alex picked is 25 2/5 kilograms.

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Answer:

18mm

Step-by-step explanation:

A^2+B^2=C^2.

144+169=313

square root of 313=17.69≈18mm

Answer:

Answer:

Slopem=−49

As a decimal:

m = -0.444444

Step-by-step explanation:

Slope m with two points

Graph of the line for y = mx + b

Point Slope Form y - y1 = m(x - x1)

Slope Intercept Form y = mx + b

Standard Form Ax + By = C

y-intercept, when x = 0

x-intercept, when y = 0

The proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal.

To answer the vice president's request, the proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal. This can be seen in the graph below, which illustrates the normal distribution of customer wait times with a mean of 20 minutes and a standard deviation of 4 minutes. In this graph, the area of the curve between 0 and 24.2 minutes represents the customers who will receive a free meal, and the area to the right of 24.2 minutes represents the customers who will not receive a free meal.

The normal distribution is a common probability distribution which follows a symmetric, bell-shaped curve. It is often used to describe real-world phenomena such as customer wait times in restaurants, since it is an effective tool for modeling variation in large datasets. The normal distribution can be determined by two parameters: the mean and the standard deviation. The mean represents the average wait time, while the standard deviation describes how the wait times vary.

In this case, the normal distribution has a mean of 20 minutes and a standard deviation of 4 minutes. This means that the average wait time is 20 minutes and that the wait times may vary by up to 4 minutes. The area of the graph between 0 and 24.2 minutes can be seen as the customers who will receive a free meal, as these customers waited longer than the advertised maximum wait time. The area of the graph to the right of 24.2 minutes represents the customers who will not receive a free meal, as these customers did not wait longer than the advertised maximum wait time.

By proposing a maximum wait time of 24.2 minutes, the company will not be losing out on any profit. This is because only 1% of customers will be receiving a free meal, and the cost of this will be more than offset by the increased customer satisfaction due to faster service.

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Answer: The graph is translated to the left 9 units

Step-by-step explanation:

When the thing is negative it will move to the right it will be positive. When it's negative it will move to the left than it will be negative.

Answer:

C,D

Step-by-step explanation:

Answer:

y = 4x + 15

Step-by-step explanation:

Using 'y=mx+c' form,

Since m = 4,

y = 4x + c

Substituting (-5, -5) into the above equation:

-5 = -20 + c

c = 15

Hence,

y = 4x + 15

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the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.

The answer is C: 24 m; 18 m. To find the shortest distance from the parking lot to the beach, one should measure the distance between the two locations. The distance between the parking lot and the beach is 24 m. To find the distance between the beach and the refreshment stand, one should measure the distance between the two locations. The distance between the beach and the refreshment stand is 18 m. Therefore, the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.

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Randy's claim is not correct Therefore, he cannot purchase 3.5 pounds of chicken salad for $23.50

To determine if Randy's claim is correct, we can use the given linear graph and points to find the equation of the line that represents the relationship between the amount of chicken salad purchased and the cost.

We can use the two points (1, 7.5) and (3, 22.5) to find the slope of the line:

slope = (change in y) / (change in x)

slope = (22.5 - 7.5) / (3 - 1)

slope = 15 / 2

slope = 7.5

Now we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line:

y = 7.5x + b

To find b, we can use one of the points on the line, such as (1, 7.5):

7.5 = 7.5(1) + b

b = 0

So the equation of the line is:

y = 7.5x

Now we can use this equation to check if Randy's claim is correct. If he can purchase 3.5 pounds of chicken salad for $23.50, we can plug in x = 3.5 and see if y = 23.5:

y = 7.5x

y = 7.5(3.5)

y = 26.25

Since y = 26.25 is not equal to $23.50

Therefore, Randy's claim is not correct

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The given question is incomplete, the complete question is:

Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.

The prοperty the equatiοn illustrates-4x-1/4=1 is multiplicatiοn inverse.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.

οr,

A mathematical expressiοn cοmpοsed οf twο expressiοns jοined tοgether by the equal sign.

Given equatiοn is (-4)×(-1/4) = 1.

The name οf prοperties are

Distributive Prοperty: a(b+c) = ab + bc

Cοmmutative Prοperty: ab =ba

Assοciative Prοperty :a(bc) = (ab)c

Identity Prοperty a×b=1

Inverse Prοperty: a×b=1

These characteristics hοld true in mathematical and algebraic expressiοns just as they dο in prοpοsitiοnal language.

In the Inverse Prοperty, the prοduct οf a number and its inverse is equal tο 1.

The given equatiοn represents Inverse Prοperty.

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Step-by-step explanation:

Use the triangle bisector theorem:

"The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle."

so 12 is to 16  as   x is to 20

12/ 16 = x/20

20 * 12/16 = x = 15 units

Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the angle into segments that are proportional to the other two sides , that is

[tex]\frac{12}{16}[/tex] = [tex]\frac{x}{20}[/tex] ( cross- multiply )

16x = 12 × 20 = 240 ( divide both sides by 16 )

x = 15

Using the dimensional analysis, 9 tsp is equivalent to 3 tbsp.

A conversion factor is a numerical ratio that relates two units of measurement for the same quantity

To convert 9 tsp to tablespoons using dimensional analysis, we can use the conversion factor that 1 tablespoon is equal to 3 teaspoons. We can set up the following proportion

1 tablespoon / 3 teaspoons = x tablespoons / 9 teaspoons

where x is the number of tablespoons we want to find. To solve for x, we can cross-multiply and simplify:

1 tablespoon × 9 teaspoons = 3 teaspoons × x tablespoons

9 tablespoons = 3x

x = 9 tablespoons / 3

x = 3 tablespoons

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1.) Yes, it will fit because the volume of the baseball is 13.36 cubic inches and the volume of the box is 64 cubic inches which is greater than the volume of the baseball.

2) The ratio of the side length of box B to the side length of box A is 1.472 inches: 6 inches.

The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.

To check whether the baseball is will still fit in the box we will check the maximum value of circumference.

[tex]2\pi r = 9.25[/tex]

Make r the subject formula

r= 1.472 inches

Volume of the baseball = [tex]\frac{4}{3\pi x^3}[/tex]

Expand:

13.35 inches^3 < 64 inches^3

So, it will fit inside the box.

2.) [tex]\sqrt[3]{216} = 6[/tex]

Therefore, V = a^3

The length of each side of the box is 6 inches.

The ratio of the side length of box B to the side length of box

A:

1.472 in : 6 inches

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Point G has the coordinates  (-2.5, 5.5), so a correct option is an option (C).

What is a coordinate plane?

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). It is possible to determine the separation between two points, divide a line into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations using coordinate geometry.

A coordinate plane is a plane in which a set of two number lines are represented, the horizontal line is called the x-axis and the vertical line is called the y-axis.

The given coordinates are (-2.5, 5.5).

The graphical representation of the points is shown below.

Point G has the coordinates (-2.5, 5.5).

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The given function of the cost represents exponential growth.

A form of growth known as exponential growth occurs when the rate of expansion is proportionate to the present value. This implies that the rate of growth increases as the present quantity increases. An exponential function, such as the one in this question (y = abx, where an is the starting value, b is the growth factor, and x is the number of time periods), may be used to describe exponential growth. In natural and social processes, such as population expansion, economic growth, and the spread of illnesses, exponential growth is frequently seen. Yet, there are always resource constraints and other factors that will ultimately reduce or stop the expansion, therefore exponential growth cannot last eternally.

The given function is y=100(1. 05)^x.

To find cost for certain year we substitute different value of x.

From the function we observe that as the value of x increases the function increases continuously.

Hence, the given function of the cost represents exponential growth.

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The complete question is:

Answer:

y = (1/x)+2.05

Step-by-step explanation:

We are only given one point, so there are an infinite number of possible equations.  But forging ahead, we can come up with at least one equation of an inverse relationship containing the point (-20,2).

By inversely, the function will produce lower values of y as x increases, or vice versa.  A good first step is to say:

 y = 1/x

As the value of x increases, the value of y decreases.  Invere accomplished.

Simple, elegant, and inverse.  If it were a person, she'd be on the cover of People Magazine.

But we want any equation to include the point (-20,2).

Let's see if we can move y=1/x to include (-20,2)

y=(1/x) + b

2 = (1/(-20)) + b

2 = -(0.05) + b

b = 2.05

The equation y = (1/x)+2.05 is an inverse equation that includes point (-20,2).

See the attached graph.  Note that when x = 0, the expression (1/x) becomes (1/0).  Division by zero is not allowed (undefined).  Use caution if in the neighborhood.

Answer:153

Step-by-step explanation

we can see height is equal to 9. if we consider height and 10sm as sides of rectangle, we can say top of trapezoid is equal to 10 as well.

Area of trapezoid is A=(a+b)/2*h

h-height=9

a-top=10

b-bottom=10+7+7=24

A=(10+24)/2*h=34/2*9=17*9=153