the graph represents an object that is shot upward from a tower and then falls to the ground. The independent variable is time in seconds and the dependent variable is the object's height above the ground in meters. 1. How tall is the tower from which the object was shot?2. when did the object hit the ground?3. estimate the greatest height the object reached and then the time it took to reach that heightindicate this situation on the graph below by drawing on the graph given

Step 1. The expression that we have is:

And we need to solve the operations to find the answer.

Step 2. We need to make the multiplications first:

(-6)(-2)=12

and

(+8)(-4)=-32

here we have applied the law of signs:

The solution to the multiplications is shown here:

The expression now is:

Step 3. Now we solve the expression considering that

(+)(-) is -

The result of the subtraction is:

Answer:

ANSWER

Current (l) = 7.81 amps (rounded to 2 decimal places)

EXPLANATION

Declaration of Variables

Let l represent the current in a wire,

v represent the voltage, and

r represent the resistance

Desired Outcome

The current (l)

Equation formation

where k is the constant of proportionality.

Determine the value of k given l = 27.5, v = 110, and r = 4.

Find the current (l) given v = 125, and r = 16.

Hence, the current (l) when the voltage is 125 volts and the resistance is 16 ohms is 7.81 amps (rounded to 2 decimal places).

The answer is (5, - 4) (Option D)

We are required to solve the system of equations:

In order to solve the equations, we need to make sure that one of the terms in both equations is the same.

In (Equation 1), there is a 4x term. In (Equation 2), there is a 2x term.

We can make 2x in (Equation 2), the same as 4x in (Equation 1), by multiplying the whole of (Equation 2) by 2

Let us perform this multiplication below:

Now that we have a similar term in both (Equation 1) and (Equation 2), we can subtract both equations to eliminate that term and then find the value of y.

This is done below:

Now that we have the value of y, we can substitute this value into Equation 1 to get the value of x

This is done below:

Therefore, the solution to the system of equations is:

x = 5, y = -4

Thus the final answer is (5, - 4) (Option D)

The volume of liquid (V1) in first container at any time 't' is given as,

The volume of liquid (V2) in other container at any time 't' is given as,

Consider the equation,

Thus, the given equation represents the situation when the volume in both the containers are equal.

Given: A graph of a function

The intercepts and the aymptotes of h(x) using the graph

From the given graph

Y-intercept is the point where the curves crosses the y-axis

From the graph, the coordinate of the y-intercep is

X-intercept is the point where the curves crosses the x-axis

From the graph, the oordinate of the x-intercept is

Answer:

x intercept= -4

y intercept= -1

Asymptote for H(x)= -5

Step-by-step explanation:

Yw;)

We must write the relation between the age and the average number of hours slept as a set of ordered pairs.

Notice that the average number of hours slept by age is the following:

To write the function as a set of ordered pairs, use the data from the domain (years) and from the range (hours) to form ordered pairs as (years,hours).

Then, the function as a set of ordered pairs is:

Since the club needs to raise $ 5, 000

And the school agrees to contribute $1000

Then if the least amount each of the 60 members of the club is represented by x

then

Solution:

Analysis:

We have a budget of $ 460. In the first step, we need to calculate the total amount of money spent on a bicycle, reflectors, and bike gloves.

When we calculate the amount spent, we can write the inequation:

X would be the number of outfits and adding to 316.78, it has to be less or equal to 460.

Now, let's

Given the inequality:

So, we will select the values of v that is less than (-7)

The solution on the number line is as shown in the following figure:

So, we will select the numbers that are shown in the following figure:

The answer is the numbers with the red color.

Answer:

B. There tended to be fewer complaints on days with more buses.

Explanation:

From the scatterplot, when the number of buses per hour increased, the number of complaints reduced.

A line of best fit drawn on the scatterplot will have a negative slope.

The diagram below illustrates a negative and positive slope on the line of best fit.

Thus, we can say that there tended to be fewer complaints on days with more buses.

The correct option is B.

SOLUTION:

Step 1:

In this question, we are given the following:

A foam cylinder, with a diameter of 3 inches and a height of 8 inches, is carved into the shape of a cone.

What is the maximum volume of a cone that can be carved? Round your answer to the hundredth place.

Step 2:

The details of the solution are as follows:

CONCLUSION:

The

Explanation

We are given the following equation:

We are required to determine the quadratic term, the linear term, and the constant term.

This is achieved thus:

We know that given the general form of a quadratic equation, we have;

Hence, the answer is:

Given: A rhombus ABCD

To Determine: The CD

Solution

Please note that the four sides of a rhombus are the same side lengths

Since all the side lengths of the rhombus are the same, then CD = 18 units

we must apply the formula

now we apply the formula to find x,

having already x now we apply the formula to find the vertex at y that intersects at point 12.

"There are 5 one-story houses and 5 two-story houses on the west side of the street, which require a total of 115 doors." translates to 5x + 5y = 115

"there are 2 one-story houses and 5 two-story houses, which require a total of 85 doors." translates to 2x + 5y = 85

Substitute x = 10 for one story houses, and y = 13 for two story houses.

Let:

M(t) = Money earned by ken as a function of time

Let's asume ken earned 20 dollars for the purchase of Bryan

And let's make a conversion:

2 min * 60 s/1min = 120s

So, the food goes up every 150s

Hence the function M(t) would be:

Let's define t2= 150s

M(t) = $20 + ($5+$10t/t2)

Because he sells his food for $5 and the price goes up by $10 every 150s

Ok, now an hour has 3600s:

So:

3600s/150s = 24

We can conclude that in one hour the food went up in price 24 times

Now, using the function:

M(t) = $20 + ($5+$10t/t2)

For t = 3600

M(3600) = $20 + ($5 + $10 * (3600)/(150))

M(3600) = $20 + ($5 + $10*24)

M(3600) = $20 + $5 + $240 = $265

Ken will make $265 in one hour

1.5 + 0.3> 3.6

1.8>3.6 is a contradiction, then the given inequality is False.

Options A, B, and E

See below the diagramatic representations of the two congruent triangles

Since △FGH ∼ △LMN:

All corresponding sides are similar

The ratio of two corresponding sides are equal

Corresponding angles are congruent

Therefore:

∵ The number of the folders = 9

∵ The cost of each folder = $2.50

∴ The cost of the folders = 9 x 2.50

The volume of a prism is equal to the area A of its base times its height h:

On the other hand, there is a formula to find the area of a triangle if the lengths of 3 sides are given.

Let a, b and c be the lengths of the sides of a triangle.

We define the semiperimeter s of the triangle as:

Then, the area of the triangle is given by the Heron's formula:

Replace a=3cm, b=6cm and c=5cm to find s:

Replace the values of a, b and c as well as s=7cm into Heron's formula to find the area of the triangular base:

Replace the value of A and h=15cm into the equation to find the volume of the prism:

Therefore, to the nearest cubic centimeter, the volume of the prism is 112 cm^3.

We know that

• The plane travels 1440 miles in 3 hours with the wind.

• It takes 4 hours against the wind to travel the same distance.

Let's call p the rate of the plane in still air, and w the speed of the wind.

Traveling with the wind would be expressed as follows.

This expression is deducted from the distance formula d = v*t.

The expression that represents against the wind would be.

To solve the system we just formed.

Let's multiply the first equation by 4 and the second equation by 3.

Now, let's combine the equations.

The rate of the plane in still air is 420 miles per hour.

Now, let's find w.

The rate of the wind is 60 miles per hour.

A function showing an exponential growth is modelled in the form,

y = Aoe^kt

where k is the rate of growth

If k is negative, then it is the rate of decay and the function would be a decay function

SOLUTION

First, we will define the terms and match the line that matches the definition.

RADIUS

A straight line from the center to the circumference of a circle

DIAMETER

A straight line passing from side to side through the center of a body(circle)

CHORD

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.

TANGENT

The tangent to a circle is defined as a straight line that touches the circle at a single point.

x will represent the number of rides Clay do

The cost of the rides must be less or equal to 50. Therefore the inequality is

ANSWER

3x<=50

Given:

The function is:

Find-:

The horizontal or vertical stretch or compression of the function

Explanation-:

The graph of a function is:

The f(x) is:

The graph of function is:

So, the both function is:

So, the graph is vertically stretch by √3

A rectange has four sides. Two sides with the same length and other two sides of the same length.

This means that if you rotate the rectangle you will obtain the same figure only for rotation of 180°.

You can notice the previous conclusion in the following image:

The rectangle with black lines is the original one, and the rectangle with red lines is the rotated rectangle with a rotation of 180°. You can observe that for such a rtation yo obtain the same figure.

In order to find the volume of a traingular prism, we do:

1/2 ( b x h x l) = 1/2 (5x2x15)

1/2(150)

= 75 m³

Letter C

Let's find the length of the side of the pool.

Let it be x, so the diagram is:

Using the pythagorean theorem, we can figure out x. Shown below:

So, 30 meters is the side length of the square (pool).

The area of a square is:

Where "s" is the side length

We found s to be 30, thus the area of the pool is:

Thus,

Given the word problem, we can deduce the following information:

Radius of a circle = 6 feet

Arc length = 6 feet

To determine the central angle, we use the formula:

where:

L=arc length

r=radius

θ= central angle in degrees

We plug in what we know:

Therefore, the angle is 57.30°.

Given

Angle = 32°

top of the ladder is 20 feet up on the building

Find

length of the ladder

Explanation

let length of ladder = h

here we use trigonometric ratio.

so ,

Final Answer

Hence , the length of ladder in nearest foot is 38 ft