A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.

y=-16x^2+248x+116

The graph of the rational function is the one in option D.

Here we have a rational function of the form:

y = (x^2 + 4x + 3)/(x + 2)

Now, notice the variable is on the denominator, and notice that the denominator becomes zero when:

x +2  = 0

x = -2

This meansthat we will have a vertical asymptote at x = -2, the only graphs with that are D and B.

Now, the y-intercept is:

f(0) =  (0^2 + 4*0 + 3)/(0 + 2) = 1.5

The y-intercept is positive, like in graph D, so that is the correct option.

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Answer:

radius = 6.5

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 42.25 ← is the equation of a circle centred at the origin

with r² = 42.25 ( take square root of both sides )

r = \(\sqrt{42.25}\) = 6.5

Answer:

£2121.8

Step-by-step explanation:

2000 X 1.03 X 1.03 = 2121.8

Primer coat is a layer of emulsified asphalt applied over the existing pavement. This layer is applied to bond the new asphalt layer with the old pavement and provide a strong foundation for construction.

Tack coat, on the other hand, is a thin layer of asphalt emulsion or liquid asphalt or cutback asphalt applied between two pavement lifts. It acts as a bonding agent, ensuring that the new pavement layers adhere to each other properly.

The percentage of the lift surface covered by the tack coat should be around 90%.

Prior to painting, materials are coated with a primer or undercoat. In addition to improving paint adherence to the surface and extending paint endurance, priming also offers extra protection for the object being painted.

A primer is made up a synthetic resin, a solvent, and additives. Some primers also contain plastic (polyethylene) for increased durability.

A paint component called primer improves the adhesion of finishing paint compared to when it is applied alone.[3] It is made to stick to surfaces and provide a binding layer that is more suitable for receiving paint. A primer can be designed to have better filling and binding capabilities with the substance beneath rather than being utilised as the outermost durable finish like paint.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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A probability model gives information about the likelihood of different outcomes of a random event or experiment.

A probability model is a mathematical tool used to describe the likelihood of different outcomes in a random event or experiment. It provides information about the distribution of probabilities associated with the different possible outcomes, and can be used to make predictions about the likelihood of specific events occurring.

Probability models can be simple or complex, depending on the nature of the event or experiment being modeled, and can be used to make predictions in a wide range of fields, from finance to physics. By providing a framework for understanding the distribution of probabilities associated with different outcomes, probability models allow us to make informed decisions and assess risk in a variety of contexts.

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By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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The integral (12x + 12y) dA over the region R, using the given transformation, evaluates to 64. The new limits of integration are u = -6 to u = 6 and v = -6 to v = 6.

To evaluate the integral (12x + 12y) dA over the region R, we need to perform a change of variables using the given transformation:

\(x &= \frac{1}{3}(u + v) \\\)

\(y &= \frac{1}{3}(v - 2u)\)

First, let's find the Jacobian determinant of the transformation:

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(\left| \frac{\partial x}{\partial u} \ \frac{\partial x}{\partial v} \right|\)

\(\[= \left| \frac{1}{3} \ \frac{1}{3} \right|\]\)

\(=\[| -\frac{2}{3} \ \frac{1}{3} |\]\)

\(=\frac{1}{3}\)

Now, let's find the new limits of integration by substituting the given vertices of R into the transformation:

When (x, y) = (-2, 4):

\(\[-2 = \frac{1}{3}(u + v)\]\)

\(\[4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = -6.

When (x, y) = (2, -4):

\(\[2 = \frac{1}{3}(u + v)\]\)

\(\[-4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = 6.

When (x, y) = (3, -3):

\(\[\begin{aligned}3 &= \frac{1}{3}(u + v) \\\\-3 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = 6 and v = 0.

When (x, y) = (-1, 5):

\(\[\begin{aligned}-1 &= \frac{1}{3}(u + v) \\5 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = -6 and v = 0.

Therefore, the new limits of integration for the integral are u = -6 to u = 6 and v = -6 to v = 6.

Now, we can rewrite the integral using the new variables:

\([\int_{-6}^{6} \int_{-6}^{6} (12x + 12y) , da = \frac{1}{3} \int_{-6}^{6} \int_{-6}^{6} \left( 12(u + v) + 12(v - 2u) \right) , dudv]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( 4u + 4v + 4v - 8u \right) \, dudv\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( -4u + 8v \right) \, dudv\]\)

Integrating with respect to u first, we have:

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -\frac{4u^2}{2} + 8uv \right) \, du\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -2u^2 + 48v \right) \, du\]\)

\(\[= \frac{4}{9}\) (864)

= 64

Therefore, the value of the integral (12x + 12y) dA over the region R is 64.

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Answer:

f(g(x)) = 9x² - 6x - 4

Step-by-step explanation:

f(g(x) )

= f(3x - 1)

= (3x - 1)² - 5 ← expand factor using FOIL

= 9x² - 6x + 1 - 5

= 9x² - 6x - 4

Answer:

0.5

3.1

16 %

Step-by-step explanation:

The chosen topic is not meant for use with this type of problem. Try the examples below.

Answer: $130

Step-by-step explanation:

Simple interest is calculated as:

= PRT/100

where P = principal = $5200

R = Rate = 5%

T = Time = 2 years

S.I = (PRT)/100

= (5200 × 5 × 2)/100

= 52000/100

= $520

Assuming the loan was obtained for 2 1/2 years, the simple Interest will be:

= (5200 × 5 × 2.5)/100

= 65000/100

= $650

This means he'll have saved:

= $650 - $520

= $130

Answer:

37.33 students were in each bus

Step-by-step explanation:

total student =229

travelled student by car =5

travelled student by 6 buses=(229-5)=224

travelled student by 1 buses=224/6=37.33

A 70% chance of rain means that there is a higher likelihood of rain occurring compared to other possible weather conditions, but it is not a guarantee.

When a forecaster says there is a 70% chance of rain, it means that, based on their analysis of various weather factors, they believe there is a 70% probability of rain occurring. This percentage represents the likelihood or chance of rain happening.

It's important to note that this is not a definitive prediction that it will rain. Weather forecasting is not an exact science, and there is always some level of uncertainty involved. The forecaster is indicating that, given the current conditions and their expertise, rain is more likely to happen than not.

To put it into perspective, if this weather scenario were repeated 100 times, it is expected that rain would occur in approximately 70 of those instances. The remaining 30 instances would not experience rain.

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Answer:

D

Step-by-step explanation:

This comes out to 4. The other ones are absolute value, meaning there are no negatives. You can think of subtracting as adding a negative. When you role a dice however, you are never really moving backward.

Answer:

A

Step-by-step explanation:

Mark Branliest Please!

Answer:

204

Step-by-step explanation:

3.4[6(4)+6^2]=

3.4[24+36]=

3.4[60]=

204

Hope this helps!

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16, RT= 32  and UV ≈ 8.2.

A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16.

Finding R T and U V is our goal.

First, let's assume that the figure RSTU is a rhombus since its perimeter and one-half of a diagonal's length are both provided. RT is the result of adding the segments RV and VT.

RT=RV + VT

We are informed that the RV is sixteen. If RV and VT are congruent, then V T equals 16. So:

R T = 16 + 16 = 32

In order to determine the UV length, we must first determine the RU length. Since a rhombus's sides are the same length, we can divide its perimeter by four to determine

RU= Perimeter/ 4

If we simplify and replace Perimeter with 72, we get:

RU = 72 / 4

RU =18

Since UB is a member of the right triangle RUV created by the intersection of the diagonals, we can now use the Pythagorean theorem to determine its length. So:

U V²+ R V² =  RU²

If R V = 16 and R U = 18, we obtain:

U V² + 16 ²= 18²

By way of summary, we have:

U V² + 256 = 324

U V² + 256 − 256 = 324 − 256

√ UV = √ 68

UV = 8.2462

UV ≈ 8.2

Our recommendations are as follows:

RT= 32

UV ≈ 8.2.

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Answer:

x = 2

Step-by-step explanation:

Equation:

3 - 2x = 2x - 5

Step 1: add 2x on each side

3 = 4x -5

Step 2: Add 5

8 = 4x

Step 3: Divide by 4

x = 2

Answer:

$54.30

Step-by-step explanation:

Given Total Donations already raised

= $30.20 + $10.50 + $5.00

= $45.70

Donations still required = Total Donations needed - Donations already raised

= $100 - $45.70 = $54.30

Answer:

slope = 1/2

Step-by-step explanation:

slope = y2-y1 / x2-x1

1 - -2 / 4 - -2 = 3/6 = 1/2

or think of it this way. for every 1 step up you take 2 steps to the right to stay on the line. 1/2

By making quarterly deposits of $5,500 into an investment fund at an interest rate of 3.25% compounded quarterly, the accumulated value after 5 years would be around $124,907.43. It's important to note that this calculation assumes the periodic deposits are made at the beginning of each quarter and that the interest is compounded quarterly.

To calculate the accumulated value of periodic deposits, we can use the formula for the future value of an ordinary annuity:

A = P * [(1 + r)^n - 1] / r,

where: A is the accumulated value, P is the periodic deposit, r is the interest rate per period, and n is the number of periods.

In this case, the periodic deposit is $5,500, the interest rate is 3.25% (or 0.0325) compounded quarterly, and the investment period is 5 years, which is equivalent to 20 quarters.

Substituting the values into the formula, we have:

A = $5,500 * [(1 + 0.0325)^20 - 1] / 0.0325.

Calculating this expression, the accumulated value of the periodic deposits after 5 years would be approximately $124,907.43.

Therefore, by making quarterly deposits of $5,500 into an investment fund at an interest rate of 3.25% compounded quarterly, the accumulated value after 5 years would be around $124,907.43. It's important to note that this calculation assumes the periodic deposits are made at the beginning of each quarter and that the interest is compounded quarterly.

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Answer:

yo thats pretty pog ngl

Step-by-step explanation:

esnjogjdrgjsrknfseoikngsdbngdmhg

answer:

a) 9

b) 12

c) -18

d) 8

e) -7

f) 0

g) -7

h) 24

Answer:

22 1/2 degrees

Step-by-step explanation:

4 x 5 = 20

(1/2) x 5 = 2.5

Answer: 22.5 degrees

Step-by-step explanation:

If it fell 4.5 degrees each hour, and there were 5 hours, 4.5x5 == 22.5

14 cubic cm because you just gotta think about how to flip these so you can count it B)

Answer:

The mark up is $2.20 and the new price of each T-shirt is $6.20.

Step-by-step explanation:

Before we find the new price of each T-shirt we must find the markup (by how much were raising the price).

The problem states each T-shirt costs $4.00, but then marks up the price of each by 55%.

Step 1 would be to find 55% of $4.00.

0.55 * 4 = 2.2

So that is the mark up, the price is going up by $2.20. To find the new price of each T-shirt, you take that $2.20 and add it to the original $4.00.

$4.00 + $2.20 = $6.20

So the mark up is $2.20 and the new price of each T-shirt is $6.20.

Answer:  the  answer  is  15m  +  35

Step-by-step explanation:

Answer:

y= 5(3m+7)

Step-by-step explanation:

The linear optimization problem is to maximize the objective function 250x + 150y, subject to the constraints x + y ≤ 60, 3x + y ≤ 90, and 2x + y > 30, where x and y are both greater than or equal to 20.

The feasible region can be determined by graphing the constraints and finding the overlapping region that satisfies all the conditions. In this case, the feasible region is the area where the lines x + y = 60, 3x + y = 90, and 2x + y = 30 intersect. This region can be visually represented on a graph.

To find the corner points of the feasible region, we need to find the points of intersection of the lines that form the constraints. By solving the systems of equations, we can find that the corner points are (20, 40), (20, 60), and (30, 30).

The optimal solution and the optimal objective function value can be determined by evaluating the objective function at each corner point and selecting the point that yields the maximum value. By substituting the coordinates of the corner points into the objective function, we find that the maximum value is achieved at (20, 60) with an objective function value of 10,500.

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Answer:

AC is included between <A and <C.

b) angle a and angle c

The required characteristic that has a high survival value in a population is likely to become dominant or common.

Statistics is the study of mathematics that deals with relations between comprehensive data.

A characteristic that has a high survival value in a population is likely to become more common over time. This is because individuals with this characteristic are more likely to survive and reproduce, passing the trait on to their offspring. Over generations, this process, known as natural selection, can lead to an increase in the frequency of the advantageous trait in the population. Over time, the characteristic that has a high survival value in a population is likely to become dominant.

Thus, the required characteristic that has a high survival value in a population is likely to become dominant or common.

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