What is the area of Rectangle PQRS in the xy-coordinate plane below?

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The time it will take the ball to reach a height of 90feet is 1.2 and 4.4secs

Given the height h (in feet) of the ball t seconds after being kicked expressed as:

h = –16t2 + 90t + 4.

If the ball is at a height of 90feet, hence:

90 = –16t2 + 90t + 4

–16t2 + 90t + 4 - 90 = 0

16t^2  -90t  + 86= 0

8t^2  -45t  + 43= 0

Factorizing the result to get the values of t:

\(t=\frac{45 \pm \sqrt{45^2-4(43)(8)} }{16} \\t=\frac{45 \pm \sqrt{2,025-1376} }{16} \\t=\frac{45 \pm {25.47}}{16} \\t=4.4s \ and\ 1.22secs\)

Hence the time it will take the ball to reach a height of 90feet is 1.2 and 4.4secs

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Answer:

  A(8, 10)

Step-by-step explanation:

Vertex A is on the vertical line x=8, so we can find the y-coordinate by solving the boundary equation ...

  5x +8y = 120

  5(8) +8y = 120 . . . use the x-value of the vertical line

  5 + y = 15 . . . . . . . divide by 8

  y = 10 . . . . . . . . . . subtract 5

Point A is (8, 10).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

Here, we have,

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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Answer:

This is the quadratic formula that is used to solve quadratic equations.

Answer:

quadratic formula

Step-by-step explanation:

\(x = \frac{-b + / - \sqrt{b^{2} - 4ac } }{2a}\) is called the quadratic formula

Answer:

The Alpha Level

Step-by-step explanation:

The critical value is obtained by applying the alpha value to an area. For example if we choose the alpha level of 0.05 the critical value would be 1.96 for a two tailed test. But if the alpha is 0.1 the critical value would be 1.645 and similarly the critical value would be 2.58 for 0.01 alpha level.

The critcal value depends on the alpha level and is set accordingly depending on one tailed or tailed test. It does not involve the use of The Obtained Statistic  or The Population Mean.

Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

Yes it is rational number becauseit it s fraction

Answer:

\( JM = 60 units \)

Step-by-step explanation:

Given:

\( JM = 9x + 6 \)

\( JK = 5x \)

\( KM = 3x + 12 \)

\( JK + KM = JM \) (segment addition postulate)

\( (5x) + (3x + 12) = (9x + 6) \) (substitution)

Solve for x

\( 5x + 3x + 12 = 9x + 6 \)

Collect like terms

\( 5x + 3x - 9x = -12 + 6 \)

\( -x = -6 \)

Divide both sides by -1

\( x = 6 \)

\( JM = 9x + 6 \)

Plug in the value of x

\( JM = 9(6) + 6 \)

\( JM = 54 + 6 \)

\( JM = 60 units \)

The number line first represents the solution to the inequality x/-1 > -6 option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The complete question is:

Which of the following number lines represents the solution set of x/-1 > -6?

For the number lines shown in the attached picture, please refer to the picture.

We have an inequality:

x/-1 > -6

x < 6  

x ∈ (-∞, 6)

Thus, the number line first represents the solution to the inequality x/-1 > -6 option first is correct.

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Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

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

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)

Answer:

Counter Clockwise Torque = 360 Nm

Clockwise Torque = 240 Nm

Step-by-step explanation:

Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

Answer:

f(g(x))=6x-8

Step-by-step explanation:

To keep it simple lets say if , for example

\(f(x)=2x-4\)

then f(2) would be what?

\(f(2)=2(2)-4\\f(2)=0\)

which means we plugged in x=2 in our f(x) this goes for same as the composite function \(f(g(x))\) where we plug in g(x) in f(x) and replace x with g(x). I'll show you

\(f(x)=2x-4\\g(x)=-3x+2\\\)

now we insert g(x) in f(x) cause we need f(g(x)) which means we replace x with the function g(x).

\(f(g(x))=-2(-3x+2)-4\)

\(f(g(x))=6x-4-4\\f(g(x))=6x-8\)

so that is our final answer.

Hope i helped

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

A:y= 2x+4 B:y= -1/3x +12

Step-by-step explanation:

Answer:

The first one is False.

Step-by-step explanation:

If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.

Answer:

c is the correct answer

Step-by-step explanation:

A is the correct option:) Three ways electrons can be transferred are conduction, friction, and polarization. In each case, the total charge remains the same. This is the law of conservation of charge. Conduction occurs when there is direct contact between materials that differ in their ability to give up or accept electrons.

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The predicted population in the year 2030 is 10 people

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

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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Answer:

it would be 6. it is closer to the 6 mark. so the answer would be B. this is the answer.

Step-by-step explanation:

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:Asa

Step-by-step explanation:because I know

The area of the circle is  \(225\pi \ in.\)

Hence, Option A is the correct answer.

A circle is a round-shaped figure that has no corners or edges. The Diameter is the longest chord of the circle. It divides the circle into two equal halves.

Diameter of the circle (d)= 30 in.

The radius of a circle is the distance from the center of the circle to any point on its circumference. The diameter is twice the radius of the circle.

The radius of the circle will be =d/2

                                             = \(\frac{30}{2}\)

                                             = 15 in.

So, the radius of the circle is 15 in.

The area of the circle is given by \(A = \pi r^2\)

So we have,

\(A = \pi r^2\)

\(A = \pi 15^2\)

\(A =225\pi \ in.\)

Hence, the area of the circle is \(225\pi \ in.\)

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An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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Mean = 33.3 g, Range = 1.9 g, Standard Deviation = 0.7 g, Relative Standard Deviation = 2.1%.

To calculate the mean of the data set, add all of the measurements together and divide by the total number of measurements. In this case, the mean is

33.3 g (33.0 + 33.5 + 32.2 + 34.1 + 32.6 + 33.2)

= 196.6 / 6

= 33.3.

To calculate the spread or range, subtract the smallest measurement from the largest measurement. In this case, the range is

1.9 g (34.1 - 32.2 )

= 1.9

To calculate the standard deviation, first calculate the difference between each measurement and the mean, square each of those differences, add them together, and then divide by the total number of measurements. In this case, the standard deviation is

0.7 g\(([(33.0-33.3)^2 + (33.5-33.3)^2 + (32.2-33.3)^2 + (34.1-33.3)^2 + (32.6-33.3)^2 + (33.2-33.3)^2] / 6 = 0.7)\). To calculate the percent relative standard deviation, divide the standard deviation by the mean and then multiply by 100. In this case, the relative standard deviation is 2.1% (0.7 / 33.3 x 100 = 2.1%).

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