The first five questions refer to the following problem:


A model rocket lifts off with an upward thrust of 35 Newtons. It has a mass of 2.5 kilograms and a weight of 25 Newtons. How quickly does the rocket accelerate?


Use your given quantities and your equations to solve the problem.


Question 5 options:


10 m/s^2


150m/s^2


24 m/s^2


4 m/s^2

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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Answer:

c took me a wiel but then realized it was just butterfly method to solve.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer is C, only need to move it up and to the right through translation.

Perimeter of triangle XRS is 100.

A triangle is said to be similar to another triangle if all the angles in one triangle is equal to the corresponding angles in the other triangle.

Corresponding sides are proportional.

Given ΔACF similar to ΔXRS.

We have to find the perimeter of ΔXRS.

Corresponding sides of AC, CF and FA are XR, RS and SX respectively.

We have,

AC = 20, CF = 32, FA = 28 and XR = 25.

Sides of similar triangles are proportional.

AC / XR = CF / RS = FA / SX

20 / 25 = 32 / RS = 28 / SX

Consider 20 / 25 = 32 / RS.

RS = 40

Consider 20 / 25 = 28 / SX

SX = 35

Perimeter of ΔXRS = XR + RS + SX = 25 + 40 + 35 = 100

Hence the perimeter is 100.

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Answer:

Any set of (x , y) whose distance from (4, -3) is 3 units lies on the circle.

Step-by-step explanation:

To find the distance , use the formula

\(distance = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}\)

If distance < 3, (x, y) lies inside the circle.

If distance > 3, (x, y) lies outside the circle.

If distance = 3 (x, y) lies on the circle.

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Answer:

I think the answer is 7/16 hope it's correct

The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

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

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)

Given:

Simplify the fraction,

Answer:

The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A

The vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.

In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:

\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)

From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).

The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.

The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is  \((x - 4)^2 - 20.\)

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After 1 year, the book value of the computer is $2,000.

To calculate the book value of the $2,500 computer after 1 year using the given MACRS rates, we need to apply the depreciation percentages for each year.

Given the MACRS rates:

Year 1: 20.0%

Year 2: 32.0%

Year 3: 19.2%

Year 4: 11.52%

Year 5: 11.52%

Let's calculate the depreciation for each year:

Year 1: 20.0% of $2,500 = $500

The computer's value after Year 1 is $2,500 - $500 = $2,000.

Therefore, after 1 year, the book value of the computer is $2,000.

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Answer:

12.6 m^2

Step-by-step explanation:

area of sector = 90/360 × 3.14 × 4^2

= 12.56

to the nearest tenth = 12.6 m^2

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} \theta =\stackrel{\textit{in degrees}}{angle}\\ r=radius\\[-0.5em] \hrulefill\\ \theta =270\\ r=4 \end{cases}\implies A=\cfrac{(270)(\stackrel{\pi }{3.14})(4)^2}{360}\implies \underset{\textit{rounded up}}{A\approx 37.7}\)

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

Answer:

The practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Step-by-step explanation:

The practical domain of the function is limited by the given constraints: Joe can purchase up to 8 boxes of hot dogs, and he cannot purchase partial boxes. Therefore, the number of boxes he can purchase is a whole number between 0 and 8, inclusive.

Substituting the values from 0 to 8 into the function, we get:

f(0) = 48(0) + 20 = 20

f(1) = 48(1) + 20 = 68

f(2) = 48(2) + 20 = 116

f(3) = 48(3) + 20 = 164

f(4) = 48(4) + 20 = 212

f(5) = 48(5) + 20 = 260

f(6) = 48(6) + 20 = 308

f(7) = 48(7) + 20 = 356

f(8) = 48(8) + 20 = 404

Therefore, the practical domain of the function is the set of integers from 0 to 8, inclusive, which is option B.

Answer:

D. x ≤ 5

Step-by-step explanation:

The closed circle means greater than or equal to (≤) or less than or equal to (≥). The open circle is greater than (<) or less than (>).

And since the circle is closed and the arrow is going to the right, than x is either greater than 5 or equal to 5

The central angle is 1.6 radian.

Given that there is a circle with radius 3.4 and an angle intercepts an arc of length 5.5.

We need to find the central angle,

So,

The arc length = central angle × radius

So,

5.5 = central angle × 3.4

Central angle = 1.6

Hence the central angle is 1.6 radian.

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Answer:

The answer is below

Step-by-step explanation:

1

a) The symmetric equations for the line that passes through the point (a, b, c) and is parallel to the vector (e, f, g) is:

\(\frac{x-a}{e}=\frac{y-b}{f} =\frac{z-c}{g}\)

Therefore using the above equation to Find symmetric equations for the line that passes through the point  (4, −4, 8) and is parallel to the vector (−1, 4, −3) we get:

\(\frac{x-4}{-1}=\frac{y-(-4)}{4}=\frac{z-8}{-3} \\\\Therefore:\\\\\frac{x-4}{-1}=\frac{y+4}{4}=\frac{z-8}{-3}\)

b)i) The line would intersect the xy plane where z = 0. Hence:

\(\frac{x-4}{-1}=\frac{y+4}{4}=\frac{0-8}{-3}\\\\\frac{x-4}{-1}=\frac{y+4}{4}=\frac{8}{3} \\\\\frac{x-4}{-1}=\frac{8}{3}\ and\ \frac{y+4}{4}=\frac{8}{3}\\\\x=\frac{4}{3}\ and\ y=\frac{20}{3} \\\\Therefore\ the\ line\ intersect\ the\ xy\ plane\ at\ (\frac{4}{3},\frac{20}{3},0)\)

ii) The line would intersect the yz plane where x = 0. Hence:

\(\frac{0-4}{-1}=\frac{y+4}{4}=\frac{z-8}{-3}\\\\\frac{y+4}{4}=\frac{z-8}{-3}=4\\\\\frac{y+4}{4}=4\ and\ \frac{z-8}{-3}=4\\\\y=12\ and\ z=-4 \\\\Therefore\ the\ line\ intersect\ the\ yz\ plane\ at\ (0,12,-4)\)

iii) The line would intersect the xz plane where y = 0. Hence:

\(\frac{x-4}{-1}=\frac{0+4}{4}=\frac{z-8}{-3}\\\\\frac{x-4}{-1}=\frac{z-8}{-3}=1\\\\\frac{x-4}{-1}=1\ and\ \frac{z-8}{-3}=1\\\\x=3\ and\ z=5 \\\\Therefore\ the\ line\ intersect\ the\ xz\ plane\ at\ (3,0,5)\)

2)

Let the points be A(−6, 4, 1) and B(2, 6, 5). Let O be the midpoint of the two points A and B. Therefore O is the average of the x coordinates, y coordinates and z coordinate.

\(0=\frac{1}{2} (-6+2,4+6,1+5)=(- 2,5,3)\\\\\)

The normal vector (n) in the direction of line between A and B is:

n = AB = B - A = (2, 6, 5) - (−6, 4, 1) = (8, 2, 4)

n = 8x + 2y + 4z

The equation of the plane based on the normal vector and the midpoint 0 is:

Plane = 8x + 2y + 4z  = 8(-2) + 2(5) + 4(3) = 6

Therefore:

8x + 2y + 4z = 6

4x + y + 2z = 3

3) The normal vectors to the plane are:

\(n_1=(1,1,-1)\ and\ n_2=(4.-1,5)\)

The point of intersection O of the two planes is normal to the normal vectors, hence:

\(O=n_1*n_2=(1,1,-1)*(4,-1,5)\\\\O=(4, -9, -5)\)

A point that lies on both plane is gotten by substituting z = 0, hence:

x + y - (0) = 3,    and     4x - y + 5(0) = 5

x + y = 3    and    4x - y = 5

Solving simultaneously gives x = 8/5, y=7/5

From this two points we get:

AB = (-2-8/5, 1 - 7/5, 1-0) = (-18/5, -2/5, 1)

The vector normal to the plane (n) = (4, -9, -5) * (-18/5, -2/5, 1) = (-11, 14, -34)

\(B=A_o=-11(x-(-2))+14(y-1)-34(z-1)\\\\0=11x+22+14y-14-34z+34\\\\11x+14y-34z =42\\\)

Answer:

$5

Step-by-step explanation:

1000/200=5

Answer:

20 cents.

Step-by-step explanation:

A fair price would be 200/1000 = 1/5 of a dollar which is 20 cents. But this does not allow for the people putting on the raffle to make any money for doing it. It would be better if the raffle went for a dollar. Most people would think that is fair and would not begrudge a dollar.

Answer: 80

Step-by-step explanation:

Answer: The correct answer is 80

Step-by-step explanation:

in parentheses 3x4 = 12 - 4 = 8

6 + 4 = 10

10 x 8 = 80

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

see below

Step-by-step explanation:

a) set the two equations equal to each other and isolate the variable

3x+8 = 7x-24

3x+32=7x

32=4x

x=8

b) Plug in the value of x we got into the equation

7(8)-24 = 56

56-24=32

c) Angle k and h are both 72 (add 20 and 502 together) so h+k=144

J and m are going to have the same measurement so we can set up and equation, we also know all angles must add up to 360

144+2x=360

2x=216

x=108

HMK=108

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Answer:

True

Step-by-step explanation:

limx→b [3f(x)-4g(x)]

limx→b [3f(x)-4g(x)]= limx→b [3f(x)] - limx→b [4g(x)]

= 3[limx→b f(x)] - 4[limx→b g(x)]

Since limx→b f(x) = 2 and limx→b g(x) = 10,

= 3(2)-4(10)

= -34

Answer:

4 by 3

Explanation:

Rows by columns

The population of interest: Male RCCC students.

Sample size: 31.

The sample mean: 69.68 inches.

Median: 69 inches.

Mode: 70 inches.

Range: 11 inches.

Standard deviation: 3.32 (rounded to 2 decimal places).

Variance: 11.02 (rounded to 2 decimal places).

We have,

Mean:

To find the mean, we sum up all the heights and divide by the total number of data points (31 in this case):

Mean = (70 + 70 + 70 + ... + 75) / 31

Mean ≈ 69.68 inches

Median:

The median represents the middle value in the dataset when arranged in ascending order. Since the dataset has an odd number of values (31), the median will be the value in the middle position when ordered:

Median = 69 inches

Mode:

The mode represents the value(s) that occur most frequently in the dataset. In this case, the mode is the height that appears most often:

Mode = 70 inches

Range:

The range is calculated by subtracting the minimum value from the maximum value in the dataset:

Range = Maximum height - Minimum height

Range = 75 - 64 = 11 inches

Standard Deviation (σ):

To find the standard deviation, we can use the formula that involves finding the difference between each value and the mean, squaring those differences, averaging them, and taking the square root:

Standard Deviation (σ) ≈ 3.32 (rounded to 2 decimal places)

Variance (σ²):

The variance is the square of the standard deviation.

We can square the value of the standard deviation to find the variance:

Variance (σ²) ≈ 11.02 (rounded to 2 decimal places)

The height dataset (in inches) for the 31 male RCCC students is as follows:

1 70

2 70

3 70

4 70

5 71

6 64

7 64

8 65

9 65

10 66

11 66

12 67

13 67

14 68

15 68

16 68

17 69

18 72

19 72

20 72

21 72

22 73

23 73

24 73

25 73

26 73

27 73

28 74

29 75

30 75

31 75

32 75

Thus,

The population of interest: Male RCCC students.

Sample size: 31.

The sample mean: 69.68 inches.

Median: 69 inches.

Mode: 70 inches.

Range: 11 inches.

Standard deviation: 3.32 (rounded to 2 decimal places).

Variance: 11.02 (rounded to 2 decimal places).

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