Jason has 17 pencils and Shannon has 43 pencils. How many pencils must Shannon give Jason
in order for them to have the same number of pencils?

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.

To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.

Using this method, we can find all the possible length and width pairs:

1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8

Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:

perimeter = 2(length + width)

For each pair, we can plug in the values for length and width to get the perimeter:

1 x 48: perimeter = 2(1 + 48) = 98

2 x 24: perimeter = 2(2 + 24) = 52

3 x 16: perimeter = 2(3 + 16) = 38

4 x 12: perimeter = 2(4 + 12) = 32

6 x 8: perimeter = 2(6 + 8) = 28

Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.

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Answer:

(800 x 9) + (10 x 9)

Step-by-step explanation:

Find out what 810 x 9 is:

810 x 9 = 7290

Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):

(800 x 9) = 7200

(10 x 9) = 90

7200 + 90 = 7290

Answer:

  you're nearly there

Step-by-step explanation:

You have obviously determined the correct entry in the top box of each pair. What you seem to have failed to observe is that the bottom box in each pair needs exactly the same entry as the top box.

_____

You figure this out by looking at the stuff that is outside the box. The numbers and symbols for the second box show how the function indicated outside the first box is evaluated. That is f(x) at the top becomes 4x at the bottom, where x (in this case) is x/4 for both.

Answer: (9, 40, 41)

Step-by-step explanation:

There are an infinite number of Pythagorean triples.

Any value a, b, c such that a² + b² = c²

Here are a few of them:

3, 4, 5

5, 12, 13

7, 24, 25

8, 15, 17

9, 40, 41

Answer:

​(x²-y²)² + (2xy)² = (x²+y²)²

Find the missing x- and y-values and Pythagorean triples using the identity given

A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).​

​We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :

​a = (x²-y²)

​b = (2xy)

​c = (x²+y²)

​Question 1)

X Value = 4​

​Y Value = 3

​Pythagorean triples: ?

We can replace the values of x and y, to determine a, b and c.​

​a = (x²-y²) = (4²-3²) = 16-9 = 7

​b = (2xy) = (2*4*3) = 24

c = (x²+y²) = (4²+3²) = 16+9 = 25​

​Answer 1 : Pythagorean triples : (7,24,25)

Question 2) ​

​X Value = 5

Y Value = ?​

Pythagorean Triples: (9,40,41)​

​Now we have a, b, and c, to determine Y

​b = (2xy) = 40

Y = 40/2x = 40/2*5 = 40/10 = 4​

Answer 2 : Y = 4​

​Question 3)

X Value = ?​

Y Value = 3​

Pythagorean Triples: (27,36,45)​

Now we have a, b, and c, to determine X​

b = (2xy) = 36​

​X = 36/2y = 36/2*3 = 36/6 = 6

​Answer 3 : X = 6

Question 4)​

​X Value = 7

Y Value = 5​

​Pythagorean Triples: ?

We can replace the values of x and y, to determine a, b and c.​

a = (x²-y²) = (7²-5²) = 49-25 = 24​

b = (2xy) = (2*7*5) = 70​

c = (x²+y²) = (7²+5²) = 49+25 = 74​

Answer 4 : Pythagorean triples : (24,70,74)​

Hope this helps!​​​​​

Step-by-step explanation:

From Spymore

Answer:

24

Step-by-step explanation:

Rect = 3*4 = 12

Rect 2 = 1*6 = 6

Triangle = (6-3)*1/2*4 = 6

6 + 6 + 12 = 24

Answer:

60°

Step-by-step explanation:

240° is between the two numbers 180°and 270°, So you're going to want to subtract 180 from 240 Thus, your answer will be 60!

hope you found this helpful :)

The reference angle is 60°. Option B

Since 240° is in the third quadrant

Formula for reference angle in the third quadrant

Reference angle = ∝ - 180°

Reference = 240 - 180

Reference angle = 60°

Thus, the reference angle is 60°. Option B

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The equation resulting from Vineet's substitution in solving the system of equations is not provided, so it is not possible to give a direct answer.

To provide an explanation and calculation, we need the specific equations and the substitution made by Vineet. Without this information, it is not possible to proceed with the calculation or analysis.

Without the equation resulting from Vineet's substitution or the specific system of equations being solved, it is not possible to provide a detailed explanation or calculation. It is important to have the complete information in order to analyze Vineet's work accurately. If you can provide the specific equations and the substitution made, I would be happy to assist you further in explaining Vineet's process and reaching a conclusion.

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Answer:

1. a)  b = 2

b) f(x) = (3x + 2)(x + 1)(x - 1)

2. a = 5,  b = -8

3. 4 ≤ x ≤ 5

Step-by-step explanation:

see attached for step-by-step

Answer:  −6894.4

Step-by-step explanation:

The given equation is\(`3x^2 + 2x + 15 = 0`\). To solve the equation graphically for all real solutions using a graphing calculator, follow these steps:Turn on the graphing calculator. Press the Y= button on the calculator.

Enter the given equation \(`3x^2 + 2x + 15` in Y1\).Step 4: Press the Window button on the calculator and set the appropriate values for the Xmin, Xmax, Ymin, and Ymax, depending on the graph's scale. Press the Graph button on the calculator to graph the function.

These values are the real solutions of the equation.Using the above steps, we can solve the given equation graphically for all real solutions. The solutions are as follows:\(a ≈ -1.76 and a ≈ 1.07\), accurate to at least two decimal places.

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Answer: the three given points are the vertices of a triangle. solve the triangle, rounding lengths tot he nearest tenth and angle measures to the nearest degree A(0,0) B(-3,5) C(3,-2)

***

Plot given points to form a triangle with angle A at (0,0), B at (-3,5) and C at (3,-2).

Using distance formula:

AB=√(0+3)^2+(0-5)^2)=√(9+25)=√34

AC=√(0-3)^2+(0+2)^2)=√(9+4)=√13

BC=√(-3-3)^2+(5+2)^2)=√(36+49)=√85

..

Law of cosine: c^2=a^2+b^2-2abcosA

(BC)^2=(AB)^2+(AC)^2-2*AB*ACcosA

√85^2=34+13-2*√34*√13cosA

85=47-2√442cosA

38=-42cosA

cosx=-38/42

A=154.8˚

..

using law of sin:

BC/sin(154.8˚)=AC/sinB

sinB=AC*sin(154.8˚)/BC=0.1665

B=9.6˚

..

BC/sin(154.8˚)=AB/sinC

sinC=AB*sin(154.8˚)/BC=0.2693

C=15.6˚

Step-by-step explanation:

Answer:

150.56

Step-by-step explanation:

I took the test

Answer:

150.56

Step-by-step explanation:

Answer:

b = 1/3

Step-by-step explanation:

The general structure of equations in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).

f(x) = mx + b

f(x) = -(2/9)x + 1/3

Answer:

a = 2

b = -3

c = -2

Step-by-step explanation:

The standard form of a quadratic equation:

ax² + bx + c = 0

…………………………

in order to determine the equation

in standard form ,we have to expand the given expression :

(2x + 1)(x - 2) = 2x² - 4x + x - 2

                     = 2x² - (4x - x) - 2

                     = 2x² - 3x - 2

Then the standard form is :

2x² - 3x - 2

Step-by-step explanation:

Hey there!

Follow the steps to get answer.

The equation of a line passing through point (2,3) is;

(y-3)= m1(x-2).......(i).

Another equation is;

\(y = \frac{ - 1}{2} x + \frac{2}{3} \)

2nd equation..

Now, From equation (ii)

We have;

Comparing equation (ii) with y = mx+c.

We get;

Slope = -1/2.

For perpendicular lines,

\(m1 \times m2 = - 1\)

\(m1 \times \frac{ - 1}{2} = - 1\)

Therefore the slope is 2.

Put value of slope (m1) in equation (i). We get;

\((y - 3) = 2(x - 2)\)

Simplify them to get equation.

\((y - 3) = 2x - 4\)

\(y = 2x - 1\)

Therefore the required equation is y = 2x-1.

Hope it helps..

Answer:

in order to know the money that he receive first the type and amount of box must be described unless the question may not have answer.

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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The degree of the polynomial f(x) = 2x(x - 3)³(x + 1)(4x - 2) is 6, and the dominant term is - 216x²

The polynomial function is given as:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

To determine the degree, we simply add the multiplicities.

So, we have:

Degree = 1 + 3 + 1 + 1

Evaluate

Degree = 6

Hence, the degree of the polynomial is 6

We have:

f(x) = 2x(x - 3)³(x + 1)(4x - 2)

Expand

f(x) = 8x⁶ - 68x⁵ + 176x⁴ - 72x³ - 216x² + 108x

The term with the highest absolute value is - 216x²

Hence, the dominant term is - 216x²

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Answer:

C) 78.5cm^2

Step-by-step explanation:

Answer:

1=137 2=43 3=137 4=43 5=137 6=43

Step-by-step explanation:

Answer:

-5, 1/2, -0.45, -0.05 would be the solution

Answer:

The perimeter of figure a is 44 inches, the perimeter of figure b is 72 inches.

Step-by-step explanation:

The sides of figure a is 8; 2; 3; 12; 2; 12; 3; 2, to get the perimeter, add all the sides together, which will be 8 + 2 * 2 + 3 * 2 + 12 * 2 = 8 + 4 + 6 + 24 = 12 + 30 = 42 inches. The sides of figure b is 3; 3; 3; 3; 13; 13; 5; 5; 5; 5; 7; 7, to get the perimeter, add all the sides together, which will be 3 * 4 + 13 * 2 + 5 * 4 + 7 * 2 = 12 + 26 + 20 + 14 = 32 + 40 = 72 inches.

Answer:

a) 44

2 + 8 + 2 + 8 + 12 + 12 = 44

b) 72

13 + 13 + 3 +3 +3 +3 +5 +5 +5 +5 +7 +7 = 72

Step-by-step explanation:

The difference between 141.2 and 79.83 is as follows:141.2 - 79.83 = 61.37The sum of 141.2 and 79.83 is:141.2 + 79.83 = 221.03The product of 141.2 and 79.83 is:141.2 × 79.83 = 11250.996 The quotient when 141.2 is divided by 79.83 is:141.2 ÷ 79.83 = 1.7696655174 (approx. 1.77)

Thus, the sum of 141.2 and 79.83 is 221.03. The difference between 141.2 and 79.83 is 61.37. The product of 141.2 and 79.83 is 11250.996. The quotient when 141.2 is divided by 79.83 is approximately 1.77.Thus, the solution can be summarized as follows: Given the two numbers 141.2 and 79.83, we are to find their sum, difference, product, and quotient.

After performing the necessary arithmetic operations, we get that their sum is 221.03, their difference is 61.37, their product is 11250.996, and their quotient is approximately 1.77.

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A shop sells packs of black pens, packs of red pens and packs of green pens. In the same way, the shop sells a pack of black and red pens, a pack of black and green pens, and a pack of green and red pens.

They charge $3.00 for a pack of black pens, $3.50 for a pack of red pens, and $4.00 for a pack of green pens. A pack of black and red pens sells for $4.00, a pack of black and green pens costs $5.00, and a pack of green and red pens sells for $5.50.

The cost of a pack of green pens is $4.00, and the cost of a pack of black pens is $3.00. The total cost of two packs of pens will be $7.00.

Therefore, the cost of a pack of green pens and a pack of black pens is $7.00

.Explanation: The cost of a pack of black pens is $3.00.

The cost of a pack of red pens is $3.50.The cost of a pack of green pens is $4.00.A pack of black and red pens costs $4.00.

A pack of black and green pens costs $5.00.A pack of green and red pens costs $5.50.

The cost of a pack of green pens and a pack of black pens is $7.00.

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Answer:

f-96=124

Step-by-step explanation:

This is the equation of the sentence that has been mentioned.

All the questions have been solved in the above pictures 7,8,9,10,11,12 & 13

Answer:

I think it would be dream shopping if you are good at math. If you are bad it's a real nightmare. At least that's what I think