The two lines graphed on the coordinate grid each represent an
equation
Problem
Which ordered pair represents a solution to both equations?

A (-3,2)

B (3,-1)


C no solution

D(3,-2)

The answer is b=18. To solve, multiply 6 by 3 to get 18. This is called doing the inverse operation. Since the equation is a division equation, we would have to multiply in order to find the missing variable.

The sum of the series 164+113+62+11+... can be represented using summation notation.

To express the series using summation notation, we need to find a pattern that describes the terms. Looking at the given series, we can observe that each term is obtained by subtracting 51 from the previous term. We can express this pattern as:

aₙ = aₙ₋₁ - 51

Here, aₙ represents the nth term of the series, aₙ₋₁ represents the previous term, and 51 is the common difference.

The first term of the series is 164, so we have:

a₁ = 164

Using the pattern, we can express the remaining terms as:

a₂ = a₁ - 51 = 164 - 51 = 113

a₃ = a₂ - 51 = 113 - 51 = 62

a₄ = a₃ - 51 = 62 - 51 = 11

...

To represent the series using summation notation, we can use the following formula:

∑(aₙ) = a₁ + a₂ + a₃ + ...

In this case, the starting index is 1, and the terms follow the pattern described earlier. Thus, the summation notation for the given series is:

∑(164 + 113 + 62 + 11 + ...)

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The graph of the function f(x) = -2sin(x) starts at the midline (y = 0) and reaches its maximum or minimum point closest to the midline at (π/2, -2).

Start by plotting the midline, which is the x-axis (y = 0). This is the starting point for the graph.

Find the maximum or minimum point on the graph closest to the midline. In this case, the maximum or minimum point is a maximum point because the coefficient of sin(x) is negative (-2). The maximum point occurs at π/2 on the x-axis.

Plot the maximum point on the graph at (π/2, -2). This point represents the highest or lowest point on the graph closest to the midline.

From the maximum point, the graph will start to decrease. Since the coefficient of sin(x) is -2, the graph will have a steeper slope compared to the graph of sin(x).

As x increases from π/2, the graph will continue to decrease until it reaches the next minimum point, which will be at 3π/2.

Continue plotting points on the graph by evaluating the function at various x-values and connecting them smoothly to create a sinusoidal curve.

Repeat the pattern of the graph for every interval of 2π, as the sine function is periodic.

Finally, label the x-axis as "x" and the y-axis as "f(x)" or "y" to indicate the function being graphed.

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Hello,

\(sin(45^o)=\dfrac{\sqrt{2} }{2} \\\\sin(45^o)=\dfrac{a}{c} \\\\\dfrac{\sqrt{2} }{2}=\dfrac{a}{6} \\\\a=6*\dfrac{\sqrt{2} }{2}=3\sqrt{2}\\\)

Answer A

Answer:

c

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

Answer:

V = pi * R^2 * h

R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm

The radius of the cylinder is 3 cm.

Given,

The volume of the cylinder is 141.3 cubic centimeters.

We need to find what is the approximate radius of the cylinder.

Use 3.14 for the approximation of pi.

It is given by:

V = π r² h

h = height of the cylinder

r = radius of the cylinder.

We have,

V = 141.3 cm³

π = 3.14

h = 5 cm

V = π r² h

141.3 = 3.14 x r² x 5

141.3 / 3.14 x 5 = r²

r² = 9 cm²

r = 3 cm

Thus the radius of the cylinder is 3 cm

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To find the equilibria of autonomous differential equations, set the derivative equal to zero and solve for the variable. Equilibria are fixed points where the rate of change is zero, and can be classified as stable or unstable based on the behavior of the solution trajectories near the equilibrium point.

To find the equilibria of autonomous differential equations, follow these steps:

1. Identify the autonomous differential equation, which is an equation in the form dx/dt = f(x), where f(x) is a function of x only.
2. Set the right-hand side of the equation (f(x)) equal to zero, as equilibria occur when dx/dt = 0.
3. Solve the resulting equation for x to find the equilibrium points.

These equilibrium points represent the constant solutions where the system remains unchanged over time.

To find the equilibria of autonomous differential equations, we first set the derivative equal to zero and solve for the variable. In other words, we find the values of the variable where the rate of change is zero. These values are called equilibria or fixed points.

For example, if we have an autonomous differential equation of the form dx/dt = f(x), where f(x) is a function of x, then we set f(x) equal to zero and solve for x. The resulting values of x are the equilibria.

It is important to note that equilibria can be classified as stable or unstable based on the behavior of the solution trajectories near the equilibrium point. If nearby solutions move towards the equilibrium point as time progresses, it is a stable equilibrium. If nearby solutions move away from the equilibrium point, it is an unstable equilibrium. The classification of the equilibrium can be determined by analyzing the sign of the derivative of f(x) near the equilibrium point.

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The given function f(x) has three different cases based on the range of x. Let's break it down step by step: For x less than 3, the function is not defined. This means that f(x) is undefined for x < 3.

For x between 3 and 4 (inclusive), the function is given by f(x) = √(x^2 + 1)/(x^2 - 9). In this case, you need to evaluate the expression inside the square root and then simplify it further if possible. Remember to exclude any values of x that make the denominator zero, as division by zero is undefined.

For x greater than or equal to 4, the function is given by f(x) = x^2 - 9. In this case, you simply need to square the value of x and subtract 9 to get the result.

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Answer:

100 points cool the answer is 30

Answer:

\(x^{2} - 25\)

Step-by-step explanation:

Area is side x side, so naturally it would be: (x+5)(x - 5)... Though to simplify, those parenthesis can be FOILed. (Reminder: "FOIL" means First - Outer - Inner - Last)

\(x^{2} - 5x + 5 x - 25\)

The 5x cancels out because 5x - 5x = 0

So that leaves us with:

\(x^{2} - 25\)

=========================================================

Explanation:

Let's say we replace the "x+5" with some other letter. Let's use L for length.

We'll keep the width x-5 the same.

area = length*width

area = L*(x-5)

area = L*x + L*(-5)

area = xL - 5L

At this point, we would then plug in L = x+5 and distribute like so:

area = x( L ) - 5( L )

area = x( x+5 ) - 5( x+5 )

area = x^2 + 5x - 5x - 25

area = x^2 - 25

Side note: (x+5)(x-5) = x^2 - 25 is an application of the difference of squares rule.

Answer:

3/2

Step-by-step explanation:

we can calculate the values of different hyperbolic trigonometric functions based on the given equation sinhx = . Using the appropriate identities, we can determine the values as follows:

a) cosh x: The value of cosh x can be found by using the identity cosh x = √(1 + sinh^2x). By substituting the given value of sinh x into the equation, we can calculate cosh x.

b) tanh x: The value of tanh x can be obtained by dividing sinh x by cosh x. By substituting the values of sinh x and cosh x derived from the given equation, we can find tanh x.

c) sech x: Sech x is the reciprocal of cosh x, which means it can be obtained by taking 1 divided by cosh x. By using the value of cosh x calculated in part a), we can determine sech x.

d) coth x: Coth x can be found by dividing cosh x by sinh x. Using the values of sinh x and cosh x derived earlier, we can calculate coth x.

e) sinh^2x: The square of sinh x can be expressed as (cosh x - 1) / 2. By substituting the value of cosh x calculated in part a), we can determine sinh^2x.

f) cosech^2x: Cosech^2x is the reciprocal of sinh^2x, so it is equal to 1 divided by sinh^2x. Using the value of sinh^2x calculated in part e), we can find cosech^2x.

These calculations allow us to determine the values of cosh x, tanh x, sech x, coth x, sinh^2x, and cosech^2x in terms of the given value of sinh x.

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The linear equation written in slope-intercept form is:

y = 8x + 5

A general linear equation written in slope-intercept form is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

For this case, we know that the values for these are:

slope = 8

y-intercept = 5

Replacing these values in the general formula for a line we will get the equation that we want, which is:

y = 8x + 5

That is the line.

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Answer:

166 per person

Step-by-step explanation:

500 divided by 3

The cost of Juan's South American stamps issued before the '70s is $10.

To determine the cost of Juan's South American stamps issued before the '70s, we need to consider the prices for stamps from Brazil and Peru, which are both South American countries. According to the information provided, stamps from Brazil and Peru cost 6 cents each.

Since the specific quantity of stamps is not given, we assume that Juan has an equal number of stamps from Brazil and Peru. Therefore, the cost of his South American stamps from these countries can be calculated as follows:

Cost of stamps from Brazil = 6 cents each

Cost of stamps from Peru = 6 cents each

Total cost of South American stamps = (Cost of stamps from Brazil + Cost of stamps from Peru) × Quantity

As the quantity is unknown, we cannot calculate the exact cost. However, the given answer options provide the closest approximation.

Looking at the answer options, the only option that falls within the range of the given prices is $10. Therefore, the cost of Juan's South American stamps issued before the '70s is $10.

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Answer: 54,454 ft^3

The volume of the cylinder is about 50265.4 and the volume of the cone is 4188.7. If you add this together you get 54,454.1. Therefore, 54,454 ft^3 is the answer

Answer:

First, we need to solve the equation in the problem for y to put it in slope-intercept form so we can determine its slope:

2y−6x=4

2y−6x+6x=6x+4

2y−0=6x+4

2y=6x+4

2y2=6x+42

2y2=(6x2)+(42)

y=3x+2

The slope-intercept form of a linear equation is: y=mx+b

Where m is the slope and b is the y-intercept value.

Therefore the slope of this equation is m=3

A perpendicular line will have a slope (let's call this slope mp) that is the negative inverse of this line. Or, mp=−1m

Substituting gives:

mp=−13

Answer:

-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

P = 2( L + W)

To solve for L first divide both sides by 2

That's

\( \frac{P}{2} = L + W\)

Move W to the other side of the equation to make L stand alone

We have the final answer as

\(L = \frac{P}{2} - W \\ \)

Hope this helps you

Answer:

Example 2:

Step-by-step explanation:

The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} . Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.

Answer:

1.

5

x

−

2

y

=

4

; (−1, 1)

2.

3

x

−

4

y

=

10

; (2, −1)

3.

−

3

x

+

y

=

−

6

; (4, 6)

4.

−

8

x

−

y

=

24

; (−2, −3)

5.

−

x

+

y

=

−

7

; (5, −2)

6.

9

x

−

3

y

=

6

; (0, −2)

7.

1

2

x

+

1

3

y

=

−

1

6

; (1, −2)

8.

3

4

x

−

1

2

y

=

−

1

; (2, 1)

9.

4

x

−

3

y

=

1

;

(

1

2

,

1

3

)

10.

−

10

x

+

2

y

=

−

9

5

;

(

1

5

,

1

10

)

11.

y

=

1

3

x

+

3

; (6, 3)

12.

y

=

−

4

x

+

1

; (−2, 9)

13.

y

=

2

3

x

−

3

; (0, −3)

14.

y

=

−

5

8

x

+

1

; (8, −5)

15.

y

=

−

1

2

x

+

3

4

;

(

−

1

2

,

1

)

16.

y

=

−

1

3

x

−

1

2

;

(

1

2

,

−

2

3

)

17.

y

=

2

; (−3, 2)

18.

y

=

4

; (4, −4)

19.

x

=

3

; (3, −3)

20.

x

=

0

; (1, 0)

Find the ordered pair solutions given the set of x-values.

21.

y

=

−

2

x

+

4

; {−2, 0, 2}

22.

y

=

1

2

x

−

3

; {−4, 0, 4}

23.

y

=

−

3

4

x

+

1

2

; {−2, 0, 2}

24.

y

=

−

3

x

+

1

; {−1/2, 0, 1/2}

25.

y

=

−

4

; {−3, 0, 3}

26.

y

=

1

2

x

+

3

4

; {−1/4, 0, 1/4}

27.

2

x

−

3

y

=

1

; {0, 1, 2}

28.

3

x

−

5

y

=

−

15

; {−5, 0, 5}

29.

–

x

+

y

=

3

; {−5, −1, 0}

30.

1

2

x

−

1

3

y

=

−

4

; {−4, −2, 0}

31.

3

5

x

+

1

10

y

=

2

; {−15, −10, −5}

32.

x

−

y

=

0

; {10, 20, 30}

Find the ordered pair solutions, given the set of y-values.

33.

y

=

1

2

x

−

1

; {−5, 0, 5}

34.

y

=

−

3

4

x

+

2

; {0, 2, 4}

35.

3

x

−

2

y

=

6

; {−3, −1, 0}

36.

−

x

+

3

y

=

4

; {−4, −2, 0}

37.

1

3

x

−

1

2

y

=

−

4

; {−1, 0, 1}

38.

3

5

x

+

1

10

y

=

2

; {−20, −10, −5}

Part B: Graphing Lines

Given the set of x-values {−2, −1, 0, 1, 2}, find the corresponding y-values and graph them.

39.

y

=

x

+

1

40.

y

=

−

x

+

1

41.

y

=

2

x

−

1

42.

y

=

−

3

x

+

2

43.

y

=

5

x

−

10

44.

5

x

+

y

=

15

45.

3

x

−

y

=

9

46.

6

x

−

3

y

=

9

47.

y

=

−

5

48.

y

=

3

Find at least five ordered pair solutions and graph.

49.

y

=

2

x

−

1

50.

y

=

−

5

x

+

3

51.

y

=

−

4

x

+

2

52.

y

=

10

x

−

20

53.

y

=

−

1

2

x

+

2

54.

y

=

1

3

x

−

1

55.

y

=

2

3

x

−

6

56.

y

=

−

2

3

x

+

2

57.

y

=

x

58.

y

=

−

x

59.

−

2

x

+

5

y

=

−

15

60.

x

+

5

y

=

5

61.

6

x

−

y

=

2

62.

4

x

+

y

=

12

63.

−

x

+

5

y

=

0

64.

x

+

2

y

=

0

65.

1

10

x

−

y

=

3

66.

3

2

x

+

5

y

=

30

Part C: Horizontal and Vertical Lines

Find at least five ordered pair solutions and graph them.

67.

y

=

4

68.

y

=

−

10

69.

x

=

4

70.

x

=

−

1

71.

y

=

0

72.

x

=

0

73.

y

=

3

4

74.

x

=

−

5

4

75. Graph the lines

y

=

−

4

and

x

=

2

on the same set of axes. Where do they intersect?

76. Graph the lines

y

=

5

and

x

=

−

5

on the same set of axes. Where do they intersect?

77. What is the equation that describes the x-axis?

78. What is the equation that describes the y-axis?

Part D: Mixed Practice

Graph by plotting points.

79.

y

=

−

3

5

x

+

6

80.

y

=

3

5

x

−

3

81.

y

=

−

3

82.

x

=

−

5

83.

3

x

−

2

y

=

6

84.

−

2

x

+

3

y

=

−

12

Step-by-step explanation:

Answer:

After filling in the formula and solving you’ll get 1.75 which is the same as 7/4

Therefore, correct response is percentage C. "For comedies that college students enjoy, she estimated the conditional relative frequency. The right response is 28%.

A number or figure that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the "%" symbol used to represent it is often employed. No dimensions exist; the % amount is flat. Percentages are essentially fractions because their numerator is 100. A percent symbol (%) should be placed in front of a number to indicate that it is a percentage. For instance, if you answered correctly 75 out of questions in total on a test, you'd get a 75%.

Here,

Given :

She determined the combined relative frequency for humor and college. For college students who enjoy comedy, the appropriate conditional relative frequency value is 28%.

For comedies that college students enjoy, she determined the conditional relative frequency. For college students who enjoy comedy, the appropriate conditional relative frequency value is 16%.

For comedies that college students enjoy, she determined the conditional relative frequency. The right response is 28%.

She determined the combined relative frequency for humor and college. The right response is 16%.

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Answer:

\(\tt volume=\boxed{6}\: units^3\)

Step-by-step explanation:

\(\tt volume=(\frac{9}{2})(\frac{4}{3} )\)

\(\tt volume=\frac{36}{6}\)

\(\tt volume=6\)

~

Summary statistics for the given data are as below; Mean is 77.19, Median is 77, The mode is 77, Range is 39, Variance is 193.95 and Standard deviation is 13.

To calculate some summary statistics for the given data, we can use the following:

Mean: The average of the data. We can calculate the mean by adding up all the scores and dividing by the total number of scores.

Median: The middle score of the data, when the scores are arranged in order from lowest to highest.

Mode: The score that appears most frequently in the data.

Range: The difference between the highest and lowest scores in the data.

Variance: A measure of how spread out the data is. We can calculate the variance by taking the difference between each score and the mean, squaring the differences, adding up the squared differences, and dividing by the total number of scores.

Standard deviation: The square root of the variance. The standard deviation gives us an idea of how spread out the data is in relation to the mean.

Using these formulas, we can calculate the following summary statistics for the given data:

Mean: (59 + 60 + 60 + 61 + 63 + 67 + 69 + 70 + 71 + 72 + 73 + 75 + 77 + 77 + 77 + 78 + 79 + 80 + 80 + 81 + 83 + 83 + 86 + 87 + 90 + 91 + 94 + 94 + 95 + 97 + 98) / 31 = 77.19

Median:-

The middle score is the 16th score when the data are arranged in order: 77.

Mode:-

The mode is 77, since it appears most frequently in the data (3 times).

Range:-

The highest score is 98, and the lowest score is 59, so the range is 98 - 59 = 39.

Variance:-

We can calculate the variance using the formula: Σ(x - μ)² / N, where Σ is the sum, x is the score, μ is the mean, and N is the total number of scores.

Using this formula, we get:

(59 - 77.19)² + (60 - 77.19)² + (60 - 77.19)² + (61 - 77.19)² + (63 - 77.19)² + (67 - 77.19)² + (69 - 77.19)² + (70 - 77.19)² + (71 - 77.19)² + (72 - 77.19)² + (73 - 77.19)² + (75 - 77.19)² + (77 - 77.19)² + (77 - 77.19)² + (77 - 77.19)² + (78 - 77.19)² + (79 - 77.19)² + (80 - 77.19)² + (80 - 77.19)² + (81 - 77.19)² + (83 - 77.19)² + (83 - 77.19)² + (86 - 77.19)² + (87 - 77.19)² + (90 - 77.19)² + (91 - 77.19)² + (94 - 77.19)² + (94 - 77.19)² + (95 - 77.19)² + (97 - 77.19)² + (98 - 77.19)² / 31

= 193.95

Standard deviation:

The standard deviation is the square root of the variance, which is approximately 13.

Summary statistics for the given data are as below;

Mean is 77.19, Median is 77, The mode is 77, Range is 39, Variance is 193.95 and Standard deviation is 13.

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Answer: Heyaa!

The Answer is 2x+2

Step-by-step explanation:

Simplify the expression.

hopefully this helps you !

- Matthew ~

answer is in the attachment hope it helps you ^_^

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

To know more about the tangent line, here

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Answer:

2,472 / 2 = 1,236

Answer:

The dimensions of the garden is 102 feet by 68 feet

Step-by-step explanation:

Here, we want to get the width and length of the garden

The perimeter is represented by the length of the fencing

From the question;

w = 2l/3

The formula for the perimeter is;

P = 2(l + w)

Thus;

340 = 2(l + 2l/3)

170 = (l + 2l/3)

Multiply through by 3

510 = 3l + 2l

5l = 510

l = 102 feet

w = 2/3 * l

w = 2/3 * 102

w = 68 feet