(Graphing Linear Equations MC)

A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.

Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?

graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100

The given vector is v = -3 4 -1 0. The given vector is not in the range of t(x).

To determine if this vector is in the range of t(x) = ax where a = 1 -2 0 3 2 1, we need to check if there exists a vector x such that t(x) = ax = v. This can be represented as the following equation:

1x1 - 2x2 + 0x3 + 3x4 + 2x5 + 1x6 = -3

We can solve this equation using Gaussian elimination. After row operations, we can obtain the following reduced row-echelon form:

1 0 0 0 0 3/2 = -3

Since the left-hand side does not equal the right-hand side, we can conclude that the given vector is not in the range of t(x).

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No, the city will not allow the tree to grow 2} more feet.

The telephone wire is a safety hazard, so the city trims back the branch so that it does not come closer than 2 feet to the wire. To calculate if the tree can grow 2} more feet, we need to find out how far the branch is currently from the wire and subtract 2 feet.

Let x = the current distance of the branch from the wire

51 - x = 2

x = 49 feet

Therefore, the branch is currently 49 feet away from the wire, which is less than 2} feet. Since the city trims back the branch when it grows closer than 2 feet to the wire, the city will not allow the tree to grow 2} more feet.

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Answer: A

Step-by-step explanation:

Using the property of exponents the numbers are determined as follows

5. x = 9

6. b = -4

7. n = 0

An exponential equation can be solved using the same bases because to the property of equality of exponential functions. It states that if all sides of an exponential equation have identical bases, then the exponents must likewise be equal.

The property is applied in the following equations

5. 8² * 8ˣ = 8¹¹

equating the powers

2 + x = 11

x = 11 - 2

x = 9

6. 5⁷ * 5ᵇ = 5³

equating the powers

7 + b = 3

b = 3 - 7

b = -4

7. x¹² * xⁿ = x¹²

equating the powers

12 + n = 12

n = 12 - 12

n = 0

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The equation represents the function on the graph is f(x)= cos 4x.

What is the function on the graph?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.

We have given,

A: f(x)= cos 1/4x

B: f(x)= sin 4x

C: f(x)= cos 4x

D: f(x)= sin 1/4x

To find the equation represent the function on the graph:

f(x) = cos 4x

let take the values on the x-axis of the graph,

x = п/2, п, 3п/2, 2п, 5п/2

For cos 360 degrees, the angle 360° lies on the positive x-axis. Thus cos 360° value = 1

Since the cosine function is a periodic function, we can represent cos 360° as, cos 360 degrees = cos(360° + n × 360°), n ∈ Z.

⇒ cos 360° = cos 720° = cos 1080°, and so on.

so, cos 4( п/2) = cos 4( 3п/2) = cos 4( 2п) = cos 4( 5п/2) = 1.

Hence, the equation represents the function on the graph is f(x)= cos 4x.

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The measure of angle ∠LMN = 105°

What is a parallelogram?

A parallelogram is a quadrilateral, which is a four-sided polygon, with opposite sides that are parallel. Additionally, opposite angles in a parallelogram are congruent (equal in measure). So, if a figure has parallel opposite sides and congruent opposite angles, then it is called a parallelogram.

In the given figure, quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°

We have get the measurement of ∠LMN

Since in a parallelogram opposite angles are equal.

Therefore 25x = 22x + 9

25x - 22x = 9

3x = 9

x = 3

From another property of a parallelogram, we know that consecutive angles are supplementary.

∠LMN + ∠ONM = 180°

∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)

∠LMN = 180 - 75 = 105°

Hence, the measure of angle ∠LMN = 105°

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On the coordinate plane , the point which lies on the y -axis is given by option ( 0 , 9 ).

As given in the question,

On the coordinate plane :

Point which lies on the y - axis is given by :

a. ( 9 , 9 )

This coordinate lies in the first quadrant. It will not lies on any of the axis.

False.

b. ( 9 , 0 )

In this coordinate has y-,coordinate is equal to zero , it lies on the x- axis.

False.

c. ( 0 , 9 )

In this coordinate has x-,coordinate is equal to zero , it lies on the y- axis.

True.

d. ( -9 ,-9 )

This coordinate lies in the third quadrant. It will not lies on any of the axis.

False.

Therefore, on the coordinate plane the point that lies on the y-axis is

( 0, 9).

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Answer:

29/14

Explanataion:

The inverse function of tangent (tan^-1) is also known as arctangent. The domain of arctangent function is all real numbers and its range is (-π/2, π/2).

The tangent function, tan(x), is defined for all real numbers x, but it's not defined when x = (nπ + π/2), where n is an integer. So the domain of the tangent function is all real numbers except (nπ + π/2), where n is an integer.

When we take the inverse of a function, we switch the roles of the domain and range, so the domain of the tangent function becomes the range of the inverse function and the range of the tangent function becomes the domain of the inverse function. The range of the tangent function is all real numbers, but it is not defined for (nπ + π/2), where n is an integer. So the domain of the arctangent function is all real numbers except (nπ + π/2), where n is an integer.

The range of arctangent function is (-π/2, π/2) because the range of arctangent function is the set of all possible values of the input of tangent function for which it is defined.

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[tex]\hspace{13em} \begin{array}{cll} term&value\\ \cline{1-2} a_5&16\\ a_6&16r\\ a_7&16rr\\ a_8&16rrr\\ a_9&16rrrr\\ a_{10}&16rrrrr=\frac{1}{2}\\ a_{11}&\frac{1}{2}r\\ a_{12}&\frac{1}{2}rr \end{array}~\hfill \\\\\\ 16r^5=\cfrac{1}{2}\implies r^5=\cfrac{1}{32}\implies r=\sqrt[5]{\cfrac{1}{32}}\implies r=\cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ a_{12}=\cfrac{1}{2}rr\implies a_{12}=\cfrac{1}{2}r^2\implies a_{12}=\cfrac{1}{2}\left( \cfrac{1}{2} \right)^2\implies a_{12}=\cfrac{1}{8}[/tex]

Answer:

x = 61

Step-by-step explanation:

Let's call the number of codes Jayvik can make, j, and the number of codes Fay can make, f. We know that since 0 cannot be used, Jayvick can have 5 number choices (1, 3, 5, 7, 9), and Fay can have 4 number choices (2, 4, 6, 8). To calculate the number of possible codes for Jayvick, we will have:

5 * 5 * 5 = 125

So Jayvick can make 125 codes. Then, for Fay we have:

4 * 4 * 4 = 64

So Fay can make 64 codes. We were told at the beginning that:

j = f + x

So, we substitute our numbers in, giving us:

125 = 64 + x

Minusing 64 from both sides gives us:

x = 61

So, x = 61.

Hope this helped!

Please give Brainliest if possible!

Answer:    10. equal 0.27

                  11. 5.12

                  12. 3.35

Step-by-step explanation:

10. 0.9 * 0.3 = 0.27

11. 1.6 * 3.2 = 5.12

12. 0.5 * 6.7 = 3.35

13. 0.81*7.3 = 5.873

14. 5.6*3.9 = 21.84

15. 1.2 * 0.05 = 0.06

Answer:

cylinder

Step-by-step explanation:

The total balance in John's account after depositing his paycheck is, 800.47.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The balance in John's account before depositing his paycheck = 249.50

And, He deposit 550.97 in his account.

Here, The balance in John's account before depositing his paycheck = 249.50

Hence, The total balance in John's account after depositing his paycheck is,

⇒ 249.50 + 550.97

⇒ 800.47

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Answer:

Step-by-step explanation:

The formula for calculating the time it will take for an investment to reach a certain amount given a rate of return and regular withdrawals is:

Time = (ln(Final Balance/Initial Balance))/(ln(1 + Rate of Return))

In this case, the Initial Balance is $100,000, the Final Balance is $0, and the Rate of Return is 2.66%.

Time = (ln(0/100000))/(ln(1 + 0.0266))

Time = (-11.51)/(0.026101)

Time = -440.17

Since the time is given in years, we need to round the answer to the nearest year.

Answer: It will take 440 years for the account to have a balance of $0.

The number of teaspoons of baking soda will be left will be 4 teaspoons.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Grace is making cookies. She has 6 tablespoons of baking soda left in the container. If she uses 2 teaspoons of baking soda for her recipe.

Then the number of teaspoons of baking soda will be left will be given as,

⇒ 6 - 2

⇒ 4

The number of teaspoons of baking soda will be left will be 4 teaspoons.

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Answer:

4 teaspoons is left.

Step-by-step explanation:

Now we have to,

→ find teaspoons of baking soda left.

Given information,

→ Total = 6 teaspoons

→ Used = 2 teaspoons

→ Left = x

Forming the equation,

→ 6 = x + 2

Then the value of x will be,

→ 6 = x + 2

→ x + 2 = 6

→ x = 6 - 2

→ [ x = 4 ]

Hence, the value of x is 4.

The image point of the point is (-12,8)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point (-3, 2) is transformed under a dilation of 4 with respect to the origin.

So the image point is (kx, ky) = (-34, 24) = (-12, 8)

So the image point of (-3,2) under a dilation of 4 with respect to the origin is (-12,8)

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To find the inverse of a fraction using cross multiplication, you first need to understand what the inverse of a fraction is. The inverse of a fraction is another fraction that, when multiplied by the original fraction, equals 1.

For example, the inverse of 3/4 is 4/3, because 3/4 x 4/3 = 1.

To find the inverse of a fraction using cross multiplication, you will need to use the property that if a/b = c/d, then a x d = b x c. To find the inverse of a fraction, you simply swap the numerator and denominator and multiply them together.

For example, to find the inverse of 3/4, you would swap the numerator and denominator to get 4/3, and then multiply them together to get 1.

So the steps would be:

It is important to note that if the original fraction is a whole number, it's inverse will be 1 over the whole number.

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Complete question:

Attempt to find the inverse of a fraction using cross - multiplying . please describe the method of finding the inverse.

Answer:

x = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{16}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 16[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 8[tex]\sqrt{3}[/tex]

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.

The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.

Here,

Given :

Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).

In order to determine what data they use,

From the information provided, it is clear that they are using second-party data.

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.

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It takes approximately 1.909 seconds for the ball to reach the right-most edge of the green.

In this problem, we are given the radius of the circular green (30 feet) and the speed of the ball (11 ft/sec). We are also given a diagram of the ball's starting point and the location of the cup, which is at the origin of the xy-coordinate system.

We can introduce coordinates by assigning the x-coordinate to be the horizontal distance from the cup (the origin) and the y-coordinate to be the vertical distance from the cup.

From the given diagram, we can see that the ball's starting point is at (x,y) = (-15, -18). The cup is at (0,0). We are asked to find the time it takes for the ball to reach the right-most edge of the green.

To find this, we first need to find the distance between the ball's starting point and the right-most edge of the green. We can use the Pythagorean theorem to do this:

d = √((x2-x1)^2 + (y2-y1)^2) = √((15)^2 + (18)^2) = 21

Now that we have the distance, we can use the formula:

time = distance / speed = 21 / 11 = 1.909 sec (approx)

So it takes approximately 1.909 seconds for the ball to reach the right-most edge of the green.

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The percentage of the total deliveries made by the Mary is equal to 95%.

As given in the question,

Total number of deliveries need to be delivered by the Mary this week = 40

Total number of deliveries completed by Mary is equal to 38

Percentage formula =  [( Number obtained ) / (Total number ) ] × 100

Substitute the value in the formula we get,

The percentage of the completed deliveries made by Mary is

= ( 38 / 40 ) × 100

= 3800 / 40

= 95%

Therefore, the total percentage of the completed delivery made by Mary is equal to 95%.

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Answer: 3 ovals and 3 rectangles and an even amount of rectangles and ovals

The rule for the given pattern is to subtract 13, then add 24.

The correct Option is (A.) subtract 13, then add 24.

A pattern or sequence in a series of numbers is called a number pattern. In general, this pattern builds a connection between all integers.

In this question we have the following pattern:

1, -12, 12, -1

Here we need to find the rule for this pattern.

Let's take the first number of the pattern, which is 1:

1

To obtain the second number of the pattern, which is -12, we must subtract 13, because:

1 - 13 = -12

To obtain the third number of the pattern, which is 12, we must add 24, because:

-12 + 24 = 12

Therefore, the correct answer is A.) subtract 13, then add 24

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The complete question is: "Which best describes the rule for this pattern? 1,-12,12,-1 A.) subtract 13, then add 24 B.) subtract -13, then add 24 C.) subtract -24, then add 13 D.) subtract 24, then add 13"

The rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.

Use the formula A=pi*r^2 to calculate the area of the circle when the radius is 44cm.

A=pi*r^2

A= 3.14159*(44 cm)^2

A= 6081.816 cm^2

Use the formula A'=2pi*r*r' to calculate the rate of change of the area.

A'=2pi*r*r'

A'= 2*3.14159*44 cm*(7 cm/s)

A'= 97.636 cm^2/s

The area of a circle is calculated by the equation A=pi*r^2, where r is the radius of the circle. At the instant when the radius of the circle is 44 centimeters, the area is 6081.816 cm^2. To calculate the rate of change of the area, we use the equation A'=2pi*r*r', where r' is the rate of change of the radius. In this case, the radius of the circle is decreasing at a rate of 7 cm/s, so r'=7 cm/s. Plugging these values into the equation, we get A'=2*3.14159*44 cm*(7 cm/s), which equals 97.636 cm^2/s. Therefore, the rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.

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The expression 2x cos 6x can be rewritten using product to sum identities as 1/2(cos(8x) + cos(-4x))

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

The product to sum identities we are going to need in this case is given by the formula:

cos(a) cos(b) = 1/2 (cos(a+b) + cos(a-b))

Since we have cos 2x cos 6x. Thus:

cos 2x cos 6x = 1/2 (cos(2x+6x) + cos(2x-6x))

                       = 1/2 (cos(8x) + cos(-4x))

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The two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.

The given equation is a quadratic equation in x, of the form ax2 + bx + c = 0, where a = 1, b = 8 and c = 20.

To solve this equation, we use the quadratic formula, which states that the two roots of the equation are:

x = [-b ± √(b2 - 4ac)] / 2a

Since a = 1, the formula simplifies to:

x = [-8 ± √(82 - 4(1)(20))] / 2

Substituting the values for a, b and c, we get:

x = [-8 ± √(-64)] / 2

Taking the positive and negative square roots of -64, we get:

x = [-8 ± 8i] / 2

Simplifying, we get:

x = -4 ± 4i

Therefore, the two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.

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The line of reflection that reflects the quadrilateral ABCD to quadrilateral A'B'C'D' is at y = 2, and it is parallel to x-axis.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

From the given figure we can observe that the figure is reflected.

Let us suppose C as the reference point. The coordinates of C and C' are:

C = (0, 2)

C' = (0, 2)

The coordinates of x for C and C' are similar hence, the line of reflection is parallel to x-axis.

To find the value of line of reflection we take the midpoint, that is:

[tex]y = \frac{y_1 + y_2}{2}\\\\y = \frac{2+2}{2} \\\\y=2[/tex]

Hence, the line of reflection lies on y =2 and it is parallel to x-axis.

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The area of the region enclosed by the inner loop of the curve is 8π/3.

The term area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Here we have Given the following values,

r = 2 + 4 sin (θ)

Now, we have to substitute the value of r = 0, then we get

⇒ 0 = 2 + 4 sin (θ)  

⇒ 4 sin (θ) = -2

⇒ sin θ = -1/2

⇒ θ = -π/6

Therefore, the limit lies in the interval -π/6 to + π/6

Now, the value of Area of polar region is calculated as,

=> A = ∫

Now, by Substituting the values

A=∫π/6−π/6 (2 + 4 sin (θ)) dθ

When we simplify this one then we get the value as,

=> A = 16 [θ + 1/6 sin6θ]

Apply the limit value, then we get

=> A = 16[(π/6 + 0) - (0 + 0)]

=> A = 8π/3

Therefore, the area of the region enclosed by the inner loop of the curve is 8π/3.

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The question is asking to express the mathematical operation: 2 plus the cube of a number, this can be written as 2+x^3. 'x' represents the unknown number, and 'x^3' depicts the cube of that number.

This question pertains to the mathematical concept known as the 'cube' of a number. It is asking for the expression of the operation: 2 plus the cube of a number. In mathematical terms, if we let x be the unknown number, then the expression can be written as 2+x^3. Here, 'x' represents any number and 'x^3' denotes the cube of that number. So if x was 2, for example, the expression would be 2+(2^3) = 2+8 = 10.

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