which graph represents the function y=-2cos(2πx)

Answer:

Graph is attached below

Step-by-step explanation:

To start off, let's find the y-intercept, which is when x=0

So, when x=0,

[tex]y=\frac{3}{4}(0)+5[/tex], which is y=5.

So we can put a point on (0, 5)

From there, since the slope is 3/4. We can go up 3 and right 4 to plot a point there, you can also do down 3 and down 4 from the y-intercept point, then keep going either, up 3 and right 4 or down 3 and left 4, which should give you a diagonal line that looks something like;

The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.

The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.

The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.

To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:

y = (4x+9x^2)(3x-7x^4)

y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4

Using the distributive property, we can simplify the expression by combining like terms:

y = 12x^2 - 28x^5 + 27x^3 - 63x^6

y = (12x^2 + 27x^3) - (28x^5 + 63x^6)

So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6

The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.

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Answer:

z = -8/3 - 5i

Step-by-step explanation:

Sorry, I don't know what a ti-84 calculator is.

But, I can solve this question normally.

Let the real part of z be x and the imaginary part be y.

z = x + iy

|z| = √(x²+y²)

z + |z| = x + iy + √(x²+y²) = 3 - 5i

Now, y has to be -5 as |z| is a real number so the only component affecting i is y. Therefore, y = -5.

Now, lets figure out the real part.

Cancel out imaginary part.

x + √(x² + 25) = 3

3 - x = √(x² + 25)

squaring on both sides,

9 + x² - 6x = x² + 25

6x = -16

x = -8/3

Hence the required complex number is -8/3 - 5i

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When the number of blue frogs increased by 60% and the number of green frogs decreased by 60%, the percentage of the overall increase is solved to be 60%

Assuming the number of blue frogs and the number of green frogs are equal and = y

Then the total number of frogs = y + y = 2y

Increasing the percentage of each by 60%, the factor for percentage increase by 60% is 1.6

hence 1.6y + 1.6y = 3.2y

percentage change

= change in price / original price * 100

= (3.2y - 2y) / 2y * 100

= 1.2y / 2y * 100

= 0.6 * 100

= 60

hence the percentage change is 60%

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The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A two-dimensional shape with horizontal and vertical axes is known as a 2d shape (x-axis and y-axis). Two-dimensional shapes have only length and width. There is no thickness or height to these shapes.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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If h(x) is equal to the composition between functions f(x) and g(x), then we must have:

f(x) = 1/x.

Here we have the function:

h(x) = 1/(x - 5)

And we know that we can write function h as a composition of other two functions:

h(x) = f( g(x) )

Where we know that:

g(x) =x - 5

Remember that the composition of two functions means that we are evaluating one in the other, in this case is rater easy to notice that we must have:

f(x) = 1/x

Then when we evaluate this in g(x) we will get:

f(g(x)) = 1/g(x)

Now we can replace g(x) by the actual function:

f(g(x)) = 1/g(x) = 1/(x - 5)

And that is h(x).

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Sherree's score on her 12th game is 86.67 in her golf game using equation.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs) (Input, Output). In algebra, relationship and function are crucial ideas. They are commonly employed in both real life and mathematics.

At games =2 score was 120

At games = 8 score was 100

so the equation is

y - 2 = (8-2)/(100-120) *(x-120)

⇒ (y-2)*(-20) = 6(x - 120)

⇒ -20y + 40 = 6x -720

⇒ 6x + 20y = 760

⇒ 3x + 10 y = 380

So, for y = 12

3x + 12*10 = 380

⇒ 3x +120 = 380

⇒ x = 260/3 = 86.67

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Answer:

85 inches

Step-by-step explanation:

7*12+1=84+1=85

The top of the hill have an altitude of 1391 feet above sea level

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

From the table, checkpoint 3 is at 1327 feet above sea level. Since the top of a hill rises 64 feet above checkpoint 3, hence:

Altitude of hill = 1327 + 64 = 1391 feet

The top of the hill is 1391 feet

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Answer:

[tex]5y^3-2x^2+2[/tex]

Step-by-step explanation:

I like to start off by rearranging the like terms next to each other, going from the greatest power to the least, so that they are more clear.

So in this case it would be: [tex]2y^3+3y^3+x^2-3x^2+1+5-4[/tex]

Now you can add them together. Remember you can only add/subtract coefficient or variable with the same base and power.

And with that in mind, the final result should be,
[tex]5y^3-2x^2+2[/tex]

Hope this helps!

Answer: To find the batting average of a player, we need to find the ratio of hits to total attempts.

Jana's ratio is 12/15, and Tasha's ratio is 9/10.

To compare these ratios, we can simplify both of them to a common denominator. In this case, the common denominator is 15.

Jana's ratio can be simplified to 12/15, which is equal to 0.8

Tasha's ratio can be simplified to (9/15), which is equal to 0.6

So, Jana has a ratio that means she has a better batting average (0.8) compared to Tasha (0.6)

Alternatively, we can convert these ratio to percentage by multiplying them by 100.

Jana's batting average is 12/15 * 100 = 80%

Tasha's batting average is 9/10 * 100 = 90%

By this way also we can see that Tasha's batting average is higher than Jana's batting average.

Step-by-step explanation:

Answer:

Step-by-step explanation:

24²=24×24

Which is 576

What else is part of the problem?

Answer

[tex] - 5 \sin(5x) [/tex]

Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.

Dimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.

Generally, the term dimension is the measurement of the length, width, and height of anything.

In this case, as given in the question

A frame is 10in wide and 6 in tall.

reduces to a width of 3 in

let us assume that the height of the frame after reducing the width to 3in be = x

then the equation becomes original width/ original length = reduced width/reduced length

put all the value, we get

[tex] = 10 \div 6 = 3 \div x[/tex]

solve the above

[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]

Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.

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Answer:

To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).

Tip = 0.24 * 73.25

= 17.58

Therefore, the tip should be $17.58 in dollars.

The geometric shape formed is a rhombus.

A quadrilateral is a four-sided shape enclosed shape, where the sum of the internal angle is 180°.

Here,
It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.
So, the construction of a quadrilateral is shown.
As seen in the figure, the figure is of a rhombus.

Thus, the geometric shape formed is a rhombus.

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The total surface area of the rectangular prism is 160 inches².

Since the base of the rectangular prism is a square, we know that the edge length of the base is the square root of the area of the base. The area of the base is 16 square inches (since it can be completely covered by 16 squares with edge length of 1 inch), so the edge length of the base is 4 inches.

Since the height of the prism is twice the edge length of the base, the height of the prism is 8 inches.

The total surface area of a rectangular prism is given by the formula:

2lw + 2lh + 2wh

Where l is the length, w is the width and h is the height

So, the total surface area of the rectangular prism is:

2(4 inches * 4 inches) + 2(4 inches * 8 inches) + 2(4 inches * 8 inches)

= 160 square inches

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The length of the rectangle is [tex]x^{4}[/tex]- 7 units.

We know that,

                  Area of a rectangle = length* width

           So,                       Length = Area/width

According to the question,

                                    Area = [tex]7x^{5} - 49x[/tex]

                                   Width = [tex]7x[/tex]

             Length of the given rectangle = Area/width

                                                                = [tex]\frac{7x^{5}- 49x}{7x}[/tex]

                                                                = [tex]\frac{7x(x^{4}- 7)}{7x}[/tex]

                                                                = [tex]x^{4} - 7[/tex]

Hence, the length of the rectangle is [tex]x^{4} - 7[/tex] units.

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The complete question is:

A rectangle has an area of [tex]7x^{5}- 49x[/tex]. Its width is 7x units. What is its length?

Answer:

The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.

Step-by-step explanation:

Answer:

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Step-by-step explanation:

The time needed to travel the entire distance is given as follows:

1.27 minutes.

Before obtaining the time, we need to obtain the entire distance.

The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.

The sides of the right triangle are given as follows:

40 yards and 70 yards.

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 40² + 70²

[tex]\sqrt{40^2 + 70^2}[/tex]

h = 80.6 yards.

Then the total distance is given as follows:

40 + 70 + 80.6 = 190.6 yards.

The time is given by the division of the distance by the velocity of 150 yards per minute, hence:

t = 190.6/150

t = 1.27 minutes.

The problem is given by the image presented at the end of the answer.

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The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.

To complete the hole on schedule the minimum amount of time the drill must continue to work is 18 hours

The rate of the drill for the remaining part of creating the whole is 56 feet per hour of digging

The remaining depth of the hole = the total hole - the depth before the rock

The remaining depth of the hole = 1012 - 2.75

The remaining depth of the hole = 1009.25

At a rate of 56 feet per hour the number of hours to dig 1009.25

56 feet = 1 hour

1009.25 feet = ?

cross multiplying

? * 56 = 1 * 1009.25

? = 1009.25/56

? = 18  

approximately 18 hours will take the drill to reach complete the hole

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Answer:

39

Step-by-step explanation:

x+x+1+x+2=120

3 consecutive numbers leading to x=39 !

The altitude of the hill whose top rises 64 feet above checkpoint -213, is 277 feet above sea level.

The altitude refers to the vertical distance or height of an object or point in relation to sea level (true altitude) or ground level (absolute altitude).

The altitude of a hill refers to its height measured from the ground level or the sea level, as the case may be.

In this situation, we can compute the altitude of the hill as the difference between the rise of the hill or mountain above the checkpoint and the given checkpoint.

The rise of the top of a hill = 64 feet

Given checkpoint = -213

The altitude of the hill = 277 feet [64 - (-213)]

Thus, the position or altitude of the hilltop in relation to the ground or sea level is 277 feet.

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Answer:

12 students

Step-by-step explanation:

The number of students surveyed: 53 + 46 = 99 students
The number of student having both: 99 - 87 = 12 students

A worker's starting wage at this job is $13.5.

$31.70 per hour can be expected after 7 years of experience.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that a worker earns $16.10 per hour with 1 year of experience.

The other worker earns $21.30 per hour with 3 years of experience.

The model that represents the wages of a worker is

y = ax + b

Where x is the number of years of experience, and y is total wages.

Now putting x =1 and y = 16.10 in y = ax + b:

16.10 = a + b .....(i)

Now putting x =3 and y = 21.30 in y = ax + b:

21.30 = 3a + b .....(ii)

Subtract equation (ii) from equation (i)

3a + b =21.30

a + b = 16.10

(-)  (-)    (-)

__________

2a = 5.2

a = 2.6

Putting a = 2.6 in equation (i)

16.10 = 2.6 + b

b = 16.10 - 2.60

b = 13.5

The model is y = 2.6x + 13.5

A worker's starting wage is $13.5 at this job.

Putting x = 7  in y = 2.6x + 13.5:

y = 2.6×7 + 13.5

y = $31.70

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Table F shows a proportional relationship and its points are plotted in the graph shown in the image attached below.

In Mathematics, the graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.

Mathematically, a proportional relationship can be represented or modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 8/4 = 10/2

Constant of proportionality, k = 2.

Therefore, the linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 7.5x

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