Question 5 please someone solve its functions and composite functions

The expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

To write the expression as a trigonometric expression using the suggested substitution, we can substitute x = cos(θ) into the expression and simplify:

√9−9x2 = √9−9(cos(θ))^2

= √9−9(cos^2(θ))

= √9(1−cos^2(θ))

= √9(sin^2(θ))

= 3sin(θ)

Therefore, the expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

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Answer: slope of the line

Step-by-step explanation: I'm not sure if we're talking about the same thing though

Answer: The slope (stands in for m)

Step-by-step explanation:

In a direct variation, the variable m (slope) is swapped for k.

The height (in inches) of a triangle with an area of 720 square inches and base of 32 inches is 45 inches.

The height of a triangle can be found using the formula for the area of a triangle: A = (1/2)bh, where A is the area, b is the base, and h is the height.

In this case, we are given the area (720 square inches) and the base (32 inches) and are asked to find the height.

First, we can plug in the given values into the formula:

720 = (1/2)(32)(h)

Next, we can simplify the equation by multiplying both sides by 2:

1440 = 32h

Finally, we can solve for the height by dividing both sides by 32:

h = 45 inches

Therefore, the height of the triangle is 45 inches.

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The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

The present value of an annuity is calculated using the following formula:

PV = A[((1+i)n-1)/(i(1+i)n)]

where A = amount of each annuity payment, i = interest rate, and n = number of payments.

For this problem, A = $500, i = 6%, and n = 15 years.

Therefore, the present value of the annuity necessary to fund the withdrawal is:

PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]

PV = $500[5.72982/0.105638]

PV = $5,354.82

Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

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Answer:

The equation y=225x represents a proportional relationship between the number of hours the field is being rented and the total cost. This means that as the number of hours increases, the total cost will increase proportionally. Therefore, statement D) "The equation shows a proportional relationship, but not a linear relationship" is true based on the given equation.

Answer:

Step-by-step explanation:

We separate into 2 congruent triangles. Both have a base of 3.5 and a height of 9 inches. Using pythagoran theorum, we will square 9 and 3.5

81 and 12.25

Add them up and it's 93.25

[tex]\sqrt{93.25}[/tex]=9.65660395791

Now since it's isosceles, the other side will also be 9.65660395791.

9.65660395791 + 9.65660395791 + 7 =26.3132079158

You want it rounded to the nearest tenth, so 26.3

The value of x for the similar triangles is 57.5 units.

The value of x is determined by applying the principle of similar triangles as shown below.

In the given diagram, we can assume the following for the similar triangles;

length 46 is congruent to length (16 + 46)

length 20 + x is congruent to length x

So we will have the following equation;

46/x = (16 + 46 ) / ( 20 + x )

46/x = ( 62 ) / ( 20 + x )

46 ( 20 + x ) = 62x

920 + 46x = 62x

920 = 16x

x = 920 / 16

x = 57.5

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Answer:

Step-by-step explanation:

its 190 because you started on page 4 and you add 186

Answer:

14.75 + 18.75x ≤ 425

Step-by-step explanation:

Total amount they have is $425

Parking for the entire group = $14.75

If x is the number of persons in the group, the cost of x tickets at $18.75 per head
= 18.75x

The total cost incurred
= Parking Cost + Ticket Cost

= 14.75 + 18.75x

This has to be less than equal to 425

So the inequality is

14.75 + 18.75x ≤ 425

i cannot make out the given answer choices clearly, it appears the constant 425 is on the left side in each answer choice - choose the one which is closest to the given answer

The empirical norm therefore states that 68% of 7-year-old kids are between 47 and 51 inches tall.

A column in a table is a collection of cells which are arranged vertically. A field, like the received field, is a sort of element that contains only one item of data. A column in a table usually contains the values for just a single field.

The empirical rule states that in a normal distribution, 68% of the data fall within one average standard deviation. In this instance, the mean difference is 2 inches, while the average height of 7-year-old kids is 49 inches.

We must identify the range among heights that is within one average standard deviation in order to apply the scientific rule. To accomplish this, we can add and subtract the standard variance from the median as follows:

Mean ± (Standard Deviation) = 49 ± 2

As a result, the height range which falls within the standard deviation from the average is between 47 and 51 inches.

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All the roots of all the polynomials in {f1, ..., fn}.

(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur) where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E.

(b) We can extend part (a) to splitting fields of arbitrary sets of polynomials by first noting that the field E must contain the coefficients of all the polynomials in the given set. This implies that for a given set of polynomials {f1, ..., fn}, the field F is a splitting field over K if and only if it is a splitting field over E, where E is the smallest field containing the coefficients of {f1, ..., fn}. In other words, F must contain all the roots of all the polynomials in {f1, ..., fn}.

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There are 14 books on the bookshelf as a result.

Assume that there are x total books on the bookshelf. Neil has read 7 out of a total of 7 + (x-7) = x-0 books, which means that he has read 7/14 of the books, according to the problem. This is reduced to 1/2.

Now that he has read 8 out of 15 books, his percentage of books read will be 8/15 if he reads one more (the original 7 books he read plus the one he read now). This implies:

8/15 = 8/(x+1)

In order to find x, we can cross-multiply:

8(x+1) = 15(8) (8)

8x + 8 = 120

8x = 112

x = 14

There are 14 books on the bookshelf as a result.

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Using the given functions, the product of (g*f)(x) is 2x³ - 11x² + 12x + 9.

A relation between a set of inputs having one output each is called a function. The product of (g*f)(x) can be found by multiplying the functions f(x) and g(x) together.

Since f(x) = 2x² - 5x - 3 and g(x) = x - 3, then the product of (g*f)(x) can be solved as follows:

(g*f)(x) = g(x)*f(x) = (x - 3)(2x² - 5x - 3)

Use the distributive property:

(g*f)(x) = 2x³ - 5x² - 3x - 6x² + 15x + 9 = 2x³ - 11x² + 12x + 9.

Therefore, the correct answer is 2x³ - 11x² + 12x + 9.

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Answer:

a) [tex]\frac{2\pi }{3}[/tex]

b) 330

Work:

a) To convert degrees to radians you multiply by [tex]\frac{\pi }{180}[/tex]

[tex]\frac{120}{1}[/tex] x [tex]\frac{\pi }{180}[/tex]

= [tex]\frac{6}{1}[/tex] x [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{2\pi }{3}[/tex]

b) To convert radians to degrees you multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{11\pi }{6}[/tex] x [tex]\frac{180}{\pi }[/tex]

= [tex]\frac{11}{1}[/tex] x [tex]\frac{30}{1}[/tex]

= 330

Graph of g(x) will be wider than f(x) is false.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The graph of f(x)=x² was transformed to create g(x)=2/3x².

The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.

This means that the graph of g(x) will be narrower than the graph of f(x), not wider.

Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).

Hence,  graph of g(x) will be wider than f(x) is false.

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Looking at the table, we can see that the addends follow a pattern where each subsequent pair of addends adds up to 1/5. Specifically, the missing addend is 2/5 - 3/10, which equals 1/10. The missing sums are 1/2 and 4/10.

The addends in the table are as follows:

1/10 + 1/5 = 3/10, 1/5 + 1/5 = 2/5

3/10 + 1/5 = 1/2

We can observe that the first two pairs of addends add up to 1/5 less than the subsequent sums. This pattern indicates that the missing addend must be

1/5 - 1/10 = 1/10

which would make the third pair of addends add up to

1/2 - 1/10 = 4/10

Therefore, the missing sums are 1/2 and 4/10, respectively. This pattern can be helpful in solving similar problems where pairs of addends add up to a specific sum or difference.

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The possible values of x are 2 and 17

The complete question is added as an attachment

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

Similar triangles

In the triangles, we have the following possible equations

15/18 = 10/(10 + x)

10/18 = 15/(10 + x)

Solving the equations, we have

15/18 = 10/(10 + x)

150 + 15x = 180

15x = 30

x = 2

10/18 = 15/(10 + x)

100 + 10x = 270

10x = 170

x =17

Hence, the values of x are 2 and 17

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Complete Question

The two triangles in the diagram are similar there are 2 possible values for x

See attachment for image of the triangle

Answer:

Step-by-step explanation:

Answer:

To find the total amount of money spent on the toy car, pizza, and pencil, we simply need to add the individual prices together:

$7.55 (toy car) + $3.75 (pizza) + $0.75 (pencil) = $12.05

Therefore, you spent $12.05 altogether on the toy car, pizza, and pencil.

Answer:

Alice paid for the 4 packs of cards with 4 x $2 = $8.

She used 3 ten dollar bills, which is 3 x $10 = $30.

Therefore, the cost of the 2 jigsaw puzzles is:

Total cost of the purchase - Cost of the packs of cards

= ($30 + $4 change) - $8

= $26

So, the total cost of the 2 jigsaw puzzles was $26.

The answer is (D) $26.

Answer:

C. $22

Step-by-step explanation:

You have $30, then you multiply 4x2=8(Price of the Cards)

next subtract the $8 from $30 (30-8)

Your final answer is 22

The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.

Grid squares are a way to represent two-dimensional space using a grid of squares, with each square representing a unit of length.

Grid squares are often used in various fields, such as computer graphics, geographic information systems, and mathematics, to represent and manipulate two-dimensional data.

Here we have

The table shows the distance traveled in a time period

The maximum time is shown in a table = 35 minutes

Let 1 unit = 5 minutes

Number of squares used to represent 35 minutes = 35/5 = 7

Therefore, the number of squares wide needs = 7 blocks

Given that the grid is 20 squares tall

The maximum distance in a table = 1.8 km  

Let's take the total distance = 2 km

The number of squares along length = 2 km/20 = 0.1

Therefore,

The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.

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The number "4" in the expression 4x - 5 represent the number of days Gerard worked.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Gerard worked the same number of hours, x, on Monday, Tuesday, and Wednesday, but on Thursday, he worked 5 hours less than the previous day.

The total number of hours Gerard worked can be found using the expression, 4x − 5

Hence:

The number "4" in the expression 4x - 5 represent the number of days Gerard worked which is Monday, Tuesday, and Wednesday and Thursday

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1[/tex]

Answer:

The difference between the LCM and the GCF of 30 and 55 are that the LCM is the smallest positive integer that is divisible and the GCF is the largest positive integer that divides each of the integers.

Step-by-step explanation:

The intersection point on the graph has an approximate x-value of 1a.

Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.

The line, also called the "curve," has a point at each point that fulfils the function.

The three lines are contemporaneous if they all cross at the same point.

From the second equation,

x = 8y + 19

Putting value of x,

2(8y + 19) + 3y = 0                              9(8y + 19) + 5y = 17

16y + 38 + 3y = 0                                 72y + 171 + 5y = 17

19y = -38                                                77y = -154

 y = -2                                                      y = -2

You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.

x = 8(-2) + 19

x = -16 + 19

x = 3

The single point that these three equations share is (3, -2).

4x - 3y = 13                     eq1

-6x + 2y = -7                   eq2

Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.

8x - 6y = 26                eq1

-18 + 6y = -21              eq2

Adding the equations to eliminate the y terms.

-10x = 5

 x = -1/2

Substituting this value of x into any of the equations to solve for the value of y.

Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.

You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.

If you were to graph these two lines, they will be intersecting at (7, -5).

Now, draw the following lines on a coordinate system:

i) A vertical line passing through the points (3, 0).

ii) A horizontal line passing through the point (0, 6).

iii) A line passing through the points (0,0) and (1, -3).

Once you have drawn these lines, look for 3 points of intersection.

Area = (base × height) / 2

Lines that have the same slope never intersect.  Put both equations in y=mx+b  form where the slope is the coefficient of x.

2x + 3y = > 3y = -2x + 23

y = (-2 / 3) x + 23/3

7x + py = 8

py = -7x + 8

y = (-7 / p) x + 8/p

Set the slopes equal to each other.

-2 / 3 = -7 / p

Cross-multiply.

-2p = -21

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The next marble's experimental probability of being blue, according to an experiment, is: 23/25.

Based on empirical data, experimental probability is the likelihood that an event will occur. A theoretical probability would be obtained by dividing the number of different ways to achieve the desired result by the total number of outcomes.

The next marble's likelihood of being blue, according to an experiment, is:

Experimental probability = Number of time blue appears / Total outcomes

Experimental probability = 23/25

Thus, the next marble's experimental probability of being blue, according to an experiment, is: 23/25.

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Answer:

We can use the properties of logarithms to simplify this expression:

log2(9x^10/y²) = log2(9) + log2(x^10) - log2(y²)

Now we can apply the power rule of logarithms to the second term:

log2(x^10) = 10 log2(x)

Substituting back into the original expression:

log2(9x^10/y²) = log2(9) + 10 log2(x) - log2(y²)

This is the simplified form of the expression.

Answer:

Your score is -9.

Step-by-step explanation:

The monthly revenue for the route, R, as a function of the ticket price, x, can be expressed as R(x) = (9000 + 50(150 - x))x.

The airline carries 9000 passengers per month, and each pays $150, so the initial monthly revenue is R(150) = 9000 x $150 = $1,350,000.

If the ticket price is decreased by $1, the airline will gain 50 passengers, so the new monthly revenue can be calculated by adding the revenue gained from these additional passengers to the initial revenue, and subtracting the revenue lost from the decrease in ticket price. The revenue gained from the additional passengers is 50(x - $150), since each passenger pays the new ticket price x instead of $150. The revenue lost from the decrease in ticket price is 9000($150 - x), since each of the 9000 passengers pays $150 - x instead of the initial price of $150.

Putting these together, we get:

[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]

R(x) = (9000 x $150) + 50x - 50($150) - 9000($150) + 9000x[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]

[tex]R(x) = (9000 + 50(150 - x))x[/tex]

Thus, the monthly revenue for the route, R, as a function of the ticket price, x, is [tex]R(x) = (9000 + 50(150 - x))x[/tex]

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