What is a table of a function?

The solution is Option B , Option D.

The equations are z/6 + w = 11 and 5y + 4 = 16 + y

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

( 10 + a ) / ( 3a + 1 )  

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

b)

z/6 + w = 11   be equation (1)

Now , the equation is having = sign along with coefficients and variables

c)

( z-2 ) / 3 < 15

The < sign represents an inequality relation

So , it is not an equation

d)

5y + 4 = 16 + y   be equation (2)

Now , the equation is having = sign along with coefficients and variables

e)

x² + 3x + 7

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

f)

5y + 1 ≤ y

The ≤ sign represents an inequality relation

So , it is not an equation

Hence , the equations are solved

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Answer: $14697.51

Step-by-step explanation:

[tex]9126(1+0.10)^{5} \approx \$14697.51[/tex]

The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).

The lowest integer that unites all of the fractions in a given collection is known as the least common denominator (LCD).

Given that,

The equation x+2/3x - 1/x-2 = x-3/3x is being multiplied by the least common denominator (LCD)

So, further solving this equation,

x+2 / 3x - 1/x-2 = x-3/3x

Here, the least common denominator (LCD) is (3x)(x-2). so we multiply the whole equation by the least common denominator (LCD).

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

We multiply each term by the least common denominator (LCD).

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

Thus, we get (x-2) (x+2)-1(3x) = (x-3) (x-2).

Therefore,The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).

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Answer:

D

Step-by-step explanation: answer is d

Answer:

first three are correct answers last two are not

Step-by-step explanation:

quadratic equations are in the for y=ax²+bx+c

y= f(X)

The equation of the line would be y = 17/7x + 1.

What is the equation of the line?

The equation of a line is a mathematical expression that describes the position of a line in a coordinate plane. It typically takes the form of "y = mx + b", where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis.

The whole question is:

Write an equation of the line passing through the point (8,7) that is perpendicular to the line  [tex]y + 7 = -\frac{7}{17}(x+8)[/tex]

To write the equation of a line that is perpendicular to a given line, we can use the slope of the given line and the point the new line passes through.

The slope of the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] can be found by isolating y and then taking the derivative, which gives us: -7/17.

The slope of a line perpendicular to this line is the negative reciprocal of the given line's slope, which is 17/7.

We also know that the new line passes through the point (8,7). Using a point-slope form of a line which is (y-y1) = m(x-x1) where m is the slope, we can write the equation of the line as:

y - 7 = 17/7(x - 8)

So the equation of the line that passes through the point (8,7) and is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] is:

y = 17/7x + 1

Hence, the equation of the line would be y = 17/7x + 1.

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The equation that represents this word sentence is n-7 = 9

The value of n = 16

An algebraic expression can be defined as an expression that is composed of variables, terms, coefficients, constants and factors.

They are also made up of mathematical or sometimes called arithmetic operations, such as;

From the information given, we have that;

9 is the difference of a number n and 7.

This is represented as;

n - 7 = 9

Now, collect like terms

n = 9 + 7

Add the values

n = 16

Thus, the value is 16

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At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.

Vector is a mathematical element that has both magnitude and direction. It is used to represent quantities such as velocity, force, acceleration, and displacement. Vector is used in physics and engineering for computing physical quantities. Vector is also used in computer graphics for representing shapes, lines, and curves. Vector can also be used in economics for representing stocks and bonds.

The vector t is the direction vector of the parametric function r(t). It is found by taking the derivative of the parametric equation:

t = (2t, 2t^2, 1)

The normal vector n is found by taking the cross product of the curvature vector and the direction vector. The curvature vector is found by taking the second derivative of the parametric equation.

k = (2, 4t, 0)

n = (4t, -2, 2)

The binormal vector b is found by taking the cross product of the direction vector and the normal vector.

b = (-8t, 4, -4t)

At the given point, (4, 16/3 , -2), the vectors t, n, and b are (2, 4, -1), (16, -8, 4), and (-32, 8, 8), respectively.

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Answer:

1. To find the gradient of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the gradient of (x+7)/(y-2) = 0, we can first rewrite the equation as y = (2x+14)/(x+7). To find the slope, we can take the derivative of y with respect to x. We get the slope or the gradient of the line as m = 2/(x+7).

b) To find the gradient of the line through (p,5) and (6,2p), we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and solve for m.

y - 5 = m(x - p)

2p - 5 = m(6 - p)

2p - 5 = 6m - mp

mp + 6m = 2p + 5

m(p+6) = 2p + 5

m = (2p+5)/(p+6)

2. To find the equation of a line, we can use the slope-intercept form of the equation: y = mx + b, where m is the gradient and b is the y-intercept.

a) To find the equation of the line with a gradient of 3, passing through (0,5), we can substitute the values into the slope-intercept form.

y = 3x + b

5 = 3(0) + b

b = 5

The equation of the line is y = 3x + 5

3. To find the value of p, if the gradient of the line joining (-1,p) and (p, 4) is 2/3, we can use the point-slope form of the equation: y - y1 = m(x - x1). We can substitute the coordinates of the two points and the gradient, and solve for p.

y - p = (2/3)(x - (-1))

4 - p = (2/3)(p - (-1))

4 - p = (2/3)p + (2/3)

(2/3)p - 4 + p = (2/3)

p = 6

Final Answer: The value of p is 6.

In the given question, none of the function exhibits an end behavior

The end behavior of a polynomial is the way the graph of the polynomial behaves as the input values become very large or very small. Generally, the end behavior of a polynomial is either up, down, or a combination of both. If the highest degree term has a positive coefficient, the end behavior is up; if the highest degree term has a negative coefficient, the end behavior is down. If the highest degree term has a coefficient of zero, the end behavior is a combination of up and down.

In the functions given, we can find the end behavior of each of these functions.

1)

y = √x

The leading coefficient test requires a polynomial and this function is not a polynomial.

2)

y = √(x - 5) - 6

The leading coefficient test requires a polynomial and this function is not a polynomial.

3)

y = -3√(x + 3) + 7

The leading coefficient test requires a polynomial and this function is not a polynomial

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The actual number of people in 10 years could be 57,000 or 56,000. The equation of the trend line is y=1.9x+21, so for any year x, the population y can be found using this equation. To find the population in 16 years, when the population is 52,900, we can plug in x=16 and solve for y to find y=52,900. To find the population in 10 years, when the population is 2,000 people from what the trend line shows, we can plug in x=10 and solve for y to find y=50,900. Since the population should be 2,000 more, the actual population in 10 years is either 57,000 (50,900 + 2,000) or 56,000 (50,900 + 1,000).

Answer:

Part A is 16

Step-by-step explanation:

The possible values of [tex]$m$[/tex] are all real numbers greater than   [tex]$\frac{2}{x^2}$[/tex]

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its unknown variable (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.

Let [tex]$y = 2x^2mx8$[/tex]

The two distinct real roots of the equation imply that y is a quadratic equation with two distinct real roots.

So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]

Using the quadratic formula , [tex]$m = \frac{8}{2x^2x}$[/tex]

The two distinct real roots of the equation imply that the discriminant of the quadratic equation, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.

So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]

[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]

So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]

Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]

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Answer:

2

Step-by-step explanation:

-4+6=2

f(g(7))

        you can see that f(7) = 4, so plug in f(7) = 4 in the equation

       you can see that f(4) = 9

Answer to this function is 9 A)

Hope it helps!

449 students were surveyed about their preferences for sports. 146 students like football, 107 students like baseball, and 49 students like both sports. there are 293  students like exactly one of the two sports.

This can be determined by subtracting the number of students who like both sports (49) from the total number of students surveyed (439). This leaves us with 390 students who like either football, baseball, or both. To find the number of students who like exactly one of the two sports, we will need to subtract the number of students who like both sports from the number of students who like either football or baseball.

To do this, we add together the number of students who like football (146) and the number of students who like baseball (107). This gives us 253 students who like either football or baseball. Subtracting this number (253) from the number of students who like either sport (390) gives us the number of students who like exactly one of the two sports (293).

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Answer: x=10

Step-by-step explanation:

120=6x

120+6x=+180=360

300+6x=360

6x=60

x=10

To write an absolute value inequality from a line graph, we need to identify the inequality sign and determine the interval(s) of x-values that make the inequality true.

Here are the steps to write an absolute value inequality from a line graph:

Identify the inequality sign: If the graph is a solid line, the inequality is "equals to", if the graph is dashed, the inequality is "not equal to", if the graph is a solid line to one side and a dashed line to the other side, the inequality is "greater than or equal to" or "less than or equal to".

Determine the interval(s) of x-values that make the inequality true: The x-values for which the graph is above the x-axis represent the solution set of the inequality when the inequality sign is "greater than" or "greater than or equal to", and the x-values for which the graph is below the x-axis represent the solution set of the inequality when the inequality sign is "less than" or "less than or equal to"

Write the inequality: Using the information from step 1 and 2, we can write the inequality in the form of |x-h| operator k, where h is the x-coordinate of the vertex, k is the distance of the vertex to the x-axis and operator is the inequality sign determined in step 1.

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For the line segment MO, the ratio of the length of MN to length of NO is 3 : 7. The ratio of the length of MN to length of MO is 3 : 10.

Ratio or proportion is the relation describing the size, quantity, or the amount of two or more variables.

For example, the ratio of sugar and flour in a cake dough is 1 : 2. It means, if there is 200 grams of sugar in the dough, the amount of flour is 2 x 200 = 400 grams.

In the given problem, the ratio of length MN to the length NO is 3 : 7.

Notice that:

MO = MN + NO

Hence, the ratio of the length of MN to the length of MO is:

MN : MO = MN : (MN + NO)

MN : MO = 3 : (3 + 7)

MN : MO = 3 : 10

The picture in your question is missing. Most likely it was like the one in the attached picture.

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The linear equation on the graph is the one in the last option, it is:

y = 6x

A general linear equation can be written as:

y = a*x + b

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

First, we can see that the line passes through the point (0, 0), thus the y-intercept is b = 0.

We can write:

y = a*x

We also can see that the line passes through the point (1, 6)

Replacing these values we will get:

6 = a*1

6/1 = a

6 = a

Then the linear equation is:

y = 6x

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Given an infinite grid, initial cell position (x, y) and a sequence of other cell position which needs to be covered in the given order.

The task is to find the minimum number of steps needed to travel to all those cells.

Note: Movement can be done in any of the eight possible directions from a given cell that is from cell (x, y) you can move to any of the following eight positions:(x-1, y+1), (x-1, y), (x-1, y-1), (x, y-1), (x+1, y-1), (x+1, y), (x+1, y+1), (x, y+1) is possible

Examples:

Input: points[] = [(0, 0), (1, 1), (1, 2)]

Output: 2

Move from (0, 0) to (1, 1) in 1 step(diagonal) and

then from (1, 1) to (1, 2) in 1 step (rightwards)

Input: points[] = [{4, 6}, {1, 2}, {4, 5}, {10, 12}]

Output: 14

Move from (4, 6) -> (3, 5) -> (2, 4) -> (1, 3) ->

(1, 2) -> (2, 3) -> (3, 4) ->

(4, 5) -> (5, 6) -> (6, 7) ->

(7, 8) -> (8, 9) -> (9, 10) -> (10, 11) -> (10, 12)

Since all the given points are to be covered in the specified order.

Find the minimum number of steps required to reach from a starting point to next point, then the sum of all such minimum steps for covering all the points would be the answer.

One way to reach from a point (x1, y1) to (x2, y2) is to move abs(x2-x1) steps in the horizontal direction and abs(y2-y1) steps in the vertical direction, but this is not the shortest path to reach (x2, y2).

The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction.

If we look closely this just reduces to the maximum of abs(x2-x1) and abs(y2-y1).

Traverse for all points and summation of all diagonal distance will be the answer.

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Answer:

Step-by-step explanation:

x=2+2[tex]\sqrt{6}[/tex] or x=2-2[tex]\sqrt{6}[/tex]

That's  0.20833 of one day./

(5/24 of a day)

No, You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.

A public, two-way personal radio service is the Citizen's Band (CB) Radio Service, usually abbreviated as CB. There are various categories for CB operating. The most popular CB method is voice communication, which rose to popularity in the 1970s. Mobile CB operating is still common, particularly in automobiles and trucks. The majority of CB operating occurs in a constrained range of frequencies around 27 MHz. This band contains 40 channels. There is excessive channel saturation.

A CB (citizen’s band) radio must be FCC type approved. Of course, I have no idea where you are, so maybe, where you are, it is ok. In the US however, CB radios are not to be “easily modified” neither to increase power out nor to allow operation outside the citizen’s band frequencies. Even as an extra class amateur radio licensee, I may not use a modified radio on the CB band. I am allowed, however to modify a CB radio to operate on amateur radio bands.

You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.

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Answer:

a) The function to represent the scenario would be:

f(x) = 56 - 8x

b) To find out how many sips Anna can take before she needs to refill, we need to find when the water bottle is empty.

To do this, we can set f(x) = 0 and solve for x:

0 = 56 - 8x

8x = 56

x = 7

So, Anna can take 7 sips before she needs to refill.

c) A graph to represent this situation would be a straight line with a slope of -8 and y-intercept of 56.

d) The domain of the function is the set of all possible input values, or in this case, the number of sips Anna takes.

As Anna can take any whole number of sips, the domain of the function is the set of all non-negative integers:

{x | x ∈ Z, x ≥ 0}

We can represent how many sips Anna takes from her water bottle with the function y = 56 - 8x. Anna can take 7 sips before she needs a refill. The graph of this function is a straight line that starts at (0, 56) and ends at (7, 0). The domain in set notation is {x|x is an integer and 0 <= x <= 7}.

a) We can represent this scenario with a function, where the amount of water in the bottle depends on how many sips Anna has taken. This is a linear function because each sip Anna takes decreases the amount of water in the bottle by a constant amount. The function could be written as: y = 56 - 8x, where y represents the amount of water in the bottle, and x represents the number of sips Anna has taken.

b) To find out how many sips Anna can take before she needs to refill the bottle, we set y to 0 in our function: 0 = 56 - 8x. Solving for x gives us x = 7. Therefore, Anna can take 7 sips before she needs to refill the bottle.

c) A graph representing this situation would be a straight line starting at (0, 56) on the y-axis, and going down 8 units for each step along the x-axis, until reaching x=7.

d) The domain in set notation for this function would be {x|x is an integer and 0 <= x <= 7}.

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(5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports. This can be solved using the concept of standard deviation.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.

Thus, (5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports.

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The complete question is as follows:

A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports?

Find the t-table here.

(4.396, 8.104)

(4.865, 7.635)

(5.097, 7.404)

(5.245, 7.256)

The value of expression (a + b + c + d) is 20

Consider given equations x + y = 4       ........(1)

and 3xy = 4        .........(2)

The solutions of given equations are of the form [tex]$x = \frac{a \pm b\sqrt{c}}{d}$[/tex]

where a, b, c, and d are positive integers and the expression is completely simplified.

From equation (2),

y = 4/3x

Substitute above value of y in equation (1),

x + y = 4

x + (4/3x) = 4

3x² + 4 = 12x

3x² - 12x + 4 = 0

After solving above quadratic equation we get,

[tex]x=\frac{6\pm 2\sqrt{6} }{6}[/tex]

Comapring this solution with [tex]$x = \frac{a \pm b\sqrt{c}}{d}$[/tex] we get,

a = 6, b = 2, c = 6 and d = 6

Now we find the value of expression (a + b + c + d)

a + b + c + d

= 6 + 2 + 6 + 6

= 20

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The population mean  of interest for this example is all of the tire pressure gauges in the shipment of 2000.

1. The problem states that 2000 tire pressure gauges were shipped to an automotive company warehouse.

2. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined.

3. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back.

4. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000.

This example involves an automotive company warehouse receiving a shipment of 2000 tire pressure gauges. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000 since this is the sample from which the percentage of defective gauges was determined.

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The required ways can 3 club members be chosen as president, vice president, and treasurer are 56.

When the order doesn't matter, the combination is a choice between all of the objects in the set or just a portion of them. As a result, the combination formula is provided by; n, and the number of combinations of n objects taken r at a time.

Total number of eligible members for these positions = 8

To choose three members,

C(8, 3)

(8×7×6)/(3×2)

336/6

= 56 ways.

Thus,the required number of ways are 56.

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The probability of getting exactly 14 heads by flipping a fair coin 20 times is 0.03696.

The number of times a fair coin is flipped = 20

The outcomes for flipping the coin once = 2

Therefore, the outcomes for flipping the coin 20 times = (2) ^ 20

Number of heads needed = 14

The number of ways of getting exactly 14 heads = 20C14

20C14 is the 20! / (14! (20-14)! = 38760

Probability of getting an event = possible outcome / total outcomes

Thus, the probability of getting exactly 14 heads by flipping a fair coin 20 times = (20C14) / (2 ^ 20) ≈ 0.03696

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Answer:

D. (1,3) and (3,7)

Step-by-step explanation:

The graphs of y = 2x + 1 and y = -(x-1)^2 + 3 intersect at the points where they have the same y-coordinate. To find these points, we can set the two equations equal to each other and solve for x.

y = 2x + 1 = -(x-1)^2 + 3

2x + 1 = -x^2 + 2x + 2

x^2 - 4x + 1 = 0

(x-1)^2 = 0

x = 1

Now we can substitute this value of x into either of the given equations to find the corresponding y-coordinate.

y = 2x + 1 = 2(1) + 1 = 3

so the point of intersection is (1,3)

So the answer is D. (1,3) and (3,7)

Please note that the solution is valid only if the two equations y=2x+1 and y=-(x-1)^2+3 are defined for the same domain.

Answer:

[tex]f(g(4) = \boxed{\bold{0}}[/tex]

[tex]g(f(3)) = \boxed{\bold{2}}[/tex]

[tex]f(f(5)) = \boxed{\bold{5}}[/tex]

[tex]g(g(1)) = \boxed{\bold{4}}[/tex]

Step-by-step explanation:

All the expressions are composite functions where the output of one function is fed as input to the other function to get the composite output

To explain better, I will use the specific values and the graphs of f(x) and g(x)

-----------------------------------------------------------------------------------------------------
f(g(4))

Let's take the first expression [tex]\displaystyle {f(g(4))}[/tex]. The innermost function, [tex]g(x)[/tex] is first evaluated at [tex]x = 4[/tex], then this value is used to find the value of the outer function [tex]f(x)[/tex]

To find the value of this expression

-----------------------------------------------------------------------------------------------------

The other expressions can be evaluated using similar reasoning.
g(f(3))

First evaluate[tex]f(x) \:at\: x = 3 == > f(3) = 0 == > g(0) = 2[/tex]

Answer:  2

-----------------------------------------------------------------------------------------------------

f(f(5))

This is a function which is a composite of itself
Find [tex]f(5) = 2 == > f(2) = 5[/tex]

Answer: 5

-----------------------------------------------------------------------------------------------------

g(g(1))

[tex]g(1) = 5 == > g(5) = 4[/tex]

Answer: 4