A table of values for a one-to-one function is given. Find the
indicated value.
x
1
2
3
4
5
6
f(x)
7
9
3
0
4
1
f −1(0) =

Step-by-step explanation:

so, let me retype this.

horizontal asymptote : y = 2

that means lim x going to ±infinity f(x) = 2.

vertical asymptotes :

x = 3

x = -4

that means the function must have these 2 points, where the expression leads to a division by 0 or something similar that would make the result undefined.

we got 4 functions :

A) y = x²/(x² + x - 12)

B) y = x²/(x² - x - 12)

C) y = 2x²/(x² + x - 12)

D) y = 2x²/(x² - x - 12)

so, for which ones we have y = 2 as limit when x goes against + or - infinity ?

that would be C and D.

A and B lead to x²/x² = 1 as limit for gigantic numbers.

C and D lead to 2x²/x² = 2 as limit.

remember, when x gets really, really big, the "±x - 12" part becomes irrelevant.

so, we look at C and D.

which one lead to a division by 0 at x = 3 and x = -4 ?

that would be C.

for x = 3

x² + x - 12 = 3² + 3 - 12 = 9 + 3 - 12 = 12 - 12 = 0

for x = -4

x² + x - 12 = (-4)² - 4 - 12 = 16 - 4 - 12 = 12 - 12 = 0

D with x² - x - 12 would have x = -3 and x = 4 as zeroes.

these are different asymptotes than requested.

so, C is the right answer.

Answer: Hayley is hosting a party. She has 50 pieces of candy she wants to give to her 10 friends. How many pieces should each friend get so everyone receives the same amount?

Answer: 0.125 and 12.5%

Step-by-step explanation:

To convert any fraction to decimal form, we just need to divide its numerator by the denominator.

Here, the fraction is 1/8 which means we need to perform 1 ÷ 8.

This gives the answer as 0.125. So, 1/8 as a decimal is 0.125

To get its percentage form, you simply multiply the obtained decimal value by 100:

0.125 x 100 = 12.5

Hence, we can learn vital information about the behaviour and shape of a polynomial function's graph by scrutinising its factors and other characteristics.

A polynomial function's factors include crucial details about the function graph. The factors specifically determine the locations where the graph intersects the x-axis, known as the function's roots or x-intercepts. By setting each factor to zero and calculating the associated value of x, these roots can be discovered.

The behaviour and structure of the graph are also influenced by the degree of the polynomial function, the signs of its leading coefficient, and other coefficients. The number of turning points in the graph, for instance, is determined by the degree of the polynomial function, whereas the concavity or convexity of the graph is determined by the leading coefficient and other coefficients' signs.

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Answer:

x > 5

Step-by-step explanation:

-2x - 2 < 8

-2x < 10

x > 5

So, the answer is x > 5

The measure of the angle ∠Z will be 88°.

Geometry is the study of two-dimensional and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles. Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.

Given that the two angles are (9p + 20)° and (7p + 32 )°. The value of angle z is calculated as,

9p + 20 + 7p + 32 = 180

16p = 180 - 20 - 32

16p = 128

p = 8

The measure of the angle ∠Z will be,

9p + 20 + ∠Z= 180

72 + 20 + ∠Z= 180

∠Z = 180 - 72 - 20

∠Z = 88°

Therefore, the angle ∠Z is 88°.

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There are 2 quart jars can he fill.

There is 4 pint jar can he fill with any leftover sauce.

Fractions are numerical values that are a part of whole.

Julian is making barbecue sauce to the can. He uses 6 cups white vinegar, 1/2 cup honey, and 1/2 cup maple syrup.

We know that

1 quarts = 4 cups

Total number of cups is;

6 + (1/2) + (1/2) = 7

The total number of jars that he can fill is;

= total number of cups/4

=7/4

=1.75

There are 2 quart jars can he fill.

There are pint jars he can fill with any leftover sauce is;

1 quart = 2 pints

So, 2 quart = 2 × 2 = 4 pints.

There is 4 pints jar can he fill with any leftover sauce.

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Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

A graph is a picture of data that illustrates the connection between two or more factors. A graph in mathematics is typically a two-dimensional coordinate system with a horizontal x-axis and vertical y-axis (vertical). Data points are represented on a graph by points that are drawn with their x- and y-coordinates. The graph can be used to display trends, correlations, and temporal shifts as well as other patterns and connections between the variables. Graphs are used to aid in the interpretation and communication of data in a wide range of disciplines, including mathematics, science, economics, and social studies.

given

Locate the vertex: The vertex of a quadratic function is the lowest or highest spot on the graph. For the x-coordinate of the vertex, use the expression x = -b / (2a), and for the y-coordinate, use y = f(x), where f(x) is the quadratic function.

The places where the graph crosses the x-axis and the y-axis are known as the intercepts. If x = 0, then calculate f to determine the y-intercept (0).

Additional information: Plug a few x values into the function to determine the associated y values. You'll have more data points to display on the graph as a result.

Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

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Answer:

Step-by-step explanation:

To find the length of the square side lengths and the diameter of the circle, we can divide the perimeter by 4:

79.04/4 = 19.76

This is the diameter of the circle. The radius is half the diameter:

19.76/2 = 9.88

Hope this helps!

Answer: 9.88 cm

Step-by-step explanation:

To find the radius, we need to find half the length of one side of the square.

The perimeter of the square is all the sides of the square added together.

Squares have 4 sides so divide the perimeter by 4 to find the length of 1 side.

79.04 / 4 = 19.76 is the length of one side.

Half of 19.76 is 9.88 so the radius of the circle is 9.88 cm.

Hope this helps!

Answer:

  B  -4.5

Step-by-step explanation:

You want the solution to 2(x -9) = 9/(-1/3).

Simplifying the equation gives us ...

  2x -18 = -27

  2x = -9 . . . . . . . add 18

  x = -4.5 . . . . . . . divide by 2

The value -4.5 for x will make the equation true.

Draw a flower

Draw a cupcake

Draw a butterfly

Draw a tree

Draw a cartoon character

Draw a heart

Draw a cat

Draw a sun

Draw a bird

Draw a landscape

Draw a cloud

Draw a house

Draw a star

Draw a fish

Draw a snowman

Draw a rainbow

Draw a car

Draw a dog

Draw a person

Draw a fruit

Remember, practice makes perfect! So, keep practicing and exploring your creativity.

Answer: sm1 took my answer down but yes draw a cartoon character or something similar to an old school drawing try giving the character a new look something u never drawn before

Step-by-step explanation:

Answer:

Not a function

Step-by-step explanation:

For this to be a function there can not be 2 of the same x values.

Our points for this are (−2, −5), (−1, −3), (−2, 6), (5, 7)

Your x value is the number on the left side of the point=

When we look at our points we see that -2 is repeating for (-2,-5) and (-2,6)

If we plot these points on a graph and use the vertical line test we see that our line passes thru the 2 points.

So this is not a function  

(a) It is possible to form a triangle with the angle measures, 30°, 80°, 70°

It is not possible for all such triangles to be congruent.

(b) It is possible to form a triangle with the angle measures, 20°, 105°, 55°

It is not possible for all such triangles to be congruent.

(c) It is not possible to form a triangle with the side lengths, 4cm, 3cm, 8cm

(d) It is possible to form a triangle with these side lengths.

All such triangles are congruent

From the question, we are to determine if it is possible for a triangle to have the given angle measures or side lengths

(a) To determine if a triangle can have the angle measures 30°, 80°, and 70°, we add the angles together to see if they equal 180°, the total degrees of a triangle.

30° + 80° + 70° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures.

It is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(b) To determine if a triangle can have the angle measures 20°, 105°, and 55°, we add the angles together to see if they equal 180°.

20° + 105° + 55° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures. However, it is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(c) To determine if a triangle can have side lengths 4cm, 3cm, and 8cm, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

4cm + 3cm > 8cm

4cm + 8cm > 3cm

3cm + 8cm > 4cm

Since all three inequalities are not satisfied (4 + 3 = 7 is not greater than 8, which is the longest side), it is not possible to form a triangle with these side lengths.

(d) To determine if a triangle can have side lengths 8cm, 15cm, and 17cm, we apply the triangle inequality theorem.

8cm + 15cm > 17cm

8cm + 17cm > 15cm

15cm + 17cm > 8cm

Since all three inequalities are satisfied, it is possible to form a triangle with these side lengths.

All such triangles are congruent, since these side lengths satisfy the conditions for a unique triangle known as a Pythagorean triple.

Hence, the triangle with side lengths 8cm, 15cm, and 17cm is a right triangle, and all right triangles with these side lengths are congruent by the Pythagorean theorem.

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The total number of participants in all the activities is represented by the expression 5.5s + 11.

The given information about the number of participants in each activity can be represented in the following table:

ActivityNumber of ParticipantsGolfing3(s-2)Snorkeling s Parasailings+14Surfing(1)/(2)(s+5)

To find the total number of participants in all the activities, we can add the number of participants in each activity:

Total number of participants = 3(s-2) + s + (s+14) + (1)/(2)(s+5)

Simplifying the expression gives:

Total number of participants = 5.5s + 11

Therefore, the total number of participants in all the activities is represented by the expression 5.5s + 11.

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The correlation coefficient relating is 0.76 thath mean  the accompaniment rates for wives and sons is the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

To find the correlation coefficient relating the accompaniment rates for wives and sons, we can use the formula:

r = (nΣxy - (Σx)(Σy)) / √[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

Where:
- r is the correlation coefficient
- n is the number of observations (in this case, 9)
- x and y are the accompaniment rates for wives and sons, respectively
- Σxy is the sum of the products of x and y
- Σx and Σy are the sums of x and y, respectively
- Σx^2 and Σy^2 are the sums of x squared and y squared, respectively

Using the data from the table, we can calculate the following:

Σx = 27.2 + 40.1 + 35.7 + 37.8 + 38 + 38.4 + 38.7 + 29.8 + 23.8 = 309.5
Σy = 2.2 + 1.5 + 0.3 + 3.5 + 5.4 + 11 + 11.9 + 8.6 + 7.4 = 51.8
Σxy = (27.2)(2.2) + (40.1)(1.5) + (35.7)(0.3) + (37.8)(3.5) + (38)(5.4) + (38.4)(11) + (38.7)(11.9) + (29.8)(8.6) + (23.8)(7.4) = 1164.41
Σx^2 = 27.2^2 + 40.1^2 + 35.7^2 + 37.8^2 + 38^2 + 38.4^2 + 38.7^2 + 29.8^2 + 23.8^2 = 11491.89
Σy^2 = 2.2^2 + 1.5^2 + 0.3^2 + 3.5^2 + 5.4^2 + 11^2 + 11.9^2 + 8.6^2 + 7.4^2 = 349.98

Plugging these values into the formula, we get:

r = (9)(1164.41) - (309.5)(51.8) / √[(9)(11491.89) - (309.5)^2][(9)(349.98) - (51.8)^2] = 0.76

This value of r indicates a strong positive correlation between the accompaniment rates for wives and sons. This means that as the accompaniment rate for wives increases, the accompaniment rate for sons also tends to increase.

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Answer:

4y^2 - 12y + 9

Step-by-step explanation:

(3-2y)^2 = (3-2y) (3-2y)

Distribute:

3(3) + (3)(-2y) + (-2y)(3) + (-2y)(-2y)

= 9 -6y -6y +4y^2

Combine like terms:

4y^2 -12y + 9

I hope this helps!

Answer:

9 - 12y + 4y²

Step-by-step explanation:

(3 - 2y)²

= (3 - 2y)(3 - 2y)

each term in the second factor is multiplied by each term in the irst factor, that is

3(3 - 2y) - 2y(3 - 2y) ← distribute parenthesis

= 9 - 6y - 6y + 4y² ← collect like terms

= 9 - 12y + 4y²

The expression [tex]20.x^25y^3+4x[/tex] is a polynomial of degree 25 and it is a binomial.

A polynomial is an expression made up of variables and coefficients, combined using addition, subtraction, and multiplication, with no division by a variable. In this expression, we have two terms, [tex]20.x^25y^3[/tex] and 4x, which are combined using addition.

Since the degree of a term is the sum of the exponents of its variables, the degree of the first term is 25 (the sum of the exponents of x and y), and the degree of the second term is 1 (the exponent of x). Since this is a polynomial with only two terms, it is a binomial.

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The variables to use in a model depend on the type of model being developed and the problem being addressed. In general, variables are the inputs to a model that are used to predict the outputs or dependent variables.

In statistical models, the independent variables, also known as predictors or features, are chosen based on their ability to explain the variability in the dependent variable. For example, in a linear regression model, the independent variables may include factors such as age, income, education, and gender, which are thought to be related to the dependent variable, such as the likelihood of purchasing a product.

In machine learning models, the variables may include a wide range of features, such as text, images, or sensor data, that are used to make predictions or classifications. The process of selecting the most relevant features, also known as feature selection, is an important step in developing effective models that can generalize well to new data.

Ultimately, the choice of variables depends on the specific problem being addressed, and may involve a combination of domain expertise, statistical analysis, and machine learning techniques to identify the most important predictors or features.

P.S: An overview was given as your information is incomplete.

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[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} x=400\\ y=10 \end{cases} \\\\\\ 10=k(400)\implies \cfrac{10}{400}=k\implies \cfrac{1}{40}=k\hspace{5em}\boxed{y=\cfrac{1}{40}x} \\\\\\ \textit{when x = 450, what's "y"?}\qquad y=\cfrac{1}{40}(450)\implies y=\cfrac{45}{4}[/tex]

Jose is in the quadrant 4 as his coordinates are (-2, -3).

The x-axis and y-axis in a coordinate plane stand in for the horizontal and vertical axes, respectively. Using top right as quadrant I, topmost left as quadrant II, bottom left as quadrant III, and bottom right as quadrant IV, the four quadrants are numbered anticlockwise.

The given coordinates are:

Cameron = (-3, 2)

Neveah = (2, -3),

Jude = (2,3) and

Jose is at (-2, -3).

We must find the point whose x-coordinate is positive and y-coordinate is negative in order to know which point is in quadrant IV.

Hence, Jose is in the quadrant 4 as his coordinates are (-2, -3).

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4/11

The probability of choosing a green marble followed by a brown marble is 4/11. Simple probability is the likelihood that an event occurs, and in this case the likelihood is 4/11. This is calculated by taking the total number of green marbles (4) divided by the total number of marbles in the jar (11).

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The solution is, volume of cone is  =113.10.

The formula for the volume of a cone is ⅓ r^2h cubic units, where r is the radius of the circular base and h is the height of the cone.

here, given that,

a cone having a radius of 3 inches

and the height of 12 inches.

now, we have to find the volume of the cone having a radius of 3 inches and the height of 12 inches.

we know that,

Volume =  ⅓ r²h

now, substituting the values of r = 3 & h = 12, in formula of volume,

we get,

            V =1/3  9 * 12

             =113.10

Hence, volume of cone is  =113.10

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The scenario that does not represent an impulse purchase is: Melissa goes to get an oil change for her car but decides to save the $60 and ask her brother to do the oil change for free.

An impulse purchase is an unplanned purchase made on the spur of the moment, without much consideration or planning. In the first scenario, Melissa goes to get an oil change but then decides to have her car windows tinted for $300, which is an additional expense that she had not planned for. This is an impulse purchase.

In the second scenario, Melissa goes to get an oil change but then decides to spend $500 on new car stereo speakers, which is again an additional expense that she had not planned for. This is also an impulse purchase.

However, in the third scenario, Melissa decides to save the $60 and ask her brother to do the oil change for free. This decision does not involve any additional expense or impulse purchase. Instead, it is a planned decision to save money by getting the oil change done for free. Therefore, this scenario does not represent an impulse purchase.

Answer:

Below

Step-by-step explanation:

The last choice is not an impulse purchase.....it is not a purchase at all.

  the first two ARE impulse purchases.... she purchases something for which she initially had no intention.

Answer:

To determine whether the given triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

side a = 40 inches

side b = 75 inches

side c = 85 inches (the longest side)

Now we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

85^2 = 40^2 + 75^2

7225 = 1600 + 5625

7225 = 7225

Since the equation is true, we can conclude that the given triangle is a right triangle.

Answer: yes

Step-by-step explanation:

To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.

a^2 + b^2 = c^2

c is the hypotenuse, the longest side of a right triangle.

a and b are the legs of the right triangle.

40²+75²=85²

1600+5625=7225

7225=722

Ben's ball lands approximately 2.5 seconds after Andrew's ball.

Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:

h(t) = -5t² + vt + h0

where;

Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:

h_max2 = 1.5h_max1

At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):

t_max1 = v₁ / (2 x 5)

t_max2 = v₂ / (2 x 5)

Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:

h_max2 = 1.5h_max1

-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)

Simplifying this equation, we get:

-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1

We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:

h(4) = -5(4)² + v1 * 4 = 0

-80 + 4v1 = 0

v1 = 80/4

v1 = 20 m/s

Solving these equations for t_max2 and v2, we get:

t_max1 = v1 / (2 x 5)

t_max1 = 20 / (2 x 5)  = 2 s

t_max2 = 1.5 * t_max1 = 3 s

v2 = 1.5 * v1 = 30 m/s

To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.

We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:

-5t² + v₂t = 0

-5t² + 30 = 0

5t² = 30

t² = 30/5

t² = 6

t = √6

t = 2.5 s

Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.

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Answer:

Step-by-step explanation:

Let's use the variable "a" to represent the number of stamps Angela has.

From the problem, we know that Nicolas has 48 stamps, and that this is 2 times 5 less than the number of stamps Angela has. "2 times 5 less than the number of stamps Angela has" can be written as:

2(a - 5)

So the equation that relates the number of stamps Nicolas and Angela have is:

48 = 2(a - 5)

We can simplify this equation by first distributing the 2:

48 = 2a - 10

Then, we can add 10 to both sides of the equation:

58 = 2a

Finally, we can solve for a by dividing both sides by 2:

a = 29

Therefore, the equation we can use to find the number of stamps Angela has is:

2(a - 5) = 48

or, simplified:

a = 29

The midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \)[/tex].

To find the midpoint of a line segment, we can use the midpoint formula: [tex]\[ M=\left( \frac{x_1+x_2}{2})[/tex], [tex]\frac{y_1+y_2}{2} \right) \][/tex] where [tex]\( x_1 \)[/tex] and [tex]\( y_1 \)[/tex] are the coordinates of point [tex]\( A \)[/tex], and [tex]\( x_2 \)[/tex] and [tex]\( y_2 \)[/tex] are the coordinates of point[tex]\( B \)[/tex].

Plugging in the values from the given points, we get: [tex]\[ M=\left( \frac{4+(-6)}{2},\frac{4+(-4)}{2} \right) \][/tex]

Simplifying the fractions gives us: \[ M=\left( \frac{-2}{2},\frac{0}{2} \right) \]

Finally, we can simplify further to get our final answer:[tex]\[ M=(-1,0) \][/tex]

Therefore, the midpoint [tex]\( M \)[/tex] of the line segment joining the points [tex]\( A=(4,4) \)[/tex] and [tex]\( B=(-6,-4) \)[/tex] is [tex]\( M=(-1,0) \).[/tex]

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The correct equation that describes the relationship in the table is option B, which is y = x2 + 3.

An equation is a mathematical statement that expresses the relationship between two or more variables. Equations are used to solve problems and represent real-world relationships.

To understand why this is the correct equation, it is important to look at the values of x and y in the table. When x increases by one, the value of y increases by the same amount. This indicates that the relationship between x and y is one of direct proportionality, wherein the value of y is directly proportional to the value of x. This can be expressed mathematically as y = kx, where k is a constant.

We can also look at the values of x and y in the table to determine the value of k. When x increases from 2 to 3, the value of y increases from 7 to 17. This means that k = 10. This can be written as y = 10x.

The value of y when x = 0 is 3, which is the constant term. This can be written as y = 10x + 3.

Therefore, the equation that describes the relationship in the table is y = x2 + 3.

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Answer:

1.5 quarts/ounce

Step-by-step explanation:

I'll assume the question wants to know the simplified conversion factor for quarts and ounces.

((3/4)quart)/((1/2)oz))

Can be rewritten as:

(3/4)/(1/2) (quart/oz)

(3/4)/(1/2) can be written as:  (3/4)*(2/1)  [Invert the denominator and multiply]

(3/4)*(2/1) = (6/4)

(6/4) = (3/2)

(3/2) [or 1.5] quarts/ounce