find lim x approaches 3
f(x) = x^2 - 2
f(x) = -3x + 15. x> 3

The vertex form of the equation of a parabola is equal to y + 1 = - (1 / 12) · (x - 2)².

In this problem we need to determine the equation of a parabola, this can be done by knowing the distance between vertex and focus and the coordinates of the focus. The vertex form of the equation of the parabola is:

y - k = [1 / (4 · p)] · (x - h)²

Where:

If we know that (h, k) = (2, - 1) and p = - 3, then the equation of the parabola in vertex form is:

y + 1 = - (1 / 12) · (x - 2)²

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Answer:

[tex](x-2)^2=-12(y+1)[/tex]

Step-by-step explanation:

From observation of the given diagram, we can see that the graphed conic section is a vertical parabola that opens downwards, with a vertex at (2, -1) and a focus at (2, -4).

The equation of a vertical parabola in standard form is:

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a vertical parabola}\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k + p)$\\\end{minipage}}[/tex]

Given the vertex is (2, -1):

Given the formula for the focus is (h, k+p), then:

[tex]\begin{aligned}(h, k+p)&=(2, -4)\\(2,-1+p)&=(2,-4)\\\\\implies -1+p&=-4\\p&=-4+1\\p&=-3\end{aligned}[/tex]

To write the equation of the graphed conic section, substitute the found values of h, k and p into the standard formula:

[tex](x-2)^2=4(-3)(y-(-1))[/tex]

[tex](x-2)^2=-12(y+1)[/tex]

Therefore, the equation of the graphed conic section is:

[tex]\boxed{(x-2)^2=-12(y+1)}[/tex]

Answer: 7 and -4

Step-by-step explanation:

Coefficients are numbers in front of variables

6 doesn't have a variable so it's a constant

7 and -4 are the coefficients

Consignment cab be used as an option for selling the clothing

Consignment involves providing your goods to an established business, like a boutique or vintage store, which then sells the items on your behalf and takes a cut of the profits. This approach lets Drew benefit from the store's customer base and avoids the need to manage a storefront.

Mail order (option a) could also work if Drew is willing to manage shipping and handling, and has a method for advertising the products effectively without a physical or online storefront.

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The coordinates of V' include the following: V' (-5, -10).

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.

In this scenario an exercise, we would dilate the coordinates of V at (-2, -4) by applying a scale factor of 2.5 that is centered at the origin as follows:

V (-2, -4) → V' (-2 × 2.5, -4 × 2.5) = V' (-5, -10).

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The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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

First = tan(θ)

Second = cos(θ)

The basis trigonometry identity is

sin²(θ) + cos²(θ) = 1

Divide through the equation by cos²(θ)

So, we have

tan²(θ) + 1 = 1/cos²(θ)

Subtract 1 from both sides

tan²(θ) = - 1 + 1/cos²(θ)

Take the square root of both sides

tan(θ) = √[-1 + 1/cos²(θ)]

Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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Answer:

8) b. 15 m²

9) c. 63.5 ft²

Step-by-step explanation:

Area of composite figure:

8) To find the area of the composite figure, we have to add the area of rectangle, area of the top triangle and the area of the below triangle.

Rectangle:

            length = 3m

            width = 2.5 m

          [tex]\boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                           = 3 * 2.5

                                           = 7.5 m²

Area of triangle:

              [tex]\boxed{\text{\bf Area of triangle =$ \dfrac{1}{2}*base*height$}}[/tex]

       Triangle1:

                    base = 3 m  ; height = 1.5 m

                   [tex]\sf Area \ of \ triangle1 = \dfrac{1}{2}*3*1.5[/tex]

                                             [tex]= 2.25 \ m^2[/tex]

       Triangle2:

               base = 3 m ; height = 2.5 + 1 = 3.5 m

               [tex]\sf Area \ of \ triangle2 = \dfrac{1}{2}*3*3.5[/tex]

                                          = 5.25 m²

Area of the figure = 7.5 + 2.25 + 5.25

                               = 15 m²

_______________________________________________________

9) To find area of the given area, add the area of rectangle1 and area of rectangle2.

      length = 5 ft ;  width =  5.5 ft

Rectangle1:

         Area of rectangle1 = 5 * 5.5

                                         = 27.5 ft²

Rectangle2:

           length = 8ft

           width = 10 - 5.5

                      = 4.5 ft²

           Area of rectangle2 = 8 * 4.5

                                           = 36 ft²

Area of the given figure = area of rectangle1 + area of rectangle2

                                       = 27.5 + 36

                                        = 63.5 ft²

The division of x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 will have a quotient of x⁴ + 9x² + 9 and a remainder of -1 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall divide x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 as follows;

x⁵ divided by x equals x⁴

x - 1 multiplied by x⁴ equals x⁵ - x⁴

subtract x⁵ - x⁴ from x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 will give 9x³ - 9x² + 9x - 10

9x³ divided by x equals 9x²

x - 1 multiplied by 9x² equals 9x³ - 9x²

subtract 9x³ - 9x² from 9x³ - 9x² + 9x - 10 will give 9x - 10

9x divided by x equals 9

x - 1 multiplied by 9 equals 9x - 9

subtract 9x - 9 from 9x - 10 will give us a remainder of -1

Therefore by synthetic division, x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 divided by x - 1 will result to a quotient of x⁴ + 9x² + 9 and a remainder of -1.

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The correct equation to determine the area, A, of the patio that will be painted is,

D. A = (x + 25)(x + 15) - 30

We have to given that;

Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted.

Here, rectangle with a length of x plus 25 and width of x plus 15 with a rectangle.

And, in the bottom right corner labeled bench that has a length of 10 and width of 3.

Hence, Area of rectangle is,

A = (x + 25) (x + 15)

And, Area of bottom right corner is,

A = 10 x 3

A = 30

Thus, The equation to determine the area, A, of the patio that will be painted is,

⇒ A = (x + 25)(x + 15) - 30

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3a. 60

3b. 4

3c. It means that the individual speeds of the trucks are pretty close to the mean.

4. The temperature is not very consistent.

5. The values in the data set are close together, and the mean is pretty consistent.

6. Evelyn and Nova are correct

Pls give brainliest

Answer:

3a. 60

3b. 4

3c. represents the difference in speed from the mean, or data is close to mean

4. The temps are not consistent, data varies a lot

5. It means that the data does not vary much, data is basically exactly the same as the mean.

6. evelyn, nova

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Answer:

  (c)  B'(3, -2); C'(7, 8); D'(-5, -1)

Step-by-step explanation:

Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.

The reflection in the line y = x has the effect of swapping the x- and y-coordinates:

  (x, y) ⇒  (y, x)

No sign changes are involved.

The reflected coordinates are ...

  B'(3, -2); C'(7, 8); D'(-5, -1)

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The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

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The least common denominator will be (x-1)(x²-1).

When two or more fractions have the same denominators, they are termed as the common denominators.

The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.

For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.

The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.

Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,

So,

-2x/x-1 + x+3/x²-1

Taking the LCM,

-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).

Hence the least common denominator will be (x-1)(x²-1).

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The likelihood of  profit and loss in the following week is 18.75%. The Option D is correct.

A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.

To get  probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.

The probability of making a profit in one week is 0.75

The probability of making a loss in the following week will be:

= 1 - 0.75

= 0.25.

So, probability of the company making a profit in one week and then making a loss in the following week is:

= 0.75 * 0.25

= 0.1875

= 18.75%.

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The author references a couple of situations that occured in the country and are occuring presently, justified by laws, which reduces the ability of social minorities to vote.

The author of this article cites several laws passed in states that make it harder for minorities, especially blacks, to vote regularly. He said that even after an amendment was passed allowing blacks to vote, he passed other laws preventing blacks from voting, such as requiring voter education.

These laws were enacted with increasing force until the passage of the Civil Rights Act in the 1960s.

Every year since civil rights, different laws have been passed making it harder for blacks, women, the working class, and homosexuals to vote among other members of social minorities. Many of these laws are still in effect.

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The outcome of 4 occurred 3 more times than expected. This is the resulting probability. Therefore, the correct option is option A.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which anything is probable to happen is basically what probability means. The outcome of 4 occurred 3 more times than expected.

Therefore, the correct option is option A.

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Sharon is correct in classifying the shape as a square, rectangle, and quadrilateral.

The shape satisfies the criteria for each classification: it has equal sides and right angles, making it a square; it has right angles, making it a rectangle; and it has four sides, making it a quadrilateral. Therefore, the shape can be accurately described and categorized using all four classifications.

Moreover, as a quadrilateral, this shape satisfies the general criteria of having four sides. Its defined boundaries encompassing an enclosed area are emblematic of a quadrilateral.

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Okay, let's break this down step-by-step:

* The distance between Marisa's house and the post office is 720 m

* Marisa walks at an average speed of 80 m/min

* To calculate the time:

** Distance / Speed = Time

** 720 m / 80 m/min = 9 minutes

Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.

The answer is C. Mean, because Desert Landing is symmetric.

A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.

To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the Mean, which measures the spread of the middle of the data.

The answer is C. Mean, because Desert Landing is symmetric. depending on the shape of the distributions. If the temperature data in Desert Landing is symmetric, then the Mean would be appropriate to measure the spread of the data. If the temperature data in Sunny Town is skewed, then the Mean would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.

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The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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After 1 second the football is 24.5 meters.

Given that, a football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +2.4

a) Here, t=1

Now, h =-4.9(1)²+27(1)+2.4

= -4.9+27+2.4

= 24.5 meters

b) Given that, h=30 meter

30=-4.9t² +27t +2.4

30+4.9t²-27t-2.4=0

4.9t²-27t+27.6=0

Factor and set each factor equal to zero.

Exact Form:

t=(135+√4701)/49, (135−√4701)/49

Decimal Form:

t=4.15436405…, and 1.35584002...

c) To find maximum height, set h=0

-4.9t² +27t +2.4=0

Factor and set each factor equal to zero.

Exact Form:

t=(135+√19401)/49, (135−√19401)/49

Decimal Form:

t=5.59770352…,−0.08749943…

Therefore, after 1 second the football is 24.5 meters.

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Cone - A cone is a three-dimensional geometric object used in mathematics that smoothly taper from a flat, typically circular base to a point known as the apex or vertex.

The following is the formula for a cone's volume:

[tex]V = (1/3)πr^2h[/tex]

where the volume is [tex]V[/tex], the radius is [tex]r[/tex], and the height is [tex]h[/tex].

In putting the values provided yields:

[tex]48 = (1/3)πr^2(9)[/tex]

By dividing both sides by [tex]3[/tex], we arrive at:

[tex]144/π = r^2(9)[/tex]

When we multiply both sides by [tex]9[/tex], we get:

[tex]16/π = r^2[/tex]

When we square the two sides, we obtain:

[tex]r = √(16/π)[/tex]

(Rounded to two decimal places) [tex]r = 2.52 feet[/tex]

As a result, the radius is roughly [tex]2.52 feet.[/tex]

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The mean monthly income is $3300, the median monthly income is $3000, there is no mode, and the range of the monthly income is $3000.

To find the mean, median, mode, and range of the monthly incomes, we'll perform the following calculations:

Mean:

The mean is calculated by summing all the values and dividing by the total number of values.

Mean = (2000 + 2500 + 3000 + 4000 + 5000) / 5

Mean = 16500 / 5

Mean = 3300

The mean monthly income is $3300.

Median:

The median is the middle value when the data is arranged in ascending order. In this case, since we have an odd number of values, the median is the middle value.

Arranging the incomes in ascending order: $2000, $2500, $3000, $4000, $5000

The median monthly income is $3000.

Mode:

The mode is the value(s) that appear most frequently in the data. In this case, there is no value that appears more than once, so there is no mode.

The data has no mode.

Range:

The range is calculated by subtracting the minimum value from the maximum value.

Range = Maximum Value - Minimum Value

Range = $5000 - $2000

Range = $3000

The range of the monthly income is $3000.

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The complete question is as follows:

Mean, Fractiles, median, and mode are called the measures of central tendency. A group of friends recorded their monthly incomes in dollars. The incomes are as follows: $2000, $2500, $3000, $4000, $5000. Determine the mean, median, mode, and range of their monthly incomes.

The expression has no solution when k < - 5.

Hence, option B is correct.

The given inequality is

|2x + 7|-k ≤ 5

We know that,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.

A function with absolute values is another name for it.

No matter what input was provided to this function, the outcome is always favorable.

Now adding k both sides of inequality,

⇒ |2x + 7| ≤ 5 + k

When we take value of k less than -5

Then the expression |2x + 7| becomes negative.

Since it always gives absolute value,

Therefore,

There is no any solution when k < -5.

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The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2y+ 3/2x + 7/4

On simplifying , we get

A = ( -4y + 3 )/2x + 7/4

Taking LCM on both sides , we get

A = ( -16y + 12 + 7 ) / 8x

Hence , the expression is A = ( -16y + 12 + 7 ) / 8x

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All the values of a 12-sided die will be represented by two 6-sided die. The probability of rolling a 7 on the 12-sided die is 1/12 and rolling a sum of 7 on the two 6-sided dice will be 1/6.

The 12-sided die which is dodecahedral consists of numbers up to 12. The 6-sided die consists of numbers up to 6. The suggestion of using two 6-sided dice instead of a 12-sided die will make a difference in the probabilities of a specific outcome.

Although, using a pair of 6-sided dice and adding their scores will represent all the values or outcomes you can get in a 12-sided die but still there will be a difference in the probabilities.

If we find the probability of rolling 7 on the 12-sided die, then it will be 1/12.

But, in the case of two 6-sided dice, we will obtain the sum of 7 in 6 outcomes which are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of outcomes, in this case, is 36.

Therefore, the probability of rolling a sum of 7 on the two 6-sided dice will be 6/36   =  1/6.

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Answer:

Step-by-step explanation:

For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:

t = 27n + 18

In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.

The margin of error for the two-proportion 95% confidence interval is 0.0662.

The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:

ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)

where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.

Using the given information, we have:

Sample 1: n₁ = 250, p₁ = 0.90

Sample 2: n₂ = 275, p₂ = 0.85

Level of confidence: 95%

Substituting these values into the formula, we get:

ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]

ME = 0.0662

Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.

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Since angles M and P are complementary, if m∠M = 3x - 45 and m∠P = 2x + 15, the value of x is 24
and the value of M and P are   27° and 63°   respectively.

Since M and P are complimentary, that means the sum of them is = 90°

So
3x - 45 + 2x + 15 = 90

Taking like terms

3x + 2x = 90 + 45 -15
5x = 120
x = 120/5

x = 24

to find M and P

since m∠M = 3x - 45

m = 3(24) -45

m = 27°

m∠P = 2x + 15

since x = 60

P = 2(24) + 15

P = 63°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Angles M and P are complementary. If m∠M = 3x - 45 and m∠P = 2x + 15, what is the value of x? What is the measure of each angle?

The simplified form of 5x³y (2x + 3y - 4) will be 10x⁴y + 15x³y² - 20x³y.

Given that:

Expression, 5x³y (2x + 3y - 4)

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Simplify the expression, then we have

5x³y * 2x + 5x³y * 3y - 5x³y * 4

10x⁴y + 15x³y² - 20x³y

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