3. Determine how many real solutions the quadratic equation has. x2 + 6x + 8
A. One solution
B. Two solutions
C. No solutions​

If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.

Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:

m₁ × m₂ = -1

Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;

m₁ × m₂ = -1

2 × m₂ = -1

Slope, m₂ = -1/2.

In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.

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The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression is

[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]

Now factories p²- 4p -12, p²-9p+18, and 6p + 12:

p²- 4p -12

= p²- (6 - 2)p -12

= p²- 6p + 2p -12

= p(p - 6) + 2(p - 6)

=(p - 6)(p + 2)

p²- 9p + 18

= p²- (6 + 3)p + 18

= p²- 6p -3p + 18

= p(p - 6) -3(p -6)

=(p - 6)(p - 3)

6p + 12

=6(p+2)

Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:

[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]

Multiply the denominator with denominator and numerator with numerator:

= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)

Now cancel out (p+2)(p - 6) from denominator and numerator:

= 18p/ 6(p - 3)

Divide denominator and numerator by 6:

= 3p/ (p - 3)

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Any line perpendicular to line C must have a slope equal to -3/2.

A general linear equation is written as:

y = a*x + b

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

Two linear equations are perpendicular if the product between the slopes is -1, then if the slope of the line perpendicular to line C is x, then we can write:

x*(2/3) = -1

Solving for x we get:

x = -3/2

That is the slope of the perpendicular line.

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The sum of both accounts' expression in its most basic form is 55w + 145.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the instructions given in the question,

Amount in savings account = 10w + 120

Amount in checking account = 45w + 25

Then, total money shaved each week will be,

(10w + 120) + (45w + 25)

10w + 45w + 120 + 25

= 55w + 145

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The next three numbers that would be generated are 13, 37, and 109.

Formula is a mathematical expression that is used to calculate the value of a particular quantity, such as a number, a quantity of a certain type of material, or a number of elements. The most common form of a formula is an equation, which contains two or more variables and is written in the form of a mathematical expression. Formulas are used in many disciplines, including physics, chemistry, engineering, and economics, to solve problems and determine relationships between quantities.
This is because the formula applies the operation of multiplying the current number by 3 and then subtracting 2. Applying this formula to 5 gives 13, and then applying the formula to 13 gives 37, and so on. The resulting sequence is 5, 13, 37, 109, and so on. This is a simple PRNG that can be used to generate sequences of random numbers.

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Answer:

29 is the correct answer

Answer:

A:Infinite solutions

Step-by-step explanation:

1.2 ( 3x + 5 ) = 3.6x + 6

1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6

3.6x + 6 = 3.6x + 6

Answer: A

Step-by-step explanation:

The perimeter of the figure with side length of 5 units is 50 units

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

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

Substitute the known values in the above equation, so, we have the following representation

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Alona is using a quantitative approach to her studies.

The goal of quantitative research is to quantify the data collection and processing process.

It is based on a deductive method that emphasizes the validation of the hypothesis and is influenced by positivist and empiricist theories.

This research technique, which is related to the natural, applied, formal, and social sciences, encourages the unbiased empirical exploration of observable phenomena to test and comprehend correlations.

This is accomplished using a variety of quantification techniques and procedures, demonstrating the wide application of this approach as a research strategy across numerous academic fields.

So, in the given situation, Alona is using the quantitative research method.

Therefore, Alona is using a quantitative approach to her studies.

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Answer:

To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles.

So to convert 54.74 kilometers to miles, you can multiply 54.74 by 0.621371:

54.74 kilometers * 0.621371 miles/kilometer = 34.09 miles

Rounded to the nearest whole number, this is 34 miles.

Step-by-step explanation:

Answer:

To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles. To convert 54.74 kilometers to miles, you can multiply the number of kilometers by the conversion factor:

[tex]54.74 kilometers * 0.621371 miles/kilometer = 34.08 miles[/tex]

Rounded to the nearest whole number, there are approximately 34 miles in 54.74 kilometers.

Step-by-step explanation:

Answer:

15/14 or 1 1/14

Step-by-step explanation:

multiple the numerators and deno

3x5=15

7x2=14

15/14 or 1 1/14

Answer:

Step-by-step explanation:

Exact form

15/14

Decimal Form:

1.07142857........

mixed number is

1, 1/14

Answer:  C. The width of the bar representing dogs is more than the widths of the other bars.

Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.

Answer:

D

Step-by-step explanation:

slope of the given line :

(-4-2)/(-1-4)

-6/-5

6/5

slope of a perpendicular line : -5/6

y-7 = -5/6 (x-(-3)

y -7 = -5/6 (x+3)

y -7 = -5/6 x - 5/2

5/6 x + y - 7 + 5/2 = 0

5/6 x + y + (-14 + 5)/2 = 0

5/6 x + y - 9/2 = 0

5x + 6y - 27= 0

5x + 6y = 27

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )

m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (- 3, 7 ) into the partial equation

7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]

y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form

multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions

6y = - 5x + 27 ( add 5x to both sides )

5x + 6y = 27 ← equation of perpendicular line in standard form

Answer:

point

vertex

one

face

face

circular

length

area

volume

In the given figure QT is of 16 units.

A line segment has two end points unlike a line which can extend indefinitely in both the directions.

According to the given question S is between Q and T and R is the midpoint of QS. RS=4 And RT= 12 we have to find QT.

As R is the midpoint of QS It will be twice of RS which

= 8 units.

And if RS is 4 units then QR is also 4 unit as R is the midpoint.

QT = QR + RT.

QT = 4 + 12

QT = 16 units.

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Therefore at $5 you selling 15 mugs will generate the maximum revenue.

In discrete mathematics, a graph is made up of points called vertices, and the connecting lines between them are called edges. Simple graphs, linked and unconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and linked and unconnected graphs are only a few of the numerous varieties of graphs.

Here,

For $0 for , 50 mugs be sold

For $10 for , 0 mugs be sold

Thus, from graph

1)  Slope= 50/-10 =-5

2) m(p)= -5(p-10) =-5p +10

=> m(p) =10 -5p

3)Revenue R(p) = m(p)

R(p) = 10 -5p

4) point(5,15)

5) at price p =0 , p=5 , we do not make any money

6)At $5 most revenue is made

7)when p=5

R(p) = 10 -5(5)

R(p) = 15

Thus , 15 coffee mugs will yield max revenue

8)Max revenue = $45

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Answer:

2, 13, 103

Step-by-step explanation:

These prime numbers are the ones.

2678 = 2 * 13 * 103

A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example,  3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.

So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.

A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.

The answer is -

    2678 = 2 * 13 * 103

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Answer:

84

Step-by-step explanation:

EFD is an iscosilies triangle therefore angle F = angle D = 48

and therefore angle E= 180-48-48=84

The volume of the solid you (the region) create by spinning about the x-axis is V = 225units³

Depends whether it is a solid with sides, height, and depth. In this case it is the multiplicarion of the three to get the volume.

If it is an irregular shaped object it is done by water displacement. Fill a container with a known amount of water, immerse the object, and the difference in volume in the water is the volume of the object.

Break the volume down into prisms and pyramids that you can calculate the volume of and sum the pieces up to get the total volume. If the shape has curved surfaces, it gets much more complicated.

This gives a y = 15

                   x = 3

The straight line equation will be y = 5x

The volume of a pyramid is given by the following equation:

where r = radius of the base

          h= height of the cone

from the graph, roating about the x - axis gives h = 3, r = 15

Volume =

            = 225  units³

Volume of cone formed is 225  units³.

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Answer:

D

Step-by-step explanation:

D. If it's not D, C. It's a negative slope with a negative y-intercept of -1

Answer:

-48 ft.

Step-by-step explanation:

-76+28= -48

Hope this helps! Had this on one of my quizzes

Answer:

-48 espero te sirva perdon por llegar tarde

Answer:

Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)

B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution

Step-by-step explanation:

Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)

B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution

The correct characterization of the limit distribution and other Questions are answered in the following steps.

For the first question, the distribution of (An-a) is approximated best by N(0, n) because the variance of the sample mean of i.i.d. standard normal variables is 1/n.

For the second question, since An converges in probability to a constant, Bn = 4An also converges in probability to 4a. Therefore, the sequence of random variables (Bn-b) does converge in distribution.

For the third question, the limit distribution of (Bn-b) is N(0, 4^2 * n) because the variance of the product of a random variable and a constant is the constant squared times the variance of the random variable.

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Two urns contains different numbers of different colour balls. Two balls are randomly chosen from both of urns. The probability that two red balls are choosen is 1/3..

We have given that

First Urn, u₁ contains 3 Red( labelled r₁,r₂,r₃) ; 1 blue ball ,(labelled b₁).

Total number of balls in urn, u₁ = 4 balls

Second Urn, u₂ contains 2 red (labelled r₄,r₅) and 2 blue (labelled b₂, b₃) .

Total number of balls in urn, u₂ = 4 balls

Assume , A = first urn , u₁ is selected

Assume, B = Second urn u₂ is selected

Assume , R = selected balls are red

Case 1 : Urn u₁ is choose and two balls without replacement are withdraw.

Probability to choose the first urn, P(A) = 1/2

Probability that the two withdraw without replacement balls are red in colour, P(A/R)

= 3/4 × 2/3 = 1/2

Case 2 : Urn u₂ is choose and two balls without replacement are withdraw.

Probability to choose the second urn, P(B) = 1/2

Probability that the two without replacement withdraw balls are red in colour, P(B/R)

= 2/4 × 1/3 = 1/6

The required probability= P(A) P(A/R) + P(B)P(B/R) = 1/2(1/2) + 1/2(1/6) = 1/4 + 1/12

= 4/12 = 1/3

Hence, the required probability is 1/3..

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Complete question:

One urn u1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn u2 contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. Probability that two red balls are choosen.

The line that is an irregular line of a blank verse is A . “ He only says , ‘Good fences make good neighbours. ”

The irregularity of the line is that it has 11 syllables while other lines have 10 syllables .

Unrhymed but metric poetry with usually always iambic pentameter is referred to as "blank verse" in literature.

Going by the definition, the three bottom lines are regular lines in a blank verse as they have 10 syllables. However, the first line, has 11 syllables, thereby making it irregular.

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1)Test Static: 1.82

2)P-Value: < 0.05

3)Decision: i. Reject the null hypothesis.

To test the claim that the population mean is greater than 90, we can use a one-sample t-test.

(a) The test statistic for the one-sample t-test is calculated as:

Plugging in the values, we get:

(b) To find the p-value for the test, we can use a t-table or a statistical software package to find the probability of observing a t-value as extreme or more extreme than the one we obtained, given that the null hypothesis is true. For a one-tailed test with α = 0.05 and df = 99 (the sample size - 1), the critical value for t is approximately 1.65. Since our test statistic (1.82) is greater than the critical value, the p-value is less than 0.05.

(c) Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that the population mean is indeed greater than 90. Therefore, the decision for this test is: i. Reject the null hypothesis.

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Answer:

The apparent nth term of the given sequence is given by the formula:

a_n = 1 / n!

where n! is the factorial of n, defined as the product of all positive integers less than or equal to n.

For example, the first term of the sequence is 1/1! = 1/1 = 1, the second term is 1/2! = 1/2 = 1/2, the third term is 1/3! = 1/6, and so on.

Therefore, the expression for the apparent nth term of the sequence is:

a_n = 1 / n!

Answer:

[tex]a_n=\dfrac{1}{n!}[/tex]

Step-by-step explanation:

Given sequence:

[tex]1,\; \dfrac{1}{2},\; \dfrac{1}{6}, \; \dfrac{1}{24}, \; \dfrac{1}{120}, \; ...[/tex]

Analyse each term in the sequence:

[tex]a_1=\dfrac{1}{1}=\dfrac{1}{1 \times 1}=\dfrac{1}{1!}[/tex]

[tex]a_2=\dfrac{1}{2}=\dfrac{1}{2 \times 1}=\dfrac{1}{2!}[/tex]

[tex]a_3=\dfrac{1}{6}=\dfrac{1}{3 \times 2 \times 1}=\dfrac{1}{3!}[/tex]

[tex]a_4=\dfrac{1}{24}=\dfrac{1}{4 \times 3 \times 2 \times 1}=\dfrac{1}{4!}[/tex]

[tex]a_5=\dfrac{1}{120}=\dfrac{1}{5 \times 4 \times 3 \times 2 \times 1}=\dfrac{1}{5!}[/tex]

The exclamation mark "!" placed after a number means factorial.

It means to multiply all whole numbers from the given number down to 1.   Example:  4! = 4 × 3 × 2 × 1

Therefore, the equation for the nth term of the given sequence is:

[tex]a_n=\dfrac{1}{n!}[/tex]

The affect of mean and median due to the birth of the 4th kitchen is B. Both the mean and median will increase, but the mean will increase by more than the median.

The median is the middle value when the values are ordered from smallest to largest. In this case, the median of the first 3 kittens is 153 because it is the middle value of (147, 153, 159). The median of all 4 kittens is 153 because it is the middle value of (57, 147, 153, 159). The median does not change because the addition of the 4th kitten does not change the position of the middle value.

The mean is calculated by adding up all the values and dividing by the number of values. In this case, the mean of the first 3 kittens is:

(147 + 153 + 159) / 3 = 153

The mean of all 4 kittens is:

(147 + 153 + 159 + 57) / 4 = 128

The mean increases because the addition of the 4th kitten with a lower mass pulls the overall average down.

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Answer:

235.5

Step-by-step explanation:

cylinder volume formula

V = pi * r^2 * h

V = 3.14 * 5^2 * 3

V = 3.14 * 25 * 3

V = 3.14 * 75

V = 235.5

Answer:

  17.86

Step-by-step explanation:

You want to find y when x=8 using the equation y = 13.06 +0.6x.

Put the value of the variable in place of the variable in the equation, and do the arithmetic.

  y = 13.06 +0.6x

  y = 13.06 +0.6·8 . . . for x=8

  y = 13.06 +4.8

  y = 17.86

The estimated value of y for x=8 is 17.86.