the topic is piecewise functions, can someone help? i’m a little confused :)

The value of k in the quadratic equation is k = 0 or k = 8

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

2x² + kx + k = 0   be equation (1)

And , the roots of the equation are equal

So , when the discriminant is zero we get just one real solution

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

( b² - 4ac ) = 0

Substituting the values in the equation , we get

k² - 4 ( 2 ) ( k ) = 0

On simplifying the equation , we get

k² - 8k = 0

Adding 8k on both sides of the equation , we get

k² = 8k

So , when k = 0 , the equation satisfies

And ,

k = 8

Therefore , the value of k are 0 and 8

Hence , the value of k in the equation is 0 or 8

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Answer: it is p

Step-by-step explanation:

4p-3p

Subtract 3p from 4p

=p

Brainliest pls

Answer:

p

Step-by-step explanation:

4p+3q-3p-3q

rearrange terms

4p-3p+3q-3q

combine like terms

1p+0q

simplify

p

hopes this helps

For at least 75% of the data, the spread will be within two standard deviations of the mean.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Generally speaking, the spread will be within two standard deviations of the mean for at least 75% of the data.

The data will be within three standard deviations of the mean for at least 89% of the time.

Data that deviates more than two standard deviations from the mean are deemed "unusual."

Therefore, for at least 75% of the data, the spread will be within two standard deviations of the mean.

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Yes, a function will have more than one inverse.

Given,

Function;

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Inverse function;

A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by f-1 or F-1 if the function is denoted by f or F.

Here,

A function may have more than one inverse, or many functions have inverses that are not functions.

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It's the first math course they take where they have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students.

We employ integers with definite or fixed values in algebra, such as 2, 9, 0.068, etc. Numerous sub-branches of algebra exist, including introductory algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

here

Because it's the first math course they take where they have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students .

Additionally, there is sometimes insufficient effort made in the classroom to relate algebra to students' daily lives and explain why it is important for them to grasp.

They have to deal with variables, complex ideas, and creative problem solving, algebra can be intimidating for many students .

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The number of different ways for each case is given as follows:

a) 1,024 ways.

b) 1,043,456 ways.

c) 1,073,739,264 ways.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, we have that for each of the 10 toppings, there are 2 options, insert or not, hence the total number of outcomes is of:

2^10 = 1024 ways.

For item b, we have that:

Hence the number of ways is given as follows:

1024 x 1024 - 10 x 512 = 1,043,456

For item c, we have that:

Hence the number of ways is given as follows:

1024 x 1024 x 1024 - 10 x 256 = 1,073,739,264

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The last statement the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela is correct.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given:

Kim and her friends watched the server making smoothies.

The given table shows the number of mangos that were used for each of the different size of smoothies that the friends ordered.

From the given statements the last statement 'the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela.'

Because,

The ratio of smoothies size to mangos used for Kim is, 21/3 = 7 and

The ratio of smoothie size to mangos used for Angela is 28/4 = 7.

Both the ratios are same.

Hence, the last statement the ratio of smoothies size to mangos used for Kim is same as the ratio of smoothie size to mangos used for Angela is correct.

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The Surface Area of Pyramid is 104 cm².

Simply calculating the areas of each face in a figure is surface area. It is considerably simpler for us to calculate because the amount is supplied to us as a net of.

So, Area of square base= (side²)

= 8²

= 64 cm²

and, Area of one triangular face

= (1/2 x b x h)

=1/2 x 8 x 5

= 20 cm²

Now, Multiply by 4 as we have 4 triangular faces

= 20 cm² x 4

= 80 cm²

Then, Surface Area of Pyramid is

= 64 cm² + 40 cm²

= 104 cm²

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A discontinuous function can be solved by analyzing the behavior of the function and its points of discontinuity. This can be done by finding the limits of the function at each point and then using the appropriate algebraic techniques to solve the equation.

Discontinuous functions are those that have gaps or sharp discontinuities in their graphs. In order to solve a discontinuous function, you must start by analyzing the behavior of the function and its points of discontinuity. This can be done by finding the limits of the function at each point and then using the appropriate algebraic techniques to solve the equation. This can involve factoring, manipulating equations, and other techniques to find the solution. Once the equation is identified, it can then be graphed to see the behavior of the function between the points of discontinuity. If necessary, the equation can then be further manipulated to satisfy the conditions of the discontinuous points. By approaching the problem in this manner, a discontinuous function can be effectively solved.

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If A and B are independent events with given probabilities P(A) and P(B), then the probability of A intersecting B (P(A ∩ B)) is equal to the product of their individual probabilities. For example, if P(A) = 0.05 and P(B) = 0.65, then P(A ∩ B) = 0.0325.

The probability of two events A and B occurring together, P(A ∩ B), can be calculated by multiplying the individual probabilities of each event, P(A) and P(B). In this case,

P(A) = 0.4 and P(B) = 0.6, so P(A ∩ B) = 0.4 * 0.6 = 0.24

.The probability of event A occurring given that event B has already occurred, P(A | B), is equal to the probability of both events occurring together, P(A ∩ B), divided by the probability of event B occurring, P(B). In this case,

P(A ∩ B) = 0.24 and P(B) = 0.65, so P(A | B) = 0.24 / 0.65 = 0.0375

which can be rounded to 0.0325.These probabilities can be used to estimate the likelihood of certain events occurring together or given certain conditions. In this case, the probability of events A and B occurring together is 0.24 and the probability of event A occurring given that event B has already occurred is 0.0325.

A. P(A ∩ B) = P(A) * P(B)

= 0.4 * 0.6

= 0.24

B. P(A | B) = P(A ∩ B) / P(B)

= 0.24 / 0.65

= 0.0375

= 0.0325

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A school cafeteria wants to find out what combinations of food and beverage students are ordering.  the probability that a student ordered a hamburger and a Slurpee is 19 over 137.Option D

Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.

From the table, we can see that 19 students ordered a hamburger and a Slurpee.

There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.

Therefore, the probability that a student ordered a hamburger and a Slurpee is 19/137, or about 0.14.

Therefore, the correct answer is d) 19 over 137.

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The value of the polynomial 5x- 4x²+3 at x=-1 is -6 by using the substitution method.

Given that,

The polynomial is 5x- 4x²+3

We have to find the value of the polynomial when x=-1.

We know that,

A polynomial is an algebraic expression whose exponents are all whole numbers. There must be non-negative integer variable exponents in all polynomials.

Take the polynomial P(x) = 5x- 4x²+3

P(x) = 5x- 4x²+3

So, we take x=−1,

P(−1)=5×(−1)−4×(−1)²+3

P(−1)=−5−4+3

P(−1)=−6

Therefore, The value of the polynomial 5x- 4x²+3 at x=-1 is -6 by using the substitution method.

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You must have held Social Security-covered employment and have a medical condition that satisfies Social Security's rigid definition of disability in order to be eligible for SSS disability benefits.

People who are unable to work for a year or more due to a handicap typically receive monthly payments. Benefits often persist until you can resume regular employment. Additionally, there are a number of unique regulations, referred to as work incentives, that offer ongoing benefits and health insurance to support your move back to employment.

When you reach full retirement age while receiving SSDI payments, your disability benefits will automatically transition to retirement benefits, but the amount will not change.

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The solution to 4x 5y 20 is 4x + 5y = 20. This can be solved by subtracting 5y from both sides of the equation, giving 4x = 20 - 5y, and then dividing both sides of the equation by 4, giving x = (20 - 5y) / 4.

4x 5y 20 is not an equation and thus cannot be solved. However, if you are looking to find the product of 4x and 5y, then the answer would be 100xy. To calculate this, you must multiply 4x by 5y. This will give you 20x + 20y, which can be simplified to 100xy. To make sure that you reach the correct answer, it is recommended to double check your work. This can be done by taking the inverse of the equation, which would be dividing 100xy by 4x and 5y. If done correctly, you will end up with the same numbers you started with: 4x and 5y.

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Option d is Correct. The other ratios of right triangle's area is 1/4 of the square's size in terms of area.

Two right triangles are similar, as demonstrated in mathematics. It follows that the triangles' side ratios are equal. The triangle's height with area m is 2m in the figure because A = 1/2bh = h/2. The base of the other triangle is x, therefore 2m/1 = 1/x. Please see the file that is provided for the figure, which is X = 1/ 2m.

Area of triangle = 1/2 * base * height

The area of that triangle, which is determined by the relationship between its area and the area of the square, is

= 1/2 × 1 × 1/2m = 1/4m

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Correct Question:

Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is:___________.

(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

Answer:

Below

Step-by-step explanation:

Domain is the x values a graph can have

   this one goes from 7 to 11   inclusive ( solid dots at each end)

7<= x <= 11  

The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

The relationship between the volume of the rectangular pyramid and the volume of the rectangular prism with the same base and height is given by : Volume of the rectangular pyramid = (1/3) of the volume of the rectangular prism.

As given in the question,

Formula need to use for the calculation of the volume of the rectangular pyramid and prism is  :

Volume of the rectangular pyramid

= (1/3) × ( rectangular base area) × height

Volume of the prism = ( rectangular base area ) × height

If the base and height of the rectangular pyramid and rectangular prism is same then,

Volume of the rectangular pyramid

= ( one - third ) × Volume of the rectangular prism

Therefore, the relationship representing the volume of the rectangular pyramid is and prism with same base and height as volume of pyramid is one third the volume of the prism.

The above question is incomplete , the complete question is:

What is the relationship between the volume of rectangular prism and pyramid which have the same height and base?

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Answer:

2a. Scale factor is 2

2b.  Scale factor is 3

Step-by-step explanation:

2a.

We see that the smaller figure to get from F' to G', it is 2 squares, and we see the larger figure to get from F to G, it is four squares, so the scale factor is 2.

2b.

We see that to get from A' to C', it is 2 squares, and we see the larger figure to get From A to C, it is 6 squares, so the scale factor is 3

Multiplicity is a mathematical concept related to the roots of a polynomial equation.

It is defined as the number of times a given root is repeated in the polynomial equation.

The formula for calculating the multiplicity of a root is :

Multiplicity = n-(degree of the polynomial equation)

where n is the order of the root and the degree of the polynomial equation is the highest exponent in the equation.

For example, if the polynomial equation is 3x^2 + 4x + 2 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:

Multiplicity = n - (degree of the polynomial equation)

Multiplicity = 2 - 2

Multiplicity = 0

This means that the root 2 is not repeated in the polynomial equation and therefore has a multiplicity of 0.

In another example, if the polynomial equation is 4x^3 + x^2 + 6x + 12 = 0 and the root is 2, then the multiplicity of the root is calculated as follows:

Multiplicity = n - (degree of the polynomial equation)

Multiplicity = 2 - 3

Multiplicity = -1

This means that the root 2 is repeated in the polynomial equation and therefore has a multiplicity of -1.

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A T1 consists of 24 telephone channels.

A T1 line is a twisted 4 wire copper circuit that carries/transfers data and voice from one point to another point throught digitilized signals.

The T1 is designed to transmit 24 voice channels at a rate of 64Kbps (Kilobits per second) which makes it 1.544 Megabits per second in total.

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f(x) = 2[tex]x^{3}[/tex] + 4[tex]x^{2}[/tex] - 22x -24 will be the equation.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The equation will be 2(x-3)(x+4)(x+1) since the function f(x) has roots of 3, -4, and -1 and a leading coefficient of 2.

so 2(x-3)(x+4)(x+1) will be the equation

That is 2(x-3)([tex]x^{2}[/tex] +5x + 4)

2([tex]x^{3}[/tex] + 2[tex]x^{2}[/tex] - 11x -12)

f(x) =2[tex]x^{3}[/tex] + 4[tex]x^{2}[/tex] - 22x -24

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Answer:

56 teddy bears

Step-by-step explanation:

If each teddy bear weighs 1/4 pounds, then the total weight of teddy bears that can be put on the display is 1/4 pounds * X teddy bears, where X is the number of teddy bears.

The maximum weight the display can hold is 14 pounds, so we need to find the value of X that satisfies the equation: 1/4 pounds * X teddy bears = 14 pounds.

Dividing both sides of the equation by 1/4 pounds, we get: X teddy bears = 14 pounds / 1/4 pounds = 56 teddy bears.

Therefore, the employee can put 56 teddy bears on the display.

Answer:  56 teddy bears on the display.

Step-by-step explanation: We can find the maximum number of teddy bears that can be put on the display by dividing the maximum weight of the display by the weight of each teddy bear. Since each teddy bear weighs 1/4 pounds and the display can hold 14 pounds, we can put a maximum of 14 / (1/4) = <<14/(1/4)=56>>56 teddy bears on display.

On observing the provided question, we can say that the the provided equation f(x) = [tex]x^3[/tex] is the basic cubic function.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

basic cubic function is =  [tex]f(x)=x^3[/tex]

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II only- the distribution of the sample data.

A sampling distribution is a probability distribution of a statistic generated from more samples taken from a specific population.

The sampling distribution shows how the sample means will vary in repeated samples.

The mean is the most common kind of sampling distribution. This kind concentrates on figuring out the mean average of all sample means, which results in the sampling distribution.

A sampling distribution mean is obtained by adding together the average of each sample and reflecting the characteristics of the entire population.

As the number of samples increases, the standard deviation falls, resulting in a normal frequency distribution or a bell-shaped graph.

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A sampling distribution is a probability distribution of a statistic generated from more samples taken from a specific population.

The sampling distribution shows how the sample means will vary in repeated samples.

The mean is the most common kind of sampling distribution. This kind concentrates on figuring out the mean average of all sample means, which results in the sampling distribution.

If the product of their slopes is -1, these lines are perpendicular to each other.

What is perpendicular ?

The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.

The equation of a straight line that is perpendicular to the line y = x is the line y = −x .

E.g. Take the line y = 2x.

Let's construct a perpendicular to the line y = 2x at the point ( 0,3 )

We can therefore state that for any two perpendicular lines y = mx + c and y = nx + c ,

mn = −1 .

If the product of their slopes is -1, these lines are perpendicular to each other.

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Answer:35°

Step-by-step explanation:55+90=145   180-145=35

Answer:

a = 35

Step-by-step explanation:

Straight angle theorem state that a straight line has an angle of 180 degrees

a + 90(right angle) + 55 = 180

a = 35

The solutions for given equation are x = 4 and y = 6

The algebraic technique for resolving many linear equations at once is called the substitution method. As the name implies, this approach involves substituting a variable's value from one equation into another.

Here we have

- 5x - 2y = - 40 --- (1)

 y = 2x + 2  ---- (2)

To solve (1) and (2)

Substitute (2) i.e y value in (1)

=> - 5x - 2(2x+2) = - 40

=> - 5x - 4x - 4 = - 40

=> -9x - 4 = - 40

=> - 9x = - 36

=>  x = 4  

Now substitute x = 4 in (2)

=>  y = 2(2) + 2  

=>  y = 6

Therefore,

The solutions for given equation are x = 4 and y = 6

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Answer: C

Step-by-step explanation:

(-3x + 9i) (x + 3i)

-3x^2 - 9ix + 9ix - 27

-3x^2 - 27

So, the answer is C