M a t h (look at image)

The quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.

For the stated values,

Sum of zeroes is 3 and product is -40​

Use formula,

x² - x (sum of zeros) + (product of zeros) = 0.

Put the values.

x² - x (3) + (-40) = 0.

x² - 3x + -40 = 0.

Thus, the quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.

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The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

What is an Equation?

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 cost of b chocolate bars be = C

Let the cost of 1 bar of chocolate bar be = $ 2.25

Let the number of chocolate bar be = b

Now , the equation to find the cost of b number of chocolate bars is ,

The cost of b number of chocolate bar =
cost of 1 bar of chocolate bar x number of chocolate bar

So , the equation is

The cost of b number of chocolate bar = 2.25b

So , the equation to find the cost of b number of chocolate bars is ,

Cost of b chocolate bars C = cost of b number of chocolate bar

C ( b ) = 2.25b

Therefore , the expression is C ( b ) = 2.25b

Hence , The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars

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Answer:

36

Step-by-step explanation:

The perimeter of ABCDE is equal to AB + BC + CD + DE + AE.

AB = 10 - 2 = 8 (The x values of A and B are the same, therefore the distance between them is the difference between their y values.)

BC = 7 - 4 = 3 (The y values of B and C are the same, therefore the distance between them is the difference between their x values.)

CD =  [tex]\sqrt{(X_D - X_C)^2 + (Y_D - Y_c)^2} = \sqrt{(15 - 7)^2 + (4 - 10)^2} = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]

DE = [tex]\sqrt{(X_E - X_D)^2 + (Y_E - Y_D)^2} = \sqrt{(7 - 15)^2 + (-2 - 4)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]

AE =

[tex]\sqrt{(X_E - X_A)^2 + (Y_E - Y_A)^2} = \sqrt{(7 - 4)^2 + (-2 - 2)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

[tex]\Delta \text{ABCDE} = \text{AB} + \text{BC} + \text{CD} + \text{DE} + \text{AE} = 8 + 3 + 10 + 10 + 5 = 36[/tex]

Step-by-step explanation:

x + y = 17

x = 17 - y

xy = 20

(17 - y)y = 20

-y² + 17y = 20

-y² + 17y - 20 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =

= (-17 ± sqrt(289 - 80))/-2 =

= (-17 ± sqrt(209))/-2

y1 = (-17 + sqrt(209))/-2 = 1.271583853...

y2 = (-17 - sqrt(209))/-2 = 15.72841615...

the 2 numbers are

1.271583853...

15.72841615...

This type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

We are asked that, what would happen if you did not take absolute values before calculating the sum of differences between group means.

As, when we calculate the differences between group means then, some of the values may be negative.

When we add those negative values while evaluating the sum then the sum can be less than the absolute and to get over from this type of problem we always take absolute values of the differences between group means and then get the sum.

Also, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

Hence, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

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The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.

We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).

y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.

Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).

Hence, the line perpendicular  to y = 5 and that passes through the point (-7, -5)  is x = -7.

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The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = 300 ± 1.96 x (45 / √26)

CI = 300 ± 17.30

CI = [$282.70, $317.30]

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Answer:

WITDTH=7

Step-by-step explanation:

width = w

length = w + 2.

w(w + 2) = 63 (area)

quadratic equation in w:

w2 + 2w = 63

w2 + 2w - 63 = 0

FACTOR:

(w + 9)(w - 7) = 0

  9-7=2

   9x(-7) = -63

Two possible solutions:

w + 9 = 0 (solution w = -9) or

w - 7 = 0 (solution w = 7)

The width must be positive, the answer is 7 units.

length = w+2

length  = 9

The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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Answer:

Step-by-step explanation:

If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

As per the question statement, a person spins a six-space spinner and then flips a coin,

And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.

Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).

And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.

Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

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The probability that in any given period of 400 days there will be an accident on one day is 0.2707

Given that;

In a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.

n = 400, p = 0.005

Poisson distribution is given by;

e P(x) = (λˣe^λ ) / x!

Here, Mean(λ) = np

                        = 400*0.005

                        =2

The probability that there will be an accident on one day;

(P(x = 1)) = (λxe-λ)/x!

             = 2*e-2

             = 0.2707

The probability that in any given period of 400 days there will be an accident on one day is 0.2707

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The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x

Equation:

An equation is made up of two expressions connected by an equal sign.

For example, y = 3x + 6 is an equation.

Given,

The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.

Here we need to find the equation that shows the total cost depends on the number of students.

Let us consider x be the number of students and y be the cost for x number of students.

Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.

So, based on these details, the equation for the total cost is calculated as,

=> y = 21.25 + 14.75x

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Answer: See the image below for the table and graph

==========================================================

Explanation:

We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.

For instance, if x = -2, then...

[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]

If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.

We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.

Repeat for x values x = -1 through x = 2.

Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.

Answer:

[tex]^4\sqrt{2}[/tex]

Answer: Option C

Step-by-step explanation: just took the test.

Answer:

  14 square units

Step-by-step explanation:

You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.

The diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:

  b = -4 -(-11) = 7

The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...

  h = 8 -4 = 4

We now have the information we need to use the area formula:

  A = 1/2(7)(4) = 14 . . . . square units

The area of ∆ABC is 14 square units.

__

Additional comment

You can use the diagram and count grid squares to find the dimensions of the triangle.

m∠C > m∠A > m∠B is correct regarding the angles of the triangle ABC.

What is the angle of the triangle?

While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°.

Here, we have

In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.

AB=4p-1 , AC=p+4 , BC=3p

where p+4 < 3p        [as p≥3]

3p < 4p-1          [as p≥3]

⇒  4p-1> 3p > p+4

⇒AB > BC > AC

Angle opposite to AB, BC, and AC is m∠C,m∠A, and m∠B.

m∠C > m∠B > m∠A    [∵Angle opposite to greater side is greater]

Hence, mC > mA > m∠B is correct regarding the angles of the triangle ABC.

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Answer:

-2x+18, and -2(x-9)

Step-by-step explanation:

4x+18-6x

4x-6x+18

-2x+18

-2(x-9)

-2x+18

Answer:  [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

90 degree counter-clockwise rotation around the origin.

===================================================

Explanation:

Focus on A(-1,2) and A'(-2,-1)

The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"

In other words, we've gone from (x,y) to (y,x) to (-y,x)

Representing this with arrows looks like:

[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]

or in short

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

which represents a 90 degree counter-clockwise rotation around the origin.

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

Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]

Sure enough, it works for point B.

Lastly, let's check if it works for point C.

We should go from C(3,-4) to C'(4,3).

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]

All points have been confirmed.

The value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.

The  given function is f(x)=x-7/2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The inverse of the given function is

y=x-7/2

Replace y with x and x with y, we get

x=y-7/2

y=x+7/2

[tex]f^{-1}(x)[/tex]=x+7/2

When x=3

[tex]f^{-1}(3)=3+7/2[/tex]

=6.5

f(6.5)=6.5-7/2

=6.5-3.5

=3

Therefore, the value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.

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In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.

Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.

An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.

Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.

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If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.

The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.

This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.

By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:

LP + PR = LR

LP = LR - PR

Substituting the given parameters into the formula, we have;

LP = 12 - 4

LP = 8.

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Complete Question:

Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain

LP = 16 because 12 + 4 = 16 according to the addition property of equality.

LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.

PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.

PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.

Answer: Lp = 8

Step-by-step explanation:

Got it right

The correct answer to this question is d. the value of the 6 in 364 is 10 times the value of the 6 in 346.

The place value of the 6 in 346 is six because it is in the place of ones, whereas the place value of the sixth in 364 is 60 because it is in the place of tens. As a result, the value of 60 is ten times that of the value of 6.

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which can result in a number having two similar digits with different values.

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Answer:

8.433 to the power of 4

Step-by-step explanation:

The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.

The equation of line parallel to the given line is found as y = -6x + 13.

The equation of the line is-

y = -6x + 1

The second line is parallel to the above line, thus the slopes of both the line are equal.

m1 = m2 = -6

The new line also passes from the point (1, 7)

(x1, y1) = (1,7)

Thus, the equation of the line will be calculated as-

y - y 1 = m2(x - x1)

y - 7 = -6(x - 1)

y - 7 = -6x + 6

y = -6x + 13

Thus, the equation of line parallel to the given line is found as y = -6x + 13.

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Using the simple interest formula, Mr. Solo received $26 interest.

In the given question we have to find how much interest Mr. Solo received.

The investment(P) = $325.

Interest rate(R) = 8%

Time(T) = 1 year

Finding the interest using the simple interest formula.

I = PRT/100

where I = interest

P = Principal Amount

T = Time

R = Interest Rate

Putting the value

I = 325*8*1/100

I = 26

Hence, Mr. Solo received $26 interest.

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Answer:

Zyndy is 14, Vyndel is 7.

Step-by-step explanation:

Let Zyndy's age be represented by 'z', and Vyndel's age be represented by 'v'.

Zyndy is twice the age of Vyndel, so z=2v

The sum of their age is twenty-one, so z+v=21

Sub the first equation above into the second to get:

2v+v=21

3v=21

v=7

Knowing v=7, we can say z=2(v)=14.

Answer:

4.76

Step-by-step explanation:

had this on a test today!

The statement that best analyzes the role this event plays in The Necklace plot is A. It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.

There are both planned and unplanned events, and the start and end times may be noted. Event types include accidents, celebrations, natural disasters, and rallies. The event is the occurrence of the event.

Loisel is well-liked and adored by all. As she walks away, she searches for the pendant and discovers it has gone missing. After days of searching, she and her husband decide to replace it with something similar. It takes her ten decades to pay for the successor, which costs the same as your salary.

In this case, it best analyzes the role this event plays in leading to the resolution where Mathilde learns a lesson about the downfall that can come from vanity and greed The plot of The Necklace.

Therefore, the correct option is A.

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Complete question

Which statement best analyzes the role this event plays in The Necklace plot?

“Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!”

It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.

It is the climax of the story since the reader is most excited at this point.

It serves as a complicating incident because Mathilde will have to suffer the consequences of her actions.

It serves as the falling action because it shows that Mathilde will have to get used to her place in life.

Answer: 600$

Step-by-step explanation:

2/5 of 600 is 240