Factor the expression completely over the complex numbers.

y4+14y2+49



Enter your answer in the box.

The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

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Answer: negative one third

Answer:

-1/3

Explanation:

There's a formula that I'll use to find the slope - it's called the slope formula.

\(\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data:

\(\sf{m=\dfrac{8-4}{-4-8}}\\\\\sf{m=\dfrac{4}{-12}\)

Simplify:

\(\sf{m=-\dfrac{4}{12}}\)

\(\sf{m=-\dfrac{1}{3}}\)

Hence, the slope is negative one-third.

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

The annual rainfall in 2016 is 336 mm.

Let the annual rainfall in 2016 be 100x mm.

Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.

So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm

Also given that the amount of rainfall in 2017 = 420 mm.

According to question the suitable equation is,

125x = 420

x = 420/125

x = 3.36

Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.

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Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B

To solve this problem, we have to know the perimeter of the polygon C.

The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The perimeter of the figures are;

Using the concept of perimeter of a rectangle;

a. figure A = 2(4 + 11) = 30cm

b. figure B = 2(8 + 4) = 24cm

c figure C = 11 + 4 + 8 + 4 = 27cm

Now, we can add A and B and then subtract c from it.

30 + 24 - 27 = 27cm

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Answer:

The y-intercept of the table shown is (0, 1).

The y-intercept of the parabola can be found by verifying if any coordinates from the table has x = 0 and y = some specific value. If there is a coordinate point such that the value of both is x = 0 and y = any value, then the value of y is the y-intercept of the parabola. Further explained in example:

Example: if a line passes through a coordinate point (0, 4), the y-intercept for that line is four because the value of x is 0 and y is 4.

Solving the Problem/Question (Applying the method stated above):

From the table, we can tell that the parabola passes through the following coordinate points: (-2, -11); (-1, -4); (0, 1); (1, 4); (2, 5); (3, 4); (4, 1).

From all the coordinates, we find that (0, 1) has the value of x as 0 and the value of y as 1. Therefore, this coordinate point (0, 1) is the y-intercept.

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The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

Answer:

The formula gives the area of a parallelogram:

Area = base x height

Substituting the given values, we get:

Area = 7.5 cm x 12.2 cm

Area = 91.5 cm^2

Therefore, the area of the parallelogram is 91.5 square centimeters.

Step-by-step explanation:

Answer:

91.5 sq cm

Step-by-step explanation:

A=bh=7.5·12.2=91.5

Answer:

I don't understand but I believe the answer is 16y^8

Step-by-step explanation:

Answer: (4 x a x a x a x a) x (4 x a x a x a x a)

HOPE THIS HELPS

Answer:

45

Step-by-step explanation:

9514 1404 393

Answer:

  (a)  45

Step-by-step explanation:

The angle where the chords cross is half the sum of the subtended arcs:

  (x +99)/2 = 72

  x +99 = 144 . . . . . multiply by 2

  x = 144 -99 . . . . . .subtract 99

  x = 45

Therefore , the solution to the given problem of slope intercept comes out to be  dy/dx = -1/2.

After you are certain if Y = mx + b, the gradient intercept approach can be employed. By using just one particular point on the line and its slope, the direction form is a way to represent an axiom for a line. The slope is defined as such rise across run and is represented first by point form (x,y), and may be calculated using the slope intercept method, y = mx + b. (0, b). By using just one specific statement on the vector and its slope, the direction form is a technique to write a linear model for a line.

Here,

Given : x² +2xy - 2y² +x =2

thus,

To find the gradient at point (-4,1) :

We have to find the dy/dx

so,

=>  2x + 2y + 2xdy/dx -2ydy/dx +1 =0

=> dy/dx (2x-2y) = -(2x+ 2y) -1

=>dy/dx = -(2x+2y) -1 / (2x-2y)

So , at the point (-4,1)

=> dy/dx = -(-8 + 2) -1 / (-8 -2)

=>dy/dx = 5/-10

=>dy/dx = -1/2

Therefore , the solution to the given problem of slope intercept comes out to be  dy/dx = -1/2.

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Answer:

P(w) = 3x + 4

Step-by-step explanation:

Answer:

La probabilidad es \(0.2508\)

Step-by-step explanation:

Sabemos que según datos de una empresa aseguradora de vehículos, dos de cada cinco accidentes son provocados por conductores en estado de ebriedad. Entonces, si definimos el evento

\(A\) : ''Accidente provocado por un conductor en estado de ebriedad''

La probabilidad de este evento es

\(P(A)=\frac{2}{5}\)     (dato del problema)

Por lo tanto, en cada accidente que ocurre, la probabilidad de que ocurra el evento \(A\) es  \(\frac{2}{5}\) .

Ahora bien, si suponemos cada uno de estos accidentes independientes y con probabilidad de ocurrencia ''p'' constante a lo largo del tiempo, estamos ante la presencia de un proceso Bernoulli.

Dado un proceso de Bernoulli, definimos la variable aleatoria discreta ''\(X\)'' como el número de éxitos del proceso Bernoulli para un número fijo de ensayos.

En este caso vamos a definir

\(X\) : ''Número de accidentes provocados por conductores en estado de ebriedad de un total de n accidentes''

Se dice que \(X\) tiene distribución binomial de parámetros ''n'' y ''p''.

Lo denotamos \(X\) ~ Bi (n,p)

En nuestro ejercicio el valor de ''n'' es 9 (son los ensayos que fijamos) y el valor de ''p'' es \(\frac{2}{5}\) (definimos como ''éxito'' que el accidente sea provocado por un conductor en estado de ebriedad).

Ahora bien para calcular probabilidad vamos a utilizar la siguiente fórmula :

\(P(X=x)=(nCx)p^{x}(1-p)^{(n-x)}\)    (I)

'' \(P(X=x)\) '' es la probabilidad de que la variable aleatoria \(X\) asuma el valor x. En particular, buscamos \(P(X=3)\) que es la probabilidad de que de nueve accidentes (fijados), tres sean provocados por conductores en estado de ebriedad.

'' \((nCx)\) '' es el número combinatorio definido como

\(nCx=\frac{n!}{x!(n-x)!}\)

Reemplazando los datos en la ecuación (I) :

\(P(X=3)=(9C3)(\frac{2}{5})^{3}(\frac{3}{5})^{6}=0.2508\)

La probabilidad pedida es \(0.2508\)

Answer: 1

Step-by-step explanation:

6a. The equation for the graph is y = 2√(x + 5).

6b. The equation for the graph is y = -|x + 1| + 5

In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;

y = a√(x - h) + k

Part 6a.

Next, we would determine value of a as follows;

4 = a√(-1 + 5) + 0

4 = a√4

4 = 2a

a = 2

Therefore, the required square root function is given by;

y = 2√(x + 5)

Part 6b.

Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:

y = a|x - h| + k

y = -|x + 1| + 5

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Answer

Step-by-step explanation:

 yl grafica

Answer:

The slope would be -7

Step-by-step explanation:

To find the slope, you find two points on a line and find the difference between x-values and y-values. Then divide the difference of y-values by the difference of x-values to acquire the slope. \(\frac{8-1}{-4+3}\) = \(\frac{7}{-1}\) or -7, so that would be the slope.

Our solution set is correct because it contains valid solutions.

We want to eliminate the inequality:

√c + 9 - √c > √3

First, we simplify the inequality's left side:

9 - √c > √3

Following that, we square both sides of the inequality:

81 - 2√c + c > 3

Now we simplify the inequality's right side:

c + 78 > 3

Finally, take 78 off both sides of the inequality:

c > -75

This gives us the following solution set:

c ∈ (-∞, -75) U (-75, ∞)

We test a value from each interval to validate our solution set:

Let's go with c = -100, which is in the range (-, -75). Putting it into context with the original inequality:

√(-100) + 9 - √(-100) > √3

Because the square root of a negative number is not defined, this choice of c is invalid.

Let us choose c = 0, which is in the range (-75,). Putting it into context with the original inequality:

√0 + 9 - √0 > √3

Because 9 > 3, this choice of c is a valid solution.

We can conclude that our solution set is correct because it contains valid solutions.

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PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

Answer: y=3x-2

Step-by-step explanation:

3y-9x=-6

First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.

Answer:

This equation in slope intercept form would be y = 3x - 2

Step-by-step explanation:

The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3

So the answer is y = 3x - 2

Answer:

  exponential function

Step-by-step explanation:

A geometric sequence is a representation of an exponential function.

__

There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.

Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.

The payment options contemplated by the employer are distributed as follows:

Option A

Option B

Note: This question is incomplete because there is some information missing. Here is the missing information:

Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

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I don’t have an answer but by any chance did you complete the assignment?

15% off of $80 is $68.00

it won't let me send this without 20 characters so just ignore this part lol.

Answer:

a) drinking caffeinated coffee

b) hyperactivity

c) experimental study

d) Non-Probability Sampling Method

Explanation:

a) An independent variable refers to the object(s) or variable that is been measured which is not affected or changed by other variables. Rather, the independent variable affects or changes other variables. That is why drinking caffeinated coffee falls under the independent variable.

b) The dependent variable on other hand is a variable that can be affected or changed by the independent variable. That is why hyperactivity falls under the dependent variable.

c) Noteworthy is the fact that in an experimental study a researcher usually alters the level of the independent variable [the caffeinated coffee]. This is evident in this case because we are told, "One group received regular coffee and the other received decaffeinated coffee."

d) The kind of sampling method used is the Non-Probability Sampling Method because they [the students] which formed the population were not randomly selected, but "intentionally balanced" into groups by the student’s year, major, and gender.

The value of the variable is 1. 40

we need to know that algebraic expressions are described as expressions that are made up of term, variables, constants, factors and coefficients.

these algebraic expressions are also made up of arithmetic operations.

These arithmetic operations are listed as;

From the information given, we have that;

7.5x/11=4.8/5

cross multiply the values, we get;

7.5x(5) = 4.8(11)

multiply the values

37. 5x = 52. 8

Divide both sides by the coefficient of x, we get;

x = 1. 40

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The direction of rotation used to create the image is 90°  counterclockwise rotation. To determine the direction and degree of rotation used to create the image, we can compare the positions of the vertices of the original triangle ABC with the corresponding vertices of the image triangle A' B' C'.

Let's analyze the changes in the coordinates of the vertices.

Original Triangle ABC:

A(-4, -4)

B(3, -3)

C(0, -10)

Image Triangle A' B' C':

A'(4, -4)

B'(3, 3)

C'(10, 0)

By comparing the coordinates, we can observe that the image triangle has undergone a 90° counterclockwise rotation.

To determine this, we can focus on a single vertex, such as A. The original point A(-4, -4) has been rotated counterclockwise by 90° to its new position A'(4, -4). This rotation is evident in the change of sign for the y-coordinate (-4 to -4) and the swapping of the x-coordinate (-4 to 4). This pattern is consistent across all three vertices.

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Answer:

Counterclockwise rotation of 90° about the origin

Answer:

I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.

Step-by-step explanation:

Step-by-step explanation:

since they are the midpoints, then the connecting line UX is also right in the middle of the lengths of TY and VW.

so,

UX = (TY + VW)/2

-p + 90 = (p + 50 + 2p + 75)/2

-2p + 180 = 3p + 125

55 = 5p

p = 55/5 = 11