Complete the statement.
The polynomial function f(x) = ____.

(x + 2)(x - 2)(x + √3)

(x + 2)(x +√3)(x-√3)

(x - 2)(x + √3)(x-√3)

(x + 2)(x - 2)(x + √3)(x-√3)

Answer:

The answer would be 19

Step-by-step explanation:

Using pythagoras theorem

15+6= 21

a^2+b^2= c^2

In this scenario,

c^2-a^2= b^2

Meaning it would be 21^2+8^2

= 377

Square root of 377 would be 19.416

?= 19.416

The missing side length of the right angle triangle is 20

Pythagoras theorem States that the square of the longest side of a triangle is equal to the sum of the square of the opposite side and no square of the adjacent side.

BC² = AB² + CA²

(15 + 6)² = x² + 8²

21² = x² + 8²

21² - 8² = x²

441 - 64 = x²

377 = x²

x = √377

x = 19.41648783894759891856148511263886343

Approximately to the nearest whole number

= 20

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Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

Here, we have,

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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Answer:

câu này là 500 nhen

Answer:

they would eat 3500 pounds of food in 1 week

Step-by-step explanation:

its simple math just multiply 500 by 7 and you would get 3500

Step-by-step explanation:

The way to approach the problem is this

After one year she has 2000*1.05

After two years she has the money from the last year plus interest, so she has 2000*1.05*1.05

After t years she has 2000*1.05

Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.

8(b - c) = 464

7(b + c) = 644

b - c = 58

b + c = 92

Adding the two together

2b = 150

b = 75

75 - c = 58

c = 17

The boat's speed is 75 mph and the current's speed is 17 mph.

7x + 3 = 9x - 3 - 2x

7x - 9x + 2x = -3 - 3

0 = -6

equation doesn't have any solution

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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1. The type of function which vest represents the data in the table is; Quadratic.

2. The statement which is true is; The second differences are constant.

3. The type of function which best represents the given table is; Linear equation.

It is evident from the task content that the functions which correctly represents each data table is required to be determined.

By definition, linear functions are functions in which case, the first differences are constant while quadratic functions are functions in which the second differences are constant.

Ultimately, the first data table represents a quadratic function while the second data table represents a linear function.

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Answer:

its 5

Step-by-step explanation:

with a y intercept of -4

The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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Answer:

it is correct I think it's right

Step-by-step explanation:

Answer:

325 cm²

Step-by-step explanation:

find area of each side even those that are not shown. then add the areas

Answer:

D, R: {11, -4, -29}

Step-by-step explanation:

According to the given set of domains, the corresponding range is found by substituting the x values into the equation and solving for y.

i.e {-2} -> 5x + y = 1, -10 + y = 1, y = 11

{1} -> 5x + y = 1, 5 + y = 1, y = -4

{6} -> 5x + y = 1, 30 + y = 1, y = -29

Answer:

The short answer is D

Answer:

157908.83

Step-by-step explanation:

RD formula is :

\(P(1+\frac{r}{m} ) [(1+\frac{r}{m} )^{N} -1 }]{\frac{m}{r}\)

where P: Principal / rd amount = $2000

r : interest = 8% = 0.08

m : no. of times compounded in a year = 1 (compounded annually)

N : time = 25 years

Amt =

\(2000(1+\frac{0.08}{1} ) [(1+\frac{0.08}{1} )^{25} -1 }]{\frac{1}{0.08}\)

\(= 2000(1.08) [1.08^{25} -1 }]{\frac{1}{0.08}\)

= 157908.83

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

\(A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2\)

Area 2:

\(A\frac{}{2} = ∫(g(x) - f(x))dx\)

\(= ∫(x - {(x - 2)}^{2} )dx\)

\( = ∫( - {x}^{2} + 5x - 4)dx\)

\(= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}\)

\( = 2.67 - ( - 0.67) = 3.34\)

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

Similar triangles have the same ratio with their corresponding sides.

The ratios of the corresponding sides are:

12√5/20 = 24/8√5 = 36/12√5

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

We can have two similar right triangles as shown in the figure.

Triangle A and Triangle B.

Now,

Triangle A:

Base = BC

BC² = (8√5)² + 16²

BC = √320 + 256)

BC = √576

BC = 24

And,

AC² = AB² + BC²

AB² = x² - 576

AB = √(x² - 576)

Triangle B:

AB² = AD² + DB²

x² +  576 = (x - 16)² + 320

x² -  576 = x² - 32x + 256 + 320

-576 = 576 - 32x

32x = 576 + 576

32x = 1152

x = 36

So,

AD = x - 16 = 36 - 16 = 20

BD = 8√5

AB =  √(x² - 576) = √(1296 - 576) = √(720) = √(144 x 5) = 12√5

AC = 36

Now,

We can make ratios as:

AB/AD = BC/BD = AC/AB

12√5/20 = 24/8√5 = 36/12√5

We see that,

6√5/10 = 3√5/5 = 3/√5

24/8√5 = 3/√5

36/12√5 = 3/√5

The ratios are the same.

Thus,

Similar triangles have the same ratio with their corresponding sides.

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The interest obtained after 4 years from a loan of $7500 is = $750

The principal amount of the loan = $7500

The rate at which the interest is paid is = 2.5%

The time that it will take to pay the interest = 4 years

Using the formula for Simple interest;

SI= P×T×R/100

SI = 7500×4 × 2.5/100

SI= 75000/100

SI=$750

Therefore, the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years is = $750

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Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Answer:

B)

Step-by-step explanation:

4y = 3x + 5 has a slope of 3/4

4y = 3x - 1 has a slope of 3/4

parallel lines have equal slopes

The equation of a straight line that is parallel to the line 4y = 3x + 5 is B. 4y = 3x - 1.

To find an equation of a straight line that is parallel to the given line 4y = 3x + 5, we need to identify the equation that has the same slope as the given line

The given line is in the form 4y = 3x + 5. We can rewrite this equation in slope-intercept form (y = mx + b) by dividing both sides by 4:

y = (3/4)x + 5/4.

The slope of the given line is (3/4).

To find a parallel line, we need to choose an equation with the same slope of (3/4). Among the options provided:

A. y = 3x + 5 - The slope of this line is 3, not (3/4), so it is not parallel.

B. 4y = 3x - 1 - This line has a slope of (3/4), making it parallel to the given line.

C. 3y = 4x - 3 - The slope of this line is (4/3), not (3/4), so it is not parallel.

D. 4y = x + 5 - The slope of this line is (1/4), not (3/4), so it is not parallel.

Therefore, the equation of a straight line that is parallel to the line 4y = 3x + 5 is B. 4y = 3x - 1.

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Answer:

\(k=-\dfrac{11}{2}\)

\(\left(x+\dfrac{7}{2}\right)\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.7 cm}\underline{Factor Theorem}\\\\If f$(x)$ is a polynomial, and f$(a) = 0$,\\then $(x-a)$ is a factor of f$(x)$.\end{minipage}}\)

Given polynomial function:

\(p(x)=x^2-kx+7\)

Apply the Factor Theorem:

\(\begin{aligned} \textsf{If $(x + 2)$ is a factor of $p(x)$ then: \quad}p(-2)&=0\\\\\implies (-2)^2-k(-2)+7&=0\\4+2k+7&=0\\2k+11&=0\\2k&=-11\\k&=-\dfrac{11}{2}\end{aligned}\)

Substitute the found value of k into the original function:

\(\implies p(x)=x^2-\left(-\dfrac{11}{2}\right)x+7\)

\(\implies p(x)=x^2+\dfrac{11}{2}x+7\)

As (x + 2) is factor of the polynomial, and the leading coefficient of the function is 1, the other factor will be (x + q) where q is a constant to be found.

\(\begin{aligned}x^2+\dfrac{11}{2}x+7 & = (x+2)(x+q)\\& = x^2+qx+2x+2q\\& = x^2+(2+q)x+2q \end{aligned}\)

Compare the constant of the given polynomial with the constant of the expanded factors:

\(\implies 2q=7\)

\(\implies q=\dfrac{7}{2}\)

Therefore:

\(\implies x^2+\dfrac{11}{2}x+7 = (x+2)\left(x+\dfrac{7}{2}\right)\)

So the other factor of the given polynomial is:

\(\left(x+\dfrac{7}{2}\right)\)

Answer:

0 because there is no black socks.

Step-by-step explanation:

Answer:

0 because there are already some in one drawer

The top of the pole from the ground is 13.314798.

Given condition, formulate :

= 14 * sin (72°)

= 4 sin 72°

= 14 * 0.951057

= 13.314798

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant, cosine , cotangent , secant , sine , and tangent .

The trigonometric function can be described as being even or odd.

Odd trigonometric functions: A trigonometric function is said to be an odd function if f(-x) = -f(x) and symmetric with respect to the origin.

Even trigonometric functions: A trigonometric function is said to be an even function, if f(-x) = f(x) and symmetric to the y-axis.

Hence, the top of the pole from the ground is 13.314798.

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The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the

Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.

Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.

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The price of a used compact disk is $9.99.

Well, this is a system of 2 equations and 2 unknowns.

Let n = the price of new compact disks and let

u = the price of used compact disks.

Then the first equation would be 6n + 2u = 127.92.

The second equation would be

3n+8u = 133.89.

So our system is,

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

6n + 2u = 127.92

3n+8u = 133.89

Since I don't like working with decimals I would multiply both equations by 100 that way it would get rid of the decimal.

Doing so results in the following system

600n+200u = 12792

300n+800u = 13389

Now we want to know how much one used disk sells for.

To do that we multiply the bottom equation by -2 and add it to the top equation.

-2(300n+800u = 13389)

=> -300n-1600u = -26778

Now we add that to the top equation

600n+200u = 12792

+(-300n-1600u = -26778)

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

-1400u = -13987

Now we solve for u by dividing both sides by -1400 and we see that

u = 9.99.

So the price of a used compact disk is $9.99.

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