g(x)=5x+2, find g(-4)g(−4).

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Work Shown:

Method 1

List out the first few powers of 'i', where [tex]i = \sqrt{-1}[/tex]

The process repeats every four terms. Divide the exponent by 4 to look at the remainder.

39/4 = 9 remainder 3

Ignore the quotient 9. The remainder is all we care about

Since we get remainder 3, this means i^39 = i^3 = -i

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Method 2

i^39 = i^(36+3)

i^39 = i^36*i^3

i^39 = i^(9*4)*i^3

i^39 = (i^4)^9*i^3

i^39 = (1)^9*i^3

i^39 = 1*i^3

i^39 = i^3

i^39 = -i

This is a bit longer method, but it helps confirm that i^39 = i^3 = -i we found earlier in the previous section.

Answer:

5 (1 + 5)

Step-by-step explanation:

It would be this because the 5 would distribute itself multiplying into the 1 and other 5 equaling 5 + 25 and it is in the distributive property.

Answer: Option 1

Step-by-step explanation:

We need to multiply each coordinate by 3/2.

Answer: The answer is in the picture!

Step-by-step explanation:

Solution :  Distance between (-1/2, -1) , (5/8, -1) = .75

Distance Formula :

Distance between two points can be evaluated if we know the c

[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex] = XY

The difference between the x-axis coordinates gives the horizontal distance and the difference between the y-axis coordinates gives the vertical distance.

Distance between the points P and Q is calculated as follows:

S and T are the points on the x-axis which are endpoints of two parallel line segments PS and QT respectively.

⇒ PR = ST

Coordinates of S and T are (x1, 0) and  (x2, 0) respectively.

OS =  x1 and OT = x2

ST = OT – OS = x2 – x1 = PR

Similarly,

PS =  RT

QR = QT – RT = QT – PS = y2 – y1

By Pythagoras theorem,

PQ2 = PR2 + QR2

PQ = √[(x2– x1)2+ (y2– y1)2]

Therefore,

Distance between two points (x1,y1) and (x2,y2) is given by:

[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex]

distance between (-1/2, -1) , (5/8, -1)

[tex]XY = \sqrt{{(-1-(-1))^{2} } +(5/8-(-1/2))^{2}]\\\\\\\\\\\\XY = \sqrt{9/16}\\\\\\XY = 3/4\\XY = .75\\[/tex]

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(A) 1.5 (IQR) is used to identify outliers in a set of data.

As it is given in the description itself, the interquartile range is the best tool to use to find all of your outliers (IQR).

Therefore, (A) 1.5 (IQR) is used to identify outliers in a set of data.

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The correct question is given below:
Which of the following is used to identify outliers in a set of data?

(A) 1.5(IQR)

(B) 1.5(range)

(C) 2(mean)

(D) 2(median)

Considering the definition of an equation and the way to solve it, the number is -3/7.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. This is, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "x" a number, and knowing that eight more than six times a number is the same as two less than 8 times the numbe, the equation in this case is:

8 + 6x= 2 - 8x

Solving:

6x + 8x= 2-8

14x= -6

x= (-6) ÷ 14

x= -3/7

Finally, the number is -3/7.

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Answer:

Answer: 3 + 7 + 12 - 2 = 20

Step-by-step explanation:

Answer:  4.1

Step-by-step explanation: You would do 8.2 m/2 because since 1cm =2m the opposite would be 2m = 1 cm so 8.2 = 4.1 because 2/2 = 1

The equation of the line in y = mx + c form is y = (-25/4)(x) + 5.

Here, we are given a line as shown in the figure.

Let us take 2 points that the line passes through. We can see that the line passes through (0, 5) and (0.8, 0)

Now, we have two points, we can find the slope of the line.

Slope is taken to be m. Thus,

m = (y2-y1)/ (x2-x1)

here, (x1, y1) = (0, 5)

and (x2, y2) = (0.8, 0)

Therefore,

m = (0-5)/ (0.8 -0)

m = -5/0.8

we can simplify this as follows-

m = -50/8

m = -25/4

Thus, the slope of the line is -25/4.

Now, we already know that  (0, 5) is a point on the line. Thus, the y intercept of the line is 5.

⇒ c = 5

Now, substituting the values in the equation we get-

y = (-25/4)(x) + 5

Thus, the equation of the line in y = mx + c form is y = (-25/4)(x) + 5.

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Answer: i got u

Step-by-step explanation:

2*8x+2=3*2x-7
16x+2=6x-7
-6x      -6x
10x+2=-7
     -2   -2
10x=-9
x=-9/10

Based on the amount that Luis earns per week, and the state flat rate income tax, Luis's state income tax for the week is $11.66

First, find out what Luis's earnings for the week were:

= Number of hours worked for the week x Earnings per hour

= 28 x 11.90

= $333.20

The state income tax is therefore:

= Amount earned weekly x State tax rate

= 333.20 x 3.5%
= $11.66

In conclusion, the state income tax of Luis for the week comes to an amount of $11.66.

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So, the polynomial with the require properties is x⁵ + x⁴ - 3x³ - 5x² - 2x

A polynomial is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² + ... + a₂x² + a₁x + a₀ where aₙ are coefficients and n ≥ 2.

Since we are given a polynomial with the following properties: fifth degree, −1 is a zero of multiplicity 3, 2 is the only other zero.

We have that it has zero at

⇒ x + 1 = 0 and x - 2 = 0

⇒ (x + 1) and (x - 2) are factors of the polynomial

We are told that the polynomial has a zero of -1 with multiplicity of 3. This implies that the factor (x + 1) is repeated 3 times. That is (x + 1)(x + 1)(x + 1)

So, multiplying all four factors we have a polynomial of fourth degree as p(x) = (x + 1)(x + 1)(x + 1)(x - 2)

= (x² + 2x + 1)(x + 1)(x - 2)

= (x³ + 3x² + 3x + 1)(x - 2)

= x⁴ + x³ - 3x² - 5x - 2

To obtain a polynomial of degree 5, we multiply through by x, so we have

g(x) =xp(x)

= x(x⁴ + x³ - 3x² - 5x - 2)

= x⁵ + x⁴ - 3x³ - 5x² - 2x

So, the required polynomial is x⁵ + x⁴ - 3x³ - 5x² - 2x

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Answer:

The maximum number of people that can be invited is 65.

Step-by-step explanation:

Based on the information given in the question, the equation to solve the question will be:

80 + 37x = 2500

80+37x=2500

Step 1: Simplify both sides of the equation.

37x+80=2500

Step 2: Subtract 80 from both sides.

37x+80−80=2500−80

37x=2420

Step 3: Divide both sides by 37.

37x/37 = 2420/37

x= 2420/37

x = 65.4

x ≈ 65

Correct answer is B. The zeros of the function g will be ( -6 and 7.)

(x-7) and (x + 6) are factors in a function g.

To locate: The function g's zeros.

Because x-a=0 x = a, we know that if (x-a) is a function's factor, then x-a is the function's zero.

The fact that (x - 7) and (x + 6) are factors in the function g is a given.

x-7=0

x = 7

Likewise, x+6=0

x = -6

As a result, the function g's two zeros are -6 and 7.

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A number system is defined as the representation of numbers by using digits or other symbols, one hundred twenty one thousand, two hundred eleven in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner

one hundred twenty one thousand, two hundred eleven is

121211

This can be written in base ten numerals.

121211

=100000+20000+1000+200+10+1

=10^5+2*10^4+10^3+2*10^2+10^1+1*10^0

Therefore one hundred twenty one thousand, two hundred eleven  in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.

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Answer: 50 ft long and 6.25 ft wide

Step-by-step explanation:

The cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.

We are given that:

Cost of 4 pounds of walnuts and 8 pounds of chocolate chips = $ 21.

Cost of 2 pounds of walnuts and 3 pounds of chocolate chips = $ 9.

Let the cost of pounds of walnuts be x and the cost of pounds of chocolate chips be y.

So, we get the following equations:

4 x + 8 y = 21    …(1)

2 x + 3 y = 9

2 x = 9 - 3 y

x = 1 / 2 (9 - 3y)   …(2)

Put the value of x in (1)

4 ( 1 / 2 (9 - 3y) ) + 8 y = 21

2(9 - 3y) + 8 y = 21

18 - 6 y + 8 y = 21

2 y + 18 = 21

2 y = 21 - 18

2 y = 3

y = 3 / 2

y = 1.5

x = 1 / 2 (9 - 3y)

x = 1 / 2 ( 9 - 4.5)

x = 1 / 2 ( 4.5)

x = 2.25

Therefore, we get that, the cost for each pound of walnuts is $ 2.25 and each pound of chocolate chips is $ 1.5.

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Answer:

The car passed the truck after 60 minutes.

Step-by-step explanation:

We should first find how far the truck was from the entrance to the highway when the car entered (after 11 minutes). We know that the distance travelled is the product of the time and speed, therefore, the location of the truck is given by [tex]d = 60 * 11 = 660[/tex].

Now we can build functions representing the distance from the entrance of both vehicles, in respect to the time travelled.

Truck's Function
[tex]x_0 = 660m \\ v = 60mph \\ \to x(t) = 660m + 60t[/tex]

Car's Function
[tex]x_0 = 0m \\ v = 71mph \\ \to x(t) = 71t[/tex]

Finally, we can equalize both functions to find out at what time the car passed the truck (when their graphs intercepted):

[tex]660 + 60t = 71t \\ \to 660 = 11t \\ \to t = 60m[/tex]

The longest part is Part B, which is a little longer than Part A.

The length is the measure of distance or total time from one point to another.

For example, when measuring dimensions, the length also shows the longest side of an object, especially the rectangle.

Together with the width, the length can be used to determine the area of an object or its perimeter.

Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

Convert all lengths (A and D) into decimals:

Part                         A                 B           C          D

Length (IN.)         1.29 (1²/₇)       1.3         1.15     1.05 (²¹/₂₀)

Part B's length is the most extended length, followed by Part A, Part C, and lastly, Part D.

Thus, the most extended length of the four parts is Part B.

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Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

Answer:

Step-by-step explanation:

Answer: the sum of one interior angle and one exterior angle is 180. x+120=180. x=180-120. x=60°. sum of angles in a triangle is 180.

The mean absolute deviation (MAD) of this data set is 3

The statement is given as

"all of the values are either 3 beats per minute above the mean or 3 beats per minute below the mean"

As a general rule, the mean absolute deviation of a dataset measures the average difference between each data element and the mean value of the dataset

From the statement, we have

Above/Below = 3 beats per minute

This means that

Mean absolute deviation = 3

Hence. the mean absolute deviation (MAD) of this data set is 3

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Saying that the populations of the U.S. and India went up by 2.6 million and 15.8 million respectively is an absolute comparison.

The relative comparison of the populations of the U.S. and India from 2015 to 2016 would be 0.81% and 1.21% respectively.

In terms of population growth, an absolute comparison is made when the increase in population is denoted through the use of whole numbers. No percentages or fractions are used.

By simply mentioning that the U.S. population rose by 2.6 million and that of India rose by 15.8 million is therefore absolute.

The relative comparison is found as:

= Change in population / Population in 2015

For the United States:

= 2.6 million  / 320.7 million

= 0.81%

For India:

= 15.8 million / 1.31 billion

= 1.21%

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Answer:

41 adults and 82 kids

Step-by-step explanation:

divide 123 by 3 two parts are kids one part is adults.

Answer:

88

Step-by-step explanation: The measure of the exterior angle is equal to the sum (adding together) of the interior angles. 42+46=88.

Answer:

That's probably false.

Answer:

y-intercept is -17

x-intercept is 17

Step-by-step explanation:

See attached

The no. of sales made by the agent if he calls 20 clients is 43.

The basic equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line and can be represented graphically. A linear equation is a straightforward way of representing a mathematical statement. Unknown quantities can be represented by any variable or symbol, but in most cases, in a linear equation with one variable, a variable 'x' is used to represent the unknown quantity.

No. of sales =18.9476+1.1842x

Here x = no. of phone calls

The agent calls 20 client.

So, x = 20

Put x = 20 in the given no. of sales. equation

No. of sales = 18.9476 + (1.1842)(20)

No. of sales = 18.9476+23.684

No. of sales = 42.6316

Since the number of sales can't be in decimal numbers, so we will round off the given no. of sales.

Therefore, the no. of sales = 43

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Answer:

Marcus Ran 1.25km farther than cindy

Step-by-step explanation:

After school, Marcus ran 3.2 km and Cindy ran 1.95 km. Who ran farther? How much farther? Marcus ran 1.25 km farther than Cindy.