What is the polar form of -2√3 -6i? Help!
2√6 (cosine (2π/3) + i sine (2π/3) )
4√3 (cosine (2π/3) + i sine (2π/3) )
2√6 (cosine (4π/3) + i sine (4π/3) )
4√3 (cosine (4π/3) + i sine (4π/3) )

The possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.

The quadratic function is defined as a function containing the highest power of a variable is two.

The function is given in the question as:

f(x) = 3x² + 2x - 1

To determine possible rational zeros for the given function.

f(x) = 3x² + 2x - 1

For finding rational zeros, f(x) = 0

3x² + 2x - 1 = 0

3x² + 3x - x - 1 = 0

3x(x +1) - 1(x +1) = 0

(x +1)(3x - 1) = 0

(x +1) = 0 and (3x - 1) = 0

x = -1 and 3x = 1

x = -1 and x = 1/3

Thus, the possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.

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Answer:  A

Step-by-step explanation:

A for 1 gram it is $1.00

B for 1 gram it is $1.25

C for 1 gram it is $1.66

D for 1 gram it is $1.25

Jose will need 40.82 in² of paper to cover the stack of coins

The area in this scenario will be:

A = 2πr² + 2πrh

Where r and h represent the radius of the coins and the height of the coin stack respectively

Given: diameter of coin = 1 inch and thickness = 1/8 inch

radius(r) = diameter/2 = 1/2 inch

Substituting values gives:

A = 2×3.14 × (1/2)² + 2×3.14 ×(1/2)×(100 ×(1/8))

A = 40.82 in²

Note: the correct thickness of the coins should be 1/8 in

Therefore, the area of paper Jose will need to cover the stack of coins is 40.82 in²

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Answer:

Step-by-step explanation:

1. Since the price goes up by whatever number it eventually become 20$ from 16$. SO subtract to get number. 20-16= 4 $

So fitting best...: 20$=p+16;p=4$= TRUE

Answer:20$=p+16;p=4$ or Choice C

PS.Hope you find it helpful!!

The points that represents a viable solution to the system of inequalities include the following:

A. (−10, 170)

B. (80, 90)

C. (250, −50)

In order to determine which points are true and viable with respect to a solution of the given system of inequalities, we would have to test the each of the points by substituting their values into the inequalities as follows;

For points (-10, 170), we have:

x + y ≥ 150

-10 + 170 ≥ 150

160 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(-10) + 3.5(170) ≤ 600

-15 + 595 ≤ 600

580 ≤ 600 (Viable).

For points (80, 90), we have:

x + y ≥ 150

80 + 90 ≥ 150

170 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(80) + 3.5(90) ≤ 600

120 + 315 ≤ 600

435 ≤ 600 (Viable).

For points (250, -50), we have:

x + y ≥ 150

250 - 50 ≥ 150

200 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(250) + 3.5(-50) ≤ 600

375 - 175 ≤ 600

200 ≤ 600 (Viable).

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The value to the system of equations is (-10, -4)

In this case, the system of equations is given as

5x -10y = 10

x + 2y = -18

Make x the subject in the second equation

So, we have the following representation

x = -2y - 18

Substitute x = -2y - 18 in the equation 5x -10y = 10

So, we have

5(-2y - 18) -10y = 10

Open the brackets

This gives

-10y - 90 - 10y = 10

Evaluate the like terms

-20y = 80

Divide by -20

y = -4

Recall that x = -2y - 18

So, we have

x = -2 * -4 - 18

Evaluate

x = -10

Hence, the solution is (x, y) = (-10, -4)

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Answer: 30

Step-by-step explanation:

1. You find the slope by picking 2 points and dividing the change in the y-axis by the change in the x-axis. (Time is ALWAYS x)

(50-40)/40-20

(10)/20)

1/2

SLOPE=1/2

2. You find the y-intercept by picking a point, and plugging them into your equation, and solving for b.

(I will be using the point (20,40) )

40=1/2(20)+b

40=10+b

b=30

Y-INTERCEPT=30

By solving a system of equations we will see that Anna works 2 hours washing cars and 5 hours landscaping.

First, we need to define the variables that we will be using, these are:

We know that she works 7 hours in total and earns $78 in total, so we can write the system of equations:

x + y = 7

x*$9 + y*$12 = $78

Isolating x on the first equation we get:

x = 7 - y

Replacing this on the other equation we get:

(7 - y)*$9 + y*$12 = $78

$63 - $9*y + $12*y = $78

$63 + $3*y = $78

$3*y = $78 - $63

$3*y = $15

y = $15/$3 = 5

Then the value of x is:

x = 7 - y = 7 - 5 = 2

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The baker needs  [tex]\frac{25}{12}[/tex]  cups of sugar.

Number of batches of cupcakes a baker needs to make = [tex]3 \frac{1}{8}[/tex]

Number of cups of sugar each recipe uses =   [tex]\\\frac{2}{3}[/tex]

Quantity of sugar required to make  [tex]3 \frac{1}{8}[/tex]  batches of cupcakes = [tex]3 \frac{1}{8}[/tex]  × [tex]\\\frac{2}{3}[/tex]

                                                                                            = [tex]\frac{25}{8}[/tex] × [tex]\frac{2}{3}[/tex]

                                                                                            =  [tex]\frac{25}{12}[/tex]

Therefore, the quantity of sugar required to make  [tex]3\frac{1}{8}[/tex]  batches of cupcakes is   [tex]\frac{25}{12}[/tex]  cups.

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Answer:

532

Step-by-step explanation:

594 [monkeys]  - 62 [birds] = 532

Answer:

Step-by-step explanation:

Ok:

Since percent can only add up to 100%, the sum must be no longer over 100%

There is no green on the spinner only red, white, and blue!

This means that 0 out of 100 percent is available for green!

Answer: 0%

The solution is Option C.

The probability of getting a green colored section on the spinner is given by the equation P ( green ) = 33 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of getting a green colored section on the spinner be represented as P ( green )

Now , the equation will be

The number of sections on the spinner = 3 sections

The 3 sections are = { red , white , green }

So , probability of getting a green colored section P ( green ) = 1 /  number of sections on the spinner

Probability of getting a green colored section P ( green ) = 1/3

Probability of getting a green colored section P ( green ) = 0.33

Probability of getting a green colored section P ( green ) = 33 %

Therefore , the value of P ( green ) is 33 %

Hence , the probability is 33 %

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Answer:

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

Since absolute value is never negative, this inequality is correct for any value of m.

Correct answer choice is B.

Answer:

All real numbers.

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.

Given inequality:

[tex]|9m|+40 > 4[/tex]

Subtract 40 from both sides to isolate the absolute value on one side of the equation:

[tex]\implies |9m|+40-40 > 4-40[/tex]

[tex]\implies |9m| > -36[/tex]

As the absolute value of a number or expression is its positive numerical value:

[tex]\implies |9m| \geq 0[/tex]

Therefore, as 9m is always greater than or equal to zero, it will always be greater than -36, regardless of the value of m.

Therefore, the solution of the given inequality is all real numbers.

If each  sides of the slab form 90° angles, The number of feet that

each diagonal measure is 34 feet.

Using Pythagoreans theorem formula to find the diagonal feet

D² =L² + W²

Where:

D = Diagonal

L= Length = 16 feet

W = Width = 30

Let plug in the formula

D² = 16² + 30²

D² = 256 + 900

D=√1156

D= 34 feet

Therefore the diagonal measure 34feet

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The standard form of a quadratic function is y = 3/2x² + 17/2x - 7

From the question, the points on the quadratic equation are given as

(2,4), (3,5) and (4,3)

The standard form of a quadratic equation is represented as

y = ax² + bx + c

So, we have

Point (2,4):

4a + 2b + c = 4

Point (3,5):

9a + 3b + c = 5

Point (4,3):

16a + 4b + c = 3

Solving using an online calculator. we have

a = 3/2, b = 17/2 and c = -7

Substitute a = 3/2, b = 17/2 and c = -7 in y = ax² + bx + c

y = 3/2x² + 17/2x - 7

Hence, the equation is y = 3/2x² + 17/2x - 7

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Answer:

x = (1/3)

Step-by-step explanation:

8ˣ = 2

8 = 2³

2³ˣ = 2¹

3x = 1

÷3   ÷3

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

       1

x = ------

       3

I hope this helps!

Answer:

quick market

Step-by-step explanation:

because it more cheaper

Minimum  number is 33+4*6= 57

Give us two positive numbers, x and y.

196 is the result: x*y = 19

The minimum is the product of the first plus four times the second: x + 4y.

The first equation results in y = 196/x. Put that into the second equation as a replacement:

x + 4y = x + 4(196/x) = x + 784/x

Taking the first derivative now, we can solve for x by setting it to zero.

d(x + 784/x)/dx = 1 - 784/[tex]x^{2}[/tex]

0 = 1 - 784/[tex]x^{2}[/tex]

0 = [tex]x^{2}[/tex]- 784 [[tex]x^{2}[/tex] multiplied on both sides]

784 = [tex]x^{2}[/tex]

[tex]\sqrt{784}[/tex] = [tex]\sqrt{x^{2} }[/tex]

Y = 196/x = 7 since we want a positive integer, hence x = 28

The factors of 196 are 196*1, 99*2, 66*3, 6*33,22*19, and 11*18 as a check.

196 + 4*1 = 200

99 + 4*2 = 107

66 + 4*3 = 78

33+4*6= 57

22 + 4*19 = 98

11 + 4*18=82

In fact, 33+4*6= 57 is minimum.

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By using GCF and distributive Property, it is obtained that

3550 = 5 [tex]\times[/tex] 710 as a product

What is Greatest Common Factor and distributive property?

Greatest Common factor (GCF) of two numbers a and b is the greatest number that divides both a and b.

Distributive property is the property over both addition and multiplication.

If a, b and c are three numbers, then distributive property is given by

[tex]a \times (b + c) = a \times b + a \times c[/tex]

3550 = 3000  + 550

Now,

[tex]3000 = 2\times 2 \times 2\times 3\times 5 \times 5 \times 5\\550 = 2 \times 5 \times 5 \times 11[/tex]

GCF of 3000 and 550 = 5

3550 = 5 [tex]\times[/tex] 600 + 5 [tex]\times[/tex] 110

3550 = 5 [tex]\times[/tex] (600 + 110) [Distributive Property]

3550 = 5 [tex]\times[/tex] 710

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There are two closed containers and four balls can just fit in each of the containers, then container A has a smaller surface area.

A three-dimensional solid shape's capacity is referred to as its volume. It is difficult to visualize in any shape, yet this can be evaluated among forms.

As per the data in the question,

Radius, r = 30 mm

Height, h = 60 × 4 = 240 mm

Use the equation of the surface area of the cylinder, SA = 2πr² + 2πrh

SA = 2π(30)² + 2π (30)(240)

SA = 50,868.

Now, calculate the area of a rectangular prism,

Area of top and bottom,

= (60 + 60) × (60 + 60) × 2

= 120 × 120 × 2 = 28,800

Area of 2 sides,

= 2 × (60 × 120) = 14,400

Area of front and back,

= 2 × (60 × 120) = 14,400

Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600

Therefore, A has a smaller surface area.

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Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.

Step-by-step explanation:

Answer:

n = 3

Step-by-step explanation:

-4n + 7 + 2n = 1

Collect like terms

-2n + 7 = 1

Subtract 7 from both sides

-2n = 1 - 7

Do the math on the right side

-2n = -6

Divide both sides by -2

n = 3

The Venn diagram is attached below.

We have four sets. The sets are represented by the alphabets "U", "N", "P", and "E". The universal set is represented by U. The sets are defined as given below.

U = {x | - 10 ≤ x ≤ 10, x ∈ l}

N = {x | -10 ≤x≤-1, x ∈ l}

P = {x | 1 ≤ x ≤ 10, x ∈ l}

E = {x | x = 2a, 1 ≤ a ≤ 5, a ∈ l}

The elements in the universal set "U" are -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The elements in the set "N" are -10, -9, -8, -7, -6, -5, -4, -3, -2, and -1.

The elements in the set "P" are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The elements in the set "E" are 2, 4, 6, 8, and 10.

We need to draw the Venn diagram. A Venn diagram is a graphic representation of the contrasts and similarities between two concepts. Venn diagrams are sometimes known as logic diagrams or set diagrams.

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The solutions for the equation (2x+3)² = 10 is:

Given:

the equation is:

(2x+3)² = 10

we need to solve the following equation.

⇒ (2x+3)² = 10

taking square roots on both sides.

⇒ √(2x+3)² = √10

⇒ 2x+3=±√10

Now solving:

2x+3=√10 and 2x+3=-√10

2x=√10-3 and 2x=-√10-3

x=√10-3/2 and x=-√10-3/2

Hence we get the solutions of the given equation.

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Answer:

Option 3 ) 18x - 9 = 72

Step-by-step explanation:

Algebraic equations:

  [tex]\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\[/tex]

Multiply each term of (30x - 15) by 3/5,

    [tex]\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72[/tex]

The given equation is same as 18x - 9 = 72

The total amount of money spent on pass and lunch for each student is $19.28.

The first step is to determine the amount that was spent on a pass for each student. The cost of one pass can be determined by dividing the total amount spent on passes by the total number of teachers and students.

Cost of one pass = total amount spent on one pass / total number of people

Cost of one pass = 526.26 / (47 + 2)

Cost of one pass = 526.26 / 49

Cost of one pass = $10.74

The second step is to determine the amount spent on lunch for one student. This can be determined by dividing the total amount spent on lunch by the total number of students.

Cost of one lunch = total cost of lunch / total number of students

401.38 / 47 = $8.54

Total amount spent on pass and lunch for each student = cost of lunch for one student + cost of a pass for one student

$8.54 + $10.74 = $19.28

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The quadratic equation is −x²+10x. Domain for the given equation is (0,10) and the Range is (0,25]. The x-intercept is (0,10) and the area is 10.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Here,

quadratic function in standard form that models f(x), the total area of the playground in square feet in terms of its width x in feet,

f(x)=−x²+10x

The graph is given below,

Domain=(0,10)

range=(0,25]

To determine the domain that must exist between them, we used the xx-intercepts. We excluded them from the domain because the area at the x-intercepts is 0.

Since an area must be greater than 0, y>0y>0 follows. Remembering that the vertex of the graph of f(x) has the maximum point of (5,25) the maximum value for y is 25.

−x²+10x is the quadratic equation. The domain and range of the given equation are (0,10) and (0,25), respectively. (0, 10) is the x-intercept, and 10 is the area.

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Answer:

101

Step-by-step explanation:

Since the total number of cheeseburgers was twice the number of hamburgers, let the number of sold hamburgers be h

Twice of h = 2(h)

Hence,

2(h) + h = 303

2h + h = 303

3h = 303

Divide both sides by the coefficient of h

h = 101

Therefore, the total number of hamburgers sold was 101

The graph of the equation p(x) = -3x- 1 has been plotted

The equation is given that

p(x) = -3x - 1

We know the slope intercept form of the line

y = mx + b

Where m is the slope of the line

b is the y intercept

Compare both equation

The slope of the line m = -3

The y intercept b = -1

At x = 1

The value of p(1) = -3(1) -1

= -3 - 1

= -4

At x = 2

The value of P(2) = -3(2) -1

= -6 - 1

= -7

Substitute the value for x and find the value of y.

Draw the graph using the points

Hence, the graph of the equation p(x) = -3x- 1 has been plotted

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the exact value of x, so that the greatest possible amount of light is admitted is 3.92 ft.

let x represents the radius of a semicircle, thus the width of the rectangle = 2x, length be y.

perimeter of the rectangular window = πx + 2y + 2x = x(π +2) + 2y

it is given that the perimeter is 28 ft.,

28 = x(π +2) + 2y

y = 28 - x(π +2) / 2

the area of the window A = 1/2 πx² = 2yx ( area of semicircle + area of rectangle)

A = 1/2 πx² + 2x [(28 - x(π +2) / 2]  (Substituting the value of y)

A = 1/2 πx² + 28x - πx² - 2x²

A = 28x - x² ( 2 + π/2 )

The maximum value of x is when dA/dx = 0

A' = 28- 2x ( 2 + π/2 )

2x ( 2 + π/2 ) = 28

x ( 2 + π/2 ) = 14

x = 3.92 ft

hence the value of x so that the greatest possible amount of light is admitted is 3.92 ft.

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(complete question)

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See the figure below.) If the perimeter of the window is 28 ft, find the value of x so that the greatest possible amount of light is admitted.