Graph the following inequality. Then click to show the correct graph.


3x - 2y ≤ 6

Write z in polar form:

z = 1 + √3 i = 2 exp(i π/3)

Taking the square root gives two possible complex numbers,

√z = √2 exp(i (π/3 + 2kπ)/2)

with k = 0 and k = 1, so that

√z = √2 exp(i π/6) = √(3/2) + √(1/2) i

and

√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i

Answer:

The marked price of the article was $ 6000.

Step-by-step explanation:

Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:

4000 x X x 0.8 = 4000 x 1.2

4000 x X x 0.8 = 4800

4000 x X = 4800 / 0.8

4000 x X = 6000

X = 6000/4000

X = 1.5

4000 x 1.5 = 6000

Therefore, the marked price of the article was $ 6000.

Answer:

D. ✔ 28

Step-by-step explanation:

E 2021

Answer:

There is significant preference among the 3 designs

Step-by-step explanation:

Given :

Design 1 Design 2 Design 3

54 38 28

H0 : no significant preference among the 3 designs

H1 : The preference among the designs are different

To test, we use the Chisquare test for independence ;

χ² = (observed - Expected)² / Expected

The sample size, n = 120

Expected = 120 / number of designs = 120 / 3 = 40

(54-40)^2/ 40 + (38 - 40)² / 40 + (28 - 40)² / 40

= 4.9 + 0.1 + 3.6

= 8.6

The Chisquare critical value at 95% = 5.99

Since ;

|χ² critical| < χ² statistic ; we reject the null and conclude that there is significant preference among the 3 designs

Answer:

8

Step-by-step explanation:

Let the unknown number be x.

Therefore, we can write the question as a mathematical statement and this will be:

3x^2 - 137 = 55.  (Note: ^2 = to the power of 2 or "squared"

(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55

Then, we add 137 first to get rid of the (-137)

Therefore:

3x^2 = 192

Then, we divide 3 from both sides to get rid of the (3) in (3x^2).

Therefore,

x^2 = 64.

So, we square root 64. This gives

x = 8.

Therefore, the answer is 8.

Answer: Number “2”

Step-by-step explanation: I took the ck-12 Applications with Inequalities

Answer:

A

Step-by-step explanation:

Answer: D

Step-by-step explanation:

set the functions to subtract

Answer:

Rewrite in vertex form and use this form to find the vertex

Rewrite in vertex form and use this form to find the vertex

(h,k).(−3,9)

Step-by-step explanation:

Answer:

m = +/- 12

Step-by-step explanation:

A quadratic function has only one x-intercept when the discriminant is equal to 0. The discriminant is b^2 - 4(a)(c).

When we plug in what we know, we have:

m^2 - 4(18)(2) = 0.

Then using algebraic properties, solve for m.

m^2 - 144 = 0

m^2 = 144

m = +/- 12

When you plug in positive or negative 12, and then factor you will see that it comes out to a difference of squares, proving that there is only one x-intercept.

Answer: C

Step-by-step explanation:

EDGE 2023

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

I hope this helps!

Answer:

It discusses the role of the God in influencing our decisions

Answer:

I believe it is choice D

Step-by-step explanation:

in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️

9514 1404 393

Answer:

  m∠3 = 63°

Step-by-step explanation:

Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.

Angle 1 is an obtuse angle; angle 3 is an acute angle.

  angle 3 = 180° - angle 1 = 180° -117° = 63°

The measure of angle 3 is 63°.

_____

Additional comment

There are a number of applicable theorems describing the different angle relationships. Taken together, they are summarized by the first statement above. For example, we could declare angles 1 and 4 to be "corresponding" (hence, congruent), and angles 4 and 3 to be a "linear pair", hence supplementary. The net result is that angle 1 is supplementary to angle 3, as we said above.

We could also get there via relations between alternate exterior angles, alternate interior angles, consecutive exterior or interior angles, and other ways. While that terminology is useful to understand in some problems, it is largely irrelevant here.

Answer:

y = -2x + 2

Step-by-step explanation:

Given the following data;

Points on the x-axis (x1, x2) = (2, -1)

Points on the y-axis (y1, y2) = (-2, 4)

To find the equation of line in slope intercept form;

First of all, we would determine the slope of the line.

Mathematically, slope is given by the formula;

[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]

[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

Substituting into the equation, we have;

[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]

[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]

[tex] Slope, m = \frac {6}{-3} [/tex]

Slope, m = -2

Next, we would use the following formula to find the equation of the line;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - (-2) = -2(x - 2)

y + 2 = -2x + 4

y = -2x + 4 - 2

y = -2x + 2 = mx + c

1 5

12 1 121

1

121

13

O A. 27

ОВ.

COIN

OC. .

12

OD. ????????????????

Median of the given data is 8.5.

In statistics, the median is the middle value of the given list of data in order. Data or observations can be sorted in ascending or descending order.

Given data,

1 , 5, 12, 1, 121, 1, 121, 13

Arranging in ascending order

1, 1, 1, 5, 12, 13, 121, 121

Number of elements N = 8

When number of elements is odd

Median = (N/2 th term + (N/2)+1 th term)/2

Median = (8/2 th term + (8/2)+1 th term)/2

Median = (4th term + 5th term)/2

Median = (5+12)/2

Median = 17/2

Median = 8.5

Hence, 8.5 is the median of the given data.

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Answer: Assuming pi is rounded off to 3.14, it is 219.8 feet; if not it is 70π feet

Circumference=one revoloution

Circumference=Diameter times pi

C=Dπ

C=3.14*70

=219.8

219.8 feet

Answer:

a÷(b+c)≠(a÷b)+(a ÷c)

Step-by-step explanation:

To verify that a÷(b+c)=(a÷b)+(a ÷c)

Using the values ;

a=10 , b=5 , 6=2​

plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;

That is, right hand side = left hand side

a÷(b+c) = 10 ÷ (5+ 2)

a÷(b+c) = 10 / 7

Also;

(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7

Given the result, it can be seen that ;

RHS ≠ LHS

10/7 ≠ 7

Answer:

[tex]0.\overline{369} = \frac{41}{111}[/tex]

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

[tex]x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}[/tex]

Answer:

N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)

Step-by-step explanation:

To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.

The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the square be represented as KLMN

Now , the coordinates of the square KLMN is

K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )

Now , let the translated square be represented as K'L'M'N'

When translating the square to three units to the left , the x coordinate of the square gets reduced by 3

So , the new coordinate of the square will be ( x - 3 , y )

Substituting the values in the equation , we get

K' = K ( -5 - 3 , 3 )

L' = L ( 1 - 3 , 3 )

M' = M ( 1 - 3 , 9 )

N' = N ( -5 - 3 , 9 )

So , on simplifying the equation , we get

The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)

Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )

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Answer:

y = 30.96

Step-by-step explanation:

take 23 degree as reference angle

using tan rule

tan 23 = opposite / adjacent

0.42 = 13/y

y = 13/0.42

y = 30.96

15 + 36 not-equals 41, so those lengths will not form a triangle.

15 squared + 36 squared = 1,521

41 squared = 1,681

Since a squared + b squared not-equals c squared, it will not be a right triangle.

15 squared + 36 squared = 297

41 squared = 82

Step-by-step explanation; did it on the website euphoria

The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the transformation of the function be a translation , where

The parent function is f ( x ) = | x |

And , the translated function is f ( x ) = | x + 6 |

So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

And , the function is translated 6 units to the left

Hence , the translated function is f ( x ) = | x + 6 |

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Answer:

A) (2x+3)(x+7) B) (3x-2)(x-5)

Step-by-step explanation:

A) 2x^2+17x+21=(2x+3)(x+7)

B) 3x^2-17x+10=(3x-2)(x-5)

Answer:

x = 6, y = 12

x = 7  y = 14

Step-by-step explanation:

im pretty sure that right, hope this helps!

Answer:

Mean = 4.8875

Median = 4.6

Mode = 4.5 and 7.7

Step-by-step explanation:

Mean is the sum of total of data divided by the sample size

Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5

Sum total = 39.1

Sample size = 8

Mean = 39.1/8

Mean = 4.8875

To get the median we need to first rearrange

1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7

Median = 4.5 + 4.7/2

Median = 4.6

Hence the median is 4.6

Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7

Answer:

a11 = 8+(11-1)6

a11 = 8+54

a11=68

hopefully this is correct

Step-by-step explanation:

Answer:

16 (sixteen) is 6 divided by 3/8.

Answer:

[tex]P(E|A)= \frac{10}{11}[/tex]

Step-by-step explanation:

Given

Two rolls of die

[tex]E \to[/tex] one of the outcomes is 6

[tex]A \to[/tex] atleast one is 6

Required

P(E|A)

First, list out the outcome of each

[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

So:

[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]

Where:

[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]n(E\ n\ A) = 10[/tex]

[tex]n(A) = 11[/tex]

So:

[tex]P(E|A)= \frac{10}{11}[/tex]

Answer:

20

Step-by-step explanation:

Let father's age be x

let son's age be y

x + y = 60 - (eq 1)

Six years ago,

(x - 6) = 5(y - 6) -(eq 2)

From (1)

x = 60-y

Therefore, 60-y - 6= 5y - 30

y = 14

in six years, y = 20