Consider the set of real numbers and the set of complex numbers. Is every real number also a complex number? Is every complex number also a real number? Explain.

Answer:

[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]

Step-by-step explanation:

A recursive formula allows a rem in the sequence to be found by multiplying the previous term by the common ratio r

For this sequence

r =  [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{-3}[/tex] = 7 , then recursive formula is

[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]

Yes, the results will be equal as it follows from the task content that both numbers were equal initially.

As evident in the task content, it follows that the numbers 77 and 88 although, not equal in the real sense, are equal according to the task content.

Hence, it follows that when equal parts are taken away from the two numbers, they would still be equal as both numbers were equal initially.

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The hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.

The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.

If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:

a² = b² + c².

In the question, we are given that a right triangle, has legs of lengths 6 feet and 4√3 feet each, and we are asked to find the length of the hypotenuse.

Thus, taking b = 6 and c = 4√3, in the above equation, we get:

a² = 6² + (4√3)²,

or, a² = 36 + 48,

or, a² = 84,

or, a² = (2√21)²,

or, a = 2√21.

Thus, the hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.

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The probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4

Let the "green" value be an x value lying on segment AC.

Now, the segment AC has the equation y = x. Then, let the "purple" value that is twice a selected x value lie on the segment AE and as such, the equation of this line is y = 2x.

It must be noted that at point E, x = 0.5 and y = 1. This means at every x value on AC greater than 0.5, the value of y on EC associated with this x value is is less than twice that x value.

Then, between segments AE and AC, every value of y will be greater than, but less than twice, its associated x value.

Since triangle ACD has an area of 1/2 and triangle BEA has an area of 1/4, then we can say that;

Triangle AEC area = 1 - (1/2) - (1/4)   = 1/4.  

Thus,  the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4

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John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

To determine how many images John must scan before his total cost is less than getting scanned images at the computer center, we can set up an equation.

Let's denote the number of images John needs to scan as "x."

The total cost for John to scan x images is given by:

John's total cost = cost of scanner + cost of supplies + cost per image scanned

John's total cost = $215.70 + ($0.34 * x)

The total cost for scanning x images at the computer center is given by:

Computer center's cost = cost per image scanned * x

Computer center's cost = $0.59 * x

We want to find the point at which John's total cost is less than the computer center's cost. In other words, we want to find the value of x for which John's total cost is less than the computer center's cost:

John's total cost < Computer center's cost

$215.70 + ($0.34 * x) < $0.59 * x

Now, we can solve for x:

$215.70 + ($0.34 * x) < $0.59 * x

$215.70 < $0.59 * x - $0.34 * x

$215.70 < $0.25 * x

Divide both sides of the inequality by $0.25:

$\frac{215.70}{0.25} < \frac{0.25 * x}{0.25}$

862.80 < x

Therefore, John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

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Answer:

55

Step-by-step explanation:

Well you just plug in 10 as n.. and you get the equation:

[tex]\frac{10(10+1)}{2} \\\frac{10(11)}{2}\\\\\frac{110}{2}\\\\55[/tex]

Answer:

Step-by-step explanation:

x=25 degrees.

A vertical angle is two angles formed by intersecting lines, just like the two that form 25 degrees and x degrees. The angles formed by vertical angles are congruent (meaning they are equivalent). So, x=25 degrees.

Answer:

see image

Step-by-step explanation:

The x-intercept is the point where the line crosses the x-axis (horizontal, left and right line with numbers, arrows at both ends, usually marked x at the right end)

The y-intercept is where your line crosses the y-axis (vertical, up-and-down line with numbers, arrows at the ends, usually marked y at the top)

Two points determine a line.

Draw a line through the two points given. See image.

Answer: C

Step-by-step explanation:

Construct the segment connecting the point where the height meets to the base to where the slant height meets the base.

This forms a right triangle with legs of length 3.5 and 6.

So, by the Pythagorean theorem, [tex]x=\sqrt{3.5^2 + 6^2} \approx 6.9[/tex]

Answer:

936 cm^2

Step-by-step explanation:

Solution

Back  (This is a rectangle)

Area = w * h

w = 7

h = 18

Area = 7 * 18 =                                                          126 cm^2

Front and Back

Area = 1/2 * B * H  (This is a triangle -- There are 2 of them)

Givens

B = 24

h = 18

Area = 1/2 * 24 * 18

Area = 216

But there are two such triangles = 2*216 =             432 cm ^2

Ramp

Formula Area = L*w (This is a rectangle)

L = 30

W = 7

Area = 30 * 7  =                                                          210 cm^2

Base

This is also a rectangle

L = 24

W = 7

Area = L*W

Area = 24 *7 =                                                            168 cm^2  

Total

168 cm^2

210 cm^2

432 cm^2

126  cm^2

936  cm^2

Answer:

1.) 3/5

Step-by-step explanation:

When know that 3/5 is equivalent to 6/10 because both the numerator and the denominator are scaled up/down by the same amount. To be precise, we can get the answer of 3/5 by dividing the numerator and denominator by 2.

6 / 2 = 3

10 / 2 = 5

Using translation concepts, it is found that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is:

[tex]y = 0.5^x[/tex]

It has a base with absolute value between 0 and 1, hence it is decreasing.

The changes to the function are given as follows:

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Answer:

d&#&#;#;'xn x;e;÷hr&÷h÷ebb ehehhbbsssshhheu73334914218899110

4398.22 cm³ the volume of cylinder.

What is volume of cylinder?

Given,

          Height of cylinder = 14 cm

         radius of cylinder = 10 cm

Now using formula volume of the cylinder = π r² h

          put value in formula,

                                               3.14 × 10× 10 × 14 = 4398.22 cm³

Therefore, 4398.22 cm³ the volume of cylinder.

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The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.

The correct option is (B).

Translation is also another form of transformation whereby all the points of a figure are shifted at exactly the same distance and in the same direction without being resized, reflected nor rotated.

given:

ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.

Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.

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Answer:

B

Step-by-step explanation:

Answer:

Yes, they are equivalent.

One way you can check this is by substituting any number into x.

For example, x = 2:

• First equation :  [tex]\frac{-x}{x + 1}[/tex]

                       ⇒  [tex]\frac{-2}{2 + 1}[/tex]

                       ⇒  [tex]\frac{-2}{3}[/tex]

• Second equation: [tex]\frac{x}{-x-1}[/tex]

                            ⇒  [tex]\frac{2}{-2-1}[/tex]

                            ⇒   [tex]\frac{-2}{3}[/tex]

As both forms of the equation give the same result after substitution, they are equivalent.

Answer:

see below

Step-by-step explanation:

24 ft * 12 in/ft     *   8ft * 12 in/ft   *  10 ft * 12 in/ft = 3317760  in^3

3 317 760 in^3  / 2220 in^3/bushel = 1494.49 bushels

Step-by-step explanation:

As all angles in a triangle add up to 180°

we can write:

(m+18)+(2m+28)+(3m+47) = 180

6m + 93 = 180

6m = 180 - 93

6m = 87

m = 87 / 6

m = 14.5

Answer: adult = 3 child = 5

Step-by-step explanation:

49 = 8a+5c

8 = a+c

use those equations to solve^^

Answer:

la verdad noce no me acuerdo

Answer:

4

Step-by-step explanation:

There are 6 grey diamonds in the row labelled "cat".

Each diamond means two hours.

6 × 2 = 12

Samanth's table shows that cats sleep 12 hours.

Tony is going to use a circle that means 3 hours.

12 ÷ 3 = 4

Tony needs 4 circles to show 12 hours.

4 × 3 = 12

Tony will use 4 circles.

The polynomial Identities and an example of a proof of an identity have been explained below.

Polynomial identities are defined as equations that are always true, regardless of the variable values. These polynomial identities are used while factorizing the polynomial or expanding the polynomial. These polynomial identities are;

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

(a + b)(a - b) = a² - b²

(x + a)(x + b) = x² + x(a + b)+ ab

Let us prove the polynomial identity (a + b)² = a² + b² + 2ab.

Now, (a + b)² is simply the product of (a + b) and (a + b).

That is; (a + b)² = (a + b) × (a + b)

This can simply be imagined to be a square whose side are (a + b) with its' area equal to (a + b)²

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answer:

oops, I accidentally messed this one up, so sorry

Answer:

"We can't use any of the patterns"

Step-by-step explanation:

You can't use [tex](U+V)^2[/tex] because that would result in some stuff in the middle. In general if you have something like that it would expand to [tex]U^2+2UV + V^2[/tex]. and same thing for the (U-V)^2 except the middle would be a negative number. You also can't use [tex](U+V)(U-V)[/tex] because it specifies "constant integers" and the "integer" part is what's really important, because you can technically rewrite the sum of squares as (U + V)(U - V) but you would need to use imaginary numbers. Because the difference of squares is defined as [tex]a^2-b^2 = (a-b)(a+b)[/tex]. But you can also think of it like this [tex]a-b = (\sqrt{a} - \sqrt{b})(\sqrt{a}+\sqrt{b})[/tex] because that's essentially what the original identity is saying. Using this definition you can write the sum of squares as [tex]a+b = a - (-b) = (\sqrt{a} + \sqrt{-b})(\sqrt{a} - \sqrt{-b}) = (\sqrt{a} + i\sqrt{b})(\sqrt{a} - i\sqrt{b})[/tex]. So with the restriction of constant integers "We can't use any of the patterns" is the correct answer

Answer:

x axis is -2.

y axis is +1.

(-1, 3)

Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation.

According to the question,

The following graph represents the linear function f(x) = x -2

Take any point on this line, say, (-1, 3).

Let us substitute (-1, 3) = (x, y) (i.e., x = -1 and y = 3) in the function f(x) = -x + 2 (note that it can be written as y = x - 2).

Then

3 = -(-1) + 2

3 = 1 + 2

3 = 3, thus, (-1, 3) satisfies the function.

In the same way, you can try taking different points and checking whether they satisfy the function. Each and every point on the line (in general called "curve") satisfies the function.

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The inequalities that will have point C as a solution are;

f(x) ≥ 3x + 4

g of x is greater than or equal to negative one half times x minus 5

We can see the inequality graph in the attached file.

Now, the two lines in the graph represent the equations;

f(x) = 3x + 4

g(x) = -¹/₂x - 5

Now, we see the point C and from inspection of the graph, we can see that it is to the right of f(x) and to the bottom of g(x) an as such the inequalities that will have point C as a solution is;

f(x) ≥ 3x + 4

g of x is greater than or equal to negative one half times x minus 5

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The attached graph represents the number line of the inequality |2x - 5] ≥ 3

The inequality is given as:

|2x - 5] ≥ 3

Remove the absolute value sign

2x - 5 ≥ 3 or 2x - 5 ≥ -3

Add 5 to both sides

2x ≥ 5 + 3 or 2x ≥ 5-3

Evaluate

2x ≥ 8 or 2x ≥ 2

Divide through by 2

x ≥ 4 or x ≥ 1

Combine both inequalities

x ≤ 1 and x ≥ 4

See attachment for the number line

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Answer:

30

Step-by-step explanation:

You take a protractor and put at c then you measure

The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is  q⁶  - r⁶s³

The expression is given as:

(q² − r²s) (q⁴ + q²r²s + r⁴s²)

Expand the expression

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)

Open the brackets

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³

Evaluate the like terms

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q⁶  - r⁶s³

Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is  q⁶  - r⁶s³

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Factor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)

Answer: 144 degrees

Step-by-step explanation:

Radian ⇒ Degree = 180/π

Degree ⇒ Radian = π/180

[tex]\frac{4\pi }{5} *\frac{180}{\pi } =\frac{4}{5} *\frac{180}{1} =\frac{720}{5} =144[/tex]

Therefore your answer is 144 degrees

Hello !

π rad <=> 180°

4π/5 rad <=> ?°

The calculation ils attached.

We found 144°.

Have a nice day ;)

Answer:

y = 5

Step-by-step explanation:

The standard form of a linear equation is Ax + By=C

But let's start with the slope-intercept form:  y = mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

M, the slope, may be calculated by using the Rise/Run between the two given points:  (1,5) and (3,5):

Rise = (5-5) = 0  [Note that the value of y does not change when x = 1 or 3.]

Run is = (3-1)=2

Rise/Run (slope, m) is (0/2) or 0.  [y does not change as a function of x.  It is a flat, horizontal line]

The equation becomes y = (2/3)x + b

We need to find a value of b, the y-intercept, that forces the line to go through both points.  This can be done by entering one of the points into the equation and solving for b:

y = (0)x + b

I'll use (1,5)

5 = (0)*(1) + b

b = 5

The equation becomes y = (0)x + 5  or y = 5

Standard form of the equation is Ax + By = C

A is 0, B is 1 and C is 5

y = 5

Based on the rules of the game, the probability that a person wins the game is 3/8 or 37.5%.

If participants can only win 25% of the time, the number that they need to get would be 32 or higher.

The probability of a winning score of 36 or higher in four consecutive attempts is 1/1,296.

To show that the game is fair, the teacher can post that every number apart from 24 and 30 has an equal chance of appearing.

There are 6 sides to dice and 4 cards. The sample space is:

Dice                            Card                 Product         Frequency of Product

1                                5                         5                          1

1                                 6                         6                         1

1                                 7                         7                          1

1                                 8                         8                         1

2                                 5                         10                         1

2                                 6                         12                         1

2                                 7                         14                         1

2                                 8                         16                         1

3                                 5                         15                         1

3                                 6                         18                         1

3                                 7                         21                         1

3                                 8                         24                         2

4                                 5                         20                         1

4                                 6                         24                         1

4                                 7                         28                         1

4                                 8                         32                         1

5                                 5                         25                         1

5                                 6                         30                         2

5                                 7                         35                         1

5                                       8                         40                         1

6                                 5                         30                        

6                                 6                         36                         1

6                                      7                         42                         1

6                                      8                         48                         1

Total                                                                                       24

24 and 30 have frequencies of 2 as they appear twice.

From the table, in order to win, a player needs to get 28 or higher.

There are only 8 numbers that are 28 or higher but including the chance that 30 has a relative frequency of 2, we have 9 chances to win the game. The probability is:

= 9 / 24

= 3 / 8

If people are to win only 25% of the time, this means that the number of products that can be picked is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

A person therefore needs to get 32 or above to win 25% of the time.

The probability of getting 36 or higher is:

= Chance of 36 + chance of 40 + chance of 42 + chance of 48

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

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