What is the real part of the complex number 18 - 6i?
• i
• -6i
• 18
•-6

Answer:

[tex]\frac{2\sqrt{2} }{3}[/tex]

Step-by-step explanation:

The sine of an angle is defined as the ratio between the opposite side and the hypotenuse of a given right-angled triangle;

sin x = ( opposite / hypotenuse)

The opposite side to the angle x is thus 1 unit while the hypotenuse is 3 units. We need to determine the adjacent side to the angle x. We use the Pythagoras theorem since we are dealing with right-angled triangle;

The adjacent side would be;

[tex]\sqrt{9-1}=\sqrt{8}=2\sqrt{2}[/tex]

The cosine of an angle is given as;

cos x = (adjacent side / hypotenuse)

Therefore, the cos x would be;

[tex]\frac{2\sqrt{2} }{3}[/tex]

Answer:

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Step-by-step explanation:

We know that [tex]sen(x) =\frac{1}{3}[/tex]

Remember the following trigonometric identities

[tex]cos ^ 2(x) = 1-sin ^ 2(x)[/tex]

Use this identity to find the value of cosx.

If [tex]sen(x) =\frac{1}{3}[/tex] then:

[tex]cos ^ 2(x) = 1-(\frac{1}{3})^2[/tex]

[tex]cos ^ 2(x) =\frac{8}{9}[/tex]

[tex]cos(x) =\±\sqrt{\frac{8}{9}}[/tex]

[tex]cos(x) =\±2\frac{\sqrt{2}}{3}[/tex]

Answer:

- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Earth and the Sun.

Step-by-step explanation:

Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.

Then:

The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Cosine of an angle.

The scientist can substitute these measurements into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], and solve for the distance "d".

Knowing that:

[tex]\alpha=x\°\\adjacent=d\\hypotenuse=y[/tex]

Then:

[tex]cos(x\°)=\frac{d}{y}[/tex]

And solving for "d":

[tex]ycos(x\°)=d[/tex]

The scientist can use the tangent function in trigonometry with the measured angle x and distance y to calculate the distance between the Earth and the Sun by rearranging the formula to solve for the opposite side of the right triangle formed.

The scientist can calculate the distance between the Earth and the Sun using the measurements of angle x and distance y through a process known as triangulation or the parallax method. The right triangle formed with vertices at the Earth, Sun, and Shooting Star allows for the application of trigonometric functions. Specifically, the scientist can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side over the adjacent side.

To find the distance between the Earth and the Sun, the scientist applies the formula:

tan(x) = opposite/adjacent

Where opposite is the distance between the Earth and the Shooting Star, and adjacent is the distance between the Sun and the Shooting Star (y). By rearranging the formula to solve for the opposite side, we get:

Distance between Earth and Sun = y * tan(x)

This calculation allows the scientist to determine the distance from the Earth to the Sun, given that they have the measurements of angle x and distance y.

Answer:

15%

Step-by-step explanation:

To calculate the percent of the bill that was left as a tip, you would divide the amount of the tip ($4.80) by the cost of the meal ($32) to get 0.15. This is then multiplied by 100 to give a tip percentage of 15%.

To determine the percentage of the bill that was left as a tip, you would divide the amount of the tip by the cost of the meal and then multiply by 100 to convert the decimal to a percentage. This would calculate as follows:

So, Michael and his friends left a 15% tip on the bill.

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Answer:

12.5 miles per hour.

Step-by-step explanation:

There are 60 minutes in 1 hour so:

12 minutes = 12/60 = 1/5 of an hour.

So his speed in mph

= distance in miles / time in hours

= 2.5 / 1/5

= 2.5 * 5

= 12.5 miles per hour.

The speed in miles per hour is 12.5 miles/hour

How to calculate speed?

We define speed as :

Speed= Distance/Time

In other words, it is the distance travelled in a unit time

Here,

Distance=2.5 miles

Time=12 minutes that is 12/60 =1/5 hours

[tex]Speed=\dfrac{2.5}{1/5}[/tex]

Speed= 2.5*5=12.5 miles/hour

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Answer:

Step-by-step explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex]              cross multiply

[tex]14(x+8)=10(2x-5)[/tex]             use the distributive property

[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]

[tex]14x+112=20x-50[/tex]           subtract 112 from both sides

[tex]14x=20x-162[/tex]           subtract 20x from both sides

[tex]-6x=-162[/tex]         divide both sides by (-6)

[tex]x=27[/tex]

Answer:

27.

Step-by-step explanation:

I just did this question and I got it incorrect by answering 12. It's 27!

Answer:

(-3,4)

Step-by-step explanation:

The axis of symmetry, or X coordinate for a parabolic function is [tex]\frac{-b}{2a}[/tex]

By plugging in 6 for b, and 1 for a, you have -3.

By then plugging back into the function you can get the Y coordinate of the vertex.

[tex]f(x)=(-3)^{2}+6(-3)+13[/tex]

Or 4.

The answer is (-3,4)

ANSWER

(-3, 4)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 6x + 13[/tex]

We complete the square to obtain the vertex form:

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 6x + {3}^{2} + 13 - {3}^{2} [/tex]

The first three terms form a perfect square trinomial.

[tex]f(x) = {(x + 3)}^{2} + 13 - 9[/tex]

[tex]f(x) = {(x + 3)}^{2} + 4[/tex]

Comparing this to the vertex form;

[tex]f(x) = {(x - h)}^{2} + k[/tex]

h=-3 and k=4

Answer:

its 1/2

Step-by-step explanation:

Final answer:

The constant of proportionality (r) in the equation y=rx can be found by dividing y by x for any given pair of values. Using the pair (14, 7), the constant of proportionality is calculated as r = 7 / 14 = 0.5.

Explanation:

The quantities x and y are said to be proportional if they relate via a constant of proportionality, which we refer to as r in the equation y=rx. To find the constant of proportionality, you can choose any given pair of values for x and y and divide them. For example, using the given pair (14, 7), we can find r by dividing 7 by 14.

r = y / x = 7 / 14 = 0.5

Therefore, the constant of proportionality r is 0.5. You can check this value with other given pairs to confirm it is consistent. For further confirmation, using the pair (30, 15), we have:

r = 15 / 30 = 0.5

which matches our previously calculated constant of proportionality.

x < 7

It's not less than or equal to, because of the open circle on the seven

can i get brainliest if not thats fine

Answer:

x < 7

Step-by-step explanation:

did this for an assigment soooo

Answer:

Part 1) The surface area is [tex]SA=35.1\ cm^{2}[/tex]

Part 2) The volume is equal to [tex]V=12.15\ cm^{3}[/tex]

Step-by-step explanation:

The question in English is

The bases of a right prism are two rectangle triangles whose legs measure 1.5 cm and 1.8 cm, respectively, the prism has a height of 4.5 cm. calculates its total surface area and volume

Part 1) Find the surface area

The surface area is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the area of the base B

[tex]B=(1.5)(1.8)=2.7\ cm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2*(1.5+1.8)=6.6\ cm[/tex]

we have

[tex]h=4.5\ cm[/tex]

substitute the values

[tex]SA=2(2.7)+(6.6)(4.5)=35.1\ cm^{2}[/tex]

Part 2) Find the volume

The volume is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

we have

[tex]B=2.7\ cm^{2}\\ h=4.5\ cm[/tex]

substitute

[tex]V=(2.7)(4.5)=12.15\ cm^{3}[/tex]

a:

Just divide both sides by 7. Since 7 is positive, you don't need to change the inequality sign:

[tex]7j>77\iff j>11\}[/tex]

In set notation, we write

[tex]\{j \in \mathbb{R}\ :\ j>11[/tex]

b:

Subtract 9 from both sides:

[tex]17\leq x+9 \iff 8\leq x[/tex]

In set notation, we write

[tex]\{x \in \mathbb{R}\ :\ x\geq 8\}[/tex]

Range: [0, ∞), {y|0 ≤ y}

Answer:

(x - 5)(2x + 3)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 15 = - 30 and sum = - 7

The factors are - 10 and + 3

Use these factors to split the x- term

2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )

= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term

= (x - 5)(2x + 3)

The factorization of the quadratic expression is presented as follows;

2·x² - 7·x - 15 is  (2·x + 3)·(x - 5)

A quadratic expression is an expression that can be presented in the form a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

In order to factorize the quadratic expression 2·x² - 7·x - 15, it is required to find two binomials with a product equivalent to the expression is to be found

The binomial can be found from the numbers p and q such that p + q = -7 and p·q = -30 (The product of the leading coefficient and the constant term)
A possible pair of such numbers is p = -10 and q = 3. Therefore, we get;

2·x² - 7·x -15 = 2·x² + (3·x - 10·x) - 15

The first two terms and the last two terms can be grouped and each group factorized separately as follows;

2·x² + (3·x - 10·x) - 15 = (2·x² + 3·x) +  (-10·x - 15)

x·(2 + 3) - 5·(2·x + 3)

The above expression can be further factorized by taking out the common factor (2·x + 3) as follows;

x·(2 + 3) - 5·(2·x + 3) = (2·x + 3)·(x - 5)

Therefore, the factored expression is; 2·x² - 7·x - 15 = (2·x + 3)·(x - 5)

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Answer:

C.

Step-by-step explanation:

Negative one is a natural number.

Answer:

from sloping up to sloping down ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Now lets solve the problem

∵ The equation of the line is y = 2x - 6

∵ The equation is changed to y = -2x - 6

- If the both signs of x and the number are changed means the

 equation is multiplied by -1

∴ The line is reflected across the x-axis

- If the sign of x only is changed

∴ The line is reflected across the y-axis

- From the equation 2x changed to -2x, but -6 not changed

∴ The sign of x only changed

∴ The line is reflected across the y-axis

* The graph is reflected across the y-axis

∴ from sloping up to sloping down

The line is reflected over the x axis

To obtain the graph of the function y = |x+2| we have to make a table of values of x to find the values of y. The absolute value or modulus of a real number is its numerical value without care its sign. For example, the absolute value of |4| and |-4| is 4.

In order to make a graph we are going to use the values (-3, -2, -1, 0, 1, 2, 3) for x.

x = -3

y = |-3 + 2| = |-1| = 1

x = -2

y = |-2 + 2| = |0| = 0

x = -1

y = |-1 + 2| = |1| = 1

x = 0

y = |0 + 2| = |2| = 2

x = 1

y = |1 + 2| = |3| = 3

x = 2

y = |2 + 2| = |4| = 4

x = 3

y = |3 + 2| = |5| = 5

 x   ║   y

-3        1

-2        0

-1         1

 0        2

 1         3

 2        4

 3        5

Obtaining the graph shown in the image attached.

.

Answer:

B.  50 km/hr

Step-by-step explanation:

speed of train relative to man = [tex]\frac{125}{10}[/tex] m/sec

= [tex]\frac{25}{2}[/tex] m/sec

= ([tex]\frac{25}{2}[/tex] x [tex]\frac{18}{5}[/tex] ) km/hr

= 45 km/hr

let the speed of the train be x km/hr (x=-5)

x -5 = 45

x -5 + 5 = 45 + 5

x = 50 km/hr

Answer:

50 km/hr.

B

Step-by-step explanation:

I get the same answer (50 km/hour) but I did it slightly differently and both solutions are worth seeing.

First of all you have to figure out how far the man runs. Assume he starts right at the tip of the cow catcher (the furthest point out on one of those old fashioned engines.

He runs at 5km / hour for 10 seconds.

5 km = 5000 meters.

5000 meters / hour * [1 hour / 3600 seconds ] = 1.38889 m/sec.

He does this for 10 seconds

d = r * t

d = 1.38889 * 10

d = 13.8889

Now look at what the train has to do. It passes him in 10 seconds. (The train has gone from the tip of the cow catcher to the end of the caboose in 10 seconds.)

d = 125 + 13.8889 meters

d = 138.8889 meters.

Now we have to convert this to km / hour

138.8889 m / 10 seconds [ 1 km/ 1000 m] *  [ 3600 sec / 1 hr.]

(138.8889 * 1 * 3600 ) / (10 * 1000 * 1 )

50.000004

So the answer is 50 km/hr.

Answer:

A

Step-by-step explanation:

It Has The Most Matching Y Values with The Intervals (I could Be Wrong Tho)

Answer:

(10,6) is a positive and (-2, -3) are negative

Step-by-step explanation:

Answer:

a0) 2

  x<0

a1) x

   0≤x<3

a2) 3

     x≥3

Step-by-step explanation:

As shown in the given graph

function of y is a straight line at y=2 line till x=0

hence a0:

y= 2 for x<0

Then function becomes linear line from x=0 till x=3

hence a1:

y= x for 0≤x<3

Now after that graph of function y again shift to straight line from x=3 onward with y-axis value of 3

hence a2:

y= 3 for x≥3 !

Answer:

[tex]\frac{1}{4096}[/tex]

Step-by-step explanation:

To solve this we are using the formula for the nth term of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

where

[tex]a_1[/tex] is the first term

[tex]r[/tex] is the common ratio

[tex]n[/tex] is the position of the term in the sequence

The common ratio is just the current term divided by the previous term in the sequence, so [tex]r=\frac{16}{64} =\frac{4}{16} =\frac{1}{4}[/tex]. We can infer from our sequence that its first term is 64, so [tex]a_1=64[/tex].

Replacing values

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

We want to find the 10th term, so the position of the term in the sequence is [tex]n=10[/tex].

Replacing values

[tex]a_n=64(\frac{1}{4} )^{n-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{10-1}[/tex]

[tex]a_{10}=64(\frac{1}{4} )^{9}[/tex]

[tex]a_{10}=\frac{1}{4096}[/tex]

We can conclude that the 10th term of the sequence is [tex]\frac{1}{4096}[/tex]

Answer:

10th term of the sequence 64,16,4... = 1/4096

Step-by-step explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here  

T₁₀ = ar⁽ⁿ⁻¹⁾

 = 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

 = 4³/4⁹ = 1/4⁶ = 1/4096

Answer:

False

Step-by-step explanation:

y = -(5/2)x

The slope is -(5/2)

Answer:

[tex]36.5\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

x----> the perimeter of the larger figure

y ----> the perimeter of the smaller figure

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=28\ cm[/tex]

[tex]y=20\ cm[/tex]

substitute

[tex]z=\frac{28}{20}=1.4[/tex]

step 2

Find the area of the larger figure

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x----> the area of the larger figure

y ----> the area of the smaller figure

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=1.4[/tex]

[tex]y=18.6\ cm^{2}[/tex]

substitute

[tex]1.4^{2} =\frac{x}{18.6}[/tex]

[tex]x=1.96*(18.6)=36.5\ cm^{2}[/tex]

Answer:

lower section

Step-by-step explanation:

Given:

Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.

Pyramid B: Base is square with 10 meter sides.

Heights are the same.

Volume of rectangular pyramid = (L * W * H) / 3

Volume of square pyramid = a² * h/3

Let us assume that the height is 10 meters.

V of rectangular pyramid = (10m * 20m * 10m)/3 = 2000/3 = 666.67 m³

V of square pyramid = (10m)² * 10/3 = 100m² * 3.33 = 333.33 m³

The volume of pyramid A is TWICE the volume of pyramid B.

If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),  

V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³

The new volume of pyramid B is EQUAL to the volume of pyramid A.

The volume of the pyramid A is twice the volume of pyramid B. If the height of B is increased to twice, the volumes of A and B are equal.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters.

The base of pyramid B is a square with 10-meter sides.

The heights of the pyramids are the same.

Volume of a rectangular pyramid = lwh / 3, where l, w and h are length, width and height respectively.

Volume of pyramid A = 10 × 20 × h /3 = 200/3 h

Volume of a square pyramid = a²h/3, where a is the side length of the base and h is the height.

Volume of pyramid B = 10²h/3 = 100/3 h

So volume of pyramid A = 2 × volume of B.

If height of B increased to twice that of pyramid A,

Volume of B = 100/3 (2h) = 200/3 h

So both are equal in this case.

Hence the volume of pyramid A is twice that of B in the first case and the volumes are equal in the second case.

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Answer:

(6,-11)

Step-by-step explanation:

Given

Point B' = (4,-8)

And the translation formula (x-2, y+3)

In order to get the coordinates of the point before translation, both given points have to be put equivalent.

So, for x-coordinate

x-2 = 4

x= 4+2

x= 6

And for y-coordinate

y+3 = -8

y = -8-3

y=-11

So the old coordinates of old point were (6,-11) ..

your answer is (6, -11)

Answer:

It's prime

Step-by-step explanation:

So there are no factors except 1 and 17

Answer:

15/36 = 5/12 = 41.66%

Step-by-step explanation:

If a die is rolled twice in a row, and the up face value of both throws are added, that's basically like if you had thrown 2 dice at the same time.

If you throw 2 dice at the same time, there are 36 possible outcomes, from (1,1), (1,2)... to (6,5), (6,6).

You just then have to calculate how many combinations are greater than 7.  We have (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5) and (6,6)... a total of 15 values above 7.

So, the probability is 15 totals  >7  out of 36 possible outcomes:

15/36 = 5/12 = 41.66%

Answer:

303.6ft²  or 347.88 ft²

Step-by-step explanation:

The question is on area

The dimensions of the living room are given as;

Length= L = 22'-0"

Width= W= 12' -0" or 13'- 9"

Area= L× W

22'×12'=264ft²

Allow 15% waste

264× 115/100 =303.6ft²

or

Length= 22' and width = 13' 9"

change 9" to ft ⇒1'=12"...........................divide by 12"

9/12=0.75'................add to 13'

13'+0.75'=13.75'

Area=L×W

22'×13.75'=302.5ft²

Add 15% allowed waste

302.5 × 115/100 =347.88 ft²

Step-by-step explanation:

Of the 1000 people randomly selected, 638 wear glasses.

638 / 1000 = 0.638

Since the sample is random, we can assume it is representative of the population.  So if there are 320 million people in the US, we would estimate the number that wears glasses is:

0.638 × 320 million ≈ 204 million

Answer:

204.16 million

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 638 of these people wear glasses.

The probability that a randomly selected person will wear glasses is:

[tex]P = \frac{638}{1000}\\\\P = 0.638[/tex]

Then, the expected number of people who wear glasses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.638[/tex]

[tex]N = 204.16\ million[/tex]

Answer:

Focus = (0, [tex]\frac{3}{4}[/tex])

Step-by-step explanation:

(± 3, 3) are at an equal distance from y-axis.

axis of parabola = y-axis

vertex = (0, 0)

Parabola will be of the form: x² = 4ay, passing through(± 3, 3)

(± 3)² = 4 × a × 3  ⇒ 9 = 12a   ⇒ a = [tex]\frac{9}{12}[/tex]

a = [tex]\frac{3}{4}[/tex]

Coordinates of focus are: (0, a)  ⇒  (0, [tex]\frac{3}{4}[/tex])

Answer:

The focus of the parabola is (0 , 3/4)

Step-by-step explanation:

* Lets revise some facts about the parabola

- The standard form of the equation of a parabola of vertex (h , k)

 is (x - h)² = 4p (y - k)  

- The standard form of the equation of a parabola of vertex (0 , 0)  is

  x² =  4p y, from this equation we can find:  

# The axis of symmetry is the y-axis,  x = 0  

# 4p equal to the coefficient of y in the given equation  

# If  p  >  0, the parabola opens up.  

# If  p <  0, the parabola opens down.

# The coordinates of the focus,  (0 , p)

# The directrix ,  y = − p

* Now lets solve the problem

∵ The vertex of the parabola is (0 , 0)

∴ The equation of the parabola is x² = 4p y

∵ the parabola passes through points (-3 , 3) and (3 , 3)

- Substitute the value of x and y coordinates of one point in the

 equation to find the value of p

∴ (3)² = 4p (3) ⇒ we use point (3 , 3)

∴ 9 = 12 p ⇒ divide both sides by 12

∴ p = 9/12 = 3/4

- Now lets find the focus of the parabola

∵ The focus of the parabola is (0 , p)

∵ p = 3/4

∴ The focus of the parabola is (0 , 3/4)