Help me ! Solve problems working with imaginary numbers

Answer:

ok

Step-by-step explanation:

why did you put it

Answer:

The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

F(-3;-6), G(3; -2)

When we have two points, the slope is given by the change in y divided by the change in x. So

Change in y : -2 - (-6) = -2 + 6 = 4

Change in x: 3 - (-3) = 3 + 3 = 6

Slope: [tex]m = \frac{4}{6} = \frac{2}{3}[/tex]

So

[tex]y = \frac{2}{3}x + b[/tex]

Finding b:

(3; -2) means that when [tex]x = 3, y = -2[/tex]. We use this to find b.

[tex]y = \frac{2}{3}x + b[/tex]

[tex]-2 = \frac{2}{3}(3) + b[/tex]

[tex]2 + b = -2[/tex]

[tex]b = -4[/tex]

The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]

Answer:

The event is mutually exclusive.

Step-by-step explanation:

Mutually exclusive events are events that cannot exist simultaneously.

Thus, events that are not mutually exclusive can exist simultaneously.

Since each student only has one major, a single student cannot be both a mathematics major and a business major.

So, the event is mutually exclusive.

Answer:

...

Step-by-step explanation:...

Answer:

0.375

Step-by-step explanation:

Check the picture below.

whenever we do division of decimals, we have to mind how many decimals are there on each amount, the dividend as well as the divisor, that way we pad with zeros the other amount accordingly whilst losing the dot, for example, to say divide 3 by 0.123, 3 has no decimals, whilst 0.123 has three decimals, so we can just divide 3000 by 0123, so dividing 3 by 0.123 is the same as dividing 3000 by 123.  Another example, if we were to divide say 23.761 by 555.89331, the dividend has 3 decimals, that means 3 zeros the other way, the divisor has 5 decimals, that means 5 zeros the other way while losing the dots, so we'd end up dividing 2376100000 by 55589331000, which we can simplify to just 2376100 by 5589331, as you can see in the picture in this case.

Answer:

Step-by-step explanation:

(2×4-6)/(3-2)=2

Answer:

[tex]{ \tt{f(x) = x - 2}} \\ { \bf{f(3) = 3 - 2 = 1}} \\ \\ { \tt{g(x) = 2x - 6}} \\ { \bf{g(4) = 2(4) - 6 = 2}} \\ \\ { \boxed{ \tt{ \frac{g(4)}{f(3)} = \frac{2}{1} = 2}}}[/tex]

Answer:

67 mph

Step-by-step explanation:

201/3 = 67

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: y = \frac{17 - 11x}{7} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]\\11x + 7y = 17[/tex]

[tex] \\➺ \: 7y = 17 - 11x[/tex]

[tex]\\➺ \: y = \frac{17 - 11x}{7} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The + 6 moves it up 6 units.

The correct answer is (D) "The graph of g(x) is the graph of f(x) shifted 6 units up."

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

When we add a constant to a function, such as in the case of g(x) = f(x) + 6, it will shift the graph of f(x) upward by 6 units.

This is because, for any value of x, the value of f(x) will be added to 6, resulting in a vertical shift of the entire graph.

Option (A) is incorrect because adding 6 to f(x) would shift the graph up, not down.

Option (B) is incorrect because adding a constant to a function does not cause it to shift horizontally.

Option (C) is incorrect because adding 6 to f(x) would shift the graph right, not left.

D. The graph of g(x) is the graph of f(x) shifted 6 units up. Adding a constant term to a function will shift the graph of the function vertically. In this case, adding 6 to f(x) will shift the graph of f(x) upward by 6 units, resulting in the graph of g(x).

Learn more about function here:

https://brainly.com/question/29633660

#SPJ7

Given:

Consider the below figure attached with this question.

The linear equation is:

[tex]y=2x-8[/tex]

To find:

The values to complete the table of ordered pairs for the given linear equation.

Solution:

We have,

[tex]y=2x-8[/tex]

Substituting [tex]x=0[/tex] in the given equation, we get

[tex]y=2(0)-8[/tex]

[tex]y=0-8[/tex]

[tex]y=-8[/tex]

So, the value for first blank is -8.

Substituting [tex]y=-2[/tex] in the given equation, we get

[tex]-2=2x-8[/tex]

[tex]-2+8=2x[/tex]

[tex]\dfrac{6}{2}=x[/tex]

[tex]3=x[/tex]

So, the value for second blank is 3.

Substituting [tex]x=2[/tex] in the given equation, we get

[tex]y=2(2)-8[/tex]

[tex]y=4-8[/tex]

[tex]y=-4[/tex]

So, the value for third blank is -4.

Therefore, the required complete table is:

     x           y

     0         -8

    3         -2

     2          -4

Answer:

f(-2) = g(-2) this is the answer

Answer:

1 ft^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the base and h is the height

A = 1/2 ( 3) * ( 2/3)

A = 3/2* 2/3

A =1

Answer:

1 ft^2

Step-by-step explanation:

The formula for the area of a triangle is as follows, a=b*h*1/2

Now, let's plug in the values to match your question. A=3*2/3*1/2

Lastly, solve. 3*2/3=6/3=2. Then divide 2 by 1/2=1.

Add the unit to make it 1 ft^2

Hope this helps!

Answer: 0.738

Step-by-step explanation:

11. Mendelian Genetics. When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value that was expected?

p0 = 428/(428 + 152) = 0.737931

If you round your answer of 0.737931 to three decimals you will

get 0.738.

Answer:

7x + 14

Step-by-step explanation:

the first thing to do is expand the parentheses/brackets.

3(5x + 2) -2(4x - 4) will be

3(5x) + 3(2) -2(4x) -2(-4)

= 15x + 6 - 8x + 8

collect like terms

15x - 8x + 6 + 8 = 7x + 14

the answer is 7x + 14

Answer:

3(5x+2)-2(4x-4)

15x+6-8x+8

15x-8x+6+8

7x+14

Answer:

C. 3/8

HOPE THIS HELPS :)

Answer:

c. 3/8

Step-by-step explanation:

first you need the denomerator by adding all marbles together which equals 32. now for the munerator you need the sum of the green and yellow marbles. this equals 12. so your fraction is 12/32. next we simplify. we can divide both numbers by 4. getting us a fraction of 3/8.

Answer:

Step-by-step explanation:

According to the Question,

Then, For any u,w ∈ V ⇒ u+w ∈ V

And u∈V and z∈C ⇒ z u ∈ V

So, If we take any z= i ∈ C

then, z,v ∉ V  ∴z,v Has Complex entries

So, the Scalar Closure axiom is not satisfied

Hence, V is not a Vector Space of C

Any u,w ∈ W ⇒ u+w ∈ V

So, The Additive Closure axiom is satisfied.

Answer:

What is the cos theta for, i would use sin to solve for theta and then we would get 41.25 degrees.

Step-by-step explanation:

Answer:

90km² only if it is parallelogram

Step-by-step explanation:

base = 9km

height=10km

area of parallelogram = b x h

=9km x 10km

=90km²

Answer:

A = 90km2

Step-by-step explanation:

Area of a rhombus is:

1. A = s x h (if given side and height)

2. A = 1/2 a x b (if given lengths of diagonals)

3. A = s^2 sin A (if given side and length)

Therefore from your problem, height and side is given thus, you'll use number 1

A = s x h

A = 9km x 10km = 90km2

Answer:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Step-by-step explanation:

Given

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

[tex]c = 6[/tex]

The geometric series centered at c is of the form:

[tex]\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.[/tex]

Where:

[tex]a \to[/tex] first term

[tex]r - c \to[/tex] common ratio

We have to write

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

In the following form:

[tex]\frac{a}{1 - r}[/tex]

So, we have:

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

Rewrite as:

[tex]f(x) = \frac{9}{3x - 18 + 18 +2}[/tex]

[tex]f(x) = \frac{9}{3x - 18 + 20}[/tex]

Factorize

[tex]f(x) = \frac{1}{\frac{1}{9}(3x + 2)}[/tex]

Open bracket

[tex]f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}[/tex]

Collect like terms

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}[/tex]

Take LCM

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}[/tex]

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}[/tex]

By comparison with: [tex]\frac{a}{1 - r}[/tex]

[tex]a = 1[/tex]

[tex]r = -\frac{1}{3}x + \frac{7}{9}[/tex]

[tex]r = -\frac{1}{3}(x - \frac{7}{3})[/tex]

At c = 6, we have:

[tex]r = -\frac{1}{3}(x - \frac{7}{3}+6-6)[/tex]

Take LCM

[tex]r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)[/tex]

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n[/tex]

Substitute 1 for a

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n[/tex]

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n[/tex]

Substitute the expression for r

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n[/tex]

Expand

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n][/tex]

Further expand:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................[/tex]

The power series converges when:

[tex]\frac{1}{3}|x - \frac{7}{3}| < 1[/tex]

Multiply both sides by 3

[tex]|x - \frac{7}{3}| <3[/tex]

Expand the absolute inequality

[tex]-3 < x - \frac{7}{3} <3[/tex]

Solve for x

[tex]\frac{7}{3} -3 < x <3+\frac{7}{3}[/tex]

Take LCM

[tex]\frac{7-9}{3} < x <\frac{9+7}{3}[/tex]

[tex]-\frac{2}{3} < x <\frac{16}{3}[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Answer:

(x,y) = (3.5, 11)

Step-by-step explanation:

(8,2)(x,y) = (28,22)

Dot product, so:

[tex](8,2)(x,y) = (8x,2y) = (28,22)[/tex]

Then

[tex]8x = 28[/tex]

[tex]x = \frac{28}{8} = 3.5[/tex]

And

[tex]2y = 22[/tex]

[tex]y = \frac{22}{2} = 11[/tex]

So

(x,y) = (3.5, 11)

Answer:

Diagram? I don't see a diagram.

Where is the diagram?

Step-by-step explanation:

Answer:

36cm^2

Step-by-step explanation:

total area: 6x(4+3)=42

total area excluding the space: 42-(2x3)=36

Answer:

36 cm squared

Step-by-step explanation:

To solve this problem, I first construct a line. (shown in yellow in the first photo)

I then find the area of the top rectangle. (6 cm * 4 cm = 24 cm squared.)

Next, I find the area of the lower rectangle. But...to do that I have to find the length of the line that I constructed. To do this, I do  6cm-2cm=4cm.

Then I can find the area of the lower rectangle. (4cm*3cm=12cm squared.)

add up the area of both of the rectangles and.........12+24=36 cm squared

Answer:

No , it is not a right angle triangle

Step-by-step explanation:

according to the pythagoras theorem in right angled triangle sum of square of two sides is equal to the square of it's hypotenuse.

using pythagoras theorem

a^2 + b^2 = c^2

9^2 + 16^2 = 25^2

81 + 256 = 625

337 = 625

since sum of square of two smallest sides of a triangle is not equal to the square of it's hypotenuse it can be concluded that the given figure does not form right angle triangle.

1. Y-Intercepts are where the graph crosses the y-axis. For a parabola, this occurs once, at (0, -3) in the graph shown.

2. X-Intercepts are where the graph crosses the x-axis. For a parabola, this occurs twice, at (-1, 0) and (3, 0) in the graph shown.

3. A parabola that is positive opens upwards, while a parabola that is negative opens downwards. Therefore, this parabola is positive.

Hope this helps!! :)