Write the real number 12 as a complex number in form of a+bi

Answer:

1. [tex]x=18, y=6\sqrt{10}[/tex]

2. x=108, y=180

Step-by-step explanation:

The height of the right triangle drawn to the hypotenuse is the geometric mean of two segments of the hypotenuse (two legs' projections)

1. Use this property, so

[tex]CD^2=AD\cdot BD\\ \\6^2=2\cdot x\\ \\36=2x\\ \\x=18[/tex]

Consider right triangle BCD. By the Pythagorean theorem,

[tex]BC^2=BD^2+CD^2\\ \\y^2=18^2+6^2\\ \\y^2=324+36\\ \\y^2=360\\ \\y=\sqrt{360}=6\sqrt{10}[/tex]

2. Consider right triangleGM*. By the Pythagorean theorem,

[tex]G*^2=GM^2+M*^2\\ \\240^2=GM^2+192^2\\ \\GM^2=240^2-192^2=(240-192)(240+192)=48\cdot 432=144^2\\ \\GM=144[/tex]

Use this property to find x:

[tex]GM^2=192\cdot x\\ \\144^2=192\cdot x\\ \\x=\dfrac{144^2}{192}=108[/tex]

Consider right triangle GMCup. By the Pythagorean theorem,

[tex]y^2=x^2+GM^2\\ \\y^2=108^2+144^2\\ \\y^2=32,400\\ \\y=180[/tex]

Answer:

Answer:  

$6 *53 = $318  

Step-by-step explanation:

Answer: $318

Step-by-step explanation:

Given : A grocer takes delivery of beverages from your truck at $6 per case.

If you  unloaded 53 cases for the grocer today.

Then the amount of money the grocer owes you will be the product of 53 and 6 .

Thus,  the amount of money the grocer owes you= [tex]53\times6=\$318[/tex]

Hence, the  grocer owes you $318 .

i think its a

hope that helps

Answer:

A.

Step-by-step explanation:

Vertex form for a absolute value function is f(x)=a|x-h|+k

The vertex is (h,k)

If a is positive it is open up

If a is negative it is open down

So looking at the a part we can rule out 2 choices B and D

Finding the vertex is enough because A and C different in that slightly

The vertex is (-2,3)

So the absolute value function should look like this f(x)=a|x+2|+3

So the answer is A.

Answer:

d

Step-by-step explanation:

i jut did it in google calculator (trust me)

Hello There!

First, our formula for finding the volume of a cylinder is Pi*radius^2*height

Now, let'd get into solving for the volume. First, we need to find the radius so in this problem, we are given the diameter so to find the radius, we just divid the diameter by 2. Once we divide, our radius comes out to 6.5.

Next, in our formula it says we have to square our radius so we would multiply 6.5 by 6.5 to get a product of 42.25.

Lastly, we need to multiply 42.25 by our height which is our last step in our formula. Once we multiply 42.25 by the height of the cylinder which is 11, we get a product of 464.75.

464.75 rounded to the nearest tenth is 464.8

Your answer is the first one

Answer:

[tex]-(4x^2)+6(x^4)y[/tex]

Step-by-step explanation:

Here apply the law of indices where ;

[tex]A^x*A^y=A^{x+y}[/tex]

Given;

[tex]\frac{48x^4y-72x^6y^2}{-12x^2y} \\\\\\\frac{-12x^2y(4x^2-6x^4y^2)}{-12x^2y} \\\\\\=-4x^2+6x^4y\\\\\\=-(4x^2)+6(x^4)y[/tex]

Answer:

I have provided two solutions both concluding the same thing.

There is no solution.

Simplest solution says this is a parabola opened up at vertex (-2,5) which means it never crosses the x-axis.  There is no solution because thee curve does not touch the x-axis.

Step-by-step explanation:

Harder solution (algebraic solution):

The vertex form a parabola is [tex]y=a(x-h)^2+k[/tex]

We are given the vertex (h,k) is (-2,5)

So we have [tex]y=a(x+2)^2+5[/tex]

Now we also know [tex]a>0[/tex] since the parabola opens up.

That is all we know about a.

Let's see what [tex]y=a(x+2)^2+5[/tex] is in standard form

[tex]y=a(x+2)(x+2)+5\\y=a(x^2+4x+4)+5\\y=ax^2+4ax+4a+5\\\\[/tex]

So we are asked to solve for the solution set of

[tex]0=ax^2+4ax+4a+5\\A=a\\B=4a\\C=4a+5\\\\[/tex]

Plug into quadratic formula

I'm going to write the quadratic formula with the capital letters to be less confusing:

[tex]x=\frac{-B \pm \sqrt{B^2-4AC}}{2A}\\x=\frac{-4a \pm \sqrt{16a^2-4(a)(4a+5)}}{2a}\\x=\frac{-4a \pm \sqrt{16a^2-16a^2-20a}}{2a}\\x=\frac{-4a \pm \sqrt{-20a}}{2a}\\x=\frac{-4a \pm \sqrt{4} \sqrt{-5a}}{2a}\\x=\frac{-4a \pm 2 \sqrt{-5a}}{2a}\\x=\frac{-4a}{2a} \pm \frac{\sqrt{-5a}}{a}\\[/tex]

This says [tex]a[/tex] has to be negative... The inside of the square root... So there was no real solution.\\

\\

Simpler solution (graph/visual)

You could have also drawn a parabola open up with vertex at (-2,5) and we should have seen that it was impossible it cross the x-axis.

Answer:

The answer is impossible so is Ф

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{1}{2}[/tex] and (a, b) = (- 7, 2), hence

y - 2 = [tex]\frac{1}{2}[/tex] (x - (- 7)) → D

y - 2 = [tex]\frac{1}{2}[/tex](x + 7)

The point-slope form of the equation will be [tex]y-2 = \dfrac{1}{2}(x-(-7))[/tex]. The correct option is D.

In mathematics, slope refers to the measure of the steepness or inclination of a line or a curve. It quantifies the rate at which one variable changes with respect to another variable. The slope is commonly denoted by the letter "m."

Given that the slope of the line is 1/2. The point through which the line is passing is (-7,2).

The general form of the equation of the line passing through the point (-7,2) and the slope is 1/2 can be written as,

[tex]y-y_1 = m(x-x_1)[/tex]

The equation of the line in point-slope form can be written as,

[tex]y - y_1 = m(x-x_1)\\y-2=\dfrac{1}{2}(x-(-7))[/tex]

To know more about slope follow

https://brainly.com/question/29421841

#SPJ2

Answer:

The answer is 7/3 or 2 1/3

Step-by-step explanation:

1) You change the ÷ into x  (so it will be 7/9 x 1/3)

2) You flip the 1/3 so it will be 3 ( 7/9 x 3)

3) There you have it the answer is 7/3

Answer:

Overestimate

Step-by-step explanation:

We draw five rectangles from x = 1 to x = 6, so each rectangle has a width of 1:

(6 - 1) / 5 = 1

We're using right endpoints to determine the height of each rectangle.  The first rectangle is from x=1 to x=2, so the height of the rectangle is f(2) = 6.  So on and so forth for the other rectangles.

The result is this:

desmos.com/calculator/vrl67vpigt

As we can see, these rectangles have areas outside of the curve, so their total area will be greater than the area under the curve.  So this will be an overestimate.

Answer:

for the first question the answer is dc

Step-by-step explanation:

Step-by-step explanation:

all work is pictured and shown

Answer:

130 degrees

Step-by-step explanation:

let the angle be x

2x+45+55=360(Sum of angles in quad)

2x=260

x=130

The measure of <Q is 130 degree.

There are four angles in a quadrilateral. Its inner angles add up to 360 degrees.

The angle sum property of a Quadrilateral states that the sum of all four inner angles is 360 degrees.

We have

<T = 55

<R= 45

let us consider the two angles are Equal.

Using angle sum Property

<T + <R + Q + <S = 360

45+ 55 + x + x = 360

100 + 2x = 360

2x = 260

x = 130

Thus, the measure of <Q is 130 degree.

Learn more about Angle sum Property here:

https://brainly.com/question/21364160

#SPJ7

Answer:

x = 8

Step-by-step explanation:

Step 1 : Simplify the equation

3(x-5) + 7x = 65

3x - 15 + 7x = 65

Step 2 : Make x the subject

3x + 7x = 65 + 15

10x = 80

x = 80/10

x = 8

!!

Answer:

The answer is B

Step-by-step explanation:

The reasoning behind this is because in the second step, if you were to add all of the numbers you would get the solution of -5x or something like that.

Hope this helps!

Answer:

7p^15 / q^12

Step-by-step explanation:

7p^9+6 q^-5-7 / 3         #28 is divided by 12

7p^15 / q^12       #Answer

Answer:

7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7

Step-by-step explanation:

Given Parameter:

28p^9 q^-5/12p^-6 q^7

Required; To simplify.

To simplify the above expression, we'll apply 2nd law of indices.

But first, let's rewrite the expression.

28p^9 q^-5/12p^-6 q^7 becomes

(28 * p^9 * q^-5) / (12 * p^-6 * q^7)

Then we collect similar indices. This is done as follows

(28/12) * (p^9/p^-6) * (q^-5/q^7)

From second law of indices (law of division);

If the two terms have the same base () and are to be divided their indices are subtracted.

For instance x^a/x^b = x^(a - b).

Applying this law; we have

(28/12) * (p^9/p^-6) * (q^-5/q^7) becomes

(28/12) * (p^(9 - (-6))) * (q^(-5-7))

(28/12) * (p^(9+6)) * (q^-12)

(28/12) * p^15 * q^-12

Simplify 28/12

(4*7)/(4*3) *p^15 * q^-12

(7/3) * p^15 * q^-12

(7/3) * p^15 * 1/q^12

7p^15/3q^12

Hence, 7p^15/3q^12 is equivalent to 28p^9 q^-5/12p^-6 q^7

Answer:

y = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given

- 3y = - [tex]\frac{6}{5}[/tex]

Multiply both sides by 5 to eliminate the fraction

- 15y = - 6 ( divide both sides by - 15 )

y = [tex]\frac{-6}{-15}[/tex] = [tex]\frac{6}{15}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

7x + 5y

Step-by-step explanation:

6x + 6y + x - y = 7x + 5y

Answer:

The answer would be the last one, or 7x + 5y

Step-by-step explanation:

Distribute the 6: 6x+6y + x - y

Simplifying gives:

7x + 5y

Hope this helps!

Answer: A, Jessica's Earning's at the end of the week

Step-by-step explanation: If Jessica earns $4 for every crate she sells that means the first term would be what Jessica earned at the end of the week minus $15 because Monte made $15 dollars less then Jessica

The amount earned by Jessica and Monte are illustrations of a linear function.

The first term represents Jessica's total earnings.

Monte's earning is expressed as:

[tex]\mathbf{4y - 15}[/tex]

From the question, we understand that:

Jessica earns $4 per crate of banana

So, 4y represents Jessica's total earnings.

Hence, the first term represents Jessica's total earnings.

Read more about linear functions at:

https://brainly.com/question/21107621

Answer: The 3rd from the left.

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

There are 9 options for the first choice and 10 options for the second. Multiply them together to get the full number of combinations, which is 90.

Answer:

Step-by-step explanation:

Put x = -7 to the equation -4x - 9y = -26, and solve it for y:

-4(-7) - 9y = -26

28 - 9y = -26            subtract 28 from both sides

-9y = -54           divide both sides by (-9)

y = 6

recall your d = rt, distance = rate * time.

w = rate of the wind

225 = rate of the plane

so the plane flies 260 miles in say "t" hours, with the wind, now, the plane is not really going 225 mph fast, is really going "225 + w" fast because the wind is adding speed to it, likewise, when going against the wind, is not going 225 mph fast is going "225 - w" because the wind is eroding speed from it, and that was also covered in "t" hours

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \stackrel{downwind}{\textit{with the wind}}&260&225+w&t\\ \stackrel{\textit{upwind}}{\textit{against the wind}}&190&225-w&t \end{array}~\hfill \begin{cases} 260=(225+w)t\\\\ \cfrac{260}{225+w}=\boxed{t}\\\\ \cline{1-1}\\ 190=(225-w)t \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting \underline{t} in the 2nd equation}}{190=(225-w)\left( \boxed{\cfrac{260}{225+w}} \right)}\implies \cfrac{190}{225-w}=\cfrac{260}{225+w} \\\\\\ 42750+190w=58500-260w\implies 190w=15750-260w \\\\\\ 450w=15750\implies w=\cfrac{15750}{450}\implies \blacktriangleright w=35 \blacktriangleleft[/tex]

Answer: the correct answer is a

The correct equation is "3y - 2 = 4," and the value of "y" (the number of kites Emilio saw yesterday) is 2.

The correct answer is option A.

In this problem, we need to translate the given information into a mathematical equation and then solve for the variable "y," which represents the number of kites Emilio saw yesterday.

We are told that Emilio saw four kites at the park today, and this is two less than three times the number of kites he saw yesterday. In mathematical terms, this can be expressed as:

3y - 2 = 4

Here's the breakdown:

"3y" represents three times the number of kites he saw yesterday.

"3y - 2" represents two less than three times the number of kites he saw yesterday.

"4" represents the number of kites he saw today.

So, option A, "3y - 2 = 4," correctly represents the relationship described in the problem.

To solve for "y," you can isolate the variable by adding 2 to both sides of the equation:

3y - 2 + 2 = 4 + 2

3y = 6

Now, divide both sides by 3 to solve for "y":

(3y)/3 = 6/3

y = 2

In summary, the correct equation to represent the problem is option A, and the value of "y" is indeed 2, as Emilio saw two kites yesterday.

For more such information on: equation

https://brainly.com/question/29174899

#SPJ3

Answer:

i think it is 60 because

Step-by-step explanation:

the angle 45 would make a perfect right angle ever two pedals and these look like they make a perfect 120

Answer:

f(3)=2(3)^2+4

f(3)=2(9)+4

f(3)=18+4

f(3)=22

Step-by-step explanation:

In this scenario, x=3 so you plug it into the other side of the equation.

ANSWER

[tex]f(3) = 22[/tex]

EXPLANATION

The given given function is

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

To find f(3), we substitite x=3 into the function f(x).

This means that wherever we see x in

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

we replace it with 3 .

[tex] \implies \: f(3) = 2 ({3})^{2} + 4[/tex]

We evaluate the square to get:

[tex] \implies \: f(3) = 2 ({9}) + 4[/tex]

Perform the multiplication

[tex] \implies \: f(3) = 18 + 4[/tex]

Now add to get:

[tex] \implies \: f(3) = 2 2[/tex]

Answer:    [tex]\frac{2(x+4)}{3}[/tex]

Step-by-step explanation:

Given the following expression:

[tex]\frac{4x+16}{6}[/tex]

You can notice that the Greatest Common Factor (GCF) in the  denominator  is 2, then you can factor it out.

Now, observe that the Greatest Common Factor in the numerator is 4, so you can factor it out.

Therefore, you get

 [tex]=\frac{4(x+4)}{2(3)}[/tex]

And finally, since [tex]\frac{4}{2}=2[/tex], you get the expression simplified. This is:

  [tex]=\frac{2(x+4)}{3}[/tex]

Answer: D. Horizontal stretch by a factor of 3.

Step-by-step explanation:

Below are some transformations for a function [tex]f(x)[/tex]:

If [tex]f(x)-k[/tex], then it is shifted "k" units down.

If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.

If [tex]-f(x)[/tex], then it is reflected across the x-axis.

If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".

If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].

Based on this, the transformations done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] are:

- It is shifted 7 units down.

- It is shifted rigth 4 units.

- It is reflected over the x-axis.

- It is vertically stretched by a factor of 3.

Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex]  to get the function [tex]g(x)=-3(x-4)-7[/tex] is:

Horizontal stretch by a factor of 3.

Answer:

Is an acute triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

G(7,3), H(9, 0), I(5, -1)

step 1

Find the distance GH

substitute in the formula

[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]

[tex]GH=\sqrt{13}\ units[/tex]

step 2

Find the distance IH

substitute in the formula

[tex]d=\sqrt{(0+1)^{2}+(9-5)^{2}}[/tex]

[tex]d=\sqrt{(1)^{2}+(4)^{2}}[/tex]

[tex]IH=\sqrt{17}\ units[/tex]

step 3

Find the distance GI

substitute in the formula

[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]

[tex]GI=\sqrt{20}\ units[/tex]

step 4

Verify what type of triangle is the polygon

we know that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle

[tex]c^{2}> a^{2}+b^{2}[/tex] ----> is an obtuse triangle

[tex]c^{2}< a^{2}+b^{2}[/tex] ----> is an acute triangle

where

c is the greater side

we have

[tex]c=\sqrt{20}\ units[/tex]

[tex]a=\sqrt{17}\ units[/tex]

[tex]b=\sqrt{13}\ units[/tex]

substitute

[tex]c^{2}= (\sqrt{20})^{2}=20[/tex]

[tex]a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]

therefore

[tex]c^{2}< a^{2}+b^{2}[/tex]

Is an acute triangle

Answer:

ACUTE !!!!!!!!

Step-by-step explanation: