Find the roots of the equation
x^2 +7= 2x
express your answer in simplest a +bi form

Answers

Answer 1

[tex]x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= \dfrac{-(-2) \pm \sqrt{(-2)^2 -4\cdot 1 \cdot 7}}{2\cdot 1}\\\\\\\implies x =\dfrac{2 \pm \sqrt{-24}}{2}\\\\\\\implies x = \dfrac{2 \pm i\sqrt{24}}2\\\\\implies x =\dfrac{2 \pm i2\sqrt{6}}2\\\\\implies x = \dfrac{2\left(1 \pm i \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\[/tex]

[tex]\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6[/tex]


Related Questions

The zoo expected to have 120,000 visitors last year. They
actually had 110,000 visitors. Determine the percent of
error. (Round to the nearest tenth of a percent, if necessary.)
A) 8.3%
B) 9.1%
C) 91.7%
D) 109.1%

Answers

I believe it’s D, because 120000divided by 110000=1.09
correct me if im wrong but it’s D because 120,000 divided by 110,000 -= 1.09 and that means 109.1%

Write an equation in slope-intercept form of the line that passed through (-3, 4) and (1. 4)

Answers

Answer:

y= 0x+4

Step-by-step explanation:

This is a horizontal line, since both coordinate pairs end in 4, so the slope is 0. The y-intercept is 4 because each point is 4.

i don't understand how to do this someone help me math!!

Answers

Answer:

-8

Step-by-step explanation:

ky^2 = -5y + 7y^2 +9y - 15y^2 -4y

ky^2 = -8 y^2

k = -8

Answer:

  8

Step-by-step explanation:

We believe the problem here requires that all of the coefficients in the expression on the left be zero. That is, the equation will be true for any value of y.

We can work this a couple of ways. One of them is to simplify the given expression. Let 'a' represent our unknown coefficient.

  [tex]-ay^2-[-5y-y(-7y-9)]-[-y(15y+4)]=0\\\\-ay^2-[-5y+7y^2+9y]+[15y^2+4y]=0\\\\-ay^2-[7y^2+4y]+15y^2+4y=0\\\\(-a-7+15)y^2+(-4+4)y=0\\\\(-a+8)y^2=0[/tex]

In order for this to be zero for all values of y, we must have (-a+8) = 0.

  a = 8

The missing coefficient is 8.

_____

Since this expression must be true for every value of y, another way to work this is to choose a value of y. This will tell us what the coefficient must be for the expression to be zero. Let y = 1.

  -a·1² -[-5·1 -1(-7·1 -9)] -[-1(15·1 +4)] = 0

  -a -[-5-(-16)] -[-19] = 0

  -a -11 +19 = 0

  -a +8 = 0

  a = 8 . . . . . . same as above

_____

Additional comment

The many minus signs are intended to make sure you're comfortable with arithmetic with negative coefficients and negative numbers. The key, of course, is that -(-a) = +a. The opposite of the opposite is the original.

We have assumed that the dash at the beginning of the line (before the answer box) is intended to be a minus sign. If that is not the case, then your answer will be -8, instead of 8.

Mattie Evans drove 160 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.

Answers

Answer:

Step-by-step explanation:

The speed of the plane was 291.13mph.

What is speed?

Speed is distance travelled per unit time. It is scalar quantity

Given

The difference in distances was 600 miles; the difference in speeds was 190mph. That means the time was 600/190 = 3.16 hours.

Since the plane flew 920 miles in that time, its speed was 920/3.16 = 291.13mph.

To know more about speed refer to:

https://brainly.com/question/13943409

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3x^4 + 9x^3 - 5x^2 - 14x - 7 divided by x + 3 using synthetic division

Answers

Answer:

[tex]3x^3 - 5x + 1 - \frac{10}{x + 3}[/tex]

or

3x^3 - 5x + 1

Remainder: -10

Step-by-step explanation:

Please see attached image for full explanation!

1.) Write the coefficient of each term.

2.) Beginning with 3, multiply by -3, or x + 3 = 0 (the divisor.)

3.) Add the product to the next coefficient and repeat until you get to the last number, -7.

4.) You should have the numbers 3, 0, -5, 1, and -10.

5.) Rewrite this quotient as an equation:

3x^3 - 5x + 1

Note that the highest power is 3, one less than that of the highest power in the original equation.

6.) Don't forget the remainder!

You can include this in the equation or not, depending on the instructions.

Therefore, the final answer is 3x^3 - 5x + 1 - 10/x+3 or 3x^3 - 5x + 1 R: -10.

What number is needed to complete the square?

x^2 + 3x + ?

Answers

The number needed to complete the square is 9/4

Given the expression x^2 + 3x + ?

Using the completing the square;

Step 2: Get the coefficient of x

The coefficient of x is 3

Step 3: Get the half of coefficient of x

Hale of the coefficient  = 3/2

Step 4: Take the square of the result

Square of the result  = ()3/2)^2 = 9/4

Hence the number needed to complete the square is 9/4

Learn more on completing the square here: https://brainly.com/question/1596209

Porfa ayúdenme a resolver lo de la ficha, plis.

Answers

Answer:

Step-by-step explanation:

Portf?

Huh yo I know the answers I smart

Find the perimeter of ABC with vertices A(0,-4), B(4,-4), and C(0,-1).
A. 7 units
B. 14 units
C. 12 units
D. 32 units

Answers

Answer:

C .12 units I think so if wrong I am sorry

c(n)=-6+5(n-1) Find the 8th term in the sequence

Answers

Answer:

-7

Step-by-step explanation:

c(8)=-6+5x7

c(8)=-1x7

c(8)=-7

PLEASE HELP. I NEEED THIS BY TOMORROW

Answers

It’s the top one as the x doesn’t repeat

Is x=−10 a solution to the equation 28x+17=157?

Answers

Answer:

no

Step-by-step explanation:

28x+17=157   Subtract 17 on both sides.

       -17  -17

28x=140

x=5

5 does not equal -10, so -10 is not a solution to the equation 28x+17=157.

Hope this helps!! Have a great day :)

Sara is going to home depot to buy some plants for her back yard. The price of 4 rose bushes is $12 and the price of 5 tulips is $20. Sara ends up buying $80 worth of roses and tulip plants. Which equation represents the relationship between the number of rose bushes, x, and the number of tulip plants, y, that Sara bought at home depot?

Answers

Answer:

3r + 4t = 80

Step-by-step explanation:

Roses cost $3 each, tulips cost $4 each

What is the equation of the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction) and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form

Answers

Answer: y = 1/2x + .75

Step-by-step explanation:

Slope-intercept form: y = mx + b

Step 1: Find the slope.

Solve for [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]y2-y1 = \frac{11}{12} -\frac{19}{20}[/tex]

[tex]x2-x1 = \frac{1}{3} -\frac{2}{5}[/tex]

To solve for the fractions you need a common denominator.

[tex]y2-y1 = \frac{11*20}{12*20} -\frac{19*12}{20*12} = \frac{220}{240} -\frac{228}{240}=\frac{-8}{240} = \frac{-1}{30}[/tex]

[tex]x2-x1 = \frac{1*5}{3*5} -\frac{2*3}{5*3} = \frac{5}{15} -\frac{6}{15}=\frac{-1}{15}[/tex]

To divide fractions you keep (the first equation), change (the division sign to multiplication), and flip (the second fraction).

[tex]\frac{y2-y1}{x2-x1}=\frac{\frac{-1}{30} }{\frac{-1}{15} } = \frac{-1}{30}*\frac{15}{-1} =\frac{-15}{-30}=\frac{1}{2}[/tex]

Step 2: Plug slope and a point into y=mx+b to solve for b.

[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{2}[/tex])*([tex]\frac{1}{3}[/tex])+b

[tex]\frac{11}{12}[/tex] = ([tex]\frac{1}{6}[/tex])+b

[tex]\frac{11}{12}-\frac{1}{6}[/tex] = b

[tex]\frac{11*6}{12*6}-\frac{1*12}{6*12}=\frac{66}{72} -\frac{12}{72} =\frac{54}{72}=.75[/tex]

b = .75

y = [tex]\frac{1}{2}+.75[/tex]

Molly has biweekly gross earnings of $839. 52. By claiming 1 more withholding allowance, Molly would have $16 more in her take home pay. How many withholding allowances does Molly currently claim? a. 1 b. 2 c. 3 d. 4.

Answers

Molly currently claims 2 withholding allowances which can be determined by using rules of allowance.

Given that,

Molly has biweekly gross earnings of $839. 52.

By claiming 1 more withholding allowance,

Molly would have $16 more in her take-home pay.

We have to determine,

How many withholding allowances does Molly currently claim?

According to the question,

Molly has biweekly gross earnings of $839. 52.

By claiming 1 more withholding allowance,

Molly would have $16 more in her take-home pay.

The withholding allowance is used by a person to pay less amount of tax on his or her income to the government.

Molly has biweekly gross earnings of $839. 52.

By claiming 1 more withholding allowance,

Molly would have $16 more in her take-home pay.

Therefore,

It is given that Molly has taken 1 more withholding allowance to pay tax less by the amount of $16.

So he must have possessed at least 1 allowance previously and added 1 more.

So, the minimum number of allowance possessed by Molly = 2

Hence, Molly currently claims 2 withholding allowances.

For more details about Income Tax refer to the link given below.

https://brainly.com/question/1708567

Can someone help me. I’ve tried doing this on paper. I don’t know what I’m doing wrong

Answers

ANSWER: x=12
EXPLANATION:
9+x/6=11
(54+x)/6=11 (finding common denominator)
x/6=11-54/6 (rearranging terms)
x/6=(66-54)/6 (finding common denominator so 6 gets cancelled from both the sides)
x=12

[tex]{ \huge \mathfrak \color {pink}{ \tt{answer}}}[/tex]

[tex] \large \color{cyan}{ \tt{x = 12}}[/tex]

Step-by-step explanation:

[tex] \color {cyan}{ \tt{9 + \frac{x}{6 = 11}}} [/tex]

multiply both sides of the equation by 6

[tex]{ \tt{54 + x = 66}}[/tex]

move the constant to the right hand side and change its sign

[tex]{ \tt{x = 66 - 54}}[/tex]

substract the numbers

[tex] \huge \color{magenta}{ \tt{ = \: \: x = 12}}[/tex]

[tex] \large \color{brown}{ \tt{hope \: \: it \: \: helps}}[/tex]

217.8 as mixed number

Answers

Answer:

27 1/8

Step-by-step explanation:

217/8= 27.125 = 27

217 - (8 x 27) = 1

We've now simplified 217/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

27 1/8

Simplifying our fraction

In this case, our fraction (1/8) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 1 and 8 is 1.

1/1 = 1

8/1 = 8

When we put that together, we can see that our complete answer is:

27 1/8

Answer:

217  4/5

Step-by-step explanation:



10 0breros construyen un complejo 336 días, ¿cuantos días les tomaría hacer el mismo complejo a 15 obreros?

Answers

Usando proporciones, se encuentra que 15 obreros hacerían el mismo complejo en 24 días.

Esta pregunta se resuelve por proporciones, usando una regla de tres. Cuanto mayor lo número de obreros, menor el tiempo, o sea, las medidas son inversamente proporcionales, lo que implica que la multiplicación es en línea.10 obreros toman 336 dias. ¿Cual el tiempo necessário para 15 obreros?

La regla de três es:

10 obreros - 336 días

15 obreros - x días

Aplicando multiplicación en línea:

[tex]15x = 336(10)[/tex]

[tex]x = \frac{336(10)}{15}[/tex]

[tex]x = 24[/tex]

15 obreros hacerían el mismo complejo en 24 días.

Para obtener más información sobre las proporciones, puedes visitar a https://brainly.com/question/24615636

graph 56x- 19= -8y + 5

Answers

Answer/Step-by-step explanation:

Solve

Before we begin graphing, we have to solve the equation. You cannot just graph the equation as it is now. Let us simplify it:

[tex]56x-19=-8y+5[/tex]

[tex]56x-19+19=-8y+5+19[/tex]                           [tex]\mathrm{Add\:}19\mathrm{\:to\:both\:sides}[/tex]                                            

[tex]56x=-8y+24[/tex]

[tex]\frac{56x}{56}=-\frac{8y}{56}+\frac{24}{56}[/tex]                                                 [tex]\mathrm{Divide\:both\:sides\:by\:}56[/tex]

[tex]\frac{56x}{56}=-\frac{8y}{56}+\frac{24}{56}[/tex][tex]\frac{56x}{56} = x\: (\mathrm{or}\: 1)[/tex][tex]-\frac{8y}{56}+\frac{24}{56}[/tex][tex]\frac{-8y+24}{56}[/tex][tex]\mathrm{Factor\:-8y+24}\\\mathrm{Rewrite\:as}\\=-8y+8\cdot \:3\\\mathrm{Factor\:out\:the\:common\:term\:8}\\=8\left(-y+3\right)\\\\=\frac{8\left(-y+3\right)}{56}\\\mathrm{Cancel\:the\:common\:factor:}\:8\\=\frac{-y+3}{7}[/tex]

[tex]\bold{x=\frac{-y+3}{7}}[/tex]

Graph

Now, we can graph. Graph the line using the slope and y-intercept, or two points.

[tex]\mathrm{Slope}: -7\\y-\mathrm{intercept}: (0,3)[/tex]

[tex]x\\0\\1[/tex]   [tex]y\\3\\-4[/tex]

Solve the following.

Answers

Answer:

Step-by-step explanation:

The scale factor is 5.3 repeating. So I divided 24 by 5.33333333333333333 and got 4.5. I don't know if it's accurate since it's a reapeating decimal but it's close enough. Then I multiplied 2 by 5.3333333333333333333333 and got 10.6666667.

What percent of the model is shaded green?

(answer quick please)

Answers

Answer:

30%

Step-by-step explanation:

3 rows out of 10 are shaded green. 3/10 is 30%

Answer:  30%

Explanation:

Ignore the horizontal lines. Think of this figure as 10 skinny rectangles line up side by side. Three of them are shaded, so we have 3/10 = 0.30 = 30% of it shaded.

If you wanted to include the horizontal lines, then we have 10*3 = 30 green little squares out of 10*10 = 100 total squares. This leads to the same answer 30/100 = 0.30 = 30%

Question 7 (Essay Worth 10 points)
(03.08A MC)
The number line shows the distance, in meters, of two divers, A and B, from a shipwreck located at point X:
1.5
B
Х
-2.5
A
Hot
-3 -2
+
-1
0
1 2 3
Distance (m)
Part A: Write an expression using subtraction to find the distance between the two divers. (5 points)
Part B: Show your work and solve for the distance using additive inverses. (5 points)

Answers

Answer:

45

Step-by-step explanation:

A. A cylindrical barrel has diameter 14 m and height 9 m. Find the cost of painting the inner side of the barrel at 132 per m? (Take = 3.14.)​

Answers

Answer:

Here is your Answer

Step-by-step explanation:

DIAMETER = 14 M

RADIUS = DIAMETER ×0.5

RADIUS = 14÷0.5 = 7

HEIGHT = 9M

AREA OF CYLINDER = 2pi*R* H

AREA = (2× 3.14×7×9) M^2

AREA =395.64 M^2

COST FOR AREA M^2 = ₹ 32

COST FOR AREA 395.64 =₹(395.64×32)

SO, ANSWERS= ₹ 12660.48

Plz Mark Me As Brainiest

Answer:

$ 12660.5

Step-by-step explanation:

We know that

Radius = Diameter/2

Radius = 14/2 = 7 m

Now,

CSA of cylinder = 2πrh

=> 2 × 3.14 × 7 × 9

=> 395.6 m²

Now,

Cost = 395.6 × 132

=> $ 12660.5

Rewrite 1/6 book over 2/3 hour as a unit rate

HELPPP please make it quickk D:

Answers

Answer:

0.25 book/hour

Step-by-step explanation:

(1/6)/(2/3)=x/1

*Simplify the equation

1/4=x

*Rearrange the equation

x=1/4

x=0.25 book/hour

Maddie baked 7 brownies. 4 of the brownies had nuts on top. What is the ratio of the number of brownies without nuts to the total number of brownies?

Answers

3:7 because L + Ratio + One Piece better

which of the equations below would have a line that passes through both (1,7) and (0,-9)

Answers

Answer:

Step-by-step explanation:

(-9-7)/(0-1)= -16/-1= 16

y - 7 = 16(x - 1)

y - 7 = 16x - 16

y = 16x - 9

Which expression is equivalent to 7x + 5x?

a. 12x
b.12x^2
c. 35x
d. 35x^2

Answers

Answer:

12x

Step-by-step explanation:

Plz help!!!! Find the equation of the linear function represented by the table below in slope intercept form

Answers

Answer:

y=-5x+2

Step-by-step explanation:

rise/run

or

y2-y1/x2-x1

-8-(-3)/2-1

-8+3/2-1

-5/1=m=slope

Slope intercept formula:y=mx+b

use point (1,-3)

-3=-5(1)+b

-3=-5+b

+5 +5

2=b

Final Answer: y=-5x+2

0 6. What is the constant of proportionality for the set of data in the table? 10 8 2 Hours 70 56 42 14 Miles 48​

Answers

Answer:

k = 7

Step-by-step explanation:

The constant of proportionality k is calculated as

k = [tex]\frac{miles}{hours}[/tex]

Using the values from the table , then

k = [tex]\frac{14}{2}[/tex] = [tex]\frac{42}{6}[/tex] = [tex]\frac{56}{8}[/tex] = [tex]\frac{70}{10}[/tex] = 7

3+1=5
false or true
brailest and points

Answers

Answer:

FALSE

Step-by-step explanation:

PLZ MARK BRAINLIOEST

The lifespan of a monarch butterfly is about 9 months. Assuming a 30-day month, how many minutes old is the butterfly?

Answers

Answer:

So 9 months is 273 days and 394200 minutes so if the butterfly spends  30 days means one month so it is 43800 minutes old .

hope it gonna help you.

Step-by-step explanation:

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