2x^2+2=3x complete the square i need full explaination ASAP

Answers

Answer 1

Answer:

x = 3/4 + √7i/4

x = 3/4 - √7i/4

Step-by-step explanation:

2x² + 2 = 3x

Subtract 3x from both sides so it equals 0:

2x² - 3x + 2 = 0

Divide both sides by 2:

x² - 3/2x + 1 = 0

Subtract 1 from both sides:

x² - 3/2x = -1

Take -3/2 and multiply it by 1/2 then square it:

(-3/2 • 1/2)²

9/16

Add this to both sides:

x² - 3/2x + 9/16 = -1 + 9/16

Rewrite the perfect square on the left and add the terms on the right:

(x - 3/4)² = -7/16

Square root both sides to get rid of the square:

x - 3/4 = ± √-7/16

Simplify the radical:

x - 3/4 = ± √7i/4

Add 3/4 to both sides:

x = 3/4 ± √7i/4

Your two solutions are:

x = 3/4 + √7i/4

x = 3/4 - √7i/4

You can also convert to decimal if you need to (but I don’t recommend it):

x = 0.75 + 0.661438i

x = 0.75 - 0.661438i

Hope this helps!


Related Questions

In a group of 80 people, 50 can speak Nepali, 45 can speak English and 7 of them do not
speak both languages.
a) Find the number of people who speak both languages.
b) Also illustrate the above information in Venn diagram.​

Answers

Answer:

Universal set is 80

Number of people that speak Nepali is 50

Number of people that speak English is 45

Number of people that do not speak both is 7

a. Number of people that speak both languages is 22

b. As above

Step-by-step explanation:

a. Let make number of people that speak both languages x

To get x

(50-x) + (45-x) + x + 7 = 80

(50-x) + (45-x) + x = 80 - 7

(50-x) + (45-x) + x = 73

Open bracket

50-x+45-x+x= 73

50+45-2x+x = 73

95 - x = 73

-x = 73 - 95

-x = -22

x = 22

Therefore, number of people that speak both languages is 22

b. To get venn diagram

Number of people that speak Nepali is 50 - 22 = 28

Number of people that speak English is 45 - 22 = 23

Therefore, total = 28+23+22+7 = 80

The function f(x) = 0.5x + 3 is used to estimate the number of pounds of potatoes a caterer plans to make depending on the number of people being served, x. The mathematical domain for the function is the set of real numbers.

Which statement describes the limitation for the reasonable domain compared to the mathematical domain?

The reasonable domain contains only positive real numbers.
The reasonable domain contains only positive whole numbers.
The reasonable domain contains only real numbers greater than 3.
The reasonable domain contains only rational numbers greater than 3.

Answers

Answer:The reasonable domain contains only positive whole numbers.

Step-by-step explanation: Domain is x-values. X stands for the amount of people. The amount of people can't be negative. There also can't be half a person so it has to be whole numbers. There can be less than 3 people coming.

Answer:

B on edge 2021

Step-by-step explanation:

The answer is 118 as well right??

Answers

Answer: 118 is the correct degree

Step-by-step explanation:

yes it is correct :)

Two shooters, Rodney and Philip, practice at a shooting range. They fire 100 rounds each at separate targets. The targets are marked with circles and each bullet hitting a particular circle gets them a particular number of points. 60 rounds are selected at random. The sample mean scores of Rodney and Philip are 8 and 10, respectively. And, their variances are 0.25 and 0.50, respectively The standard error of the difference between their mean scores is ______________ (Round your answer to two decimal places.) The 95% confidence interval for the difference between the mean scores Rodney and Philip is ________ _____________: (Enter a minus sign if your answer is negative. Round your answer to two decimal places.)

Answers

Answer:

A) SE = 0.1118

B) 95% Confidence interval is;

-2.22 < μ1 - μ2 < -1.78

Step-by-step explanation:

We are given;

Sample size; n = 60

Sample mean 1; x1 = 8

Sample mean 2; x2 = 10

Variance 1; v1 = 0.25

Variance 2; V2 = 0.5

Now,

Standard deviation is given by the formula ;

σ = √variance

Thus;

σ1 = √0.25

σ1 = 0.5

σ2 = √0.5

σ2 = 0.7071

Formula for standard error of mean is;

SE = σ/√n

Thus;

SE1 = 0.5/√60

SE1 = 0.06455

SE2 = 0.7071/√60

SE2 = 0.0913

The standard error of the difference between their mean scores would be;

SE = √[(SE1)² + (SE2)²]

SE = √(0.06455² + 0.0913²)

SE = 0.1118

Formula for 95% confidence interval is;

(x1 - x2) - ((Z_α/2) × SE) < μ1 - μ2 < (x1 - x2) + ((Z_α/2) × SE)

Where Z_α/2 is the critical value. At confidence interval of 95%, we have a critical value of 1.96 from tables.

Thus, plugging in the relevant values, we have;

(8 - 10) - (1.96 × 0.1118) < μ1 - μ2 < (8 - 10) + (1.96 × 0.1118)

-2.22 < μ1 - μ2 < -1.78

1 5/16 divided by 7/12

Answers

2.25 this is the correct answer

Express the number 7,980 in scientific notation.

Answers

Answer:

7.98x10^3

Step-by-step explanation:

10^3=1000

Answer:7.980 × 10^3

Step-by-step explanation:

In Mrs. Munson's 9th hour science class there are 15 girls and 9 boys. Which of the
following is the ratios of girls to boys IN SIMPLEST form?
O 5:1
15:9
O 5:3
30:18

Answers

Answer:

15-9

Step-by-step explanation:

Answer:

5:3

Step-by-step explanation:

[tex]15 \div 3 = 5[/tex]

[tex]9 \div 3 = 3[/tex]

Olga has $40 in her wallet. She has one more $5 bill than $10 bills, and two more $1 bills than $5 bills. If Olga has only three types of bills, how many bills of each denomination does she have?

Answers

Answer:

Number of $10 bills = 2

Number of $5 bills = 3

Number of $1 bills  = 5

Step-by-step explanation:

Given:

Total amount = $40

Number of $10 bills = x

Number of $5 bills = x + 1

Number of $1 bills = x + 1 + 2 = x + 3

Find:

Number of each bills

Computation:

10(x) + 5(x+1) + 1(x+3) = 40

10x + 5x + 5 + x + 3 = 40

16x = 32

x = 2

Number of $10 bills = x = 2

Number of $5 bills = x + 1 = 3

Number of $1 bills  = x + 3 = 5

Answer:

# of $10 bills = 2

# of $5 bills = 3

# of $1 bills  = 5

Step-by-step explanation:

A 40 ​-inch board is to be cut into three pieces so that the second piece is 4 as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.

Answers

Answer:

4*4=16 INCHES FOR THE SECOND PIECE. 5*4=20 INCHES FOR THE LONGEST PIECE.

Step-by-step explanation:

x = 20 inch, the length of the first piece

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

given,

Total length = 40 inch

let first piece be = x inch

second piece = 4 times of first piece = 4x inch

third piece = 5 times of first piece = 5x inch

So,

x + 4x + 5x = 200

10x = 200

x = 200/10

x = 20

Therefore, the length of the first piece is 20 inch

Read more about mathematical expression here :

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Solve and show the steps to the picture attached

Answers

Answer:

The image of point (2, 4) after transformation is (-2, 13) ⇒ D

Step-by-step explanation:

Let us revise some transformation

Translation right-left OR up-down

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  ⇒ add x-coordinate of every point by hIf the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  subtract x-coordinate of every point by hIf the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  add y-coordinate of every point by kIf the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k  ⇒ subtract y-coordinate of every point by k

A vertical stretching and a vertical compression (or shrinking)

If m > 1, the graph of y = m • f(x) is the graph of f(x) vertically stretched by factor m.  ⇒ multiply every y-coordinate by mIf 0 < m < 1 (a fraction), the graph of y = m • f(x) is the graph of f(x) vertically shrunk (or compressed) by factor m  ⇒ multiply every y-coordinate by m

Let us use these rules to solve the question.

∵ Point (2, 4) lies on y = x²

∵ The image of y = x² is y = 3(x + 4)²+1

→ The rules of transformation is y = m(x + h)² + k

m is the scale factor of a vertical stretched

m = 3

→ By using the 5th rule above

∴ The y-coordinate of point (2, 4) should multiply by 3

∴ The image of the point is (2, 4 × 3) = (2, 12)

∵ h is the horizontal translation to the left

h = 4

→ By using the 2nd rule above

∴ The x-coordinate of point (2, 12) should subtract by 4

∴ The image of the point is (2 - 4, 12) = (-2, 12)

∵ k is the vertical translation up

k = 1

→ By using the 3rd rule above

∴ The y-coordinate of point (-2, 12) should add by 1

∴ The image of the point is (-2, 12 + 1) = (-2, 13)

The image of point (2, 4) after transformation is (-2, 13)

1. Refer to the equation 3x − 5y = 15. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line. Work for Point 1 Work for Point 2 Work for Point 3 Work for Point 4

Answers

Answer:

We have the equation:

3x - 5y = 15

a) We want to create a table with at least 4 points.

To do this, first, let's write the equation as a function: We must isolate one of the variables. Let's isolate y.

5y = 3x - 15

y = (3/5)*x - 3.

Then we have a linear equation.

Now, we can input different values of x, and see what value takes y in each case, then in this way we can be sure that the points will be on the line.

x = 0.

y = (3/5)*0 - 3

y = -3

Then we have the point (0, -3).

x = 1.

y = (3/5)*1 - 3 = 3/5 - 15/5 = -12/5

y = -12/5

Then we have the point (1, -12/5)

x = 5

y = (3/5)*5 - 3 = 3 - 3 = 0

y = 0

then we have the point (5, 0)

x = 10

y = (3/5)*10 - 3 = 6 - 3 = 3

y = 3

Then we have the point (10, 3).

Now we can create the table

[tex]\left[\begin{array}{ccc}x&y\\0&-3\\1&-12/5\\5&0\\10&3\end{array}\right][/tex]

Below you can see a graph, where the blue dots are our 4 points, and the green line is the line that represents the equation.

7(10x+5-9x)=70
I rly need help on this

Answers

Answer:

x = 5

Step-by-step explanation:

1. Combine like terms

2. Multiply by 1

3. Distribute

4. Subtract  3

5  from both sides of the equation

5. Simplify

6. Divide both sides of the equation by the same term

7. Simplify

Answer: x=5

Step by Step Explanation:
7(10x+5-9x)=70 distributive property
70x+35-63x=70 subtract common terms
7x+35=70 subtract both sides by 35
7x=35 divide both sides by 7
x=5

How can a transformed quadratic equation be used real life situation?​

Answers

Answer:

Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.

Step-by-step explanation:

write in standard form -4 + y +2x = 0

Answers

Answer:

the answer is 2x+y=4

Step-by-step explanation:

2x+y=4

Answer:

y = -2x + 4

Step-by-step explanation:

t> -5
can someone show step by step how to solve this equation?

Answers

Answer: The equation cannot be simplified any further.

Explanation: The variable(t) is greater than any number than negative five.

Plz mark brainliest:)

Ten less than a number is twice the same number​

Answers

Answer:Less ten a number; 20 - 10.10 ×2 = 20

Meaning lees 10 from 20 and multiply

Hi there!

First of all, let the unknown number be z.

Now, subtract 10:

z-10

This expression is equal to twice the same number:

z-10=2z

Solve this equation:

z-2z=10

-z=10

Divide both sides by -1 in order to get rid of the minus sign:

z=-10

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Rewrite the following using the GCF and the distributive property
:32 + 54

Answers

Answer:

GCF: 2

Step-by-step explanation:

GCF: 2

(2*16) + (2*27)

Please help guys this has to be do in 10:00 please help

Answers

she drank 14 ounces of her water, she has 28 ounces left, just divide 42 by 3

Answer:

1)14oz

2)28oz

Step-by-step explanation:

1) To find the amount of water is left in the bottle you want to substract 1/3 so the first thing you want to do is find what 1/3 of 42 is. So do this: (This is also 42/3)

42*1/3=14

So we now know that 14 is 1/3 of 45 which is the first answer. To find the second answer you want to substract 14 from 42 which is 28.

So that means she has 28 oz of water left when she gets there.

If f(x) = 2x2 + x-1, then f(-5)
= ?

Answers

Answer:

-54

Step-by-step explanation:

(-5)^2 = -25

2(-25)+ -5 +1 =-54

Answer:

f(-5) = -2

Step-by-step explanation:

f(-5) = 2x2 + -5 -1

f(-5) = 4 - 6

f(-5) = -2

4. Gabby ate 25 % of a whole pepperoni pizza.
Lebron ate 1/8 of the pizza.
What fraction of the pizza was left for Mohamed to eat?

Answers

Answer:

There is 5/8 left for Mohamed to eat.

Step-by-step explanation:

Let's put everything into fractions of 1/8. knowing that 25% is 1/4 or 2/8, 1/8 + 2/8= 3/8. and to find the answer, you need to subtract 3/8 from 8/8 or 1.

As a result, 5/8.

1/8 = 12.5%

12.5% + 25% = 37.5%

We need to know how much is left.

37.5% is gone, so 100% - 37.5% = 62.5%

62.5% is left for Mohamed to eat.

62.5% = 5/8.

5/8 of a pizza is left for mohamed to eat.

Lines E, F, and G are parallel lines cut by transversal H as shown below. What is the value of
a+b+c+d?

Answers

Answer:

okay now i get it its not easy at first but look at it for a bit and yoll get it

4 1/8÷2 3/4 convert the mixed numbers to improper fractions​

Answers

Answer:

Check picture

Step-by-step explanation:

9514 1404 393

Answer:

  1 1/2

Step-by-step explanation:

  [tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]

Then the improper fraction 3/2 can be written as the mixed number 1 1/2.

  (4 1/8) / (2 3/4) = 1 1/2

_____

Comment on division of fractions

Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.

If we were to "invert and multiply", the computation would be ...

  (33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2

Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:

  (33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2

How much mixed spice will she need for 6 spice

Answers

Answer:

who

Step-by-step explanation:

The ratio of chocolate
chip cookies to total
cookies on a tray is 3:5.
What percent of the tray
is chocolate chip
cookies?

Answers

Answer:

The percent is 75%

Step-by-step explanation:

please i need in under 20 mintute quick

Answers

Answer:

its been over twenty minutes. did you figure it out ?

A proposed change in income tax suggests charging 20% on a person's income up to $30,000 and then 40% on any
income above that. If a person has an income of $47,000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Provide your answer below

Answers

Answer:

If you get tax you should know the details of the what the tax is FOR

Step-by-step explanation:

Not enough details in question

Answer:

Step-by-step explanation:

Since the person earns over $30,000, they will be charged 20% on $30,000 plus 40% on ($47,000−$30,000)=$17,000. Hence the total amount of tax that they'd need to pay under the proposal is

Total Income Tax=$30,000×20%+$17,000×40%=$30,000×20100+$17,000×40100=$6,000+$6,800=$12,800.

Find the mean of these numbers:
2,57, 38, 42,6

Answers

Answer:no

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

add all of those numbers and divide it by the value of how many numbers there are in total.

Convert 6 feet to meters.
Conversion table:
1 meter = 3.281 feet

Answers

Answer:

6 feet = 1.8288 meters

Step-by-step explanation:

Hope this helps and have a phenominal day!

The density of a certain material is such that it weighs 5 kilograms for every 8.5 fluid
ounces of volume. Express this density in ounces per liter. Round your answer to the
nearest whole number.

Answers

Answer:

701 ounces per liter

Step-by-step explanation:

it's from delta math

The required density in ounces per liter is 140 onces per liter.

The density of a certain material is such that it weighs 5 kilograms for every 8.5 fluid ounces of volume.
To determine density in ounces per liter.

What is volume?

Volume is defined as the ratio of the mass of an object to its density.

As given that, t weighs 5 kilograms for every 8.5 fluid ounces of volume.
1 KG = 7.0474 ounces
5kg = 35.247
8.5 fluid of ounces = 0.251 liter

Density is given as,
= mass / volume
= 35.274 / 0.251
= 140 ounces per liter.

Thus, the required density in ounces per liter is s140 ounces per liter.

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I need help please ​

Answers

The value of X must be 0. Hope this helps and a Brainliest would be appreciated
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