can someone help with this? there is also a part two. picture is provided :) (not pt 2)

Can Someone Help With This? There Is Also A Part Two. Picture Is Provided :) (not Pt 2)

Answers

Answer 1

Solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to   3 + i or 3 - i.

As given in the question,

Given equation is:

x² -6x +10 = 0

Complex number i² = -1

Using perfect square method:

x² -6x + 9 +10 -9 =0

⇒x² -6x +9 =-1

⇒ (x - 3)² = (i)²

⇒x-3 = ± i

⇒ x= 3 ± i

Using quadratic formula,

x = [ -(-6) ±√ (-6)² -4(1)(10)] / 2(1)

  =( 6 ± √-4)/ 2

  = (6± √4i²) /2

  = (6 ± 2i) / 2

  = 3 ± i

Therefore, solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.

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Related Questions

Given that f(x)=x+4 and g (x)=3x/x+1 (1) determine the value of f(9)​

Answers

The value of f(9) is 13

The function f(x) = x + 4

The function g(x) = 3x / x+1

The function is the mathematical statement that show the relationship between one variable and another variable. If one variable is independent variable and another variable will be dependent variable. Also the function is the equation that shows the relationship between the input  and output.

The function

f(x) = x + 4

We have to find the value of f(9)

We have to substitute the value of x = 9 in the function

f(9) = 9 + 4

Add the terms

f(9) = 13

Hence, the value of f(9) is 13

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there is a number written on the board. one student increased the number by 12. another student multiplied the number written on the board by 3. the first student's result is 2 greater than the second student's result. what is the number written on the board?

Answers

From the given condition of number written on the board, first student increased it by 12 and second multiply by 3 the result of first one is greater than the second by 2 then number written on the board is 5.

As given in the question,

Let x be the number written on the board.

First student increased the number on board by 12 = x +12

Second student multiply the number on board by 3 = 3x

Required equation as per given condition is:

x +12 = 3x + 2

⇒ 3x -x = 12 -2

⇒ 2x = 10

⇒ x = 10/2

⇒ x= 5

Therefore, for the number written on the board, first student increased it by 12 and second multiply by 3 the result of first one is greater than the second by 2 then number written on the board is 5.

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will give u brainliest

Answers

Answer:

224 in²

Step-by-step explanation:

The formula for the area of a triangle is 0.5bh, where b is the base and h is the height. Here the base is '4t' and the height is '7t'. Subbing in 4 for t, we get

Base = 4(4) = 16

Height = 7(4) = 28

Subbing this values into our formula for the area of a triangle, and we have:

Area = 0.5(16)(28) = 224 in²

Use the properties of logarithms to rewrite the following expression as a single logarithm. Please see attached pic.

Answers

Answer:

log4 (70)

Step-by-step explanation:

log4(7) + log4(10) = log4(7 * 10 ) = log4(70)

At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.

Answers

Answer:

yes

Step-by-step explanation:

Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
2
(13q² +82q - 55) ÷ (q + 7)

Answers

The division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].

What is the quotient of polynomials?

Any quotient of polynomials a(x)/b(x) can be expressed as q(x)+r(x)/b(x), where r(x) is a real number and b is a real number (x). For instance, x-2+3 can be used to represent (x2-3x+5)/(x-1) (x-1).

We have,

              [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

By dividing,

           [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)} / \frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

                  [tex]= 13q + \frac{-9q - 55)}{ (q + 7)}[/tex]

                   [tex]\frac{-9q - 55}{q+7} / \frac{-9q - 55}{q+7}[/tex]

                   [tex]= 13q - 9 + \frac{8}{q+7}[/tex]

Hence, the division of the given polynomial is  [tex]13q - 9 + \frac{8}{q+7}[/tex].

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Write an absolute value equation which means t is 7 units
from zero.

Answers

The absolute value of t = |t| = 7

The purchase price of a diamond ring increases by £20 when the rate of VAT is increased from 12% to 20%. Find the original purchase price of the ring

Answers

The original price of the ring is  £250.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, the purchase price of a diamond ring increases by £20 when the rate of VAT is increased from 12% to 20%.

Let the original price of the ring be x, then according to question,

120% of x - 112% of x = 20

1.2x - 1.12x = 20

0.08x = 20

x = 20/0.08

x = 250

Hence, The original price of the ring is  £250.

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PLEASE HELP 50 POINTS PLUS BRAINLEST ANSWER ASAP Multiply (2.36 x 10^−9)(8.4 x 10^15). Write the final answer in scientific notation.

1.9824 x 10^7
19.824 x 10^6
1.9824 x 10^−134
19.824 x 10^−135

Answers

The explanation is above

Answer:

THE CORRECT ANSWER IS 1.9824 x 10^7

Step-by-step explanation:

award as brainliest

John bought a pair of jeans on sale for $10 off. The original price of the jeans was $45. What was the sale price of the jeans?

Answers

Answer:

$35

Step-by-step explanation:

All you have to do is subtract 10 from 45 because it was $10 off and the original price was $45.

8) I bought 4 baseball cards for y dollars each and 3 card holders for $2.50
each. I paid a total of $19.50. What is the cost per baseball card?
PROVE IT!! SHOW YOUR WORK!!!!!
A) $3 B) $4 C) $5.50 D) $6

Answers

Answer:

$3

Step-by-step explanation:

Total of all = $19.50

3 Card holders total = $7.50

4 Baseball card total = ?

We know that 19.50 is the sum of the holders and cards together so we subtract $7.50 from $ 19.50.

$19.50-$7.50=$12 for ALL four baseball cards

We know that 4 baseball cards are $12, but if we DIVIDE 12 by four, we get the individual price per card.

12/4 = $3

Fine the values of x and y.

Answers

Answer:

x = 55

y = 20

Step-by-step explanation:

Angles on a straight line sum to 180°.

Finding x

⇒ 75° + (2x - 5)° = 180°

⇒ 75 + 2x - 5 = 180

⇒ 2x + 70 = 180

⇒ 2x + 70 - 70 = 180 - 70

⇒ 2x = 110

⇒ 2x ÷ 2 = 110 ÷ 2

x = 55

Finding y

⇒ 75° + (4y + 25)° = 180°

⇒ 75 + 4y + 25 = 180

⇒ 4y + 100 = 180

⇒ 4y + 100 - 100 = 180 - 100

⇒ 4y = 80

⇒ 4y ÷ 4 = 80 ÷ 4

y = 20

High-fiber foods have at least 5 g of fiber per serving. Let f be the
Number of grams of fiber per serving of high-fiber food. Which inequality
Describes this situation?
A.) f > 5
B.) f < 5
C.) f ≤ 5
D.) f≥ 5
A.
B.
C.
D.

Answers

The inequality that describes this situation is f ≥ 5

How to calculate the inequality ?

Use the steps below to solve an inequality:

Step 1: Subtract all fractions by multiplying each term by the sum of all fractions' least common denominators.

Step 2: Simplify the inequality by merging like terms on each side.

Step 3: Add or subtract amounts to get the unknown and the numbers on either side.

As per the question it tells the High- fiber should have at least 5g of fiber per serving

f = Number of grams of fiber per serving of high-fiber food

∴ f ≥ 5

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In a school of 320 children, 45% of the children speak a language other
than English at home.
(i) Calculate the number of children in the school who speak a
language other than English at home.
(ii) Of the children who speak a language other than English at home,
24 speak Polish. Write the number of children who speak Polish as
a fraction of the number of children who speak a language other than English at home.
Give your answer in its simplest form.

Answers

The number of children in the school who speak a language other than English at home is 144.

The fraction of children who speak Polish is 1/6.

How many children speak a language other than English?

Percentage is the ratio of a quantity expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.

Number of children in the school who speak a language other than English at home = Percentage of the students who speak a language other than English x number of children

Number of children in the school who speak a language other than English at home = 45% x 320

Number of children in the school who speak a language other than English at home = 0.45 x 320 = 144

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

Fraction of the students who speak Polish = number of students that speak Polish / total number of students who speak a language other than English.

Fraction of the students who speak Polish = 24 / 144 = 1/6.

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What is your country name?

Answers

The United States of America

19 is what percent of 500?

Answers

Answer:95

step by step explanation

Can I have some help asap?

Answers

Answer:

I will help you okay????

I've been stuck on this problem for awile can anyone help?
7z-4=12+3z

Answers

7z - 4 = 12 + 3z
-3z
4z - 4 = 12
+4
4z = 16
/4
z = 4

Answer:

z = 4

Step-by-step explanation:

7z - 4 = 12 + 3z

1) We want to first move the z values to one side of the equation. This means we would subtract 3z from both sides to move it to the left side. This would give us 4z - 4 = 12.

2) We then want to isolate the z value. This means we want to move the -4 to the right side. We would add 4 to both sides and get 4z = 16.

3) We can then divide both sides by 4 and get the value for z.

This gives us z = 4.

absolute value 2x - 6 less than 0

Answers

The solution set for the inequality is (-3, 3)

How to solve the absolute value inequality?

Here we have the absolute value inequality

|2x| - 6  < 0

To solve this, we need to isolate the variable, which in this case is x.

Adding 6 in both sides we get:

|2x| -6 + 6 < 0 + 6

|2x| < 6

This can be decomposed in the inequality:

-6 < 2x < 6

Now to competely solve the inequality, we will divide both sides by 2, so we get:

-6/2 < 2x/2 < 6/2

-3 < x < 3

So the solution set is (-3, 3)

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Find all real numbers x such that
(3^x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3

Answers

All the real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) is x = 1 .

In the question ,

it is given that the expression is

(3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)

By using the identity a³ + b³ [tex]=[/tex] (a + b)(a² - ab + b² )

we get ,

[(3x - 27 + 27x - 3)] × [(3x - 27)² - (3x - 27)(27x - 3) + (27x - 3)² ] = 30x - 30

(30x - 30)×[(3(x - 9))² - (3(x - 9) × 3(9x - 1)) + (3(9x - 1))²] = 30x -30

using the identity (a-b)² [tex]=[/tex] a² -ab + b²

(30x - 30) × [9( x² - 18x + 81) - (9(9x² - 82x + 9)) + (9(81x² - 18x + 1)) = 30x-30

9(30x - 30)×[x² - 18x + 81 - 9x² + 82x - 9 + 81x² - 18x + 1] = 30x - 30

270×(x - 1)×[ 73x² + 46x + 73] = 30(x - 1)

taking (x-1) terms to LHS ,
we get

(270 - 30)×(x - 1)[ 73x² + 46x + 73 ] = 0

(240) (x - 1) [ 73x² + 46x + 73 ]  =  0     ....because 270-30 = 240

Dividing both sides by 240

we get ,

(x - 1) [73x² + 46x + 73] = 0

So , either x - 1 = 0    or      73x² + 46x + 73 = 0

on solving 73x² + 46x + 73 = 0

we get the discriminant of 73x² + 46x + 73  a negative number , so it cannot have real root .

hence x -1 = 0

x = 1

Therefore , the only real solution is x = 1 .

The given question is incomplete , the complete question is

Find all real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)   ?

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Zack and his friends went to a movie on Thursday afternoon. It took 25 minutes to drive to the theater. They arrived at the theater 1 hour and 15 minutes before the movie started. Once it started, the movie lasted for 1 hour and 20 minutes and ended at 4:20 P.M. What time did Zack and his friends leave for the movies

Answers

Answer:

2:20

Step-by-step explanation:

The movie started at 3:00 PM they got there at 2:45. and it took them 25 mins to get there meaning they left at 2:20.

Answer: 1:20 P.M.

Minutes: 25 + 60 + 15 + 60 +20 =180minutes
180/60=3
3hours
4:20 - 3h= 1:20
So they left at 1:20 P.M.

Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.

$69
$90
$420
$1,080

Answers

Answer: The answer to this question is $90.

Step-by-step explanation:

The Simple interest is $90.

What is Simple Interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.

Given:

P= 1500

R = 12%

T= 6 month = 1/2 year

Using, formula of Simple Interest

I = P x R x T /100

I = 1500 x 12 x 1/ 2x100

I = 18000/200

I = 90

Hence, the interest is $90.

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Premise 1: If a person lives in San Francisco, then they live in California. Premise 2: Fred does not live in San Francisco. Conclusion: Fred does not live in California. Let A be the set of people who live in San Francisco, and let B be the set of people who live in California. (a) Draw the Venn diagram that can be used to demonstrate the above information. Include labels for both circles and mark the location of the X. Then choose which option matches your answer? ? C X B (A) B (B) B (C) B (D) А X B (E) (b) Is this argument valid or invalid? Explain on your work paper how you made this conclusion. Invalid​

Answers

Nice work on selecting "invalid" as the correct answer.

The reason why this argument is invalid is because the 'x' could be in circle B or could be outside circle B. There's simply not enough information.

The venn diagram would either be (A) or (D).

The only information we know is that Fred is does not live in San Francisco, so the 'x' will not be placed inside circle A.

Ignore any diagram where x is on the edge of a circle. That isn't allowed in venn diagrams because a person is either in San Francisco, or they aren't (same goes with California). We can't have blurry boundaries like that. This means venn diagrams (B) and (C) are nonsensical.

ou get an auto loan at 6% interest for 5 years; please answer the following. You can afford a $350 per month car payment; how expensive a car can you afford? (Round to two decimal places and do not include a dollar symbol)

Answers

You can afford a car at a price of 13,016.79

What is the monthly payment formula?

The monthly payments are given by the equation presented as follows:

[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]

where R = r / 12

P is the initial amount , r is the interest rate , n is the number of payments.


Given data ,

A = $ 350

R = 6 %

r = 6 / 12 %

 = 0.5 %

 = 0.005

n = 5 years

  = 5 x 12 months

  = 60

Therefore , the maximum value of the car is calculated as

[tex]A=P\frac{R(1+R)^{n} }{(1+R)^{n}-1 }[/tex]

[tex]250=P\frac{0.005(1+0.005)^{60} }{(1+0.005)^{60}-1 }[/tex]

[tex]250=P\frac{0.0067}{1.3488501-1}[/tex]

[tex]P = \frac{250*0.348850}{0.0067}[/tex]

[tex]P=\frac{87.2125}{0.0067}[/tex]

P = 13016.79

Hence , you can afford a car at a price of 13,016.79

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Which expressions are equivalent to 4n+5?
Select two correct answers.

5n+4

4n+20

1/4(16n+20)

4+n+5

5+4n

Answers

Hopefully this will help you

HELPP PLEASE IM ACTUALLY STUCK???

Answers

Answer:

[tex]d=-8[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]258[/tex] and the second term is [tex]250[/tex], then each successive term in the sequence is [tex]8[/tex] less than the previous term. Therefore, the common difference is [tex]-8[/tex] ( [tex]d=-8[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-8n+266[/tex]

Therefore:

Term 1: [tex]a_1=-8(1)+266=-8+266=258[/tex]

Term 2: [tex]a_2=-8(2)+266=-16+266=250[/tex]

Term 3: [tex]a_3=-8(3)+266=-24+266=242[/tex]

Term 9: [tex]a_9=-8(9)+266=-72+266=194[/tex]

Simplify. 5-[-(-2)] ​

Answers

Answer:

3

Step-by-step explanation:

Answer: 3
Step 1: remove the parenthesis
5---2
Step 2: when there are two negative it equals a positive, so it cancels out to 5-2
Which =3

The rectangle below has an area of y² + 8xy + 7a² square meters and a length of y + x
meters.
What expression represents the width of the rectangle?

Answers

The width of a rectangle is (7x+y) meters.

What is the area of a rectangle?

A flat surface of a specific shape can be thought of as the area it occupies in space. In terms of the "number of" square units, it is measured (square centimeters, square inches, square feet, etc.) The number of unit squares that can fit inside a rectangle is the area of that shape. The flat surfaces of laptop monitors, chalkboards, canvases, and other objects are a few instances of rectangular shapes.

Area of the rectangle is = (7[tex]x^{2}[/tex]+8xy+[tex]y^{2}[/tex]) square meter

length of the rectangle is = (x+y) meters

we know, the area of the rectangle= length×width

So, the width of the rectangle = (7[tex]x^{2}[/tex]+8xy+[tex]y^{2}[/tex])/(x+y) meters

=(7x+y)(x+y)/(x+y) meters

=(7x+y) meters

Hence, The width of a rectangle is (7x+y) meters.

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Translate (in terms of x) then solve the algebraic equation:
Nine is subtracted from twice some number and the result is the sum of the number
and 7.

Answers

The Algebraic Equation is correct

What is Algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.

Two times a certain quantity

When a number is divided by two, ten is subtracted: 2x-9

The equal sign is a result.

The number and its sum equals 7+x.

Put everything together (except for the first 2x, that was used to find the second part).

2x-9=7+x

Get all of your like terms on the same side first. Because dealing with a negative variable can result in an additional step at the end, I personally dislike dealing with them. As a result, I'll take the n on the right and shift it to the 2x on the left.

2x-9=7+x

x-9=7

The -9 must now be positioned on the other side of the equal sign.

x = 7 + 9

x=16

Connect the 16 to the original equation to make sure you're doing it correctly.

2(16)-9=7+(16)

32-9=7+16

23=23

It is accurate.

Hence, The algebraic equation is correct

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Which of the quotients is equivalent to -5/8? Select all that apply.

Answers

The equivalent quotient to -5/8 are; -5/8 and .5/-8.

The correct answer options are options A and C

How to find equivalent quotient?

A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.

A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.

Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.

Complete question:

Given options:

A. -5/8

True

B. 5/8

False

C.5/-8

True

D. -(5/-8)

False

E. -5/-8

False

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