Mathematics College

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Which are the solutions of the quadratic equation?

x2 = 9x + 6



Answers

Answer 1
Final answer:

The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.

Explanation:

To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +- sqrt(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:

x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))

Simplifying further:

x = (9 +- sqrt(81 + 24)) / 2

x = (9 +- sqrt(105)) / 2

So the solutions of the quadratic equation x^2 = 9x + 6 are:

x = (9 + sqrt(105)) / 2

x = (9 - sqrt(105)) / 2

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Answer 2
Final answer:

The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.

Explanation:

The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.  

If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.

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Related Questions

Each side of a square is increasing at a rate of 5 cm/s. at what rate is the area of the square increasing when the area of the square is 49 cm2? 70 cm2/s

Answers

This problem is solved using the chain rule. the area of the square is f(t) and the length of the side is g(t) f(t)=g(t)^2 g'(t)=5 Using the chain rule f'(t)=2*g(t)*g'(t) The value of g(t) is sqrt(49) which is 7. g'(t) is given as 5 cm/s f'(t)=2*7*5=14*5=70cm^2/s

Celine's Cereal Company is launching a new brand of cereal and she is considering two different sizes for the base of the boxes. Box 1: The length is 3 times the width. Box 2: The length is 1 less than 4 times the width. The dimensions of the base of Box 1 are: width: x; length: 3 width: x; length: x + 3 width: x; length: x – 3 width: x; length: 3x

Answers

Answer:

D. Width = x and Length = 3x

Step-by-step explanation:

We are given that,

The length of Box 1 is 3 times the width of Box 1.    ..................(1)

Let the width of Box 1 = x

So, from (1), we have,

Length of Box 1 = 3 × Width of Box 1

i.e. Length of Box 1 = 3x

Thus, the dimensions of Box 1 are : Width = x and Length = 3x

Hence, option D is correct.

In this exercise we have to identify which of the alternatives best represents the equation, like this:

Letter D

So we have that it is the area of ​​a box, where we have:

The length of box is 3 times widthThe width of the box is  X

So is the same as:

[tex]L= 3W\\W=X\\L=3X[/tex]

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"sam's furniture was destroyed by a fire. the furniture cost $1200 when it was purchased, but similar new furniture now costs $1800. assuming the furniture was 50 percent depreciated, what is the actual cash value of sam's loss?"

Answers

deprecated means the price is decreased, so if something is deprecated by 50% (which just means 1/2 is taken away) its original price is just cut in half. so half of 1200 (1200 divided by 2) is 600. i think the answer is 600 :-)

The actual cash value of Sam's furniture loss is $600.

To calculate the actual cash value of Sam's furniture loss, we first determine the amount of depreciation applied to the original purchase price. Since the furniture was 50 percent depreciated, we calculate this amount to be 50% of $1200, which is $600. This means the depreciated value of the furniture is $1200 - $600 = $600. However, because the replacement cost of new, similar furniture is now $1800, this does not affect the actual cash value of the lost furniture, which remains at the depreciated value of $600. So the actual cash value of Sam's loss is $600.

Greg drank 5 cups of water on Monday. He drank 4 cups of water on Tuesday. How many 1/4 cup servings of water did Greg drink on Monday and Tuesday combined?

Answers

Start the problem by first finding out how many 1/4 cups of water equal 1 full cup of water. [tex]\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 1[/tex], therefore we can see that every 1 cup of water is equivalent to 4 1/4 cups of water. Now we will find the total number of cups of water Greg drank on monday and tuesday by adding 5 + 4 = 9. Multiply this number by 4 and you have the total number of 1/4 cups of water Greg drank on Monday and Tuesday combined.
So what I did was take 5 and 4 and then add them which would be 9, after that take 1/4 and make 9 one/forth. So it would look like 1/4+ 1/4+ 1/4+ 1/4+ 1/4 + 1/4+ 1/4+ 1/4+ 1/4= 2.25

The length of a rectangle is 4 centimeters more than twice its width. If the perimeter of the rectangle is 86 centimeters , find the dimensions of the rectangle

Answers

P = perimeter = 2L + 2W = 86 cm.  Also, L = W + 4.  Subst. W + 4 for L, 

P = 2(W + 4) + 2W = 86 cm.  Then 2W + 8 + 2W = 86 cm, and 4W = 78 cm.

Finally solving for W, W = (78 cm)/4, or 19.5 cm.

If W = 19.5 cm, then L = W + 4 cm = 19.5 cm + 4 cm = 23.5 cm

The rectangle's dimensions are 19.5 cm by 23.5 cm.

a square has the side measurment of s = 2 3 over 2 using the formula 1= s^2 find the area of the square

Answers

check the picture below.

[tex]\bf A=s^2\qquad s=2\frac{3}{2}\qquad A=\left( 2\frac{3}{2} \right)^2\implies A=\left( \frac{2\cdot 2+3}{2} \right)^2 \\\\\\ A=\left( \frac{7}{2} \right)^2\implies A=\cfrac{7^2}{2^2}\implies A=\cfrac{49}{4}\implies A=12\frac{1}{4}[/tex]

30 + (.0825 x 30) + (15% x 30) =

Answers

Your answer is gonna be 36.975
30+(.0825 times 30) +(15% times30)
30+2.475 +(0.15 times 30)
32.475+ 4.5=36.975

Convert 604,800 seconds to weeks using Dimensional analysis

Answers

I think it would be 1 week.

Two negative integers are five minutes apart on the number line, and their product is 126. What is the sum of the two integers?

Answers

First I will assume that this problem can be reworded as follows:  "Two negative integers are five units apart on the number line."

Let the first (the smaller) negative integer be x and the second y.  Note that y, being bigger than x, can be represented by y=x+5.

First find the 2 integers.  Their product is 126, so x(x+5)=126.
Expanding, x^2 + 5x - 126 = 0.  Using the quadratic formula to solve this, 

          -5 plus or minus sqrt(529)        -5 plus or minus 23
x = --------------------------------------- = -----------------------------
                           2                                              2
                                                                                          -5 -23
We are interested only in negative integers, so take x = ------------
                                                                                               2

Then x = -28/2, or x = -14.  Then y is x+5, or -14+5 = -9.

Check:  does the product of -9 and -14 equal 126, as it must?   YES.

Last year, Amanda had
$10,000
to invest. She invested some of it in an account that paid
6%
simple interest per year, and she invested the rest in an account that paid
10%
simple interest per year. After one year, she received a total of
$760
in interest. How much did she invest in each account?

Answers

Let $x be invested in the account that paid 5% simple interest.
Let $y be invested in the account that paid 10% simple interest.

The total invested is $10,000, therefore
x + y = 10000            (1)

The interest amounts earned are respectively
x*1*0.06 = 0.06x
y*1*0.10 = 0.10y

The total interest earned is $760, therefore
0.06x + 0.10y = 760     
Multiply through by 10 to obtain
0.6x + y = 7600              (2)

Subtract (2) from (1).
x + y - (0.6x + y) = 10000 - 7600
0.4x = 2400
x = $6,000
From )1), obtain
y = 10000 - 6000 = $4,000

Answer:
$6,000 in the account paying 6% simple interest, and
$4,000 in the account paying 10% simple interest.

Suppose you buy a piece of office equipment for $9,000.00. After 5 years you sell it for a scrap value of $2,000.00. The equipment is depreciated linearly over 5 years. The value of the piece of equipment after 2 years is (rounded to the nearest whole dollar)

Answers

Residual value = $2000

$7000/5 = $1400

Yearly depreciation = $1400

So in 2 years total depreciation = $2800.

Value = Purchase Price - Total Depreciation
Value = $9000               -    $2800
Value after 2 years = $6200

The value of the piece of equipment after 2 years is $6,200.00.

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The equipment is depreciated linearly, which means that its value decreases at a constant rate each year. We can find the rate of depreciation by subtracting the scrap value from the purchase price, and then dividing by the number of years of useful life:

Rate of depreciation = (Purchase price - Scrap value) / Useful life

Rate of depreciation = (9000 - 2000) / 5

Rate of depreciation = 1400

This means that the equipment loses $1,400 of value each year. After 2 years, the value of the equipment will be:

Value after 2 years = Purchase price - (Rate of depreciation x Number of years)

Value after 2 years = 9000 - (1400 x 2)

Value after 2 years = 6200

Therefore, the value of the piece of equipment after 2 years is $6,200.00.

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The first three values in a selected series are 3, 6, and 9. what are the next three va;ies that will be inserted by autofill?

Answers

the answer is 12, 15. and 18

Answer:

the answer is 12, 15. and 18.

Step-by-step explanation:

x+2y=8 in slope intercept form

Answers

This question is super easy, all you need to do is isolate the y variable. When you want to isolate it, you have to get rid of other numbers by doing the opposite sign.
x+2y=8     Subtract the x.
2y=8-x      Divide by two.
y=4-1/2x

[tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].

Slope

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

Given to us,

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

To find the slope-intercept form

To find the function, simply isolate y.

[tex]x+2y=8\\2y = 8-x\\y = \dfrac{8-x}{2}\\\\y = \dfrac{8}{2}-\dfrac{x}{2}\\\\y = 4-\dfrac{x}{2}[/tex]

Hence, [tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].

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The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels and shared the cost equally. How much did each person pay?

Answers

$4.68 because each pretzel is $1.17 so 8 pretzels are 9.36 ÷ by 2 = $4.68

Earth is about 4.5 billion years old and written human history extends back about​ 10,000 years. Suppose the entire history of Earth is represented with a 1000​-meter-long ​timeline, with the birth of Earth on one end and today at the other end.
2 billion years is represented by how many meters of the timeline?

Answers

444.44 meters.

Hope that helps

10 11/12 + 7 1/4 =

A. 3 8/12
B. 3 2/3
C. 17 1/4
D. 18 1/6

Answers

It's D if you  need an explanation let me know
10 11/12 + 7 1/4 
= 10 11/12 + 7 1/4 
= 10 11/12 + 7 3/12
= 17 14/12
= 18 2/12
= 18 1/6
answer
D. 18 1/6

-3.1 * (- 2.9) Please help! Math.

Answers

8.99 would be your answer

The answer is

(-3.1)(-2.9)

=8.99

1. 3/5x -7 = 23

A. x = 40
B. x = 45
C. x = 50
D. x = 55

2.When Patrick and Cameron went bowling at Victory Lanes, they spent a total of $42. This included rental of shoes at $3.50 per pair. Patrick bowled 2 games, and Cameron bowled 3 games.
How much did each game cost?
A. $6.00
B. $7.00
C. $7.70
D. $8.75
3.A local movie theater offers a special deal for birthday parties. The price, which covers the cost of the tickets and a box lunch, includes a flat fee of $75 plus $5 per ticket. Sarah’s parents spent $150 altogether at the theater to celebrate her birthday.

Which equation can be used to determine how many children, x, were in the group?
A. 75/150=5x
B. 150/75=5x
C. 150 = 5x – 75
D. 150 = 5x + 75

4. 35 + 0.25x = 53.75
A. x = 75
B. x = 140
C. x = 215
D. x = 250

5.T he perimeter of this isosceles triangle is 47 cm.
top point. (B) left bottom point (A) right bottom point (C) in between 12cm
What is the length of each of its legs (it doesn't have legs)?
A. 15 cm
B. 17.5 cm
C. 19.5 cm
D. 35 cm

Answers

3/5x - 7 = 23
3/5x = 23 + 7
3/5x = 30
x = 30/(3/5)
x = 30 * 5/3
x = 150/3
x = 50 <==
=====================
3.50(2) + 5g = 42
7 + 5g = 42
5g = 42 - 7
5g = 35
g = 35/5
g = 7 <== each game costs $ 7
===================
150 = 5x + 75
===================
35 + 0.25x = 53.75
0.25x = 53.75 - 35
0.25x = 18.75
x = 18.75 / 0.25
x = 75 <===
===================
if one leg is 12.....and an isosceles triangle has 2 equal sides....(47 - 12) / 2 = 35/2 = 17.5 <==


Bob is a high school basketball player. his probability of making a free throw is 0.70. let x denote the number of hits in 10 shots. . find the probability that bob makes at least 9 hits. the probability is _____________.

Answers

Xjxjjxjxbdbdndbdbbdndhdhdhxhdhdhhdhdhdhdbdhdhdhdhhd

At full power, how long would it take for the car to accelerate from 0 to 64.0 mph ? neglect friction and air resistance. express your answer in seconds.

Answers

The amount of time it would take for a car to accelerate from 0 to 64.0 mph can vary based on the vehicle. Basic vehicles generally can accelerate in under 6 seconds to 64 mph, while exotic cars can reach that speed somewhere in between 3 and 4 seconds.

Find two numbers with a sum of 20 and a difference of 14.

Answers

17 and 3 is your answer

17 + 3 = 20

17 - 3 = 14

hope this helps

What is the place value of the 4 in the number 5,679.04

Answers

the 4 is in the hundreth place
Hi. The 4 is in the hundredths place. When dealing with place value that has a decimal just remember that everything to the left of the decimal starts as ones, tens, hundreds, etc. Starting with the first number on the right we have tenths, hundredths, thousandths, etc. So for your numbers, we have the following:

5 = thousands
6 = hundreds
7 = tens
9 = ones
0 = tenths
4 = hundredths

Hope this helps.

Take care,
Diana

For a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases c. as the annual rate increases, the monthly payment stays the same b. as the annual rate increases, the monthly payment decreases d. no correlation

Answers

 If the annual rate increases nothing will happen to the monthly payment, so the answer is C as the annual rate increases, the monthly payment stays the same. Once the fixed-rate payment (loan) is processed there is no chance for any changes as this procedure means that lender is under a fixed-rate loan each payment period.

The point(3,7) is reflected in the y axis what are the coordinates now

Answers

When a point P(a, b) is reflected about the y-axis, the coordinates of the reflected point are P'(-a, b).

Thus, the reflection of point (3, 7) is (-3, 7), as shown in the picture.


Answer: (-3, 7)


The graph of y = –3x + 4 is:
A. a point that shows the y-intercept.
B. a line that shows the set of all solutions to the equation.
C. a point that shows one solution to the equation.
D. a line that shows only one solution to the equation.

Answers

Answer: The answer is B, just got this one on a test.



Step-by-step explanation:


which pair of fractions is equivalent to this pair : 3/5 and 2/7

a. 21/35 & 10/35
b. 10/35 & 7/35
c. 7/35. & 5/35
d. 24/35 & 12/35

Answers

I believe the answer would be A.
Hope this helps!
First you want to get a common denominator. In this case it is 35. So multiply whatever number works to get them equal to 35.

3/5(7/7) = 21/35
2/7(5/5) = 10/35

A.21/35 and 10/35

Hope this helps!

Is 25/99 a terminating or repeating decimal

Answers

25/99 = 0.2525252525

Do you see that 25 repeats?

Repeating decimal for sure.

You are planning a party and want to know how many cans of soda to buy. a genie offers to tell you either the mean number of cans guests will drink

Answers

Is there more to this question??

You purchase three packs of batteries at $11.99/pack. You have a coupon for 10% off and the sale tax is 7% how much is the total cost of your purchase?

Answers

The answer is 34.64. C.

The entire purchase of the three items cost about $34.

How to determine the total cost?

The given parameters are:

The cost of one packs of batteries is $11.99/pack.

Coupon = 10% off

The total cost is then calculated using:

Total = (three packs of batteries) * (1 - Coupon)

So, we have:

Total = (11.99 + 11.99 + 11.99 ) * (1 - 10%)

Evaluate,

Total = 34.47

Approximate

Total = 34

Hence, the entire purchase of the three items cost about $34.

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X/2-18=(-28)
What is x?
X=?

Answers

X = -20

Step 1: Write the division as a fraction
x ÷ 2 - 18 --> x/2 - 18

Step 2: Multiply both sides of the equation by 2
x - 36 = -56

Step 3: Move contact to the right side and change its sign
x = -56 +36

Step 4: Solve
x = -20
X would be -20 in this problem.
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