Which statement best explains why the solutions of this quadratic equation are irrational?

Which Statement Best Explains Why The Solutions Of This Quadratic Equation Are Irrational?

Answers

Answer 1

The solution of the quadratic equation is irrational because 11² - 4*3*9 is not a perfect square.

What is an irrational quadratic equation?

An irrational quadratic equation is an equation that contains two irrational solutions making the equation not to be able to be solved through factorisation.

Using the quadratic equation formula to solve, the irrational solutions are gotten below,

X = -b +√b²- 4ac/2a

where a = 3; b= 11 ; C = 9

X = -3+√11²-4*3*9/2*3

X= -3+√ 121-108/6

X= -3 +√13/6

X =-3/6 +√13/6

X= -1/2 + √13/6

Therefore,X = -1/2 +√13/6 or

X = -1/2 - √13/6

The solution are two irrational numbers that are not prefect squares.

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Related Questions

The volume of this cone is 602.88 cubic inches. What is the radius of this cone?
Use a = 3.14 and round your answer to the nearest hundredth.
9 in
r
inches

Answers

Answer:

8

Step-by-step explanation:

Volume of a cone formula: V = [tex]\pi r^{2} \frac{h}{3}[/tex]

where,

h is the height             9 in  (assuming)

r is the radius              want

v is the volume            602.88 cubic inches

[tex]\pi[/tex] is                              a = 3.14

Plug in everything:

[tex]602.88 = 3.14r^{2} (\frac{9}{3} )\\602.88 = 3.14r^{2} (3)\\1808.64 = 28.26r^{2}\\\frac{1808.64}{28.26} = \frac{28.26r^{2}}{28.26} \\r^{2} = 64\\r = \sqrt{64} \\r = 8\\or\\r =-8[/tex]

Write down a number that has the same value as:
1-13.51

Answers

Answer:

The answer would have to be 5 but im not sure cause there are no answer choices.

Step-by-step explanation:

Find the probability of each event
A fair coin is flipped ten times. What is
the probability of the coin landing tails up
at least nine times?

Answers

Answer:

11/1024.

Step-by-step explanation:

Binomial Probability distribution.

This is the probability of 9 tails or 10 tails being flipped.

Prob ( 10 tails) = (1/2)^10 = 1/1024

Prob ( 9 tails) = 10C9 * 1/2^9* 1/2 = 5/512

Required probability =  1/1024 + 5/512

= 11/1024.

A(x)=x(10-x)
When is A(x) at its maximum? Explain
Or show how you know.

Answers

Answer:

A(x) is at its maximum at x = 5, or (5, 25)

Step-by-step explanation:

Putting A(x)=x(10-x) back into its standard form gives A(x) = -x^2 + 10x. The equation to find the x value in vertices in these types of functions is -b / 2a, the letters pertaining to the coefficients. In this case, this graph would have a maximum at -(10)/2(-1), or -10/-2 = 5 --> Thus, when x=5, the downwards facing graph is at its maximum

(Might not be important but another method to solve:)
Take the derivative of the function A(x) = x(10-x) and set it equal to 0 to find the x value of all vertices. In this case, A'(x) = -2x + 10,
-2x + 10 = 0
-2x = -10
x = 5
A(x) is at its maximum at x=5 because it is when A'(x), the derivative, is equal to 0 and thus has a flat slope (or vertex)

Answer:

(5, 25)

Step-by-step explanation:

A(x) is a parabola meaning the max point would be called the vertex

Expand A(x)

[tex]x(10 - x) = 10x - x^{2}\\x^{2} -10x[/tex]

The vertex point is (h, k)

To find h:

[tex]h =- \frac{-b}{2a} \\b = -10\\a = 1\\h = - \frac{-10}{2(1)} \\h = - \frac{-10}{2} \\h = 5[/tex]a and b are from the equation [tex]ax^{2} + bx[/tex]

To find k, plug in h values:

[tex]k = \\f(5) = 5^{2} - 10(5)\\f(5) = 25[/tex]

vertex = (h, k) = (5, 25)

graph attached as well for a visual

g/6 = 8 what does g equals do

Answers

Answer:

g = 48

Step-by-step explanation:

Step 1: Multiply both sides by 6.

g6=8

(g6)*(6)=(8)*(6)

g=48

If x < 5, then which of the following must be true?

- x < 5
- x > -5
- x > 5
- x < -5

Answers

Let's check the options :

[tex] - x < 5[/tex]

Divide both sieds by - 1

[tex] \frac{ - x}{ - 1} > \frac{ 5}{ - 1} \\ [/tex]

[tex]x > - 5[/tex]

False

_____________________________________________

[tex] - x > - 5[/tex]

Divide both sides by - 1

[tex] \frac{ - x}{ - 1} < \frac{ - 5}{ - 1} \\ [/tex]

[tex]x < 5[/tex]

True

_____________________________________________

Divide both sides by - 1

[tex] \frac{ - x}{ - 1} < \frac{5}{ - 1} \\ [/tex]

[tex]x < - 5[/tex]

False

_____________________________________________

[tex] - x < - 5[/tex]

Divide both sides by - 1

[tex] \frac{ - x}{ - 1} > \frac{ - 5}{ - 1} \\ [/tex]

[tex]x > 5[/tex]

False

What is the square root of 5?

Answers

Answer:

2.2360679775

used a calculator

Step-by-step explanation:

Factor -1/4 out of -1/2x - 5/4y

Answers

The factor from the provided expression of the variable x and y is taken out. The resultant expression is -1/4(2x-5y).

What is a factor of equation?

The factor of a equation is the terms or number which is common in all the terms of the that equation.

The first term of the equation is,

-1/2x

Multiply with 2 in numerator and denominator of this term as,

-2/4x

(-1/4)2x

Now the second term of the equation is,

-5/4y

Rewrite this term as,

(-1/4)5y

Thus, the expression become,

1/2x - 5/4y

(-1/4)2x- (-1/4)5y

-1/4(2x-5y)

Hence, the factor from the provided expression of the variable x and y is taken out. The resultant expression is -1/4(2x-5y).

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What kind of shape is this ?

Answers

Answer:

prism

Step-by-step explanation:

when all the sides are joined, it will reveal the shape to become a prism.

Prism because it is a three dimensional shape

could i get help pleaseeeee

Answers

aboustouly tell me ur problem


A grocery store usually orders 1500
frozen dinners every week. They have
been selling out and have decided they
need to order 2100 each week to keep
up with demand. What is the percent
increase?

Answers

Answer:

40%

Step-by-step explanation:

The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts. So if the original value increased by 14 percent, the value would increase by 14 for every 100 units, 28 by every 200 units and so on. To make this even more clear, we will get into an example using the percent increase formula in the next section.

Answer:40&!!!!!!

Step-by-step explanation:40%!!!!!!!

2. Three times some number, decreased by five is no less than 16.

Written as a inequality, what will it be?

Answers

Answer:

Read explanation

Step-by-step explanation:

The equation is written as: [tex]3x-5\geq 16[/tex]

You can make it a 2 step equation.

[tex]3x-5\geq 16\\[/tex]

16+5=21

[tex]3x\geq 21[/tex]

21/3

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

         3 times some number decreased by 5 is no less than 16.

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

3n-5≥16

[tex]\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}[/tex]

              First, notice it says "no less than 16"

So the expression can't be less than 16, so it's greater than or equal to 16.

Now, let the number be n.

Multiply 3 times n:

3n

"Decreased by 5" means you subtract 5:-

3n-5

Inequality:- 3n-5≥15

Solve:

3n-5≥15

3n≥15+5

3n≥20

n≥20/3

Good luck.

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

What’s a 1/3 as a whole number

Answers

Answer:

a repeating term of .3

Step-by-step explanation:

1/3 = 1 divided by 3

1 divided by 3 = .33333333333333333333

that is called a repeating term

[tex]\frac{1}{3}[/tex] = .3

Answer: 1/3 is .3333333 on going

it cant be a whole number

PLEASEEE HELPPPP ASAP IM LOSING MY MIND RN

Answers

Answer:

Option 4 (D)

Step-by-step explanation

Text book Formula !

square root of 3 diveded by the square root of 2

Answers

Answer:

1.2 or if you round it is 1

Answer:

1.224744871 or (square root of 6)/2

Step-by-step explanation:

35% of salt is in feta cheese. What percentage of salt is in that 350 g cheese?

Answers

The amount of salt is in the 350 g of feta cheese, when there is 35% of salt is in cheese, is 122.5 grams.

What is percentage of a number?

Percentage of a number is the part of the whole number which is expressed in the fraction of hundredth. It is represented with "%" symbol.

35% of salt is in feta cheese. The percentage of salt is in that 350 g cheese has to be found out.

Let suppose there is x grams of slat in feta cheese of 350 g. Thus, the amount of salt (35% of 350) is,

[tex]x=\dfrac{35}{100}\times350\\x=122.5\rm\; gm[/tex]

Thus, the amount of salt is in the 350 g of feta cheese, when there is 35% of salt is in cheese, is 122.5 grams.

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the price of an item has been reduced by 20%. the origianal price was 76

Answers

Answer:

$60.8

Step-by-step explanation:

Twenty percent of 76 is,

→ 20% of 76

→ (20/100) × 76

→ 1520/100

→ [ $15.2 ]

The reduced price of the item is,

→ 76 - 15.2

→ [ $60.8 ]

Hence, the price is $60.8.

please help will give brainliest and fifty points

Refer to the table above. Determine the marginal distribution of Gender. In paragraph form, how you calculated the marginal distribution. Include your calculations in your explanation.

Answers

The likelihood of an occurrence regardless of the result of another variable is known as marginal probability.

What is marginal probability?

The likelihood of an occurrence regardless of the result of another variable is known as marginal probability. The likelihood of one event occurring in the presence of another is known as conditional probability.

We already know that marginal probabilities are calculated by dividing marginal frequencies by total frequency.

As a result, in this situation, the gender's marginal probability distribution is given by,

P(Gender=x) ≈ 0.5308                     if x = Male

                     ≈ 0.4692(1-0.5308)    if x = female

                     = 0 otherwise

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Sarah has 4 shirts, 2 pairs of jeans and 3
pairs of shoes. How many different outfits
can Sarah put together?

Answers

Answer:

24

Step-by-step explanation:

4 times 2 times 3

4(2)=8

8(3)+24

Answer:

20: But here is how.

Logically. <Which as you practice means you won’t have to write anything for this type of problem =) >

“Every shirt could come with any one of the pants.” (notation: sn is shirt number n)

s1 with 4 pants, so 4 outfits

s2 with 4 pants, so 4 outfits

s3 with 4 pants, so 4 outfits

s4 with 4 pants, so 4 outfits

s5 with 4 pants, so 4 outfits

Total of 5×4

TASK 3
Movie Theme
Find the area AND perimeter of each triangle.
CODE Type the numeral answer. NO LABELSI Use a comma and a space between
all your answers. Begin with part a area, permeter, part b area, perimeter
For example 30, 33, 24,17

Answers

The area will be equal to Area = (28)(21) / 2 = 294 square inches.

What is the area?

To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:

Hypotenuse = 7 + base = 14 + height

Perimeter = 84 inches

The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,

Perimeter = height + base + hypotenuse = 84

We let x = height and y = base. We calculate area as follows:

84 = x + y + (7 + y)

77 = x + 2y

x = 77 -2y

The Hypotenuse is related to the other sides by the Pythagorean theorem.

Hypotenuse^2 = (x^2 + y^2)

(14 + x)^2 = x^2 + y^2

(14 + (77-2y))^2 = (77-2y)^2 + y^2

(91-2y)^2 = (77-2y)^2 + y^2

Solving for y and x

y = 28

x = 21

Area = (28)(21) / 2 = 294 square inches

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Please help me on this!

Answers

Answer:

Answer is in attachment

Pls Mark brainliest :)

An employee of a store's gift wrapping center is wrapping 8 gifts
same size box. The dimensions of the box are shown to the right
A Find the volume of the box to see how much space is available to place
packages. Show your work
B. How much wrapping paper is needed to wrap ONE box? Show your
work
If there is only 160 square feet of wrapping paper left, will the employee
be able to wrap all of the gifts? Explain.

Answers

Part A:

The area A of a rectangle is A = bh, where b is the base of the rectangle and h is the height. The area of each rectangle with side lengths 1.5 ft and 2 ft is 1.5 × 2 = 3ft2. Since there are two rectangles with these dimensions, the combined area is 2 × 3 = 6 ft2. The area of each rectangle with side lengths 1.5 ft and 2.5 ft is 1.5 × 2.5 = 3.75 ft2. The area of each rectangle with side lengths 2 ft and 2.5 ft is 2 × 2.5 = 5 ft2. Since there are two rectangles of each type, the combined area is 2 × 3.75 + 2 × 5 =17.5 ft2. So, the total surface area of the box is 6 ft2+ 17.5 ft2 = 23.5 ft2

Part B:

The employee needs to wrap 8 boxes, each with a surface area of 23.5 ft2. So, the combined surface area needing to be wrapped is 8 × 23.5 = 188 ft2. Since there is only 160 square feet of wrapping paper left, the employee will not be able to wrap all of the gifts

Help me
Solves multi-step equation
119=7(2e+7)

Answers

Answer:

e=+5

Step-by-step explanation:

119=7(2e+7)

We move all terms to the left:

119-(7(2e+7))=0

We calculate terms in parentheses: -(7(2e+7)), so:

7(2e+7)

We multiply parentheses

14e+49

Back to the equation:

-(14e+49)

We get rid of parentheses

-14e-49+119=0

We add all the numbers together, and all the variables

-14e+70=0

We move all terms containing e to the left, all other terms to the right

-14e=-70

e=-70/-14

e=+5

Step-by-step explanation:

the other answer is right but it seems a bit overly complicated how the result was achieved.

119 = 7(2e + 7)

119 = 14e + 49

70 = 14e

e = 70/14 = 5

that's really it.

Elena drops her pencil in her cup and notices that it just fits diagonally. the pencil is 17cm long and the cup is 15cm tall. what is the diameter of the cup

Answers

Hence the answer is 480ml

Step-by-step explanation:

Given Elena wonders how much water it will take to fill her cup. She drops her pencil in the cup and notice it just fit diagonally. The pencil is 17cm long (hypotenes) and the cup is 15cm tall.

To find how much water it can hold

SOLUTION

s

[tex] \sqrt{x {} ^{ 2} + x {}^{2} + 15 {}^{2} = 17 } [/tex]

[tex]2x {}^{2} = 64[/tex]

[tex]x {}^{2} = 32[/tex]

[tex]x = 5.66[/tex]

therefore volume of the cup

[tex]5.66 \times 5.66 \times 15cm| [/tex]

480cm³= 480ml

The nth term of a sequence is 3(n + 2).
What are the first four terms?
What is the 20th term?
th
Which is the first term to be larger than 100?


Answers

Answer:

3 ( n + 2 )

3 x n = 3n

3 x 2 = 6

3n + 6 = 9n

Step-by-step explanation:

Find the value of x in each triangle. . X= 60° 60° x° ​

Answers

Answer:

60 degrees

Step-by-step explanation:

Triangle = 180 degrees

60+60+X=180

120+X=180

X=60

a 3. A card is pulled from a standard deck of cards.
Can you find P(queen or hearts)? (make sure you aren't double counting!!!)l

Answers

Answer:    4/13

Explanation:

There are 13 hearts, including the queen of hearts. Then there are 3 more queens to get us to 13+3 = 16 cards we're after.

There are 16 cards we want out of 52 total, so the probability is 16/52 = (4*4)/(4*13) = 4/13


David needs to choose a tie for a wedding. He has 4 solid color ties, 5
striped ties, and 3 cartoon ties. If his wife picks a tie for him at random,
what of the following is the probability that she will NOT choose a solid
color tie?
elect one:

Answers

The probability of not choosing the solid color tie by David's Wife will

be [tex]\frac{2}{3}[/tex].

What is Probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Number of solid Color ties= 4Number of cartoon ties= 3Number of stripped ties= 5

Total Number of ties= 4+3+5 =12

Probability of not choosing the solid color tie

=[tex]\frac{Total\; ties- \; Number\; of \;Solid\; ties}{Total\; number \;of \;ties}[/tex]

=[tex]\frac{12-4}{12}[/tex]

= [tex]\frac{8}{12}[/tex]

=[tex]\frac{2}{3}[/tex]

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help me please please

Answers

13 in 14 in 16 21 the cyclist

The Simpsons rented a trailer that was 8 feet long and 5 feet wide. If they load the trailer with 1-by-1-by-1-foot boxes to a height of 3 feet, how many boxes can be loaded onto the trailer?​

Answers

The total number of boxes that can be loaded onto the trailer is 27.

Here we have to determine the maximum number of boxes.

That can be stored in a locker by the volume of one box.

From the given information volume of the box is Vb and the volume f the locker is Vl.

What is the volume of the box?

[tex]Volume=Length\times width\times height[/tex]

Therefore we get,

[tex]V_b=4\times3\times2\\V_b=24ft^3[/tex]

The volume of the locker is

[tex]V_L=12\times6\times 9\\V_L=684ft^3[/tex]

Therefore the number of the maximum boxes are

[tex]\frac{VL}{V_b} =\frac{648}{24} \\=27[/tex]

Therefore, The total number of boxes can be loaded onto the trailer are 27.

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A certain machine is to contain two wheels, one of radius 2 inches and one of radius 8 inches. Themanufacturer of this machine needs to produce a belt that will fit snugly around the two wheels,as shown in the diagram below. How long should the belt be? what can you say about the motion of an object if its speed time graph is a straight line parallel to the time axis ? Also draw a diagram and plese do it on paper , in above picture Q 2 is an example you can do Q3 according to Q2 Find the sum of the infinite series below.URGENT!!!!!!!!!!!!!!!! In an experiment, 16 babies were asked to watch a climber attempt to ascend a hill. On two occasions, the baby witnesses the climber fail to make the climb. Then, the babywitnesses either a helper toy push the climber up the hill, or a hinderer toy preventing the climber from making the ascent. The toys were shown to each baby in a randomfashion. A second part of this experiment showed the climber approach the helper toy, which is not a surprising action, and then the climber approached the hinderer toy,which is a surprising action. The amount of time the baby watched the event was recorded. The mean difference in time spent watching the climber approach the hinderertoy versus watching the climber approach the helper toy was 1.22 seconds with a standard deviation of 1.58 seconds. Complete parts a through c. find the circumference of the circle 5cm Factor the polynomial Compare and contrast histosols and aridosols, the soils of bogs and peat marshes versus those of deserts and arid regions respect Give two examples of how the United States prepared to fight World WarIl before war was declared. A straw is placed inside a rectangular box that is 3 inches by 5 inches by 1 inches, asshown. If the straw fits exactly into the box diagonally from the bottom left corner tothe top right back corner, how long is the straw? Leave your answer in simplestradical form. Read the following excerpt from the Emancipation Proclamation:And by virtue of the power, and for the purpose aforesaid, I do order and declare that all persons held as slaves within said designated States, and parts of States, are, and henceforward shall be free; and that the Executive government of the United States, including the military and naval authorities thereof, will recognize and maintain the freedom of said persons.To which states do the words designated States, and parts of States refer?A. Northern statesB. loyal slave statesC. all slave statesD. rebel slave statesi can only pick one What volume of hydrogen (in l) is produced from the complete reaction of 56.49 g of magnesium metal at stp? The three wooden cubes are made out of the same type of wood.cm2 cmcmEach wooden cube is placed in a beaker of tap water.Which question can be answered by observing whether or not each cube floats?O A. Are all kinds of wood able to float in tap water?What is the total surface area of each wooden cube?Do wooden cubes float in both tap water and salt water?D. Does the size of wooden cube affect whether or not it will float? or Oxalic acid (h2c2o4) has a ka of 5. 9102, while the hydrogen oxalate anion (hc2o4) has a ka of 6. 1105. Is an aqueous solution of a hydrogen oxalate salt (e. G. Nahc2o4) acidic, basic, or neutral? Which statement describes an important belief in Hinduism?A.It is never acceptable to use violence against another person.B.It is a terrible sin to worship more than one god.C.A person's soul is reborn in a new body after death.D.Hard work should allow anybody to rise up in society. What was a Southern advantage during the Civil War?A. having a higher population and more soldiersB. having a coastline that was difficult to blockadeC. having a political system that gave more power to the leaderD.having a diverse economy with lots of industry and agriculture How does respiratory failure affect the muscular system?. Two squares have areas of 4 cm?and16 cm?. What is the ratio of the side length ofthe smaller square to the side length of thelarger square? David is a statistician. he has a sample size of 40 (which he cannot change). what element of his hypothesis test can he adjust to minimize the probability that he incorrectly rejects the null hypothesis? the mean of the population the mean of the sample the standard deviation of the population the significance level of the test 30 points Please do it right. Rewrite the Gettysburg Address in your own words, using the language of today.Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. using the language of today. Re write it thanks Which inequality is graphed on the number line?