For the equation 2x^3 -11x^2 + 12x + 9 = 0 , the root 3 has a multiplicity of
A. 1
B. 2
C. 3

Please explain!

Answer:

Step-by-step explanation:

There are several ways in which you could do this.  

One involves finding the x- and y-intercepts, plotting them and drawing a straight line through them.  Starting with 4x + 2y = 16, let x = 0 to find the y-intercept:  2y = 16, or y = 8.  The y-intercept is (0,8).  Next, let y = 0 in 4x + 2y = 16 and solve for x; this leads to the x-intercept.  4x = 16, so x = 4.  The x-intercept is then (4, 0).  Plot (4,0) and (0, 8) and draw a straight line through these two points.

Another involves solving 4x+2y=16 for y, obtaining the equivalent in slope-intercept form of this equation.  Subtracting 4x from both sides, we get 2y = 16 - 4x.  Dividing all terms by 2 results in y = -2x + 8.

As before, the y-intercept is (0,8).  Plot this point.  Now use the slope, m = -2, to find another point on this line:  Starting at (0,8), move 1 unit to the right (increasing x by 1) and then move 2 units down, arriving at (1, 6).  Plot this point.  Now draw a straight line through (1,6) and (0,8).  Your result should look the same as the previous graph you drew.

Answer:

$1453.2

Step-by-step explanation:

I assume you mean the accumulated value on a principal of $1400 with 3.8% interest in 1 year.

1400 * (100%+3.8%) = 1400 * 1.038 = 1453.2

Answer:

x = 1/6

Step-by-step explanation:

2(3x+1)=3

Distribute.

6x + 2 = 3

Subtract 2 from both sides.

6x = 1

Divide by 6 on both sides.

x = 1/6

Hello there!

Question:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

Distribute:-

[tex]\sf \longmapsto \: (2)(3x)+(2)(1)=3[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 6x + 2 = 3[/tex]

Subtract 2 from both sides :-

[tex]\sf \longmapsto 6x+2 - 2=3 - 2[/tex]

On Simplification:-

[tex]\sf \longmapsto6x + 0 = 3 - 2[/tex]

[tex]\sf \longmapsto6x = 1[/tex]

Divide the two sides by 6:-

[tex]\sf \longmapsto \: \dfrac{6x}{6} = \dfrac{1}{6} [/tex]

Cancel 6/6, leave x, answer is 1x. 1/6 can't be cancelled.

[tex]\sf \longmapsto \: \dfrac{ \cancel6x}{ \cancel6} = \dfrac{1}{6} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{1}{6} [/tex]

In Decimal:-

[tex]\sf \longmapsto \: x = 0.16[/tex]

______________________________________

Henceforth,the value of x is :-

[tex]\boxed{\huge\tt x = \dfrac{1}{6}} [/tex]

[tex] \bold{OR,}[/tex]

[tex]\boxed{\huge\tt x = 0.16}[/tex]

_____________________________________

Please let me know if you have any questions.

~MisterBrian

Answer:

D b = sqrt(c^2 -a^2)

Step-by-step explanation:

We are using the Pythagorean theorem,

a^2+b^2=c^2

We want to solve for b

Subtract a^2 from each side

a^2 -a^2+b^2=c^2-a^2

b^2 = c^2 -a^2

Take the square root of each side

sqrt(b^2) = sqrt(c^2 -a^2)

b = sqrt(c^2 -a^2)

Answer:

answer A : b=√(c-a)

Step-by-step explanation:

a²+b²=c²

subtract a² from both sides to isolate b²

b²=c²-a²

take the square root of both sides to get from what b² equals to what b equals

b=√(c-a)

Answer:

3750 ft

Step-by-step explanation:

Denote Stops as points A(-2,1), B(-2,-7), C(5,-7) and D(5,1) and find all distances between two consecutive points:

The total distance Paolo walked is

[tex]8+7+8+7=30\ units.[/tex]

Since 1 unit on the coordinate grid equals 125 feet, then the total distance Paolo walked is

[tex]30\cdot 125=3750\ ft.[/tex]

Answer:

The $3485.52 money did Meg have at the end of the account term.

Step-by-step explanation:

Formula for compounded monthly

[tex]Amount = P(1+\frac{r}{365})^{365n}[/tex]

Where P is the principle , r is the rate of interest in the decimal form and n is the number of years.

As given

Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years.

Principle = $3000

3% is written in the decimal form

[tex]= \frac{3}{100}[/tex]

= 0.03

Time = 5 years

Put in the formula

[tex]Amount = 3000(1+\frac{0.03}{365})^{365\times 5}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+ 0.0000822)^{1825}[/tex]

[tex]Amount = 3000(1.0000822)^{1825}[/tex]

[tex]Amount = 3000\times 1.16184[/tex]

Amount = $ 3485.52

Therefore the  $ 3485.52  money did Meg have at the end of the account term.

Answer:

The Answer is $3,485 btw

Step-by-step explanation:

Answer C

Answer:

Step-by-step explanation: to covert improper fractions to normal fractions.

29/6 would be 4 wholes and 5/6

You count how much 6’s are in the 29 which is 4. And then the left over would be 5 so 5/6

Answer:

Step-by-step explanation: sec^2A-tan^2A+1

=1+1

=2

Answer:

Hello :

secA= 1/cosA

tanA = sinA / cosA

- tan²A + 1 + sec²A  = - (sinA / cosA)² + 1 + ( 1/cosA)²

                                 = - sin²A / cos²A  + 1 + 1 /cos²A

                                 = ( - sin²A  + cos²A +1)/cos²A

                                = ( 1 - sin²A + cos²A ) / cos²A

but : 1 - sin²A = cos²A   because : sin²A + cos²A = 1

so : - tan²A + 1 + sec²A  = ( 2 cos²A) / (cos²A)

- tan²A + 1 + sec²A  = 2

Answer:

The correct option is C.

Step-by-step explanation:

In a triangle, then sum of two smaller sides is greater than the length of third greatest side.

Let, in a triangle ABC, If the length of sides are [tex]a<b<c[/tex], then

[tex]c<a+b[/tex]

In option A,

[tex]8\nless 2+4[/tex]

Therefore option A is incorrect.

In option B,

[tex]6\nless 2+4[/tex]

Therefore option B is incorrect.

In option C,

[tex]7<3+5[/tex]

Therefore option C is correct.

In option D,

[tex]9\nless 3+5[/tex]

Therefore option D is incorrect.

Answer:

C. 3, 5, 7

Step-by-step explanation:

We know that in a triangle, 'the sum of lengths of two sides is always greater than the length of the third side'.

So, according to our options:

A. In 2, 4, 8. We have 2 + 4 = 6 < 8

B. In 2, 4, 6. We see that, 2 + 4 = 6

C. In 3, 5, 7. We see that, 3 + 5 = 8 > 7

D. In 3, 5, 9. We see that, 3 + 5 = 8 < 9.

Therefore, only option C satisfies the property of the triangle stated above.

Hence, 3, 5, 7 are the side lengths of a triangle.

Answer:

speed = 7.5 miles per hour

Step-by-step explanation:

To find the speed, we divide the distance by the time

speed = distance/time

speed = 15miles/2 hours

speed = 15/2 miles per hour

speed = 7.5 miles per hour

Answer:

30

Step-by-step explanation:

Answer:

It is 50,000

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

first do 28+32.

Next it equals 60. So change 60 to percentage form. It would be 60%

Answer:

B

Step-by-step explanation:

It's B.

Answer:

Step-by-step explanation:

its b

Total of 90 fish:

c + p = 90

Charlie gave 1/4 c to Peter.  Now

Charlie has c - (1/4) c

Peter has p + (1/4) c

Peter gave 2/5 of his to Charlie. Now

Peter has p + (1/4) c - 2/5( p + (1/4) c )

Charlie has c - (1/4) c + 2/5( p + (1/4) c )

And then they had equal number:

c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )

Let's do the easy subtractions then multiply by 20 to clear the fractions,

(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )

15c + 8p + 2c = 12p + 3c

14c = 4p

7c = 2p

c + p = 90

2c + 2p = 180

2c + 7c = 180

9c = 180

c = 20

p = 70

Answer: Charlie started with 20, Peter with 70

Check:

Initially C:20, P:70

1/4(20)=5 to P

C:15, P:75

(2/5) 75 = 30 to C

C:45, P45

Good

Answer:

The height of aquarium is [tex]\frac{3}{5}[/tex] of its length

Step-by-step explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium = [tex]\frac{4}{5}[/tex] of length

                              = [tex]\frac{4}{5} (5) = 4[/tex] decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is [tex]\frac{2}{3}[/tex] of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

[tex]\frac{2}{3}[/tex] of volume of aquarium = 40

[tex]\frac{2}{3}(20x)=40[/tex]

[tex]\frac{40x}{3} =40[/tex]

multiply both side by 3

[tex]40x= 3(40)[/tex]

[tex]40x=120[/tex]

divide both side by 40

[tex]x=\frac{120}{40}[/tex]

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

[tex]\frac{height }{length} =\frac{3}{5}[/tex]

[tex]height = \frac{3}{5} length[/tex]

hence the height of aquarium is [tex]\frac{3}{5}[/tex] of its length

The given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

An angle is formed when two rays have the same end point. The common end point is called vertex.

Given is to identify the positive angle.

Any angle measured clockwise with respect to + x axis is negative. Similarly, any angle measured anti - clockwise with respect to + x axis is negative.

Since only one angle is shown in the image, we will describe about it. It can be seen that the angle is measured clockwise with respect to + x axis. Hence, it is negative.

Therefore, the given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

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Answer:

The first pair of events are independent, the second pair of events are independent and the third pair of events are dependent.  

Step-by-step explanation:

Independent events are events that do NOT rely on previous events.  So, the chances of each of event happening in a pair of events is independent, or has no effect, on the chances of the other event.  In the case of rolling a number cube and then rolling it again, your chances would be the same each time you roll the number cube as to what number you would get.  Just because you rolled a '1' on the first roll, doesn't mean you can't get the same number (or another number) on another roll.  The same reasoning applies to the coin flip and the spinner.  These two events are not related and in no way would rely on each other.  A coin flip will not affect the chances of spinning an odd number.  However, if we have several coins in a bag and select a quarter, but do not replace it, our chances of selecting another coin changes because there are not only less coins in the bag, but there are less quarters to choose from.  In the case of events with NO replacement, these events are dependent.  

Answer:

D

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=5, b=4 and c=-1.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-4+/-\sqrt{(4)^2-4(5)(-1)} }{2(5)}\\x=\frac{-4+/-\sqrt{16+20} }{10}[/tex]

We will now simplify and solve.

[tex]x=\frac{-4+/-\sqrt{36}}{10}\\x=\frac{-4+/-6}{10}[/tex]

x=-1 and x=0.2

5x - 7y =58

y =-x +2

Using the substitution method, replace y in the first equation with the second equation:

5x - 7(-x+2) = 58

Simplify by using the distribution property:

5x - (-7x) - 14 = 58

Simplify by combining like terms:

12x -14 = 58

Add 14 from each side of the equation:

12x = 72

Divide both sides by 12:

X = 72/12

x = 6

Now you have x, replace x in the second equation and solve for y:

y = -x +2

y = -6 +2

y = -4

X = 6, y = -4

Answer:

-7

Step-by-step explanation:

Use slope equation m=y2-y1/x2-x1 aka m=rise/run.

Insert in the correct values.

-1-(-3)=2=run

-8-6=-14=rise

SO, -14/2=m

Simplify:-14/2=-7

m=-7

Answer: 1

Step-by-step explanation:

Only one line segment can be drawn between two points. Any other line segments would be overlapping and the same segment

Answer:

sqrt2/2 ( cos b - sin b)

Step-by-step explanation:

I know thats the answer but I have no idea how you solve to get it. Im looking for help too.

35kg - a mass of sugar syrup

30% of 35kg it's a mass of sugar

30% = 30 : 100 = 0.3

30% of 35kg = 0.3 · 35kg = 10.5kg - a mass of sugar

Add xkg water. Then we have (35 + x)kg of sugar syrup and still 10.5kg of sugar.

10.5kg is 25% of (35 + x)kg .

(35 + x) -- 100%

10.5  -- 25%     multiply both sides by 4

42   -- 100%

Therefore we have the equation:

35 + x = 42      subtract 35 from both sides

x = 7

Answers:

The sign is 4 ft on a side

The poster is 2 ft on a side

================================================

Explanation:

s = side length of the sign

p = side length of the poster

The poster "has sides measuring 2 ft less than the sides of the square sign", so p = s-2. Whatever the value of 's' is, we subtract off 2 to get the value of p. For example, if the sign has side lengths of s = 10 ft, then p = s-2 = 10-2 = 8 ft is the side length of the poster

We don't know s or p right now, so they are simply placeholders for some numbers.

If s is the side length of the sign, then s*s = s^2 is the area

If p is the side length of the poster, then p*p = p^2 is the area of the poster. We can replace p with s-2 since p = s-2. So we end up with p^2 = (s-2)^2 = s^2 - 4s + 4 after using the FOIL rule

Now subtract the two areas and set that difference equal to 12. Solve for s

(area of sign) - (area of poster) = 12

(s^2) - (s^2 - 4s + 4) = 12

s^2 - s^2 + 4s - 4 = 12

4s - 4 = 12

4s - 4+4 = 12+4

4s = 16

4s/4 = 16/4

s = 4

The sign's side length is 4, so its area is 4^2 = 16

If s = 4, then p is

p = s-2

p = 4-2

p = 2

The poster's side length is 2, so its area is 2^2 = 4

Subtract the areas: 16 - 4 = 12

The answer is confirmed

Answer:

I would say 49 is your answer

Step-by-step explanation:

53 plus 78 qould equal 131

subtract 131 from 180 and you get 49

add up all your numbers including x then they should all equal 180

Answer:

9 bags of trail mix

Step-by-step explanation:

I would take the fraction 3/4 and make it have a common denominator with 1/12. In order to do that, multiply each number in 3/4 by 3. It results in 9/12.

You can put 9 of 1/12 in 9/12

To find out the number of bags Maya can fill with 3/4 pound of trail mix, divide 3/4 by 1/12. The division equates to multiplication by the reciprocal, so (3/4) x (12/1) = 9. Therefore, Maya can fill 9 bags of trail mix.

This problem can be solved by division. Maya has 3/4 pound of trail mix and each small bag holds 1/12 pound of trail mix. Therefore, divide 3/4 by 1/12 to find out exactly how many bags Maya can fill.

To perform this division, you could first convert the fractions to decimals or do it directly. But let's stick with fractions and apply the principle of multiplying by the reciprocal. Change the division to multiplication and multiply 3/4 by the reciprocal of 1/12.

(3/4) x (12/1) = 9

So, Maya can fill 9 bags of trail mix.

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1. The range of the Domain: x I x ≤ -2

2. The range of the Domain: (-5, ∞)

3. The range of the Domain: (-2, 3)

Leftmost Graph:

Domain: x I x ≤ -2

Range: All real numbers (-∞, ∞)

Visual: A solid line extending infinitely to the left from a closed circle at -2, indicating all values less than or equal to -2.

Interpretation: Includes -2 and all numbers to its left (negative infinity).

Middle Graph:

Domain: (-5, ∞)

Range: All real numbers (-∞, ∞)

Visual: A solid line starting with an open circle at -5 and extending infinitely to the right, indicating all values greater than -5.

Interpretation: Includes all numbers greater than -5, but not -5 itself.

Rightmost Graph:

Domain: (-2, 3)

Range: All real numbers (-∞, ∞)

Visual: A solid line between open circles at -2 and 3, indicating values between those points but not including those endpoints.

Interpretation: Includes all numbers strictly between -2 and 3, but not -2 or 3 themselves.

Answer: attachment

Step-by-step explanation:

Answer:

45=5t

Step-by-step explanation:

im doing it right now and got it right

Answer:

-2b/(a-b)

Step-by-step explanation:

1− (a+b/a−b)

We need to get a common denominator of a-b

1 = (a-b)/(a-b)

Replace 1 with (a-b)/(a-b)

(a-b)/(a-b) - (a+b)/(a-b)

Put over the common denominator

(a-b) - (a+b)

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

(a-b)

Distribute the minus sign.

(a-b) - a-b)

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

(a-b)

a-a-b-b

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

a-b

-2b

----------

a-b