my Christmas present to you​

The remainder of the equation is [tex]\rm 28x+30[/tex].

Given that,

When the equation [tex]\rm 3x^3-2x^2+4x-3[/tex] is divided by [tex]\rm x^2+3x+3[/tex].

We have to find,

The remainder of the equation?

According to the question,

The equation [tex]\rm 3x^3-2x^2+4x-3[/tex] is divided by [tex]\rm x^2+3x+3[/tex].

On the division of the polynomial, the remainder is,

[tex]\dfrac{\rm 3x^3-2x^2+4x-3}{\rm x^2+3x+3}[/tex]

Factorize the equation to convert this into the simplest form,

[tex]\rm 3x^3-2x^2+4x-3\\\\3x^3-11x^2+9x^2+9x+28x-33x-33+30\\\\Taking \ the \ common \ terms \ and \ simplify\ the\ equation\\\\3x^3+9x^2+9x+11x^2+33x-33+28x+30\\\\3x(x^2+3x+3) - 11(x^2+3x+3) + 28x+30\\\\(3x+11) (x^2+3x+3) +28x +30[/tex]

Now, the equation can be written as,

[tex]\rm = \dfrac{(3x+11) (x^2+3x+3) +28x +30}{ x^2+3x+3}\\\\= \dfrac{(3x+11) (x^2+3x+3) }{ x^2+3x+3} + \dfrac{28x +30}{ x^2+3x+3}\\\\= (3x+11) + \dfrac{28x +30}{ x^2+3x+3}\\\\[/tex]

The relation between the divisor, remainder, and quotient is,

[tex]\rm = Quotient + \dfrac{Remainder}{Divisor}[/tex]

On comparing with the equation,

The remainder becomes 28x +30.

Hence, The required remainder of the equation is [tex]\rm 28x+30[/tex].

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3:7  

This means that for every 7 blue chairs, there are 3 red chairs.

the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade is 14%.

Given, the members of the junior varsity swim team wear glasses is 55%.

And the members of junior varsity swim team who do not wear glasses and in 10th grade is 30%.

Let the total no. of members be x.

So, the members of the junior varsity swim team wear glasses (55%),will be

[tex]0.55x[/tex].

The total number of members not wearing glasses, will be

[tex]x - 0.55 x = 0.45 x[/tex].

Now, the no. of members not wearing glasses and in 10th grade will be,

[tex]\frac{0.45x\times30}{100} =0.135x[/tex]

We know that the probability of an event E, P(E) will be,

[tex]P(E)=\frac{No.\ of Favourable\ outcomes}{total \ no. \ of \ outcomes}[/tex]

So, the probability for no. of members not wearing glasses and in 10th grade will be,

[tex]P(E)=\dfrac{0.135x}{x}[/tex]

[tex]P(E)=0.135\\\\P(E)=13.5 \%[/tex]

Hence the nearest whole percent of probability is 14%.

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Answer: The answer is 1 1/5

Step-by-step explanation: Hope that helps :)

Answer:

4

Step-by-step explanation:

note that [tex]\sqrt{x^2}[/tex] = x , then

[tex]\sqrt{(2-\sqrt{5})^2 }[/tex] + [tex]\sqrt{(2+\sqrt{5})^2 }[/tex]

= 2 - [tex]\sqrt{5}[/tex] + 2 + [tex]\sqrt{5}[/tex] ← collect like terms

= 4

Answer:

If you are not in Iceland, then you are not in Reykjavik.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The contrapositive of a statement is as follows:

"Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."

So, for this one, we need to switch as well!

If you are in Reykjavik, then you are in Iceland.

If you are NOT in Iceland, then you are not in Reykjavik.

The answer would be D

Answer:

3rd option

Step-by-step explanation:

(x + 7)(x - 9) = 25 ← expand left side using FOIL

x² - 2x - 63 = 25 ( add 63 to both sides )

x² - 2x = 88

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = 88 + 1

(x - 1)² = 89 ( take square root of both sides )

x - 1 = ± [tex]\sqrt{89}[/tex] ( add 1 to both sides )

x = 1 ± [tex]\sqrt{89}[/tex]

Answer:

The second one. 30 minutes ÷ 6 miles.

Step-by-step explanation:

You want to find how long it took Jamaal to run one mile.

30 minutes ÷ 6 miles = 5 minutes.

So Jamaal can run one mile in 5 minutes.

Option B, 30mins/6miles

Answer:

 3²

Step-by-step explanation:

The factors 3³ in the numerator and denominator cancel each other. Anything divided by itself is 1. Anything multiplied by 1 is unchanged.

  [tex]\dfrac{3^3\cdot3^2}{3^3}=\dfrac{3^3}{3^3}\cdot3^2=1\cdot3^2=3^2[/tex]

_____

Additional comment

The exception is that 0 divided by itself is indeterminate.

answer: 1/16

If you flip a coin 4 times, the probability of getting all heads is 1/16.

Answer:

Option A

Step-by-step explanation:

Given equation is:

[tex]x^2+1=2x-3[/tex]

Setting it up as a quadratic equation.

[tex]x^2+1-2x+3=0\\\\x^2-2x+4=0[/tex]

Comparing it with quadratic equation [tex]ax^2+bx+c=0[/tex], we get:

a = 1 , b = -2 , c = 4

Putting the values in quadratic equation:

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

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

A

Step-by-step explanation:

a = 1, b = -2, and c =4

d = -b +- sqrt (b^2 - 4*a*b)

= - (-2) +- sqrt ((-2)^2 - 4*1*4)

Answer:

1400

Step-by-step explanation:

two ways to do this

1, find the area of the shaded place.

2, find the area of the whole thing, subtract by the area of the corners.

          this way is easier so its what ill do

whole box is 60*30=1800

3 corners are 10*10=100    15*10=150    and   15*10=150

1800-150-150-100 = 1400

or you could do it the first way

bigger box is 20*45=900

long box is 10*35=350

small box is 15*10=150

900+350+150=1400

Step-by-step explanation:

[tex] \large\tt\underline\blue{a} \underline\pink{n} \underline\green{s} \underline\red{w}\underline \purple{e} \underline\orange{r}[/tex]

A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

The equation that can be used to determine the sales price of the bracelets is $22.5

Amount in her account = $150

Amount in her account after sales = $235

Change in account balance = $235 - $150

= $85

cost of necklace = $22.5

let

bracelet = x

necklace = y

The equation:

Total sales = 5x + y

85 = 5x + 22.5

85 - 22.5 = 5x

62.5 = 5x

x = 62.5/5

x = $12.5

Therefore, the cost of each bracelet is $12.5 and the cost of necklace is $22.5

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Answer:

  (c)  3,477.4 cm³

Step-by-step explanation:

The formula for the volume of a sphere is ...

  V = 4/3πr³ . . . . where r is the radius

The radius is half the diameter, so is 18.8 cm/2 = 9.4 cm.

Using this value and the value for pi in the formula, we have ...

  V = (4/3)(3.14)(9.4 cm)³ = (4/3)(3.14)(830.584 cm³) ≈ 3477.4 cm³

_____

Additional comment

You will do well to learn how to use a formula, and how to use your calculator to evaluate it. It can be useful to keep perimeter, area, and volume formulas handy for the usual plane and solid figures.

Answer: D hope this helps

Answer:

it's d

Step-by-step explanation:

multiply 0.31 by the amount of minutes used (27) and add the flat fee to it.

0.31×27+(0.57)= 8.94

D10W has a concentration 10%

So

Dextrose amount=

[tex]\\ \sf\Rrightarrow 10\%\:of\:756[/tex]

[tex]\\ \sf\Rrightarrow 0.10(756)[/tex]

[tex]\\ \sf\Rrightarrow 75.6ml[/tex]

Answer:

I think -24 for the hourly change

Step-by-step explanation:

10-24= -14

Answer: -4

Step-by-step explanation:

Subtract 10 by -14 to get -24 then divide by 6 because ben was at work for 6 hours to get -4

CT=90°

BTA=90°

x=29

CT=37

TA=20

CA=57

Step-by-step explanation:

they say BT is an altitude ( or height) . Altitudes are perpendicular meaning that:

BTC =90°

BTA=90°

Therefore:

(3x+3)°=90°

3x=90-3

3x=87°

x=29

CT:

x+8

=29+8

=37

TA:

x-9

=29-9

=20

CA:

=CT+TA

=37+20

=57

 The combined amount of cats sold is 117.

Ratio expresses the relationship between two variables. It shows the frequency of which that one value is contained within another variable.

The ratio of  Siamese cats to house cats = 4 : 9

Number of Siamese cats = 36

Number of combined cats = c

This equation can be formed using the above information:

4/13 x c = 36

4c = 468

c = 468 / 4

c = 117

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Answer:

45 percent

Step-by-step explanation:

Have an awesome day!

Answer:

f(x) = (2/3)x-2

Step-by-step explanation:

Pick any two points and calculate the slope.  I chose:  (-3,-4) and (3,0).  The Rise/Run, or slope, is (0-(-4))/(3-(-3) or 4/6:  2/3

The y-intercept of the graph is -2 ( the value of y when x=0).

Given y = mx + b

we have

y = (2/3)x - 2

Option 3

The total cost, if one drink costs $3 is $27.75

If kiyo bought a pizza for 12.75 and four medium drinks to Pauli’s pizza, this expressed as x + 4y

Since a pizza costs $12.75, hence x = $12.75

The function becomes 12.75 + 5y

f(y) = 12.75 + 5y

To get the total cost if one drink costs $3, hence;

f(3) = 12.75 + 5(3)

f(3) = 12.75 + 15

f(3) = 27.75

Hene the total cost, if one drink costs $3 is $27.75

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Answer:

I believe it's written y = 1/2x - 1

Hope this helps :)

Answer:

$2,691

Step-by-step explanation:

Interest (I) = Principal x Rate x Time

Total Amount (A) = Interest + Principal

I = 2600(.005)(7)

I = 91

A = 2600 + 91

A = 2691

Answer:

11

Step-by-step explanation:

(f/g)(5)=

f(5)=(5)2+1÷g(5)=5-4

10+1/1

11/1

(f/g)=11

The required simplified value of the given function as (f/g)(5)  is 26.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x² +1

f(5) = 5² + 1
f(5) = 26

g(x) = x - 4
g(5) = 5 - 4 = 1

f/g(5) = f(5) / g(5)
       = 26 / 1 = 26

Thus, the required simplified value of the given expression (f/g)(5)  is 26.

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Answer:

[tex](x-2)(x-3)[/tex]

Step-by-step explanation:

[tex]x^2-5x+6[/tex]

[tex]x^2-3x-2x+6[/tex]

[tex]x(x-3)-2(x-3)[/tex]

[tex](x-2)(x-3)[/tex]