Put the numbers in order from smallest to largest.

50.57
150
15.2
5.899

The polynomial divided by (x + 3), with quotient is x² - x + 8, and remainder of -5 is f(x) = x³ + 2x² + 5x + 19

The polynomial division algorithm states that for two polynomials, f(x) and g(x), where the degree of g(x) a divisor is less than or equal to the degree of f(x), there exist unique polynomials, q(x) the quotient and r(x) the remainder, such that f(x) = g(x)q(x) + r(x) and the degree of r(x) is less than the degree of g(x). This is also known as synthetic division.

f(x) = (x + 3)(x² - x + 8) + (-5)

but expansion;

f(x) = x³ + 3x² - x² + 8x - 3x + 24 - 5

f(x) = x³ + 2x² + 5x + 19

Therefore, the polynomial f(x) = x³ + 2x² + 5x + 19 divided by (x + 3), will give the quotient x² - x + 8, and remainder of -5.

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Answer: 15.4

Step-by-step explanation: d= [tex]\sqrt{(-18)^{2} - 18^{2}) +((-19)^{2} - 11^{2})\\[/tex]

[tex]\sqrt{361 - 121}[/tex]

[tex]\sqrt{240}[/tex]

15.4

The speed of the cheetah based on the information provided is 12.85 feet per second.

The speed of a body in movement can be expressed using different units such as:

Based on this, it is necessary to find how much distance the cheetah covers every second by dividing the distance given by the time given as it follows:

Therefore, the speed of the cheetah is 12.85 feet per second

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The mass of the liquid in the container is 18.17 g, correct to 3 significant figures

Calculate the volume of the container:

Volume = πr2h

Volume = π x (5 cm)2 x 20 cm

Volume = 3,142 cm3

Calculate the total volume of liquid A and B:

Total volume of A and B = 4:11

Total volume of A and B = 4 + 11 = 15 cm3

Calculate the volume of liquid A:

Volume of A = 4/15 x 15 cm3

Volume of A = 4 cm3

Calculate the volume of liquid B:

Volume of B = 11/15 x 15 cm3

Volume of B = 11 cm3

Calculate the mass of liquid A:

Mass of A = Volume of A x Density of A

Mass of A = 4 cm3 x 1.05 g/cm3

Mass of A = 4.2 g

Calculate the mass of liquid B:

Mass of B = Volume of B x Density of B

Mass of B = 11 cm3 x 1.27 g/cm3

Mass of B = 13.97 g

Calculate the total mass of liquid C:

Total mass of C = Mass of A + Mass of B

Total mass of C = 4.2 g + 13.97 g

Total mass of C = 18.17 g

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.

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If Ken's pay remains constant, he should expect to earn $69,600 in two years.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 14,500/5

Constant of proportionality, k = 2,900

In two (2) years, Ken's wages is given by:

y = kx

y = 2,900(24)

y = $69,600.

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Answer:

To solve the equation:

39 - 3x12²÷24

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

12² = 12*12 = 144

Then we can substitute that value into the equation:

39 - 3x144÷24

Next, we can simplify the expression inside the parentheses:

144÷24 = 6

Then we can substitute that value into the equation:

39 - 3x6

Now we can solve the equation by performing the multiplication and subtraction:

39 - 18 = 21

So the solution is 21.

Steps:

1. 12² = 144

2. 144÷24 = 6

3. 39 - 3x6 = 39 - 18 = 21

So, 39-3*12²÷24 = 21

Answer:

36

Step-by-step explanation:

39 - 3 x [tex]12^{2}[/tex] ÷ 24  First simplify the exponent

39 - 3 (12 x12) ÷ 24

39 - 3 x 24 ÷ 24  Next do multiplication and division going from left to right

39 - 72 ÷ 24

39 - 3  Subtract 3

36

You will pay back $100.00

We know that the formula for the compound ineterst:

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

where, A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

n = number of compounding periods

t = time in years

First, convert R as a percent to r as a decimal

r = 5.2/100

r = 0.052 rate per year,

Now we solve the equation for A

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

[tex]A = 95\times (1 +\frac{0.052}{2})^{2\times 1}[/tex]

A = 95.00 × (1 + 0.026)²

A = 100.004

A ≈ 100

Therefore, the total amount accrued with compound interest on a principal of $95.00 at a rate of 5.2% per year compounded semi annually is $100.00.

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Answer

1: 3x-y=0
2: 5x+y= -4
3: y=-x+4

Step-by-step explanation:

Answer: There would be 345 students because 85+200+60=345

Step-by-step explanation: it equal 245

The average speed is S=2.033 m/s

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time.

The unit of speed is a meter/second.

Speed formula can be used to find the speed of objects, given the distance and time taken to cover that distance.

To calculate the average speed we have a general formula:

speed = distance ÷ time.

Given distance=100m

time=49.17 s

Plugging the values in the above formula:

speed=100/49.17

speed=2.033

Therefore, the average speed is 2.033 m/s.

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The value of α2ββ2α2 is -20. a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation.

Given,

p(x) = 4x2 − 5x − 1

α and β are the zeroes of the quadratic polynomial p(x).

Therefore,

α + β = -5/4

and

αβ = 1/4

Therefore,

α2ββ2α2 = (α+β)2αβ = (-5/4)2(1/4) = (-5/4)(-5/4)(1/4) = 25/16 = -20

Given a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation. To find the value of α2ββ2α2, we first need to find the sum and product of the two zeroes, which can be done by solving the equation. The sum of the zeroes is -5/4 and their product is 1/4. We can then use these values to calculate the value of α2ββ2α2, which is equal to (-5/4)2(1/4) = 25/16 = -20. Thus, the value of α2ββ2α2 is -20.

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The fraction of the bag of sugar that Rick's dad pour into the water is 2/3

An equation is an expression that shows the relationship between numbers and variables.

Fractions is a part of a whole number. It is the ratio of two numbers. The top number is the numerator while the bottom number is the denominator. Hence:

Fraction = numerator / denominator

Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water. Hence:

Fraction of sugar poured into water = amount of sugar poured in water / total amount of sugar

Substituting:

Fraction of sugar poured into water = 2 cups / 3 cups = 2/3

Ricks dad pour 2/3 of the sugar into the water

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Answer: t=2

Step-by-step explanation:

-4t+14= -9t+24

+9t     =+9t

5t+14=24

    -14=-14

5t=10

5t/5       10/5

t=2

The coordinates of point C are C(0,-sqrt(36 - x²))

An equilateral triangle has all sides of equal length and all angles of 60 degrees. Since the triangle is in the fourth quadrant, so we know that both the x and y coordinates of point C must be negative.

We can use the distance formula to find the length of the sides of the triangle:
AB = sqrt((0 - 0)² + (-6 - 0)²) = 6
BC = sqrt((x - 0)²+ (y - 0)²) = AC = sqrt((x - 0)² + (y - (-6))²) = sqrt(x² + (y + 6)² = 6

We may now use the notion that all angles in an equilateral triangle equal 60 degrees. We know that point A is at (0,-6) and point B is at (0,0), therefore we can use the slope of line AB and the length of the side to compute point C's coordinates.


Line AB has a slope of (0 - (-6))/(0 - 0) = 6/0 = undefined.The slope of a line perpendicular to AB is the negative reciprocal of AB's undefined slope; so, line AB is parallel to the x-axis. So C(x,y) has the same x-coordinate as B(0,0) but a different y-coordinate.

The length of the side is 6, so we can use this information to find the y-coordinate of point C:
y = sqrt(6² - x²) = sqrt(36 - x²)= -sqrt(36 - x²)

So, the coordinates of point C are C(0,-sqrt(36 - x²))

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As the cable between the towers has the shape of a parabola, the height of the cable 200 feet from a tower is 40 feet.

Consider the origin of coordinate system at the bridge level midway between the towers and the cable has the shape of a parabola. It is the vertex of the parabola. The general equation of a parabola is given by y = a(x – h)^2 + k where (h, k) denotes the vertex. Hence, based on the provided information, the equation is;

y = a^x^2

The height of the tower above the road is 160 feet which is 400 feet from the vertex. Hence, x = 400 feet and y = 160 feet.

Substituting the values,

160 = a^(400)^2

a = 0.001

Hence, the equation of the given parabola is:

y = 0.001x^2

In order to calculate the height of the cable at 200 feet from the tower, the value of x = 400 – 200 = 200 feet

y = 0.001(200)^2 = 40 feet

Note: The question is incomplete. The complete question probably is: The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 feet from a tower?

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The father had read the most, having finished half the book. The mother had read a third of it, while the daughter was still in the first chapter. The son had only read a few pages.

They discussed their progress and made an agreement to read a certain number of chapters each week to ensure they finished the book at the same time.

Therefore, the father had read the majority of the book, having completed it. While the daughter was still in the first chapter, the mother had already read about a third of it. Only a few pages have been read by the son.

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Answer:

c

Step-by-step explanation:

it wouldnt just be 9, thats marias books, to get what jim ahs and hers its 9+b

b representing the amount jim read

The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.

To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.

We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.

To summarize, the formula used to calculate the number of pieces Lucy needs is:

(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.

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For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.

The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

The equation is given as,

2(c² + d²)x² + (c - d)x + 9 = 0

Then the discriminant is given as,

D < 0

(c - d)² - 4 × 2(c² + d²) × 9 < 0

(c - d)² > 72 (c² + d²)

The expresssion (c - d)² must be positive. Then we have

(c - d)² > 0

c - d > 0

c > d

For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.

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The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

The account balance after eleven years would be ₱14,925.08.

1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.

2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.

The account balance after eleven years would be ₱14,925.08.

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Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously therefore Serenity would need to invest $400 to the nearest hundred dollars, for the value of the account to reach $670 in 11 years.

This is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

We can solve the problem by :

1+(0.044÷365)= 1.0001205479

Yearly impounding factor, 1.0001205479^365=1.0449795838

For a period of 11 years, maturity factor,1.0449795838^11 = 1.6225043167.

$1 becomes $1.6225043167.

If Maturity value is to be,$670 which is amount to be invested,

670÷ 1.6225043167 = 412.942

To the nearest 100 dollars is $400.

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Nareh should give his brother $80. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

Subtract the amount of money that Urch has from the amount of money that Nareh has:

300 - 220 = 80

Nareh should give his brother $80 so that both of them will have the same amount of money.

Nareh currently has $300 and Urch currently has $220, so Nareh should give Urch $80 in order to make them have the same amount of money. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

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Answer:

$4

Step-by-step explanation:

Given;

Dozen long stemmed roses cost $48

Question:

What is the cost per rose?

Solve:

Based on the given, we can see that it states that a dozen long stemmed roses cost $48.

Knowing that - Dozen = 12

Since, we know that dozen equal 12. Hence, 12 long stemmed roses cost $48.

Now, divide the cost by the amount to find the cost per rose.

Thus,

48 ÷ 12 = 4.

Therefore, the cost per rose is $4.

RevyBreeze

The simplified form of expression -2.6f +0.7f - 14 - 9 is -1.9f - 23

We know that an expression is nothing but a mathematical statement that consists of at least two terms( variables or constants) along with one algebraic operation.

As we know simplifying an expression means rewriting the same expression in a compact manner with no like terms.

To simplify expressions, we combine all the like terms ; solve all the given brackets, if any.

In the simplified expression, we left with unlike terms which cannot be reduced further.

Consider an expression:

-2.6f +0.7f - 14 - 9

We simplify above expression.

-2.6f +0.7f - 14 - 9

= (-2.6 + 0.7)f - (14 + 9)              .........(combine like terms)

= -1.9f - 23

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Answer:

A

Step-by-step explanation:

Answer:

248 children

296 adults

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}\;\;\;\;\:\:\:x+y=544\\1.5x+2y=964\end{cases}[/tex]

Rearrange the first equation to isolate x:

[tex]\implies x=544-y[/tex]

Substitute the found expression for x into the second equation and solve for y:

[tex]\implies 1.5(544-y)+2y=964[/tex]

[tex]\implies 816-1.5y+2y=964[/tex]

[tex]\implies 816+0.5y=964[/tex]

[tex]\implies 0.5y=148[/tex]

[tex]\implies y=296[/tex]

Therefore, 296 adults swam at the public pool.

Substitute the found value of y into the equation for x and solve for x:

[tex]\implies x=544-296[/tex]

[tex]\implies y=248[/tex]

Therefore, 248 children swam at the public pool.

The required inequality is d + b ≥ 11 representing the possible values for the number of donuts and brownies purchased.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can represent the number of donuts purchased as d, and the number of brownies purchased as b. The inequality that represents the minimum number of donuts and brownies that must be purchased altogether is:

d + b ≥ 11

This inequality states that the total number of donuts (d) and brownies (b) purchased must be greater than or equal to 11.

This inequality can be represented graphically on a number line, with point 11 being the boundary between the solutions that satisfy the inequality and those that do not.

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Rectangle with the given ratio of length to diagonal has measure of the width equals to 27.35 feet.

Actual length of the rectangle = 6 feet

Ratio of the length to diagonal = 3 : 14

⇒Length/ diagonal = 3:14

⇒6/ diagonal = 3:14

⇒Diagonal = (14×6)/3

⇒Diagonal = 28 feet

Let 'x' be the width of the rectangle.

Length , width , and diagonal forms a right angle triangle in a rectangle.

Using Pythagoras theorem ,

Width² = Diagonal² - length²

⇒x² = 28² - 6²

⇒ x = √784 -36

⇒x = 27.35 feet ( nearest hundredth )

Therefore, the width of the given rectangle with the given ratios and dimensions is equal to 27.35 feet.

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1. The value of n in 3n + 19 = 28 will be 3.

2. The value of b in 34 - 4b = 18 will be 4.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The value of n in 3n + 19 = 28 will be:

3n + 19 = 28

Collect the like terms

3n = 28 - 19

3n = 9

Divide

n = 9 / 3

n = 3.

The value of b in 34 - 4b = 18 will be:

34 - 4b = 18

4b = 34 - 18

4b = 16

Divide.

b = 16 / 4

b = 4

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