Find the quotient and remainder using long division.
x + x - 13
x - 2
The quotient is
The remainder is

Answer:

it is 18

Step-by-step explanation:

Answer: The numbers are 2 and 2.5

Explanation:

Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]

[tex]\rule{185}{2}[/tex]

Their product :

[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]    

[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]

Their sum :

[tex]\hookrightarrow \sf x + y = 4.5[/tex]

[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]

Solve them simultaneously:

[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]

cross multiply

[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]

distribute inside parenthesis

[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]

multiply by -1

[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]

factor them out

[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]

set to 0

[tex]\rightarrow \sf y = 2.5, \ 2[/tex]

Another number:

When one number is 2.5, then another: 4.5 - 2.5 = 2

When one number is 2, then another: 4.5 - 2 = 2.5

Check:

The numbers obtained by the given condition that the product of two numbers is 5 if their sum is 9/2 will be x =( 2 or 5/2) and y = ( 2 or 5/2).

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the first number is x and the second is y then

Product xy =  5

Sum x + y = 9/2

substitute y = 9/2 - x into first

x( 9/2 - x) = 5

2x² - 9x + 10 = 0

2x² -5x -4x + 10 = 0

x( 2x - 5 ) -2( 2x -5 ) = 0

(x -2)(2x -5) = 0

x =2 and x = 5/2

Corresponding to x y will be y = 2 and y = 5/2.

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[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]

Substitute the values according to the formula.

[tex]r=\frac{94}{2}[/tex]

[tex]\large\boxed{r=47 \: cm}[/tex]

Now, let's find the area.

[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]

So, we'll have to multiply π, 47 and 47.

Substitute the values according to the formula.

[tex]a= \pi{47}^{2}[/tex]

[tex]a= 6939.778172 \: {cm}^{2}[/tex]

[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]

Hence, the area of the given circle is 6939.8 square centimeters.

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We are asked to find the radius & area of the circle.

To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:

[tex]\star~\bf{94\div2}[/tex]

[tex]\star~\bf{Radius=47}\star[/tex]

Now that we have the radius, let's compute the area! :)

///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\

                            Calculating the Area

We can work out the area of a circle by using this formula:

[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]

Where

[tex]\dag[/tex] A=Area of a circle

[tex]\dag[/tex] [tex]\pi =3.14...[/tex]

[tex]\dag[/tex] r=radius

Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.

Now it's time to substitute the values:

[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]

Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)

Here's what it stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

2 is an exponent.

So what do you think we should do first?

[tex]\square[/tex] Square 47.

[tex]\square[/tex] Multiply 3.14 times 47 and then square.

That's right, we should square 47 first. :)

[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]

Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:

[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]

Remember, the area of any shape is measured in units squared.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]

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[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]

Answer:

see the attachment photo!

After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fit:

y = 2.5 + 1.25x

Plug x = 7 weeks

y = 2.5 + 1.25(7)

y = 11.25 units

Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

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Answer:

6, 8, 10

Step-by-step explanation:

Where:

a = 6

b = 8

c = 10

Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

[tex]6^2 + 8^2 = c^2[/tex]

[tex]36 + 64 = c^2[/tex]

[tex]100 = c^2[/tex]

c = [tex]\sqrt{100}[/tex]

c = 10

Based on the cost of the contract and the probability to win it, the total expected value of the contract proposal is -$2500.

The general formula to calculate the expected value is:

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Answer:

C. As the radius of a circle increases, circumference of the circle increases.

Based on the items appearing in Gravano Engineering's Statement of Financial Position at the year-end, the totals for the following are:

1. Non-current Assets = $192,000

2. Current Assets = $64,000

A Statement of Financial Position is a financial statement that shows an entity's assets, liabilities, and equity.

Assets are items owned by an individual or entity that generate current, future, or potential economic benefits.

Liabilities are financial obligations that an individual or entity owes creditors.

Equity is the difference between assets and liabilities, which refers to the financial benefits accruing to the stockholders.

1. Trade payables                                    $39,000

2. Cash at bank                                         14,000

3. Motor vans                                           25,000

4. Inventories                                             7,000

5. Bank overdraft                                     13,000

6. Property                                              96,000            

7. Trade receivables                              43,000            

8. Plant and equipment                        26,000            

9. Trademarks                                        28,000

10.   Fixtures and fittings                        17,000

11.   Mortgage on property                   45,000​

2. Cash at bank                                          14,000

4. Inventories                                              7,000

7. Trade receivables                                43,000            

Total current assets =                           $64,000

3. Motor vans                                          25,000

6. Property                                              96,000                      

8. Plant and equipment                         26,000            

9. Trademarks                                        28,000

10.   Fixtures and fittings                         17,000

Total non-current assets =                $192,000

Thus, the total non-current assets are $192,000 and the current assets total $64,000.

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The answer to the given question is as below:-

Polynomials:-

x³-7x²+9x-5x⁴-20

x⁵-5x⁴+4x³+2x-1

3x²-5x⁴+2x-12

Non-polynomial:-

x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

[tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

[tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.

So the table will be formed as:-

Polynomials:-                            Non-polynomial:-        

x³-7x²+9x-5x⁴-20                     x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1        

x⁵-5x⁴+4x³+2x-1                        [tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

3x²-5x⁴+2x-12                           [tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

Therefore the polynomials and non-polynomials are shown in the table above.

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Answer:

Depositors

Step-by-step explanation:

Answer:

Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.

Answer:

D) [tex]22\:\text{m/s}^2[/tex]

Step-by-step explanation:

Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:

Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]

Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]

Acceleration of Particle: [tex]a(t)=6t-8[/tex]

After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]

The acceleration of the particle after 5 seconds is 38 m/s².

Acceleration is the rate of change of velocity or the slope of velocity.

We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.

∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.

Now, s = t³ + 4t² + 2t + 8 meters.

ds/dt = 3t² + 8t + 2 m/s.

d²s/dt² = 6t + 8m/s²

Now, at t = 5 seconds d²s/dt² = 6t + 8 is,

d²s/dt² = 6(5) + 8 m/s².

d²s/dt² = 38 m/s².

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Answer:

x>-7

Step-by-step explanation:

Answer:

x>-7

It wont always be easy, but always try to do what ' s right!

   In a world of worriers, be the warrior!

        When nothing goes right, go left.

Family background refers to the culture and tradition of the family into which a person is born.

Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.

My family is strictly conservative having  had a Southern Baptist orientation. My dad believes deeply in  religion and a moralist and perfectionist.

As a  result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.

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3.75 quarts of paint does Argelis have left with her.

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces.

Here, we know that,

1 gallons = 4 quarts

so, 1/2 gallons = 1/2 X 4 = 2 quarts.

and 1/4 gallons = 1/4 X 4 = 1 quarts.

Now, total paint left with Argelis = 1/2 gallons + 3/4 quarts + 1/4 gallons

                                                     =  2 quarts + 3/4 quarts + 1 quarts

                                                    = 3 quarts + 3/4 quarts

                                                    = 15/4 quarts or 3.75 quarts

Thus, 3.75 quarts of paint does Argelis have left with her.

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The values of the functions are:

1. y = f(-7) = 128

2. y = f(5) = 0.0313

We can evaluate a function by substituting the given value into the equation of the function, then simplify.

Given the function, y = f(x) = (1/2) ^ x

1. Find the value of f(-7):

y = f(-7) = (1/2)^-7

y = f(-7) = 2^7

y = f(-7) = 128

2. 1. Find the value of f(5):

y = f(5) = (1/2)^5

y = f(5) = 0.0313

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Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

[tex](-1)^{n}[/tex]

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

Answer:

If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.

Step-by-step explanation:

[tex]10.10 * 15 = x[/tex]

[tex]10.10 * 15 = 151.5[/tex]

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We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So we divide the cost of three notebooks (30.30) by 3:

[tex]\star~\large\pmb{30.30\div3}[/tex]

[tex]\star~\large\pmb{10.10}[/tex]

That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).

[tex]\star~\large\pmb{10.10\times15}[/tex]

This gives us:

[tex]\star~\large\pmb{151.5}[/tex]

That's the cost of 15 notebooks if the cost of one notebook is 10.10.

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Answer:

2.

[tex]x = \frac{11}{4} = 2 \frac{3}{4} = 2.75[/tex]

3.

[tex]x = \frac{5}{2} = 2 \frac{1}{2} = 2.5[/tex]

4.

[tex]x = \frac{3}{7} ≈0.428571429[/tex]

Answer:

M is target to the circle

The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

Complex numbers are square root of negative numbers. They are expressed as a + bi

Using the expression

(4+7i)-2i(2+3i)

Expand

4 + 7i - 4i -2i(3i)

4 + 3i - 2(-3)

4 + 6 + 3i

10 + 3i

Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

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Answer:

5

Step-by-step explanation:

This is a 3,4,5 triangle

and to prove that;

3^2 + 4^2 = 5^2

25 = 25 is a correct statement

The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)

The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).

When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.

Thus, the correct one is;

(0.5 + 0.8)/2 = 0.65

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A function assigns the values. The function will move down by 3 units.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.

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Answer:

The mode is 9 letters: True

The median is 7.5 letters: True

The mean is 7 letters: False

The graph is skewed right with an outlier of 2: False

Step-by-step explanation:

1) The mode is 9 letters. (True)

The mode is the value that shows up the most. 9 letters shows up the most as the length of a child's last name.

2) The median is 7.5 letters. (True)

The median is one of the middle points of a data set. This can be found by writing out all of the results from least to greatest, and crossing out each number starting from the ends.

2, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9

Once you meet in the middle, you should be left with 7 and 8. In this case, we find the mean of the two numbers, which is 7.5. (In cases where the data set has an odd amount - if there were 13 children instead of 12), you'd just use the middle piece of data.

3) The mean is 7 letters. (False)

The mean is also a middle point of a data set. However, this one is different. The mean can be found by adding up all of the numbers in the data set ([tex]2+6+6+7+7+7+8+8+9+9+9+9[/tex]) and then dividing that number by the amount of numbers are in the data set. Setting this up as an expression would look like: [tex]\frac{2+6+6+7+7+7+8+8+9+9+9+9}{12}[/tex]. By plugging this into a calculator you'd get 7.25 instead of just 7.

4) The graph is skewed right with an outlier of 2.

Although the outlier of 2 part of the statement is correct, the graph is not skewed right; it is skewed left.

Answer:

y = 9

Step-by-step explanation:

given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 6

12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction

72 = k

y = [tex]\frac{72}{x}[/tex] ← equation of variation

when x = 8 , then

y = [tex]\frac{72}{8}[/tex] = 9

Answer:

50.13

Step-by-step explanation:

We can easily find the area of our square, so to get that over with, 6*6=36. Now, for our circle, a full circle would be A=pi*r^2, but we only have half a circle. That means our equation will be A= 1/2(pi*r^2). We have our diameter, but we need our radius. Radius is just half the diameter, so 6/2=3. Now, we multiply. 3^3 is 9, and 9*3.14 is 28.26. All we have to do now is divide that by 2. If we do that, we get 14.13. The area of the semi-circle is 14.13. But we still have to add it to the area of the square, which will be our final step. 36+14.13=50.13, which is your area.

Hope this helps!

The volume of a piece of the cake will be 588.75 cm³.

The complete question is attached below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A birthday cake in the shape of the right-circular cylinder of radius 15 cm and thickness 10 cm is cut into smaller pieces.

One of the piece is shown.

Then the volume of piece of the cake will be

V = (30 / 360) x π x 15² × 10

V = 588.75 cm³

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