Mrs. McDonald passed out 189 photos that she had taken during the school year. If each of her 21 students received the same number of photos, how many did each receive?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

How are polynomials and non-polynomials categorized?

There are two ways to categorize polynomials: by degree and by number of terms. According to degree, polynomials can be classified as zero, linear, quadratic, or cubic. Monomials, binomials, trinomials, etc. are the different types of polynomials based on the quantity of terms.

A polynomial is, in general, an expression containing more than one term and non-negative integral exponents of a variable. A polynomial expression might look like this: ax + by + ca, x3 + 2x + 3, etc.

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Answer:

(1,3)

Step-by-step explanation:

You can use the distance formula to help you solve the answer

Answer:

(1; 3)

Step-by-step explanation:

x = (-1 + 3)/2 = 1

y = (6 + 0)/2 = 3

Answer:

E

Step-by-step explanation:

[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]

12, 68.12, 78

Answer:  22:2, 33:3 and, 44:4

Step-by-step explanation:

Answer:

Step-by-step explanation:

22 : 2

33 : 3

44 : 4

Step 1

Given;

Required; To find the measure of angle F

Step 2

Answer;

[tex] \huge\underline\mathcal{Answer \: -} [/tex]

We know that ,

exterior angle equals sum of two interior opposite angles.

therefore ,

[tex]\bold{x + x + 14 = 136\degree} \\ \\ \longrightarrow \: 2x + 14 = 136\degree \\ \\ \longrightarrow \: 2x = 136\degree - 14 \\ \\ \longrightarrow \: 2x = 122\degree \\ \\ \longrightarrow \: x = \cancel\frac{122}{2} \\ \\ \longrightarrow\boxed{ \: x = 61\degree}[/tex]

hence , the first option is correct.

hope helpful ! ;-;

Answer:

First find the last angle of the triangle.

180 - 136 = 44° (sum of angles on a straight line=180)

Form an equation with the unknown angles with the knowledge that sum of angles in a triangle add up to 180°.

x + (x + 14) + 44 = 180

Simplify and solve for x.

2x + 58 = 180

2x = 122

x = 61

3 equations that can be used to solve the given scenario are:

So, equations that can be used to solve the following scenario are:

Then,

Therefore, 3 equations can be used to solve the given scenario are:

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The solution for the algebraic expression 2 1/3 - 4/7 is 37/21

Given,

The algebraic expression ; 2 1/3 - 4/7

We have to solve this expression;

First lets solve the mixed fraction 2 1/3

2 1/3 = (2 x 3) + 1 / 3 = 6 + 1 / 3 = 7/3

Mixed fraction;

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Now,

7/3 - 4/7 = (7 x 7) / (3 x 7) - (4 x 3) / (7 x 3) = 49/21 - 12/21

That is,

49/21 - 12/21 = (49 - 12) / 21 = 37/21

That is,

The solution for the algebraic expression 2 1/3 - 4/7 is 37/21

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Answer:

x = 18

The number is 18.

Step-by-step explanation:

Convert the words into an equation.

let x;

( 3x - 10 )( 2 ) + 2 = 5x;

6x - 20 + 2 = 5x;

6x - 18 = 5x;

Subtract both sides by 5x.

6x - 5x - 18 = 5x - 5x;

x - 18 = 0;

Add 18 to both sides.

x - 18 + 18 = 18;

x = 18;

The number of times one needs to use completely filled cone to completely fill the cylinder with water is 24

The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.

Given that radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters.

The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.

The volume of cylinder is πr²h

For a volume of cone it is 1⁄3πr²h.

So volume of cylinder = 22/7×(10)2×20=3.142×100×20

=6284

volume of cone it is 1⁄3πr²h=1/3×3.142×(5)^2×10=261.16

Number of times one needs to use the completely filled cone to completely fill the cylinder with water =

= Volume of cylinder/Volume of cone

6284 / 261.16 = 24

Hence the number of times one needs to use completely filled cone to completely fill the cylinder with water is 24

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The line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.

So, the equation is as:

Then, the equation can be:

(Refer to the graph attached below)

If you solve will become:

Therefore, the line of the equation which passes through the point (0, 4) and is parallel to the x-axis is 2y = 8.

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Answer:

Step-by-step explanation:

Answer: A. 100/x^2 = h, B. v(x) = x^2*h

Step-by-step explanation:

A. Volume = b * h

100 cm^2 = x^2 * h

100/x^2 = h

B. v(x) = x^2*h

The equation that represents the total amount of money Papi's made selling pizzas on Saturday is (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

Equation:

An equation is the mathematical statement which is made up of two expressions connected by an equal sign.

For example, 3x – 2 = 16 is an equation.

Given,

There are three types of pizza varieties are small, medium and large. And the price of them are $9.99, $11.99 and $13.99 respectively.

On Saturday, Papi's sold 39 small pizzas, 62 medium pizzas, and 83 large pizzas.

So, we have to write the equation for the total amount of money Papi's made selling pizzas on Saturday.

To calculate the price of the pizza we have to multiply it by the number of items sold by the cost.

So, the equation to calculate the cost of pizza,

=> number of items sold x cost.

Here we have to write the equation for three types and we have to find the total cost for it,

So, the equation is looks like,

=> (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

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Answer:

25 bricks

Step-by-step explanation:

Calculate the volume of one brick:

Volume = (11')(8")(5") = 440 in^3

Divide the volume of a one brick into the volume of concrete that will be used:

(11000 in^3 concrete)/(440 in^3 concrete/brick) = 25 bricks

At x=0

at x=1

at x=2

a=1/2

So correct option is (c).

Answer:

C. No because two points with the same x-value have different y-values.

Step-by-step explanation:

(view my screenshot attachment too please)

A function can't have same x-values that appear for multiple different y-values.

In the diagram, (10, 6) and (10, 9) indicate that it isn't a function.

This is because the same 10 appears twice (x-value) but with multiple different y-values (6 and 9).

The acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

Differentiation is a process to find the instantaneous rate of change in function based on one of its variables.

The hypotenuse of a right triangle is growing at a constant rate of a centimeters per second

[tex]\frac{dH}{dt} = a[/tex]

One leg is decreasing at a constant rate of b centimeters per second

[tex]\frac{dy}{dt} = -b[/tex]

From the right triangle

sin θ = [tex]\frac{y}{H}[/tex]           (y is the perpendicular and H is the hypotenuse)

Differentiate both sides with respect to t

cos θ*dθ/dt = (H*dy/dt - y*dH/dt) / H²

cos θ*dθ/dt =  [H(−b)−y(a)] / H²........................(1)

If the both legs are 1 cm.

∴ H= [tex]\sqrt{ 2[/tex],cosθ=sinθ=1/[tex]\sqrt{2}[/tex]

Thus , Equation (1)

cos θ*dθ/dt =  [H(−b)−y(a)] / H²

1/√2*dθ/dt = [√2 (−b)−(a)] / 2

dθ/dt = √2  [(√2 (−b)−(a)) / 2]

Therefore, we can conclude that the acute angle between the hypotenuse and the other leg changing at the instant when both legs are 1 cm is dθ/dt = -b - a/[tex]\sqrt{2}[/tex] fast.

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Answer:

The actual area of the warehouse would be:

[tex]72000~\text{feet}^{2}[/tex]

Step-by-step explanation:

Step 1:  Convert all the blueprint lengths into real lengths:

Each inch in the blueprint represents 20 feet in the real world.

So, the real-life length (18 inches in blueprint) would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]

Similarly, the real-life width would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]

Step 2: Calculate the area

The area of the warehouse would be given by:

[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The length is 360 feet, and the width is 200 feet, so the total area would be:

[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]

Albert borrowed $17 from his friend.

Given,

Albert brought some items:

Cost of blanket = $32.75

Cost of pillow = $12.75

Cost of glove = $16.25

Amount paid by Albert = 50

Amount borrowed by Albert from his friend = x

Cashier gave back the change = $5.25

We have to find the amount borrowed by Albert from his friend:

This is simply arithmetic operations:

Total cost in shop = 32.75 + 12.75 + 16.25 = $61.75

Total amount given to the cashier = 61.75 + 5.25 = 67

Amount borrowed by Albert from his friend = Total amount given to the cashier - Amount paid by Albert

x = 67 - 50

x = 17

That is,

Albert borrowed $17 from his friend.

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Answer:

29/49

Step-by-step explanation:

x:y = 3:4

let x = 3x , y = 5k

3x+4y/8x+5y

= 3(3k)+4(5k)/8(3k)+5(5k)

= 9k+20k/24k+25k

=29/49

Answer:

Given equation is, x+3y=6

To determine whether each order pair is a solution of the equation

(3,1)

we have that, when x=3 we get y=1

Let us check this in the equation.

Put x=3, we get

Hence (3,1) is the solution of the equation.

(6,0)

Put x=6, we get,

Hence (6,0) is the solution of the equation.

(-2,2/3)

Put x=-2, we get,

Hence (-2,2/3) is not the solution of the equation.

Solution

The question would like us to evaluate the following expression

- We should deal with the modulus and bracket separately.

- After that, we can then perform the subtraction operation on the results of the modulus and bracket.

- This is done below:

Also,

Thus, combining both results, we have:

Final Answer

The answer is -6

Answer:

-6 hope it helps

thank you

Answer:

p = 3

Step-by-step explanation:

y = mx + b They gave us the slope of -1.  We need to find the y intercept.  We will use the x of 9 and the y of 2 to find b.  We will plug these numbers in to find b.

y = mx + b

2 = -1(9) + b

2 = -9 + b  Add 9 to both sides

11 = b

y = -x +11

Now, plug in 8 for x

y = -1(8) + 11

y = -8 + 11

y = 3

In this case p is 3.

Two hours after depart, the distance between two ships is 39.2 miles and the relative speed of ship A seen by ship B is 19.6 mph heading to 18.4⁰ South of East.

The situation can be depicted on the attached picture.

Let North - South be the y-axis and East - West ne the x-axis.

The velocities vector can be represented as:

Ship A, 20 mph 30⁰ west of north:

vA = - 20 . cos( 60⁰) i + 20 . sin( 60⁰) j

vA = -10 i + 10√3 j

Ship B, 25 mph 20⁰ east of north:

vB = 25 . cos( 70⁰) i + 25 . sin( 70⁰) j

vB = 8.55 i + 23.5 j

b) The speed of ship A relative to ship B is:

vAB = vA - vB

       = ( -10 i + 10√3 j) - (8.55 i + 23.5 j)

       = -18.55 i - 6.18 j

or vAB = sqrt (18.55² + 6.18²) = 19.6 mph with the angle tan⁻¹ (6.18/18.55) = 18.4⁰ South of East.

a) The distance between 2 ships after 2 hours:

d = vAB . 2 hours

d = 19.6 . 2 = 39.2 miles

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Answer:

y=2x+6

y=2x+6

Explanation:

Given the equation:

The equation written as a system of equations is:

Opening the bracket in the first equation gives:

Answer:

y = -x

Step-by-step explanation:

Answer: Y=-X

Step-by-step explanation:

So we want to find the vertical asymptotes of the function:

Remember that there's a vertical asymptote at points of x where the denominator of the rational function is 0.

So, equal the denominator to zero:

And solve this equation for x as follows:

We could factor

Now, notice that any of both factors could be zero, so:

Therefore, the function has vertical asymptotes at x=6 and x=3.