Given <2=13, which lines, if any, must be parallel based on
the given information? Justify your conclusion.

The container is large enough to hold 1 cup of liquid.

From the information, Justin is designing a drink container in the shape of a rectangular prism and the container must be made out of 254 cm² of plastic.

In this case, since 1 cup = 236cm², it can be seen that 254cm² is more than 236cm².

Therefore, the container is large enough.

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The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

Polynomial function:

The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.

Given,

Here we have the following things,

Degree = 5

Root of multiplicity 2 is x = -4

Root of multiplicity 1 at x = -1

Root of multiplicity 2 at x = -2

y-intercept of (0, 128)

Here we need to find the polynomial equation of the function.

According to the given roots of multiplicity, we have the factors of the polynomials are,

=> (x + 4)² (x + 1) (x + 2)²

So, the general form of the polynomial function can be written as,

=> f(x) = A (x + 4)² (x + 1) (x + 2)²

In order to find the 5 degree polynomial function, we have to calculate the value of A.

To Find the value of A, we have to apply the y - intercept point on the equation then we get,

=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²

=> 128 = A (4)² (1) (2)²

=> 128 = A (16 x 1 x 4)

=> 128 = 64A

=> A = 2

Now, the polynomial function is written as,

=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²

When we expand this one then we get,

=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]

Therefore, the resulting polynomial function is,

=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

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The expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

In this question, we have been given a synthetic division of x^2 + 5x and x

We need to find the quotient.

    x  + 1  + 1 + 1 + 1 + 1        

x) x^2    x   x   x   x   x

 - x^2                                  

    0      x

         -  x                            

            0   x

             -  x                    

                  0  x

                  -  x                

                      0    x

                       -    x            

                             0  x

                             -    x      

                                   0

Therefore, the expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

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According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.

Volume of Cylinder

The formula to calculate the volume of the cylinder is

Volume of a cylinder = πr²h cubic units.

where

r refers the radius

h refers the height.

Given,

Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.

While we looking into the given question, we know the following values,

Diameter = 2 3/5

When we simplify it, then we get the value of diameter as

d = 13/5 or 2.6

Similarly, the value of height is rewritten as,

h = 5.25

So, based on the formula of volume of cylinder,

We get the value as,

=> V = π x (2.6/2)² x 5.25

Apply the value of π as 3.14, then we get,

=> V = 3.14 x (1.3)² x 5.25

=> V = 16.485 x 1.69

Therefore, the volume in cubic inches is 27.86 cubic inches.

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Answer:

[tex]s \approx \$182.14[/tex]

[tex]c \approx \$435.72[/tex]

Step-by-step explanation:

Set up a system of equations, where s is the cost of a sheep and c is the cost of a cow:

[tex]4s + 2c = \$ 1660[/tex],  [tex]3s + 5c = \$ 2925[/tex]

First, isolate c in the first equation.

[tex]4s + 2c = \$ 1660[/tex]

[tex]2c = \$ 1660 - 4s[/tex]

[tex]c = \$ 840 - 2s[/tex]

Next, substitute this value into the second equation:

[tex]3s + 5c = \$2925[/tex]

[tex]3s + 5(\$840 - 2s) = \$2925[/tex]

and simplify.

[tex]3s + \$4200 - 10s = \$2925[/tex]

[tex]-7s = -\$1275[/tex]

[tex]7s = \$1275[/tex]

[tex]s \approx \$182.14[/tex]

Finally, plug this value into the first equation to get the value of c:

[tex]4(\$182.14) + 2c = \$1660[/tex]

[tex]2c = \$1600 - \$728.57[/tex]

[tex]c \approx \$435.72[/tex]

So, a sheep costs about $184.14, and a cow costs about $435.72.

Answer:

$262.50

Step-by-step explanation:

20 : 105 = 50 : x

x = (50 * 105)/20

x = (5 * 105)/2

x = 525/2

x = 262.50

Answer: $262.50

Step-by-step explanation:

What I did was divide the $105 by 20 and got $5.25. I then multiplied $5.25 by 50 since that's how many she's going to sell and got $262.50.

Answer:

slope = (1/3)

Step-by-step explanation:

(-8, 2), (-11, 3)

(x₁, y₁)   (x₂, y₂)

m = slope

        y₂ - y₁          3 - 2              1              1

m = ------------ = -------------- = ----------- = -------

        x₂ - x₁         -11 - (-8)       -11 + 8        3

I hope this helps!

The selling price of the two washing machies are

I will buy the first because it has a lower selling price

The question is a percentage problem

The first washing machine has a mark down by ​40%

= 40 percent

= 40 / 100

= 0.4

marked down factor = 1 - 0.4 = 0.6

selling price of the first machine = 550 * 0.6 = 330

the second washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 550 * 0.7 = 385

marked down again

10% = 0.1

the  factor here is = 1 - 0.1 = 0.9

selling price of the second washing machine at second mark down

= 385 * 0.9 = 346.5

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The expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

What is algebraic expression?

  When terms are combined using operations like addition, subtraction, multiplication, division, etc., the result is an algebraic expression (or variable expression). Let's look at the formula 5x + 7 as an illustration. Consequently, we can state that 5x + 7 is an illustration of an algebraic statement. Here are some more examples: 5x + 4y + 10

Here the given product of two and a number. Lets us take number as x. Then ,

=> 2*x= 2x

Product of two and a number divided by 5. Then,

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

Hence the algebraic expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

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Answer:

y-intercept (0,-3)

x-intercept (3,0)

Step-by-step explanation:

Let x = 0

-y =3

y = -3

(0,-3)

Let y = 0

x = 3

(3,0)

Answer:They are all the same because 40/100 divided by 10 on both sides is just 4/10 and 4/10 as a decimal is equal to 0.4

Step-by-step explanation:

Answer:

0.4 is the decimal form of [tex]\frac{4}{10}[/tex], which means that 4 ÷ 10 = 0.4, shown below.

If you multiply the numerator and denominator of [tex]\frac{4}{10}[/tex] by 10, you would get [tex]\frac{4*10}{10*10} =\frac{40}{100}[/tex]. This is equal in value to [tex]\frac{4}{10}[/tex] because 40 ÷ 100 = 0.4.

The fractions have a LCD of 84 is option C, 2/21,1/4,1/3.

Given:

3/14,1/42,1/6

= 3/14 + 1/42 + 1/6

= 9+42+7 / 42

The LCD  is 42 not 84.

2/84,1/16,1/42

= 6+21+8 / 336

The LCD  is 336 not 84

2/21,1/4,1/3

= 8+21+28 / 84

The LCD is 84

2/3,1/6,1/7

= 28+7+6 / 42

The LCD is 42 not 84

Therefore the fractions have a LCD of 84 is option C, 2/21,1/4,1/3.

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Answer:

[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]

Step-by-step explanation:

The least common denominator (LCD) is the smallest number that is exactly divisible by each denominator of a set of fractions.

To find the LCD of a set of fractions, reduce the fractions to their smallest equivalent, list the multiples of each denominator, then locate the smallest common number.

[tex]\textsf{A)} \quad \dfrac{3}{14}, \dfrac{1}{42}, \dfrac{1}{6}[/tex]

Multiples of 14:  14, 28, 42, 56, 70, 84, 98, ...

Multiples of 42:  42, 84, 126, 168, 210, ...

Multiples of 6:  6, 12, 18, 24, 30, 36, 42, 48, ...

Therefore, the LCD is 42.

[tex]\textsf{B)} \quad \dfrac{2}{84}, \dfrac{1}{16}, \dfrac{1}{42}=\dfrac{1}{42}, \dfrac{1}{16}, \dfrac{1}{42}[/tex]

Multiples of 42:  42, 84, 126, 168, 210, 252, 294, 336, ...

Multiples of 16:  16, 32, 48, 64, 80, 96, 112, ... , 336, ...

Therefore, the LCD is 336.

[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]

Multiples of 21:  21, 42, 63, 84, 105, 126, 147, ...

Multiples of 4:  4, 8, 12, 16, 20, 24, 28, ... , 84, 88, ...

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, ... , 84, 87, ...

Therefore, the LCD is 84.

[tex]\textsf{D)} \quad \dfrac{2}{3}, \dfrac{1}{6}, \dfrac{1}{7}[/tex]

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, ... , 42, 45, ...

Multiples of 6:  6, 12, 18, 24, 30, 36, 42, 48, ...

Multiples of 7:  7, 14, 21, 28, 35, 42, 49, 56, ...

Therefore, the LCD is 42.

Answer:

At x = 0 and at x = 2 there are points of inflections. In the intervals of

(negative infinity, 0) and (2, positive infinity) it is concave up.

In the intervals of (0, 2) it is concave down.

Step-by-step explanation:

Inflection points are point where h'(x) changes from increasing to decreasing and vise versa.

When a graph is concave up, h'(x) is increasing.

When a graph is concave down, h'(x) is decreasing.

The zeros of the function f(x) = x⁴− x² − 2 are  ±√2 or x = ±i option third positive or negative square root of 2,  ±i is correct.

What is a complex number?

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a function:

f(x) =  x⁴− x² − 2

Assume u = x²

f(x) = u² - u - 2

(u + 1)(u - 2)

(x² + 1)(x² - 2)

x² = -1

x = √1

x² = 2

x = √2

x = ±√2  or  x² = -1 ⇒ x = ±i

Thus, the zeros of the function f(x) = x⁴− x² − 2 are  ±√2 or x = ±i option third positive or negative square root of 2,  ±i is correct.

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The set of side measurements that could be used to form a right triangle is

This gotten by  Pythagoras theorem, with the formula stated as

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

50² = (√18)² + (√32)²

50² = 18 + 32

50² = 50 - incorrect

(√50)² = 6² + (√14)²

50 = 36 + 14

50 = 50 - correct

20² = 8² + 4²

400 = 64 + 16

400 = 80 - incorrect

6² = 5² + 4²

36 = 25 + 16

36 = 41 - incorrect

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Answer:

concave down: ( negative infinity, 0)

concave up: (0, positive infinity)

minimum: x = 4

maximum: x=-6

Step-by-step explanation:

Answer:

[tex] \huge{ \bold{y = - 43x - 25}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = - 43

In order to find c we substitute the point (0,−25) into the equation y = mx + c

That's

[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = - 43x - 25}[/tex]

Hope this helps you

The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

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The value of of V in the equation is P / I.

The equation given is P = IV and we were asked to solve for V. This means we should make V the subject of the formula in the equation.

The subject of a formula is the variable which is expressed in terms of the other variables.

Therefore, we have to express V in terms of other variables.

Hence,

P = IV

divide both sides by I

[tex]\frac{P}{I} = \frac{IV}{I}[/tex]

Hence,

V = p / I

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Answer:

f(-2) = 2

Step-by-step explanation:

 -2 is the input/ domain value

It's corresponding value from the graph is 2.

Answer:

150

Step-by-step explanation:

I had this on one of my quizzes, hope this helps :D

The total cost of the shoe after tax is $79.50

From the question, we are to determine the total cost of the shoes after tax.

From the given information,

Jason bought new shoes priced at $75

and

The sales tax is 6%

The total cost of the shoe = Price of the shoe + Sales tax

Sales tax = 6% of $75

Sales tax = 0.06 × $75

Sales tax = $4.50

Thus,

Total cost of the shoe = $75 + $4.50

Total cost of the shoe = $79.50

Hence, the total cost is $79.50

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14000 student tickets and 6500 general admission tickets were purchased during the football game

An equation is an expression that can be used to show the relationship between variables and numbers.

Let x represent the amount of students tickets and y represent the amount of general admission tickets.

A total of $176,000 was collected from ticket sales. Hence:

7x + 12y = 176000   (1)

A college football game is played to a sell-out crowd of 20,500 people. Hence:

x + y = 20500    (2)

From the two equations:

x = 14000, y = 6500

14000 student tickets and 6500 general admission tickets

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The length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.

According to the question,

We have the following information:

Jessica found that the perimeter of her kitchen table was 18 feet she found the area of her kitchen table to be 18 ft.²

Now, let's take the length of the table to x ft and the width of the table to be y ft.

So, we know that following formulas are used to find the perimeter and area of rectangle:

Perimeter = 2(length+width)

2(x+y) = 18 ...(1)

Area = length*width

xy = 18

x = 18/y

Putting this value of x in equation 1:

2(18/y+y) = 18

18/y + y = 9

([tex]y^{2}[/tex]+18) = 9y

[tex]y^{2}[/tex]-9y+18 = 0

[tex]y^{2}[/tex]-6y-3y+18 = 0

y(y-6)-3(y-6) = 0

(y-6)(y-3) = 0

y-6 = 0 and y-3 = 0

y = 6 ft and y = 3 ft

Now, putting this value of y in x = 18/y:

x = 18/6

x = 3 ft

x = 18/3

x = 6 ft

Hence, the length and width of Jessica's kitchen table are 6 ft and 3 ft or 3ft and 6 ft.

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Answer:

z=38

Step-by-step explanation:

Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.

Angles in a triangle add to 180°, so:

[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]

Answer: hi

Step-by-step explanation:

this is it

Answer:

$205.6

Step-by-step explanation:

20.56hours × $10/hour = $205.6

Ji-Min will spend a total of $235.62 to fence or cover the area of the circular window.

What is the area of the a circle?

The area of circle is equal to pi times square of its radius, i.e. πr². To find the area of circle we have to know the radius or diameter of the circle.

Let's find the area of the circle first;

radius = diameter / 2

radius = 5 / 2

radius = 2.5ft

The area of the circle is;

A = πr²

A = π * 5²

A = 25π

A = 78.54ft²

For every square foot, the glass cost $3, this implies that 3 * 78.54 will be the total cost to cover the window.

cost = 3 * 78.54 = $235.62

She will spend $235.62 to fence the window

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If she decides to use double strength glass costing $ 3 per square foot. the total cost for the glass is $58.88.

Given data:

Diameter = 5ft

Glass costing = $3 per square foot

Hence,

Let the radius be 5/2 feet

Area = π × (5/2)²

Area = 25π /4 ft²

So,

Total cost = ( π × 25 /4 × $3)

Total cost = $58.875

Total cost = $58.88

Therefore $58.88 is the total cost.

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The slope for the following question is = 4.

acc to our question-

hence the value of slope=4

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The cost of Falafel wraps is $5.5, the cost of Turkey BLT sandwiches is $7.5, and the cost of hot Ham and Swiss paninis is $6.

In order to determine the cost of each sandwich, we would assign variables to the cost of sandwiches ordered, and then translate the word problem into algebraic expression as follows:

Therefore, translating the word problem into an algebraic expression, we have the following;

For the first month ⇒   5f + 15t + 20h = 260      ......equation 1.

The next month     ⇒   8f + 18t + 14h = 263         ......equation 2.

For the third month ⇒ 12f + 16t + 12h = 258       ......equation 3.

Next, we would solve the system of algebraic expressions simultaneously.

Multiplying equation 1 by 12/5 and subtracting it from equation 3, we have:

6.25t - 24h = -366    ......equation 4.

Multiplying equation 2 by 5/8 and subtracting it from equation 1, we have:

3.75t + 11.25h = 95.625    ......equation 5.

Solving equation 4 and equation 5, we have:

Falafel wraps, f = $5.5

Turkey BLT sandwiches, t = $7.5

Hot Ham and Swiss paninis, h = $6.

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