6.2: The Return of the Box
Earlier, we learned we can make a box from a piece of paper by cutting squares of side
length x from each corner and then folding up the sides. Let's say we now have a piece of
paper that is 8.5 inches by 14 inches. The volume V, in cubic inches, of the box is a
function of the side length x where V(x) = (14-2x)(8.5-2x)(x).
1. Identify the degree and leading term of the polynomial. Explain or show your
reasoning.
2. Without graphing, what can you say about the horizontal and vertical intercepts of
the graph of V? Do these points make sense in this situation?

Answers

Answer 1

The leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

A sheet of paper measuring 8.5 inches by 14 inches is currently in our possession. The box's volume V, measured in cubic inches, depends on the side length x, where V (x) = (14-2x)(8.5-2x)(x).

So, we have :

V (x) = (14-2x)(8.5-2x)(x)

[tex]V(x) = (14-2x)(8.5-2x)(x).\\V (x) = (14-2x)(8.5x-2x^{2} )\\V(x) = 4x^{3} -45x^{2} + 119x[/tex]

Thus, the leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.

Now, we have :
[tex]V(x) = 4x^{3} -45x^{2} + 119x\\V(x) = x ( 4x^{2} -45x +119)\\V(x) = x (x-7)(4x-17)[/tex]

Now, For intercepts, V(x) = 0

[tex]V(x) = x (x-7)(4x-17) = 0\\x (x-7)(4x-17) = 0\\\\x = 0, 7, 4.25[/tex]

Now when x = 0, V(x) =0

when x = 7, f(x) = 135

when x = 4.25, f(x) = 252.89

So, the points are (7, 135) and ( 4.25, 252.89)

These points represent the value of x and their corresponding value of V.

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Related Questions

What kind of transformation converts the graph of f(x)=3x+9 into the graph of g(x)=3x–10?

Answers

The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up

How to determine the transformation?

The equations of the functions are given as

f(x) = 3x + 9

g(x) = 3x - 10

Let the translations from f(x) to g(x) be h and k

So, we have

g(x) = f(x + h) + k

This gives

f(x + h) = 3(x + h) + 9 + k

Open the brackets

f(x + h) = 3x + 3h + 9 + k

Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k

g(x) = 3x + 3h + 9 + k

This means that

3x + 3h + 9 + k = 3x - 10

Evaluate the like terms

3h + 9 + k = - 10

This gives

3h + k = - 19

Express -19 as -21 + 2

3h + k = -21 + 2

Express 21 as 3 * 7

3h + k = -3 * 7 + 2

By comparison, we have

h = -7 and k = 2

This means that the transformation is 7 units right and 2 units up

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Logan is having his dog professionally groomed and wants to tip the groomer 15%. What equation can Logan use to calculate the tip, y, if his total bill is x dollars?

Answers

Answer:

y = 1.15x

Step-by-step explanation:

15% = 0.15

100% = total bill

Total bill + 15% = 115% or 1.15

x × 1.15 = y

Consider the following definite integral.sxex²+1d'dx0Identify the definite integral that will result after making a u-substitution.

Answers

[tex]\begin{gathered} \text{ u = x}^2\text{ + 1} \\ du\text{ = 2x} \\ \frac{du}{2}\text{ = x}dx \\ \int e^u\frac{du}{2} \\ \frac{1}{2}\int e^udu \end{gathered}[/tex]

The first choice is the correct result

5x/6 = 30 solve for x simplify your answer as much as possible

Answers

Answer:

x = 36

Step-by-step explanation:

Simplify:

  To find the value of 'x', isolate 'x'.

[tex]\sf \dfrac{5}{6}x = 30\\\\ \text{Multiply both sides by 6,}\\\\ 5x = 30*6\\\\\text{Divide both sides by 5,}\\\\ x = \dfrac{30*6}{5}\\[/tex]

x = 6 * 6

x = 36

 

Find the circumference of the circle. Use 3.14 for x

17 ft

Answers

The circumference of the circle with a radius of 7 ft is 106.76 ft

What is circumference?

The circumference of a circle is the perimeter of the circle

How to calculate the circumference?

The given parameters are

Radius = 17 ft

As a general rule, radius are represented by the variable r

So, we have the following representation equation

r = 17

The circumference of the circle is then calculated as

C = 2πr

Next, we substitute the value of the variable r in the above equation

i.e. r = 17

So, we have the following equation

C = 2π * 17

From the question, we have

π = 3.14

So, we have the following equation

C = 2 * 3.14 * 17

Evaluate the products

So, we have the following equation

C = 6.28 * 17

Evaluate the products

So, we have the following equation

C = 106.76

Hence, the circumference is 106.76 ft

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2. Write ONE algebraic rule that represents triangle JKL being translated to triangle J"K"L".

Answers

The original coordinates of JKL:

J(-3, -3), K(-4, 2) and L(2,1)

First, it is translated by the algebraic rule (x,y)->(x+2, y-3):

J(-3, -3)-> J'(-3+2, -3-3)=J'(-1, -6)

K(-4, 2) -> K'(-4+2, 2-3)= K'(-2, -1)

L(2,1) -> L'(2+2, 1-3)= L'(4, -2)

Then, this image is translated by (x,y)-> (x-2, y-1)

J'(-1, -6) -> J''(-1-2, -6-1) = J''(-3, -7)

K'(-2, -1) -> K''(-2-2, -1-1)= K''(-4, -2)

L'(4, -2) -> L''(4-2, -2-1)= L''( 2, -3)

Coordinates for triangle J''K''L'':

J''(-3, -7), K''(-4, -2) and L''( 2, -3)

2. To find algebraic rule that represents JKL to J''K''L'':

[tex]\begin{gathered} J^{\doubleprime}(-3,-7)\text{ and J(-3, -3)} \\ (x,y)\rightarrow(x,\text{ y+4)} \end{gathered}[/tex]

Given f(x)=3x2−5x−2.

What is the value of f(−2/3)?

Answers

Answer:

[tex]2\frac23[/tex]

Step-by-step explanation:

Hello!

Evaluate the function for -2/3, by plugging it in for x in the equation.

Evaluate[tex]f(x) = 3x^2 - 5x - 2[/tex][tex]f(-\frac23) = 3(-\frac23)^2-5(-\frac23)-2[/tex][tex]f(-\frac23) = 3(\frac49) + \frac{10}{3} - 2[/tex][tex]f(-\frac23) = \frac{4}3 + \frac{10}3 - 2[/tex][tex]f(-\frac23) = 4 \frac23 - 2[/tex][tex]f(-\frac23) = 2\frac23[/tex]

The evaluated value is [tex]2\frac23[/tex].

Answer:

Step-by-step explanation:

The absolute value of negative two third is really 2/3 but if your trying to reduce it to the lowest term its 0.66 or 0.67  However I would just put only 2/3 in the box, confidently knowing it would be scored correct.  

What is the slope of the line that passes through the points (2, 8) and
(-3, 14)? Write your answer in simplest form.

Answers

Answer:

-6/5

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (14 - 8)/(-3 - 2)

slope = 6/(-5)

slope = -6/5

The solution is -6/5

The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the first point be A

Now , the value of A is A ( 2 , 8 )

Let the second point be B

The value of B is B ( -3 , 14 )

And , the slope of the line between 2 points is given by the formula,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 14 - 8 ) / ( -3 - 2 )

On simplifying the equation , we get

Slope m = 6 / ( -5 )

Slope m = -6/5

Therefore , the slope of the line is m = -6/5

Hence , The slope of the line that passes through the point A ( 2 , 8 ) and B ( -3 , 14 ) is slope m = -6/5

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3) Identify the following by using the given figure
a) Two pairs of adjacent angles
b) Two pairs of supplementary angles
c) Linear pairs ​

Answers

Step-by-step explanation:

a) angles that share 1 side and are next to each other

<DBA, <ABE

<ABE, <EBC

b) two angles whose measures add to 180°

<ABE, <EBC

<ABD, <DBC

c) two adjacent angles whose noncommon sides lie on a line

<ABE, <EBC

<ABD, <DBC

Simplify the complex rational expression. Type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent.\frac{\left(\frac{2c}{c+2}+\frac{c-1}{c+1}\right)}{\frac{\left(2c+1\right)}{c+1}}

Answers

We will simplify the complex expression shown below:

[tex]\frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}}[/tex]

The simplification process is shown below >>>>

[tex]\begin{gathered} \frac{\frac{2c}{c+2}+\frac{c-1}{c+1}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c(c+1)+(c-1)(c+2)}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{2c^2+2c+c^2+2c-c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{\frac{3c^2+3c-2}{(c+2)(c+1)}}{\frac{2c+1}{c+1}} \\ =\frac{3c^2+3c-2}{(c+2)(c+1)}\times\frac{c+1}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)\cancel{c+1}}\times\frac{\cancel{c+1}}{2c+1} \\ =\frac{3c^2+3c-2}{(c+2)(2c+1)} \end{gathered}[/tex]

If we multiply out the denominator, we have:

[tex]\begin{gathered} \frac{3c^2+3c-2}{(c+2)(2c+1)} \\ =\frac{3c^2+3c-2}{2c^2+c+4c+2} \\ =\frac{3c^2+3c-2}{2c^2+5c+2} \end{gathered}[/tex]Answer

The numerator is

[tex]3c^2+3c-2[/tex]

The denominator is

[tex]2c^2+5c+2[/tex]

How long is the hypotenuse?

Answers

The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.

How to determine  hypotenuse?

To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).

The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

a² + b² = c²

⇒ c = √(a² + b²)

Where, a = 30 and b = 40, then

substitute the  values in the above equation, we get

30² + 40² = c²

900 + 1600 = c²

2500 = c²

50 = c

Therefore, the hypotenuse exists c = 50.

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Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?

Answers

The statement that is true regarding Rick's votes is D. Rick has 32 more votes than Jami.

How to calculate the value?

From the information, three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes

Rick = h + 10

Jami = h - 22

In this case, it's important to note that the difference between Jami and Rick will be:

= 10 - (-22)

= 10 + 22

= 32

Therefore, Rick will have 32 more votes.

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Three students are running for class president at Madison High School. Helen has h votes, Jami has h - 22 votes, and Rick has h + 10 votes. Which of the following statements is true regarding Rick's votes?

A. Rick has 10 more votes that Jami

B. Rick has 22 more votes that Jami

C. Rick has 5 more votes than Helen

D. Rick has 32 more votes than Jami.

a local salesman receives a base salary of $875 monthly. he also receives a commission of 10% on all sales over $1800. how much would he have to sell in a month if he needed to have a monthly income of $1500?

Answers

The total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.

What is termed as the sales commission?Sales commission is indeed the amount of cash as well as money paid to salespeople for exceeding a predetermined sales target. For instance, a company may agree to pay it's own salespeople a 4% commission on monthly sales exceeding Y.

The total monthly earnings for salespeople can be calculated as follows:

Monthly salary = base salary + sales commission

Given that what a local salesman generates a base salary of $875 and a 10% sales commission on any and all sales above $1,800, the salesman must make the following sales in order to earn $1500 in a given month:

Let the sales done by 'x'.

Then,

875 + 7% (x - 1800) = 1500

875 + (7/100) (x - 1800) = 1500

7(x - 1800) = 62500

x - 1800 = 8928.7

x = 894657.14

Thus, the total sell in a month if salesman needed to have a monthly income of $1500 is $894657.14.

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9t + 5(t + 3) = -(t + 13) + t

Answers

If we solve the given equation for t we get that t=-2

The equation given,

9t+5(t+3) = -(t+13) +t

⇒9t + 5t + 15 = -t -13 +t

⇒14t + 15 = -13                    (∵-t+t=0)

⇒14t = -13-15                       (bringing 15 from left hand side to right hand      side the sign is flipped and 15 becomes -15)

⇒14t = -28

⇒[tex]t=\frac{-28}{14}[/tex]                            (dividing both sides by 14)

⇒t = -2

Thus on solving the equation we get t = -2

Your question was incomplete but most probably your full question was

Solve for t when this equation is given, 9t+5(t+3) = -(t+13) +t

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write the equation of the line that is perpendicular to 5x-4y=4 and passes through the point (-8, 2)

Answers

The linear equation perpendicular to 5x-4y=4 is:

y = (-4/5)*x + 42/5

How to get the linear equation?

We want to find a line perpendicular to:

5x - 4y = 4

Solving this for y, we get:

y = 4 - 5x

y = (4 - 5x)/-4 = -1 + (5/4)*x

We can see that the slope of this line is 5/4, the slope of a perpendicular line will be the inverse of the opposite, so we get:

slope = -4/5.

Then the line is something like:

y = (-4/5)*x + b

To find the value of b, we use the fact that the line passes through (-8, 2)

2 = (-4/5)*-8 + b

2 = (-32/5) + b

2 + 32/5 = b

10/5 + 32/5 = b

42/5 = b

The linear equation is:

y = (-4/5)*x + 42/5

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3. (02.02)
Angle ABC is formed by segments AB and BC on the coordinate grid:
90 degree
m/ABC 180 degrees
Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle AB'C'. Which statement shows the measure of angle A'B'C' (4 points)
OmzABC 90
m/ABC= mzABC
5-
OmzABC-2 m/ABC
8

Answers

The statement that shows the correct measure of ∠A'B'C' is
m∠ABC = m∠A'B'C'.

What type of transformation does rotation do?
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point. A rotation produces a new figure known as the image. The picture matches the original figure exactly.
The rotation will typically be at a similar angle, even if a figure can be rotated by any number of degrees. Positive degrees will cause the figure to revolve counterclockwise. The graphic will turn clockwise if the degree value is negative. Any point on the figure can be rotated.

Given, ΔABC with co-ordinates (3, 4), (5, 3) and (3, 2); also ∠ABC = 53.13°
Again, ΔABC is rotated counter-clockwise by 90° to make the  ΔA'B'C'.
Thus, new triangle having co-ordinates (-4, 3), (-3, 5) and (-2, 3) is obtained.
Rotation retains congruence since it is a transformation that does not alter side length or angle measure.
Thus, we have ∠A'B'C' = 53.13°
Therefore, ∠ABC = ∠A'B'C' = 53.13° i.e. m∠ABC = m∠A'B'C'.

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The midpoint of AB is M(1, 1). If the coordinates of A are (-2,5), what are the
coordinates of B?

Answers

The coordinates of B are (4 , -3) .

A cartesian coordinate system, which uses signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length, uniquely identifies any point in a plane by a pair of numerical coordinates.

The origin of each reference coordinate line, known as an axis of the system or simply an axis (plural axes), is the intersection of the ordered pairs (0, 0). The coordinates can also be determined by looking at the locations of the perpendicular projections of the point onto the two axes, which are shown as signed distances from the origin.

Let the coordinates of B be (x, y)

As M is the mid point of AB , we know from the distance formula that the coordinates of M will be:

abscissae of M = (-2 + x) /2

or, 1 =   (-2 + x) /2

or, x = 4

Ordinate of M = (5 + y)/2

or , 1 = (5 + y)/2

or, y = -3

Therefore the coordinates of B are (4 , -3)

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Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per
gigabyte. She wants to keep her bill under $60 per month. Write and solve an
inequality which can be used to determine g, the number of gigabytes Ella
can use while staying within her budget.
> ≤ >
Inequality: 5g +37.5 < 59
9 4.3
Submit Answer
attempt 2 out of 2

Answers

The gigabyte needed will be g<2.2 as per the given condition that is- " Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month."

What is inequality?

A mathematical statement of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. The five inequality symbols in Maths are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).

How to solve inequality?

Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the numbers on the other by adding or subtracting quantities.

Here,

Under her cell phone plan, Ella pays a flat cost of $49 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.

So the inequality will be,

49+5g<60

5g<11

g<2.2

The required gigabyte will be g<2.2 under the following circumstances: "Ella's cell phone plan has a fixed monthly fee of $49 and a per-gigabyte charge of $5. She wants to keep her monthly bill under $60."

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The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 4500 pounds on Planet​ A, find the​ elephant's weight on Planet B.

Answers

Based on the ratio of the weights of objects in Planet A to Planet B, an elephants weighing 4,500 pounds on Planet A would weigh 135 pounds on Planet B

How to find the weight?

The ratio of the weight of an object in Planet A is 100 to 3 on Planet B. This means that every 100 pounds on Planet A is 3 pounds on Planet B.

If an elephant on Planet A is 4,500 pounds, on Planet B it would weigh:

Weight on Planet B = (4,500 x 3) / 100

Weight on Planet B = 13,500 / 100

Weight on Planet B = 135 pounds

In conclusion, the weight of the elephant on Planet B would be 135 pounds.

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Please help me with this math problem!! Will give brainliest!! :)

Answers

Answer: 1/2

Step-by-step explanation:

Answer:

The correct answer seems to be 1/2

One spring day, Grayson noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 58° F. For the next 5 hours, the temperature rose 1° per hour. For the next 3 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 63° at midnight. On the set of axes below, graph Grayson's data.

Answers

On the graph that is included with the solution, the temperature fluctuations are depicted.

A graph is a representation of the relationship between two variables, often measured along one of two right-angled axes each.

It is 56° at 6 a.m.

It rises to 61° for the next 5 hours because it is increasing by 1° per hour, and after another 4 hours it will rise to 69° because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it fell for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

It is 56° at 6 a.m. The temperature rises to 61° for the next 5 hours because it is increasing by 1° per hour, and then after 4 hours it will rise to 69° again because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it dropped for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

The final graph is shown in the below attached figure.

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Items 11-15. Lines a, b, c, and d
intersect as shown.

11. Which pairs of lines are parallel?

(a) a and b
(b) a and c
(c) c and d
(d) b and d

12. What is x?

13. What is y?

(a) 37
(b) 84
(c) 88
(d) 92

14. What is z?

(a) 84
(b) 92
(c) 96
(d) 109

15. If the slope of line d is given, the slope of which other line is known?

LEFT SIDE OF PAPER!!

Answers

Answer:

11. (c) c and d

12. x = 109°

13. (b) 84

14. (c) 96

15. C

Step-by-step explanation:

11. Parallel means that if the lines continued on forever, the lines will never cross. They have the same slope.

12. x is an alternate exterior angle to the angle labeled 109°. this means that the angles are equivalent.

13. y is the last unknown angle in the triangle. The interior angles of a triangle always add up to 180°.  So 180° = 55° + 41° + y.

y = 180° - 55° - 41° = 84°

14. z is a supplementary angle to y, meaning that y + z = 180°.

180° - 84° = 96° = z

15. Lines d and c are parallel meaning they have the same slope, therefore if you know the slope of one, you know the slope of the other.

write 2 quadratic equations (of any form) that are not equivalent, each with a vertex of (4,5)

Answers

Answer:

[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]

Step-by-step explanation:

Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)

So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]

we can change the function by changing the value of the constant "a".

we can use two arbitrary values, but in this example I'll use -1 and 1.

this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]

these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.

In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form

[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]

We can also expand the other function similarly.

[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]

Can someone answer this! Its due in 34 minutes!!!!

Answers

I WILL BE USING LAWSOF EXPONENTS.

[tex] = {3}^{3} \times (3^{2})^{3x} \\ = {3}^{3} \times 3^{2 \times3 x} \\ = {3}^{3} \times {3}^{6x} \\ = 3^{3 + 6x} [/tex]

IF IT SAID THAT K IS THE IS THE EXPRESSION IN TERMS OF K THEN THE EXPRESSION NOW IS

[tex]3 +6 x[/tex]

HOPE THIS HELPS

simplify the following: [tex]\frac{(7^2.3^-1)^4.7^5}{(3^2.7^-6)^3}[/tex]

(. means multiply)

Answers

The simplification of the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex] is 2453.5.

How to simplify the equation?

Consider the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex]

Solve for Numarator [tex](7^{2} .3-1)^{4}[/tex]= [tex](7^{2} .3-1)^{2} (7^{2} .3-1)^{2}[/tex]

= [tex](147-1)^{2}[/tex][tex](147-1)^{2}[/tex]

= (21316) (21316)

Solve for Denominator [tex](3^{2}.7-1)^{3\\}[/tex]

= [tex](63-6)^{3}[/tex]

= 57³

Solve both, and simplify the equation.

= [tex]\frac{(21316) (21316)}{185193}[/tex]

= 2453.5

∴ Simplification is 2453.5

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At the beginning of baseball season, the
concession stand had inventory of
4,250 bags of popcorn. At the end of the
season, 1,250 bags remain. What is the
percent of decrease in the number of
bags of popcorn? Round to the nearest
tenth if necessary.

Answers

Answer:

70.6% decrease

Step-by-step explanation:

4250-1250 = 3000

4250x = 3000

x=70.6%

70.6% decrease

:]

James sells 6 cupcakes for £5
Maddie sells 4 cupcakes for £3.50
Which is better value?
You must show all your working.

Answers

James

6 = 5
1 = ? Crisi cross

6? = 5. Divide both side by 6
? = 5/6 = 0.966

Maddie

4 = 3.5
1 = ?

4? = 3.5

? = 0.875

0.966 > 0.875 so James is selling with bigger price

I need help asap!!!!

Answers

The answer is -1 and 5

Oscar
and maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles one entry in the table paired 152 km with 95 miles if k represents the number of kilometers and m represents the number of miles who wrote the correct equation that would relate kilometers to miles

Answers

The answer to the given question is Oscar wrote the correct equation that would relate kilometers to miles.

Calculation and Parameters

1. Table

km         miles

152          95

2.  Set the proportion with / and solve for k

/ = 152 km / 95 miles

/ = 1.6 km / 1 miles

= 1.6 , where  1.6 / 1 represents kilometers per mile.

So, Oscar is right.

Maria is wrong because:

If we solve the proportionality:

/ = 152 km / 95 miles

/ = 95 miles / 152 km

= 0.625 , where 0.625 represents miles per kilometer

Read more about kilometers and distance here:

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The complete question is:

"Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If represents the number of kilometers and represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.

Oscar wrote the equation = 1.6, and he said that the unit rate 1.6 / 1

represents kilometers per mile.

Maria wrote the equation = 0.625 as her equation, and she said that 0.625 represents kilometers per mile."

♾️ How is the infinite possible? Has anyone ever counted numbers their whole life?

Answers

Answer: False, not possible.

The human was never meant to calculate or go beyond their fingers in search of great numbers, taking count for themselves, giving them names, appropriating. If you wanted to go higher for a laugh, it was called guessing. "Give me ZERO of this, give me 14,739,628,837 of that" are words that nobody says and words that stand behind delusion.

The only "anyone" to be counting their whole life is a divine. Keep math, numbers, and geometry sacred.

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