Unit 5 Day 4 - Exit Ticket 5.3 - Dividing Polynomials
Perform the operation shown below.

Hint: Shift 6 for exponents and put remainders in (),

Ex. 2x^2+(4/x+2)

(x3+10x2+13x+36)÷(x+9)

The the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.

When rounding to one significant figure, we keep only the leftmost digit that is not zero. Therefore, rounding 33.72 and 8.19 to one significant figure gives 34 and 8 respectively so the estimated answer is;

34 + 8 = 42

Actual answer answer is derived as;

33.72 + 8.19 = 41.91

In conclusion, the estimated answer is 42 and the actual answer is 41.91. The answer 41.91 is very close to the estimated answer of 42, so it looks sensible.

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The length of GH on the triangle is 12 units

From the question, we have the following parameters that can be used in our computation:

The similar triangles

Assuming that

The smaller triangle with length DF gives the larger triangle with length GH

This means that

GH = 3 * DF

Substitute the known values in the above equation, so, we have the following representation

GH = 3 * 4

So, we have

GH = 12

Hence, the length is 12 units

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Answer:

12 ft

Step-by-step explanation:

keep it simple, just givin' the answer :)

The range of values for length when the perimeter is between 82 feet and 124 feet is: 27 ≤ l ≤ 48

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter. The perimeter of the shape can be calculated by summing the measurements of its sides and edges. A rectangle's perimeter is equal to twice the product of its length and width.

Given a rectangular fence.

The perimeter P is at least 82 feet and is no more than 124 feet.

82 ≤ P ≤ 124

The width is 14 feet.

The range of values of the length is to be found.

Now,

Perimeter of rectangle = 2( length + width)

The lowest value of the perimeter is 82

82 = 2(l + 14)

82 = 2l + 28

54 = 2l

l = 27

The highest value of perimeter is 124

124 = 2(l + 14)

124 = 2l +28

96 = 2l

l = 48

Therefore the range of values for length when the perimeter is between 82 feet and 124 feet is:

                  27 ≤ l ≤ 48

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Answer:

To determine whether the shaded triangle is a right triangle, we need to use the fact that the three right triangles together form a rectangle.

Let's label some of the dimensions as shown in the diagram:

[asy]

unitsize(0.25cm);

pair A = (0,0), B = (10,0), C = (8,6), D = (6,0), E = (8,0), F = (10,6), G = (8,2);

draw(A--B--F--C--cycle);

draw(D--E);

draw(C--G);

label("$10$", (A+B)/2, S);

label("$6$", (C+F)/2, N);

label("$8$", (B+E)/2, E);

label("$2$", (C+G)/2, E);

label("?", (D+G)/2, NE);

label("$?$", (G+E)/2, S);

fill(C--G--D--cycle, gray(0.7));

[/asy]

The dimensions of the rectangle are 12 units by 14 units, so we know that:

\begin{align*}

10 + 8 &= 18 \\

6 + 2 + ? &= 14

\end{align*}

Simplifying the first equation, we get $8 = 14 - 6$. Substituting this into the second equation, we get:

$$2 + ? = 8$$

Therefore, the length of the shaded side of the triangle is 6 units. Now we can use the Pythagorean theorem to determine whether the shaded triangle is a right triangle. Letting $x$ be the length of the other leg of the shaded triangle, we have:

\begin{align*}

x^2 + 6^2 &= 8^2 \\

x^2 + 36 &= 64 \\

x^2 &= 28 \\

x &= 2\sqrt{7}

\end{align*}

Since $2\sqrt{7}$ is not an integer, we can conclude that the shaded triangle is not a right triangle.

The solution is, he had 68 marvels.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

he added 36 marvels, now, he has 104 in total,

we have to find that, how many he had.

let, he had = x

so, we know, added = 36

i.e. now total is = x+36

ATQ, we get,

x+36 = 104

or, x = 104 - 36

or, x = 68

Hence, The solution is, he had 68 marvels.

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The highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Hence, inequality emerges from a lack of balance.

So, what we can do is add 6 in 285 till it reaches 300.

258 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 300

6 is added 7 times, then:

6*7 = 42

Then the correct inequality would be x  < 42.

Therefore, the highest number of days this institution can continue to accept cats without going over its allowed occupancy is included in the inequality (C) x<42.

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Answer: D - The mean of the date is greater than the median

Step-by-step explanation:

First, you line all the numbers up from least to greatest:

25, 26, 31, 33, 38, 39, 48, 58

Next, you find the median, or in this case, 35.5

Now you find the mean, and do that by adding all the numbers up (298) and then divide that by the number of people, or 8, which would be 37.25

Thus, the mean is greater than the median

Answer:

D

Step-by-step explanation:

Original data set:

25, 26, 31, 39, 33, 56, 38, 48

Data in increasing order:

25, 26, 31, 33, 38, 39, 48, 56

mean = (25 + 26 + 31 + 39 + 33 + 56 + 38 + 48)/8 = 37

median = (33 + 38)/2 = 35.5

mode = no mode

Answer: D

Arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.

An arrangement is a way of organizing or arranging a set of objects in a specific order or sequence.

When arranging the tiles in 3 rows of 4, there are more possible ways to create rectangular arrays using the tiles. For example, you could create a 4x3 array, a 3x4 array, a 2x6 array, a 6x2 array. These different arrays can be useful in a variety of mathematical contexts, such as exploring multiplication and division.

Therefore, arranging the twelve 1 tiles in 3 rows of 4 instead of any other arrangement of twelve 1 tiles, such as 2 rows of 6, makes sense because it allows for more flexibility and creativity in exploring mathematical concepts and creating visual representations.

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The measurement of angle x in the given figure is 11°

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

Given is a figure, we need to find the measure of angle x,

The labeled figure is attached,

We have,

∠ 1 = 85° [vertically opposite angles]

∠ 3 = 96° [corresponding angles between parallel lines]

∠ 2 + ∠ 3 = 180° [linear pair angles]

∠ 2 = 180°-96°

∠ 2 = 84°

Now,

∠ 1 + ∠ 2 + x = 180° [angles sum property of a triangle]

85° + 84° + x = 180°

x = 180°-169°

x = 11°

Hence, the measurement of angle x in the given figure is 11°

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The solution to the system 2xy+3=4y 3xy+2=5y is  (x, y) = (22/5, -30/29).

Starting with the first equation:

2xy + 3 = 4y

We can rearrange it to solve for one of the variables in terms of the other:

2xy - 4y = -3

2y(x - 2) = -3

y = -3/(2(x - 2))

Now we can substitute this expression for y into the second equation:

3x(-3/(2(x - 2))) + 2 = 5(-3/(2(x - 2)))

Multiplying both sides by 2(x - 2) to clear the fraction:

-9x + 4(x - 2) = -30

-9x + 4x - 8 = -30

-5x = -22

x = 22/5

Now we can use this value of x to solve for y:

y = -3/(2(22/5 - 2))

y = -30/29

Therefore, the solution to the system is (x, y) = (22/5, -30/29).

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You have $28.75 left to spend on diapers for Jake.

What is the percentage?

Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.

The total percentage of money spent on the blanket, toys, and clothes is 15% + 25% + 40% = 80%.

Therefore, the amount of money spent on Jake's supplies is $115, which is 80% of the total budget. We can set up the equation:

0.8x = 115

Solving for x, we get:

x = 115 ÷ 0.8 = $143.75

So, the total budget for Jake's supplies is $143.75.

To find out how much money is left for diapers, we need to subtract the amount spent on blanket, toys, and clothes from the total budget:

$143.75 - 15% of $143.75 - 25% of $143.75 - 40% of $143.75

= $143.75 - $21.56 - $35.94 - $57.50

= $28.75

Therefore, you have $28.75 left to spend on diapers for Jake.

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Answer:

Below

Step-by-step explanation:

y = 4x^2

dy/dx = 8x  

   at x = 2 this is    16   <===== not sure what they mean by 'estimate' !

Answer:

  y = -3

Step-by-step explanation:

You want the equation of a line with slope 0 through the point (-2, -3).

The point-slope form equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Adding k to both sides gives the "y =" form ...

  y = m(x -h) +k

When m=0 and (h, k) = (-2, -3), this becomes ...

  y = 0(x -(-2)) + (-3)

  y = -3 . . . . . . simplified

__

Additional comment

Anything times 0 is 0. So, the product 0(x +2) is 0.

Anything added to 0 is unchanged. So, the sum y = 0 -3 is y = -3.

When the slope is zero we get y= -3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

As, the Point-slope form

The point-slope form equation for a line with slope m through point (h, k) is

y = mx + b

When m=0 and (h, k) = (-2, -3)

y = 0(x -(-2)) + (-3)

y = -3

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Answer:

25 horse shoe magnets

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 2: 5 (bar magnet: horse shoe magnet) then we can use this ratio to solve for how many horse shoe magnets there are if there are 10 bar magnets.

To solve for '?', we can use this expression:

We multiply by 5 because in order to go from 2 to 10 (2: 5, 10: ?), we multiply the 2 by 5.

Therefore, for every 10 bar magnets, there are 25 horse shoe magnets.

The coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).

A(2, 3)  ⇒ A'(2, -3),

B(5, 5)  ⇒  B'(5, -5),

C(7, 3)  ⇒  C'(7, -3),

D(5, 2)  ⇒ D'(5, -2).

Thus, the coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).

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The correct question is-

Figure ABCD is reflected across the x-axis. What are the coordinates of A′, B′, C′, and D′?

The figure is attached.

The retailer estimates that about 254,623 regular cell phones will be sold 7 years from now.

Since the retailer estimates that 28% fewer regular cell phones will be sold every year, this means that the number of regular cell phones sold each year will be 72% of the number sold the previous year. We can use this information to find the number of regular cell phones sold 7 years from now as follows:

Let x be the number of regular cell phones sold 7 years from now. Then we have:

x = 0.72^7 * 917160

where 0.72 is the percentage of regular cell phones sold each year.

Using a calculator, we get:

x ≈ 254,623

Therefore, the retailer estimates that about 254,623 regular cell phones will be sold 7 years from now.

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Answer:

91,997

Step-by-step explanation:

y = a(1–r)t

y = 917,160(1–0.28)7 Plug in values

y = 917,160(0.72)7 Subtract

y = 917,160(0.10030…) Simplify

y = 91,996.77023… Multiply

Round to the nearest whole number.

91,996.77023… → 91,997

To the nearest whole number, 91,997 regular cell phones will be sold.

Answer:

$45

Step-by-step explanation:

I = prt

I = interest earned

p = principal = amount invested

r = interest rate; 5.25% = 5.25/100 = 0.0525

t = time in years; 6 months = 0.5 years

$4,000.00 at 5.25% interest

I = 4000 × 0.0525 × 0.5 = 105

$105 interest in 6 months

$2,000.00 at 6.00% interest

I = 2000 × 0.06 × 0.5 = 60

$60 earned in 6 months

$105 - $60 = $45

The difference is $45.

If the total amount spent by the eight students in Ms. Reese's class is $121.00, using a system of equations, the number that purchased from the:

A system of equations is two or more equations solved at the same time or concurrently.

It is also known as simultaneous equations.

The total number of students in Ms. Reese's class who decided to purchase their textbook from two different sources = 8

The unit cost per textbook from the college bookstore = $16.50

The unit cost per textbook from an online discount store = $11.00

The total spending by the eight students = $121.00

Let the number of students who purchased from the college bookstore = x

Let the number of students who purchased from an online discount store = y

x + y = 8 …Equation 1

16.5x + 11y = 121 …Equation 2

Multiply Equation 1 by 11:

11x + 11y = 88 …Equation 3

Subtract Equation 3 from Equation 2:

16.5x + 11y = 121

-

11x + 11y = 88

5.5x = 33

x = 6

Substitute x = 6 in either equation:

x + y = 8

6 + y = 8

y = 2

Thus, 6 students purchased their textbooks from the college bookstore while 2 purchased online.

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Answer:

The inverse of the function is

[tex]f^{-1} (x)=x^2-3[/tex]

Step-by-step explanation:

Given

[tex]f(x)=\sqrt{x+3}[/tex]

Find the inverse.

Write the function as an equation equal to [tex]y[/tex].

[tex]y=\sqrt{x+3}[/tex]

Interchange the variables.

[tex]x=\sqrt{y+3}[/tex]

Square both sides of the equation.

[tex]x^2=y+3[/tex]

Subtract [tex]3[/tex] from both sides of the equation.

[tex]y=x^2-3[/tex]

Replace [tex]y[/tex] with [tex]f^{-1} (x)[/tex].

[tex]f^{-1} (x)=x^2-3[/tex]

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Answer:

Step-by-step explanation:

300000000000000000000000000

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}[/tex]

The graph of the triangle is on the image at the end.

Remember that the area of a triangle of base B and height H is:

A = B*H/2.

Here we want to have an area of 21, then we can use:

B = 6

H = 7

Then:

A = 6*7/2

A = 3*7 = 21

So we must have a base of 6 units and a height of 7 units, then the vertices that we can have are:

(-3, 0), (3, 0), (-3, 7)

So we will have a right triangle such that the vertices are on the first and second quadrant, the graph of the vertices is below.

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Answer:

-21

Step-by-step explanation:

given

To evaluate (h.g(5)), we first need to find g(5) and then apply h to the result.

g(x) = 4x + 3, so g(5) = 4(5) + 3 = 23.

Now we apply h to g(5):

h(g(5)) = h(23) = -(23) + 2 = -21

Therefore, (h.g(5)) = -21.

Answer:

Step-by-step explanation:

To find (h o g)(5), we need to first find g(5), and then evaluate h at that value.

We are given that g(x) = 4x + 4, so we can find g(5) by substituting x = 5:

g(5) = 4(5) + 4 = 24

Now we evaluate h at g(5):

h(g(5)) = h(24)

We know that h(x) = -x + 2, so we can evaluate h(24) by substituting x = 24:

h(g(5)) = h(24) = -(24) + 2 = -22

Therefore, (h o g)(5) = -22.

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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The function is decreasing on the interval -6 < x < 0

increasing on the interval 0 < x < 4, and increasing on 4 < x < 9

[tex]A = 9(12) - 4^{2} = 108 - 16 = \bf 92 \ in^{2}[/tex]

By answering the supplied question, we may infer that the response is square  Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.

What is a square?

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is sometimes referred to as a rectangle with two adjacent sides of the same length.

A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are those that are 90 degrees or straight.

The diagonals of the square are also equally spaced and divided at a right angle. a nearby rectangle with two sides of identical length.

a quadrilateral with four equal-length sides and four right angles. two neighboring, equal sides that create a right angle in a parallelogram. an equilateral rhombus.

By dividing the base area by the height, one may get the volume of a square-based box. Thus, we can use the following formula to determine the juice box's volume:

Volume equals base area times height.

We may enter the numbers 22 cm² for the base area and 12 cm for the height into the formula to obtain the following results:

Volume equals 22 x 12 cm²

These values are multiplied together to produce:

Size = 264 cm³

Hence, Because 1 cm³ = 1 mL, one of the new juice cartons has a capacity of 264 cubic centimeters or 264 milliliters.

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Answer: its really simple the answer is 478cm^3

Step-by-step explanation:

Answer:

478cm^3

Step-by-step explanation: