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The simplified expressiοn is [tex]-3x^3y^2 - 4x^2y + 8y[/tex].

Mathematical statements are called expressiοns when they cοntain at least twο terms that are cοnnected by an οperatοr and cοntain either numbers, variables, οr bοth. The mathematical οperatοrs can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn. Fοr instance, the expressiοn x + y is an expressiοn where x and y are terms with an additiοn οperatοr in between.

In mathematics, there are twο types οf expressiοns: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables.

Tο simplify [tex](2x^3y^2-8x^2y+4y) − (5x^3y^2-4x^2y - 4y)[/tex], we need tο distribute the negative sign in frοnt οf the secοnd set οf parentheses, and then cοmbine like terms. This gives:

[tex]2x^3y^2 - 8x^2y + 4y -5x^3y^2 + 4x^2y + 4y[/tex]

[tex]= (2x^3y^2 - 5x^3y^2) + (-8x^2y + 4x^2y) + (4y + 4y)[/tex]

[tex]= -3x^3y^2 - 4x^2y + 8y[/tex]

Therefοre, the simplified expressiοn is [tex]-3x^3y^2 - 4x^2y + 8y[/tex].

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Answer:

its C −3x3y2 − 4x2y + 8y

Step-by-step explanation:

FO = 18. In order to solve this problem, we must first understand the concept of triangle trigonometry.

Trigonometry is the branch of mathematics that focuses on the relationships between angles and sides of triangles. It is based on the measurement of triangles and the calculation of the angles and lengths of their sides.

A triangle is a two-dimensional shape composed of three straight lines. When the three lines of a triangle meet at a single point, it is called a vertex. Each line of the triangle is called a side, and the angle between two sides is called an angle.

In this problem, we are given a triangle AFOX with one right angle at point O and an angle m/F of 40°. We also know that FX = 15. To solve for FO, we must use the Law of Sines which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal in all triangles.

Using this law, we can determine that FO = (15/sin40°) = 18. Therefore, the answer to the question is FO = 18.

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The value of the a  in the mixed form is [tex]-1 \frac{5}{43}[/tex].

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To solve for a, we can begin by isolating the variable on one side of the equation.

First, we can subtract 3 from both sides to get:

-7/12 - 3 = 4/a

Next, we can simplify the left side by finding a common denominator of 12:

-7/12 - 3 * 12/12 = 4/a

-7/12 - 36/12 = 4/a

-43/12 = 4/a

To solve for a, we can multiply both sides by a/4:

(-43/12) * (a/4) = 1

Multiplying the left side gives:

-43a/48 = 1

Dividing both sides by -43/48 gives:

a = -48/43

To express this as a mixed number, we can divide the numerator by the denominator:

-48 ÷ 43 = -1 with a remainder of 5

Therefore, the value of the a  in the mixed form is [tex]-1 \frac{5}{43}[/tex].

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Complete question:

Challenge) Solve for a. Answer as a mixed number. A=?

-7/12 = 4/a+3.

Sarah is incorrect, the sum will be a rational number, the first option is the correct one.

We say that some sets are closed under the addition if, when we add two elements of that set, the outcome also belongs to that set.

For example, the set of real numbers is closed under addition, and also happens for the case of rational numbers.

If we add two rational numbers, the outcome must be rational.

In this case the two numbers are rational, thus, the outcome of the sum will be rational, not irrational, so Sarah is incorrect. The correct option is the first one.

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The estimations for the given function are:

For a function y = f(x) we define the maximum as the value of f(c) such that:

f(c) ≥ f(x) for any value of x.

And the minimum as:

f(k) ≤ f(x) for any value of x.

Usin the graph it is easier, just select the value at the top for the maximum and the value at the bottom for the minimum, we can see that:

maximum ---> y  ≈ 120

minimum ---> y ≈ -175

Remember, these are estimations.

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Answer:

Alice is correct because area of shaded region of both the gameboards are equal.

Step-by-step explanation:

Here it is given that both the gameboards are of same shape and size and Alice stated that the area of shaded regions of both the gameboards are same.

Let us take the length of the board be "l" and its breadth be "b" .

Initial area of the gameboard will be lb since it is a rectangle.

1st case :-

breadth of the shaded region= b

length of the shaded region = l/2 (since the length becomes half )

Area of the shaded region = b*l/2 = lb/2 .

2nd case :-

breadth of the shaded region = b/2 ( since breadth becomes half. )

length of the shaded region = l

Area of the shaded region = l/2

Area of the shaded region = b/2*l = lb/2 .

As we can see that the area of shaded region in both shaded region in both cases are equal also it is half of the total area of the rectangle. Hence Alice was correct.

Hence the area of the shaded regions in both the cases are similar and half of board in case is shaded .

Therefore, if your percentage test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.

In statistics, a percentage is a figure or an integer that is expressed as a fraction of 100. Additionally, the words "pct.," "pct," but also "pc" are rarely used. The "%" symbol, however, is commonly used to denote it. There are no dimensions; the percentage total is flat. Percentages are really just numbers because the numerator is 100. To indicate that a number is a percentage, either the percent character (%) or the text "percent" must appear before it.

Here,

Using the following formula, we can determine how little classwork you need to complete to receive an overall score of 80%:

Tests account for 40% of the final grade, classwork for 40%, and homework for 20%.

=> 80% = (91.5%) x (40%) + (40%) for classwork + (97.2%) x (20%)

When the numbers are multiplied by the corresponding weights:

=> (0.4 times classwork) + (0.32) + (0.1944) = 0.8

Simplifying:

=> 0.8 - 0.32 - 0.1944 = 0.4 x Classwork

=> 4. times classwork equals 0.2856

=> multiplying by 0.4

=> Work in class = 0.714

Therefore, if your test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.

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Answer:

Step-by-step explanation:

There are different methods to approach this problem, but one possible way is:

First, find the number of weeks in a century: 100 years × 52 weeks/year = 5200 weeks

Then, find the fraction of a century that is 13 weeks by dividing 13 weeks by 5200 weeks: 13/5200 = 1/400

Therefore, 13 weeks is 1/400 of a century.

The equation of the line of best fit is given as follows:

y = 1.5x + 4.5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Two points on the line for this problem are given as follows:

(1,6) and (3,9).

When x increases by 2, y increases by 3, hence the slope m of the line is given as follows:

m = 3/2

m = 1.5.

Hence:

y = 1.5x + b.

When x = 3, y = 9, hence the intercept b of the line is obtained as follows:

9 = 1.5(3) + b

b = 9 - 4.5

b = 4.5.

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Answer:

the answer is c

Step-by-step explanation:

The group of rotations and symmetries of a geometric configuration is the group of isometries.

According to the above paragraph, "the group of rotations and symmetries of the configuration" refers to the group of isometries of a geometric configuration that preserve the configuration itself, without involving any translations. This group consists of rotations about a fixed point and symmetries about a straight line that pass through that point.

This group is formed by combining isometries of the configuration through the operation of composition, and it satisfies certain properties, such as closure, associativity, identity, and inverses. It is a useful tool for studying the symmetries and transformations of the configuration, and it is used in fields such as crystallography and quantum mechanics.

In summary, the group of rotations and symmetries of a geometric configuration is the group of isometries that preserve the configuration and can be composed with each other to obtain new isometries.

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Each row will have 4 blueberry bushes and 7 raspberry bushes.

What is Greatest common divisor?

Greatest common divisor (GCD) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest positive integer that is a factor of two or more integers.

We are required to find the greatest common divisor (GCD) of 56 and 98.

we can factorize these numbers as follows :

56 = 2 x 2 x 2 x 7

98 = 2 x 7 x 7

The GCD is the product of the common prime factors, raised to the lowest power they appear in either factor:

GCD = 2 x 7 = 14

Therefore, Gemma can plant 14 rows. To find how many blueberry and raspberry bushes will be in each row, we can divide the total number of bushes by the number of rows:

No. of blueberry bushes per row = 56 / 14 = 4

No. of raspberry bushes per row = 98 / 14 = 7

So, each row will have 4 blueberry bushes and 7 raspberry bushes.

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Answer:

Step-by-step explanation:

[tex]\tt z + 2 < 8[/tex]

Subtract 2 from both sides:-

Simplify :-

Therefore, the solution of the inequality z + 2 < 8 is z < 6.

_______________________

Hope this helps!

Answer:

The rocket splashes down after [tex]\boxed{24}[/tex] seconds

The rocket peaks at [tex]\boxed{769}[/tex] meters above sea-leval

Step-by-step explanation:

The relationship between height and time is given by the equation
[tex]h(t) = -4.9t^2+112t+129[/tex]

The splashdown will occur when [tex]h(t) = 0[/tex]

Therefore solve t for
[tex]-4.9t^2+112t+129 = 0[/tex]

This is a quadratic equation which can be solved with the aid of a quadratic formula calculator

The solution set for this equation is
[tex]t=-1.09894 \;and\;\:t=23.95609\right)[/tex]

Omitting the negative value we get
[tex]\text{t=23.95609 \;seconds}\\\\= 2\text{4 \;seconds \;rounded}}[/tex]

For the second part, the maximum value of h(t) can be found by finding the first derivative h'(t) and setting it equal to 0 and solving for t; then plug this value of t into h(t) to find the max height

[tex]h'(t) = \dfrac{d}{dt}\left(-4.9t^2+112t+129\right)\\\\= \dfrac{d}{dt}\left(4.9t^2\right)+\dfrac{d}{dt}\left(112t\right)+\dfrac{d}{dt}\left(129\right)\\\\= - 9.8t + 112 + 0\\\\= -9.8t + 112\\\\[/tex]

Setting  the above expression to 0 gives
[tex]-9.8t+112=0\\\\-9.8t = -112\\\\t = \dfrac{-112}{-9.8}\\\\t = 11.4286 \;seconds[/tex]

Plugging this value back into h(t) gives

[tex]h(11.4286) = -4.9\cdot \:11.4286^2+112\cdot \:11.4286+129\\\\= 769 \;meters \;(rounded)[/tex]

Answer:

 [tex]y=\frac{5}{2} x[/tex]

Step-by-step explanation:

Notice is a line, The equation for a line can be found as the following:
[tex]y-yo=m(x-xo)[/tex]
We need to find the slope.

First take two points of the graph
(0,0) the origin and (4,10) for example. Notice i do assume the X value is 4 for Y=10, since the cropping for the picture doesn't show the exact values for X .
Then the slope is given by equation:
[tex]m=(y-yo)/(x-xo)\\[/tex]

[tex]m=\frac{10-0}{4-0} =5/2[/tex]

then the equation is

[tex]y-0=\frac{5}{2} m(x-0)[/tex]  

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

Answer:

y=5/2x or y=2.5x

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

The y-intercept is the cost of a one time fee for renting bowling shoes.

Answer:

it's B Or D Id say it's D

Step-by-step explanation:

It's D because it's definitely not a drink so not A and when you read y is something that it's not shoes so the most one I think is correct is D

The time the softball will spend in the air is 2 seconds

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

Rate = 2(t - 2)(t + 5)

To determine the time, we set the rate to 0

So, we have

2(t - 2)(t + 5) = 0

Divide by 2

(t - 2)(t + 5) = 0

The above means that

t - 2 = 0 or t + 5 = 0

Evaluate

t = 2 or t = -5

Time cannot be negative

So, we have

t = 2

Hence, the time is 2 seconds

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The triangle with side lengths 6, 9, and 12 is an obtuse triangle. To classify the triangle as acute, right, or obtuse, we need to determine the type of triangle based on the lengths of its sides.

Recall that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side for it to be a valid triangle.

Let's check if the given triangle with side lengths 6, 9, and 12 satisfies the triangle inequality:

1. Sum of two shorter sides: 6 + 9 = 15 (greater than the length of the longest side, 12). Valid.

2. Sum of the two longer sides: 9 + 12 = 21 (greater than the length of the remaining side, 6). Valid.

3. Sum of the longest side and the shortest side: 6 + 12 = 18 (greater than the length of the remaining side, 9). Valid.

Since all three inequalities are satisfied, the given side lengths form a valid triangle.

Now, to classify the triangle, we can use the Pythagorean theorem. In a right-angled triangle, the square of the length of the longest side is equal to the sum of the squares of the other two sides.

In this case, the side lengths are 6, 9, and 12. To determine if it is a right-angled triangle, we can check if:

[tex]12^2 = 6^2 + 9^2\\144 = 36 + 81\\144 \neq 117[/tex]

Since the Pythagorean theorem is not satisfied, the triangle is not a right-angled triangle.

Now, let's check if it is an acute or obtuse triangle. In an acute triangle, all three angles are less than 90 degrees, while in an obtuse triangle, one angle is greater than 90 degrees.

To determine this, we can use the law of cosines, which states that in any triangle:

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

where c is the longest side (12 in this case), a and b are the other two sides (6 and 9), and C is the angle opposite the longest side.

Calculate the value of cos(C):

[tex]12^2 = 6^2 + 9^2 - 2 * 6 * 9 * cos(C)\\144 = 36 + 81 - 108 * cos(C)\\144 = 117 - 108 * cos(C)\\108 * cos(C) = 117 - 144\\108 * cos(C) = -27\\cos(C) = -27 / 108\\cos(C) = -0.25[/tex]

Since the value of cos(C) is negative, the angle C is obtuse. Therefore, the triangle is an obtuse triangle.

In summary, the triangle with side lengths 6, 9, and 12 is an obtuse triangle.

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The water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35) by solving the expression formed.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that are written in a certain order. Expressions can be evaluated or simplified by following the rules of arithmetic or algebra. Examples of expressions include "2x + 3", "(a + b) / c", and "5^2 - 3".

According to given information :

Let's use the variable "r" to represent the water output rate for the Rodriguez family's sprinkler.

Then, the water output rate for the Barnes family's sprinkler can be represented as "50 - r", since the sum of the two rates is 50 L per hour.

Using the formula:

rate x time = amount of output, we can set up two equations:

r x 15 = amount of water output for the Rodriguez family

(50 - r) x 35 = amount of water output for the Barnes family

We also know that the total amount of water output is 1050 L, so we can set up a third equation:

r x 15 + (50 - r) x 35 = 1050

Now we can solve for "r".

First, simplify the third equation

15r + 1750 - 35r = 1050-20r = -700r = 35

Therefore, the water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35).

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By calculating, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.

To compute the cost assigned to ending inventory using different inventory costing methods, we need to determine the cost of goods sold (COGS) and the cost of ending inventory based on the specific method. Here is the calculation for each method:

(a) FIFO (first-in, first-out) method:

We assume that the earliest inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the earliest inventory items, while the cost of ending inventory is based on the cost of the most recent purchases. Here are the calculations:

COGS: 110 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 70 units x $61.20 = $23,216

Ending inventory: 90 units x $61.20 + 160 units x $63.20 = $12,272

(b) LIFO (last-in, first-out) method:

We assume that the most recent inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the most recent inventory items, while the cost of ending inventory is based on the cost of the earliest purchases. Here are the calculations:

COGS: 90 units x $61.20 + 270 units x $86.20 + 230 units x $56.20 = $43,104

Ending inventory: 110 units x $51.20 + 140 units x $96.20 + 50 units x $86.20 = $13,048

(c) Weighted average method:

We calculate the weighted average cost per unit for all the inventory purchased during the period, and use this average cost to determine the cost of goods sold and ending inventory. Here are the calculations:

Weighted average cost per unit = ($51.20 x 110) + ($56.20 x 230) + ($86.20 x 270) + ($61.20 x 90) + ($63.20 x 160) / (110 + 230 + 270 + 90 + 160) = $72.62

COGS: 590 units x $72.62 = $42,878.80

Ending inventory: 0 units (all units have been included in COGS)

(d) Specific identification method:

We identify the specific cost of each unit sold based on its purchase price. Here are the calculations:

COGS: 70 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 90 units x $61.20 + 80 units x $63.20 + 20 units x $96.20 = $43,708

Ending inventory: 80 units x $63.20 + 70 units x $96.20 = $9,772

Therefore, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.

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Answer:

Step-by-step explanation:

area of square=side ×side

we have, side=x+8

also we have area of square=64cm²

∴  (x+8)cm×(x+8)cm=64cm²

⇒x²+16x+64=64                            ∵( a+b )²=a²+b²+2ab

⇒x²+16x=0

⇒x(x+16)=0

∴x=0 or x=-16

Answer: 64,000

Step-by-step explanation:

[tex] \mathbb{ANSWER:}[/tex]

LCM: 168

HCF: 28

Answer: 306

Step-by-step explanation:

Each child has 34 stickers and 9 bottles. To find the total number of stickers, we need to multiply the number of stickers per child by the number of children.

34 stickers x 9 children = 306 stickers

So there are 306 stickers in total.

The amount Jon and Ron earn are $22,000 and $ 74,000 respectively.

Word problem is a mathematical problem expressed entirely in words typically used as an educational tool.This word problem is interpreted into mathematical equation or expression.

Represent the amount Jon earn by j and Ron earn by r

j+r = 96000 equation 1

r = 8000+ 3j equation 2

from equation 1

r = 96000-j

substitute 96000-j for r in equation 2

96000-j = 8000 +3j

collect like terms

96000-8000 = 3j +j

88,000 = 4j

j = 88000/4

j = $22,000

from equation 1

22000+r = 96000

r = 96000-22000

r = 74,000

Therefore the amount Jon and Ron earn are $22,000 and $ 74,000 respectively.

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