The simplified rational expression of the square root of 16y^7 is given as follows:
[tex]4y^3\sqrt{y}[/tex]
How to simplify the rational expression?The rational expression for this problem is defined as follows:
[tex]\sqrt{16y^7} = (16y^7)^\frac{1}{2}[/tex]
The power of power rule states that when an exponential expression is elevated to a power, the powers are multiplied.
4 is the square root of 16, hence:
16 = 4².
Meaning that the expression is of:
(4²y^7)^0.5.
Then the simplified radicals are of:
4^(2 x 0.5) = 4.y^(7 x 0.5) = y^(3.5) = [tex]y³\sqrt{y}[/tex]Then the simplified expression is given as follows:
[tex]4y^3\sqrt{y}[/tex]
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HELP
18 kg of apples cost $106.20. How much would 31 kg cost?
Answer:
31kg will cost $ 182.9
Step-by-step explanation:
If 18kg = $106.20
than 31kg = ?
= 31kg/18kg × $106.20
= 3,292.2 /18
=$182.9
The sum of three consecutive numbers is 69. If the first number is n find the three Numbers
Answer:
22
Step-by-step explanation:
n + (n+1 )+( n+2) = 69
3n+3 =69
3n=66
n=66/3
n=22
Answer:
first number is 21
second number 23
third number 25.
Step-by-step explanation:
The sum of three consecutive numbers is 69
Let the first number be n
the second number be 2 + n
the third number be 4 + n
n + (2 + n) + (4 + n) = 69
=n + n + n + 2 +4 = 69
=3n + 6 = 69
=3n = 69 - 6
=3n = 63
=3n/3 = 63/3
n = 21
therefore the first number n = 21
the second number 2 + n = 2 + 21 = 23.
the third number 4 + n = 4 + 21 = 25.
What is the value sin 45?.
The Sin 45 value is 1/√2.For the purpose of determining the Sin 45 value, let's use the ABC right angle triangle.
The ratio of a triangle's opposing side's length to its hypotenuse is known as the Sin of an angle.
Sin ϴ = Opposite side or perpendicular / Hypotenuse
Sin ϴ = AC/AB
Sin ϴ = B/C
Calculation of the Value of Sin 45 Degree in Fraction
Sin 45 = √2/
= 1 / √2
Consider a right triangle with angle X= 45°,then it is obvious that third will also be 45°.hence the side length of triangle are L, L, √2L .then apply
sin 45°= L/√2L
Sin 45°= 1/√2
Sin 45°=0.7071
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Nate has $50 to go spend at the grocery store. He feels shopping cart with items total and $46. I’ll check out he will have to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart?
Nate have enough money to buy everything in his cart because his total expenses is lees than 50 dollars.
How to check if his money is enough to buy the grocery using the sales tax?Nate has $50 to go spend at the grocery store. He fills his shopping cart with items total and $46. He will have to pay a sales tax of 6% on al items on the cart.
Therefore, let's check if Nate have enough money to buy the groceries.
Hence,
sales tax amount = 6% of 46
sales tax amount = 6 / 100 × 46
sales tax amount = 276 / 100
sales tax amount = 2.76 dollars
Therefore,
the amount in total of the grocery = 46 + 2.76 = 48.76 dollars
Therefore, he has enough money to pay for his groceries.
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The marked price of a car i $49500 a peron can pay a depoit of 30% and imple interet at 12% per annum i charged on the outtanding balance. The total amount payable i to be paid in 2 1/2 year. Calculate the amount of each intallment
Each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.
given simple interest is 30%
Installments every month
a. Recurring payment
30 months in 2 1/2 years
First move
Payment due: [49,500 * (1-.30)] / 30 months
Amount due = (49,500 *.70) / 30 months
$34,650 payments over 30 months
Amount due: $1,155
Second action
Monthly payment equals [$1,155* (1+0.12)]
Monthly payment equals $1,155 * 1.12
The monthly payment is $1,293.6
The monthly payment equals $1,294 (Approximately)
Hire-purchase (b)
Hire purchase equals $1,155 * .12 over 30 months
=> 1155 * 0.12* 30
$4,158 for a hire buy
As a result, each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.
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Is 2x³ a polynomial?.
Answer:
Yes
Step-by-step explanation:
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Is a triangle always 360 degrees?.
A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.
No, a triangle is not always 360 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.
This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.
For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).
Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.
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2. Use function notation to represent each statement.
a. Six hours after it started raining, the amount of rain was 37 millimeters.
b. The amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining
a. Let t represent the time in hours when it started raining. We can use function notation to represent the amount of rain r at any time t with r(t) = 37 millimeters. This is because after 6 hours, the amount of rain was 37 millimeters. Therefore, we can use the equation r(t) = 37 millimeters to represent this statement.
b. We can use function notation to represent the amount of rain at any time t with r(t) = r(t-1.5). This is because the amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining. Therefore, we can use the equation r(t) = r(t-1.5) to represent this statement.
This type of function notation is useful for representing relationships between different values related to the same property or phenomenon. It allows us to quickly and easily analyse and compare data, as well as make predictions about future values. It is also useful for describing how certain parameters are changing over time.
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Workout the maximum number of hiker who could have walked between 6 mile and 17 mile
The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 and the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
The minimum number refers to the smallest value that is possible, allowed, or required based on the given interval. The maximum number refers to the largest value that is possible, allowed, or required based on given interval. The provided table provides intervals for the number of miles x the number of hikers can walk and the corresponding number of hikers.
In order to determine the minimum and maximum number of hikers that could walk between 6 miles and 17 miles, we look at the intervals which include the range between 6 miles and 17 miles.
a) The minimum value is determined by considering the common interval 10 ≤ x < 15 (5 ≤ x < 10 and 15 ≤ x < 20 are not considered as it includes values outside the range). Hence the corresponding number of hikers is 9.
b) The maximum value is determined by considering all the intervals which include the range between 6 miles and 17 miles, i.e. 5 ≤ x < 10, 10 ≤ x < 15, 15 ≤ x < 20. Hence, the maximum number of hikers is 2 + 9 + 8 = 19.
Note: The question is incomplete. The complete question probably is: The table below shows information about the distance walked by some hikers. a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.
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Which equation goes through the point (-6,2) and is perpendicular to y=3x-8
A. Y - 2 = 1/3 (x+6)
B. Y = 3x - 5
C. Y - 2 = -1/3 (x + 6)
D. Y = -3x + 6
Correct option is C, the correct equation is Y - 2 = -1/3 (x + 6).
Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation. Y = m x + b y=mx+b y=mx+by, equals, m, x, plus, b, where m is the slope and b is the y-intercept, is the slope intercept form.
Given points are (-6,2)
The required line should be perpendicular to y=3x-8.
When two lines are perpendicular,
their slopes are such that,
m1 = - 1/m2 [1]
⇒ slope of line 2 =
⇒ -1/3 [using (1) relationship ]
Now substituting the points are slope in the equation of line -
y - y₀ = m (x - x₀)
⇒ y - 2 = -1/3 (x + 6)
⇒ 3y - 6 = -x - 6
⇒ 3y + x = 0
⇒ x = -3y
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I need help on this asap!
Receives some cash from his mother for his journey. He has already put aside a total of $\$ 220$ for the trip. There is a 55-gallon gas purchase cap .
What is the greatest number of gallons ?[tex]$$\begin{aligned}& 3.25 \mathrm{~g}+40 \leq 220 \\& -403.25 \mathrm{~g} \\& \frac{3.25}{3.25} \leq \frac{180}{3.25} g \leq 55.38 \approx 55\end{aligned}$$[/tex]
Chang-to has a gas purchase limit of 55 gallons.
[tex]$$\begin{aligned}& 3.25 g+40 > 92 \\& \frac{-40}{\frac{3.25 g}{3.25} > \frac{-40}{32}} \\& \mathrm{~g} > 16\end{aligned}$$[/tex]
More than 16 gallons of gas could have been purchased by him .
[tex]$$\begin{aligned}& 3.259+40 \leq 170 \\& \frac{3.2 / 59}{3.2^{\prime} 5} \leq \frac{130}{3.25} \\& g \leqslant 40\end{aligned}$$[/tex]
He only allowed to purchase 40 gallons of gas during the journey.
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Solve x2 + 2 = 6 by graphing the related function.
A) 2
B) there are two solutions +v8
C) no real number solutions
D) +2
The solutions of the given equation are 2 or -2
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x²+2 = 6
x²+2 = 6
Solving we get,
x²+2 = 6
x² = 6-2
x² = 4
x = ±2
Hence, there are two solutions of the equation 2 or -2
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Which number line shows |x - 21| < 3
The line showing this inequality is B.
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality, |x - 21| < 3
Solving, the inequality,
|x - 21| < 3
x-21 < 3 and x-21 > -3
x < 24 and x > 18
Since, we get 18 < x < 24,
Hence, the line showing this inequality is B.
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What are the symbols used in graphing linear inequalities?.
The symbols used in graphing linear inequalities are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways.
Not equal ≠ Less than (<) Greater than (>) Less than or equal to (≤) Greater than or equal to (≥)Learn more about Linear inequalities:
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What does FG mean in algebra?.
In algebra, the notation "FG" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F" and the notation is represented as "F(G(x))".
The composition of functions is a way to combine two functions to create a new function. The output of the first function "G" is used as the input for the second function "F". This process is represented by the notation "F(G(x))", where "x" is the input for both functions. The function "F" is applied to the output of the function "G". This composition of functions is useful for modeling complex systems and can simplify mathematical expressions.
It also allows for the creation of more complex functions by combining simpler functions. However, not all functions can be composed and the order of the functions also matters. It's important to note that the order of the functions in composition matters and can change the result of composition.
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(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and
(
−
6
,
−
3
)
(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions on either side of an equals sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates, we get m = (7 - (-3))/(-9 - (-6)) = 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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Complete Question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is the equation?A mathematical statement that expresses the equivalence of two expressions is known as an equation. It typically consists of two expressions on either side of an equal sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7), and (-6,-3)(−6,−3) can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y₂ - y₁)/(x₂ - x₁). Plugging in the coordinates, we get
m = (7 - (-3))/(-9 - (-6))
= 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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The complete question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
What is the formula for number pattern?.
The formula for number pattern is an = dn - c.
A series or sequence that frequently repeats itself is referred to as a pattern. In our daily lives, we notice patterns in things like colours, behaviours, shapes, numbers, etc. They can be finite or infinite and related to any phenomenon or thing. A group of integers that are arranged in a pattern according to a predetermined rule are called a pattern in mathematics. These guidelines specify how to compute or resolve issues. For instance, every number in the series 3,6,9,12, increases by 3. The pattern predicts that the final number will be 12 + 3 = 15.
The most frequent kind of mathematical pattern is a number pattern, in which a list of numbers is arranged in a certain order according to a rule. Algebraic or mathematical patterns, geometric patterns, and the Fibonacci pattern are the various sorts of number patterns.
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how do i do 4/2 + 8?
Answer:
If that means division then here
Step-by-step explanation:
4/2=2
then,
2+8=10
Write the ratio 1.8 : 4.2 inches Simplest for
The most simplified form of the given ratio 1.8: 4.2, which is a ratio of lengths in inches is 3/7.
What is meant by ratios?
In mathematics, a ratio shows how frequently one number appears in another. When expressed as a:b, a fraction has the form of a ratio. A ratio is a comparison or compressed version of two identical values. Like fractions, ratios can be entirely simplified. Divide all of the numbers in a ratio by the same number to make it simpler. Divide each integer in a ratio by their largest common factor to fully simplify the ratio. The ratio's numbers must always be whole numbers.
Given the ratio, 1.8: 4.2
The ratio can be simplified by dividing both the terms in the ratio by the highest common factor.
The highest common factor of 1.8 and 4.2 is 0.6.
So we divide both terms by 0.6.
1.8: 4.2 = 1.8/0.6 : 4.2/0.6 = 3:7
Therefore the simplified form of the given ratio, 1.8: 4.2 is 3:7.
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what’s a geometry concept you’ve learned or found really helpful
Hey there!
There are various concepts that are used in the world of Geometry, however there are some simple concepts that may be easier to work with.
Simple Concepts in GeometryPoints - In geometry, a point is a location represented often by a dot on a x-y graph. The point does not have any length, width, shape or size, it only has a position.Lines - In geometry, a line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.Segments - In geometry, a line segment is a piece or part of a line having two endpoints. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units such as feet or inches.Rays - In geometry, a ray is usually taken as a half-infinite line (also referred to as a 'half line') with one or the two points and taken to be at infinity._____________________________________________________
So, in summary to all of this, it really depends on what concepts in geometry you are currently learning and which concept(s) you personally find the most useful and helpful.
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
x^3-9x^2+27x-27; x-3
Answer:
(x-3)^3
Step-by-step explanation:
[tex]= x^3-9x^2+27x-27 \\ =(x − 3) (x² + 3x + 9) − 9x (x - 3) \\ =(x − 3) · (x² + 3x + 9 − 9x) \\ =(x-3)·(x²-6x+9) \\ =(x − 3) · (x − 3)^2 \\ = {(x - 3)}^{3} [/tex]
Or Apply cube of difference rule
[tex]{x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} [/tex]
Answer:
[tex](x-3)^3[/tex]
Step-by-step explanation:
Given polynomial:
[tex]x^3-9x^2+27x-27[/tex]
Given (x - 3) is a factor of the polynomial, divide the polynomial by the factor using long division to find the other factor:
[tex]\large \begin{array}{r}x^2-6x+9\phantom{)}\\x-3{\overline{\smash{\big)}\,x^3-9x^2+27x-27\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-3x^2)\phantom{-b0000000)}}\\-6x^2+27x-27\phantom{)}\\-~\phantom{()}\underline{(-6x^2+18x)\phantom{0000.}}\\9x-27\phantom{)}\\-~\phantom{()}\underline{(9x-27)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore:
[tex]x^3-9x^2+27x-27=(x-3)(x^2-6x+9)[/tex]
Factor (x² - 6x + 9):
[tex]\implies x^2-6x+9[/tex]
[tex]\implies x^2-3x-3x+9[/tex]
[tex]\implies x(x-3)-3(x-3)[/tex]
[tex]\implies (x-3)(x-3)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies x^3-9x^2+27x-27=(x-3)(x-3)(x-3)[/tex]
[tex]\implies x^3-9x^2+27x-27=(x-3)^3[/tex]
NEED HELP ASAP!!
Which ratio is equal to the ratios plotted on the graph?
A- 4/2
B- 2/3
C- 1/2
D- 10/14
Answer:
Hi i found the answer 3/2 could you please check your options?
if you apply the slope formula here,
12-6/8-4 gives you the value 6/4 which is 3/2
good luck!
I round two number to the nearet 1000000 and then add them together to get a total of 7000000. If both number were rounded up and one number wa le than 3000000 to tart with, what are the greatet number each could have been before being rounded?
The larger number could have been before rounding is 4000001.
We know that both numbers were rounded up to the nearest million and added together to get 7000000.
Since one number was less than 3000000 to start with and both numbers were rounded up, the greatest that the smaller number could have been before rounding is 2999999.
We can use the equation:
(x + y) = 7000000
Where x is the smaller number and y is the larger number before rounding.
We know that x < 3000000 and x = 2999999
So we can substitute these values into the equation:
(2999999 + y) = 7000000
Solving for y:
y = 7000000 - 2999999
y = 4000001
So the greatest that the larger number could have been before rounding is 4000001.
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NEED HELP ASAP! CMON
Answer:
A: x < 3
Step-by-step explanation:
Answer: x < 3
Step-by-step explanation:
We start by subtracting 6 from both sides -
x + 6 - 6 < 9 - 6
Then, we get this -
x < 3
Which is the answer
Find the length of the third side. If necessary, round to the nearest tenth. 24 10
The length of the third side will be equal to 21.81 units.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that the bigger side of the triangle is 24 and one of the legs is 10 units. The length of the third side will be calculated as,
Use the Pythagorean theorem,
B² = H² - P²
B² = (24)² - (10)²
B² = 576 - 100
B = √476
B = 21.81 units
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There was a total of 640 students at a school on Friday. Every student either walked or
ode in a bus to the school. If 45% of the total number of students walked to the school
on Friday, how many of the students rode in a bus to the school?
The answer is, the no: of students who took the bus is =352 .The given question is a percentage calculating problem.
How to calculate the Percentage?There were a total of 640 students at a school on Friday.
Every student either walked or took the bus
45% of the total number of students walked to school
Since, 45% of them walked to the school,
Therefore, percentage of the students took the bus =
100%-45% = 55%
Now, finding the number of students took the bus,
55% of 640 = 640×55/100 = 352
Hence, There were 352 students who took the bus
A ratio or value that can be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The Symbol "%" stands for it.
There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Percentage formula = (Value/Total value) × 100
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Assignment Simplity [8q² -2 [q²-2 (3q²-3q+5)
The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5) is 18q² −12q + 20.
What is simplified from?Reduce a fraction to its simplest form to simplify it. A fraction is said to be in its simplest form if both its numerator and denominator only contain the number one. As we attempt to solve fractional problems, the process of simplifying difficulties is crucial. Even after we simplify them, the fraction's value will not change. This shows that the true fraction and the simplified fraction are two equivalent fractions.
Lets Simplify
= [8q² -2 [q²-2 (3q²-3q+5)
= [8q² -2(q²−6q² +6q−10)
= 8q² + 10q² −12q + 20
= 18q² −12q + 20
Thus, The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5) is 18q² −12q + 20.
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Find the missing length.
ADEF~AVUT
D
140
37
50
U
E
60
168
T
F
DELL
Think of a career that interet you, and you would like to learn more about. What information would you mot like to learn about that career? with 5 entence
These the five sentence about the most important thing to learn about the software engineer career:
Programming language that people most neededWay to code in the most needed programming language Way to bridge an exist database to database on the program we buildWay to determine people needed and change it into programWay to build long term IT plan for corporate or companyWhat does software engineer do?Software engineer is a branch of computer engineer science that mainly work to create, secure and manipulating a software. The career on this field mostly start from :
Junior programmer or Junior developerSenior programmer or Senior developerTim managerSystem AnalystSoftware ArchitectLearn more about software engineer here
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