Answer:
25x^6y^2
Step-by-step explanation:
Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.
how many 1/3 inch cubes does it take to fill a box with width 1 1/3 inches, length 1 1/3 inches, and height 1 2/3 inches?
The number of 1/3 inch cubes that will fill the box is 26.
Volume of an object.The volume of an object is the amount or quantity of substance that it would conveniently contain. Different objects has their method of determining their volume depending on their shapes.
Given a cube of length 1/3 inch. The volume of the cube can be determined as;
volume of a cube = length x width x height
The volume of the cube = 1/3 * 1/4 * 1/3
= 1/9 cube inches
The volume of the box can be determined as;
Volume of the box = length x width x height
= 1 1/3 * 1 1/3 * 1 2/3
= 2.963 cubic inches
Volume of the box = 2.963 cubic inches
The number of 1/3 inch cubes that will fill the box = 2.963/ (1/9)
= 26.667
The number of 1/3 inch cubes that will fill the box is 26.
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What is the image of ( 12 , − 4 ) (12,−4) after a dilation by a scale factor of 1 4 4 1 centered at the origin?
What is the image of ( 12 , − 4 ) after a dilation by a scale factor of 1/4 centered at the origin is (3, -1)
What is transformation?Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease of a figure by a scale factor k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.
The point (12, -4) is dilated by a scale factor of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)
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How do you calculate the number of seeds per acre?
1. Convert lb./acre to grams/acre
2. Use the TKW to calculate seeds per acre.
What is acre?The imperial system and US customary systems both use acres as a measure of land area.
According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.
A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.
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A cereal box is designed to hold a volume of 4096 cubic centimetres of cereal.
What dimensions will minimize the cost of producing the box?
Answer:
Refer to the step-by-step
Step-by-step explanation:
To minimize the cost of producing the box, we would want the box to be a cube.
Where the volume, [tex]V=s^{3}[/tex], where s is the length of one side of the box.
We were given the value, [tex]V=4096 cm^{3}[/tex], plug this into the equation above so we can find the dimensions of the box...
[tex]4096=s^{3} = > s=\sqrt[3]{4096} = > s=16[/tex]
Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.
What is the domain of the function f/x )= log?
The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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Number 9 is very confusing for me
Answer:
The value of x is 2/7 or 0.285
Step-by-step explanation:
Here, we will make equivalent expressions in the equation that all have equal bases.
6²⁽⁶ˣ⁻¹⁾ = 6⁵ˣ
Since, The bases are the same i.e., 6. So, exponent are also same
2(6x - 1) = 5x
Solve for x
12x - 2 = 5x
12x - 5x - 2 + 2 = 5x - 5x + 2
7x = 2
7x/7 = 2/7
x = 2/7 = 0.285
Thus, The value of x is 2/7 or 0.285
For verification
36⁶ˣ⁻¹ = 6⁵ˣ
36⁶⁽⁰°²⁸⁵⁾ ⁻ ¹ = 6⁵⁽⁰°²⁸⁵⁾
36¹°⁷¹ ⁻ ¹ = 6¹°⁴²⁵
36⁰°⁷¹ = 6¹°⁴²⁵
12.7 = 12.7
Hence, L.H.S = R.H.S
VERIFIED!!
What is the product of 2x 3y )( 2x 3y )? *?
The product of (2x-3y)(2x+3y) is 4x^2-9y^2.
the solution of the question is as follows,
Product = (2x-3y)(2x+3y)
Product =2x(2x+3y)-3y(2x+3y)
Product = 2x(2x)+2x(3y)-3y(2x)-3y(3y)
{using distributive property of multiplication}
Product = 4x^2 +6xy - 6xy -9y^2
solving 6xy-6xy=0,
Product = 4x^2 - 9y^2
4x^2-9y^2 is the product of (2x-3y)(2x+3y).
distributive property of multiplication
This property states that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a - b)(a + b) is equal to a^2 - b^2. This result is used as an identity.
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Which cube root function is always decreasing as x increases?
○ f(x) Jm³√x – 8
O
f(x) = 3√√x-5
f(x)=√√-(5-x)
f(x) = -3√x+5
Option D) f(x) = -3√x+5 is the cube root function is always decreasing as x increases
What is the Formula of Cube Root Function? f(x) = x is the formula for the fundamental (parent) cube root function. After transformations, it can alternatively take the form f(x) = a (bx - h) + k. Here, the transformations are denoted by the real numbers a, b, h, and k.The symbol "" designates the cube root. For instance, 8 Equals (2 + 2 + 2) = 2. Finding the cube root of a number is simple since 8 is a perfect cube number.You need to discover a number that, when multiplied twice by itself, equals the original number in order to get the cube root of a given integer. To get the cube root of 8, then, you need to identify the integer that, when multiplied by itself twice, equals 8. Therefore, since 2 2 2 = 8, the cube root of 8 is 2.Given data :
y = ³[tex]\sqrt{x}[/tex] is an increasing function as when the value of x increases the value of y increases
And when the value of x decreases , the value of y also decreases.
Now if we have (x+a) or (x-a) instead of x, the function shall have a horizontal shift.
So it shall either move left or right but shall not flip.
So
y = ³[tex]\sqrt{(x - 8)}[/tex] and y = ³[tex]\sqrt{(x - 5)}[/tex]
are increasing functions.
Only when x becomes -x, that the function shall flip & shall become a decreasing function.
But then it must be - (x-a) or -(x+a) inside.
So
y = ³[tex]\sqrt{-(5 - x)}[/tex] is also increasing
Only
y = ³[tex]-\sqrt{(x + 5)}[/tex] is a decreasing function.
Option D) is the right answer.
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A standard six-sided die is rolled, and P is the product of the five numbers that are visible. What is the largest number that is certain to divide P?
A. 6 B. 12 C. 24 D.14 E.720
The largest number which certain to divide P is 12. The correct option is B.
The product of all six numbers of the six-sided die is 6! = 720.
The products of numbers which can be visible are:
720 / 1, 720 / 2, …, 720 / 6.
In this case, the answer is the largest common divisor, that is:
720 / L
where L = the least common multiple of {1,2,3,4,5,6}.
So, it is clear that L = 60.
Thus, the answer is:
= 720 / L
= 720 / 6
= 12
Hence, the largest number which certain to divide P is 12, it is option B.
What is the largest number in the world?A Googolplex is studied to be the largest number in the world. It is stated as 10^googol. The number 10^googol can also be written in the exponential format which will equal 10^10^100. When writing the number googol in normal number writing format, the probability of losing count is very high. Thus, it is more convenient to write it in the form of exponent and powers.
The number googolplex is so extremely large which is unimaginable to be expressed in number writing format. Hence, the number remains a concept as it is of no use in mathematics for basic calculations.
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What is the domain of exponential function f/x )= BX?
The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).
What is interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .
Given exponential function is f(x) = B^x.
A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.
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Which techniques can be used to evaluate the expression 12. 75÷1. 5? Select all that apply.
The division technique can be used to evaluate the given expression
12.75÷1. 5
The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/).
“p divided by q” can be written as: (p÷q) or (p/q).
The method of verification can be expressed as:
Dividend = (Divisor × Quotient) + Remainder.
The given equation is:12.75÷1.5
We'll first write the above decimal numbers in fractional form.
12.75÷1.5
1275/100÷15/10
2. Now we'll divide it further.
⇒1275/100÷15/10
⇒1275/100×15/10
⇒1275/10×15
⇒225/10×3
⇒88/10
3. And finally, we'll write our quotient in decimal form.
⇒88/10
⇒8.8
ㅤ
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(2x + 5) (4x − 3) (5x - 4) can be expanded and fully simplified to give an expression of the form ax³ + bx² + cx + d.
Work out the values of a, b, c and d.
Answer:
To expand (2x + 5) (4x − 3) (5x - 4), you can use the distributive property and the FOIL method.
The distributive property states that for any two algebraic expressions a and b, and for any two numbers x and y, (a+b)(x+y) = ax + ay + bx + by.
The FOIL method is a way to multiply two binomials. It stands for First, Outside, Inside, Last, and it involves multiplying the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.
Using these methods, you can expand (2x + 5) (4x − 3) (5x - 4) as follows:
(2x + 5) (4x − 3) (5x - 4) = (2x)(4x)(5x) + (2x)(4x)(-4) + (2x)(-3)(5x) + (2x)(-3)(-4) + (5)(4x)(5x) + (5)(4x)(-4) + (5)(-3)(5x) + (5)(-3)(-4)
This can be simplified to:
= 40x³ - 32x² - 60x³ + 48x² - 20x³ + 15x² + 60x - 20x + 100x² - 20x + 12
Combining like terms, we get:
= -12x³ + 143x² + 100x + 12
So, the values of a, b, c, and d are a = -12, b = 143, c = 100, and d = 12.
Step-by-step explanation:
In a '15% off sale, Freya bought a DVD player for £179. 99. What was the original price of this
DVD player?
The original cost of the DVD player is $ 211.75.
Calulating Original price:
To calculate the original price of an item in case of giving a discount we can use the following formula
Original Price = Selling Price / (1 - Percentage Discount/100)
(Or)
We can calculate the original price by taking a variable as the cost of the item as given below
Here we have
In a '15% off sale, Freya bought a DVD player for £179. 99
Let 'x' be the cost of the DVD player
Then the cost of the DVD player after giving a 15% discount
= x - 15% of x
= x - (15/100) x
= x - 0.15x
= 0.85x
Given that
Freya bought a DVD player for £179. 99
=> 0.85x = 179. 99
=> x = 211.75
Therefore,
The original cost of the DVD player is $ 211.75.
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Find C using Special right triangles
The length c of the right angle triangle is 9 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.
The sides of a right angle triangle can be found using trigonometric ratios as follows:
Therefore,
sin 60° = opposite / hypotenuse
where
opposite side = c
hypotenuse side = 6√3 ft
Hence,
sin 60° = c / 6 √3
cross multiply
c = 6√3 × sin 60
c = 6√3 × √3 / 2
c = 6 × 3 / 2
c = 18 / 2
Therefore,
c = 9 units
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A square has an unknown side length, 2x. Write a simplified expression for its perimeter (distance around the
outside of an object. Remember, side plus side plus...)
The simplified expression for its perimeter and area are 8x.
What is the perimeter of a square?The perimeter of a square is the sum of the lengths of all the sides of a square. Thus, by summing the lengths of a square's four sides, we can get its perimeter.
An equal number of sides make up a square. As a result, the side of a square is added four times to determine the square's perimeter.
The formula for finding the Perimeter of square = 4*a
= 4 * 2x
= 8x
Perimeter of square = 8x
Hence, the simplified expression for its perimeter is 8x
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25
1 point
(3x + 32)
(5x - 8)
Select the correct equation to solve for x,
3x + 32 + 5x - 8 = 180
3x + 32 = 5x - 8
3x + 32 + 5x - 8 = 90
The value of x is 20
Now, According to the question:
The given equation is:
3x + 32 = 5x - 8
To solve the equation for finding the value of x .
32 + 3x = -8 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
32 + 3x -5x = -8 + 5x -5x
Combine like terms:
3x -5x = -2x
32 -2x = -8 + 5x -5x
Combine like terms: 5x -5x = 0
32 -2x = -8 + 0
32 -2x = -8
Add '-32' to each side of the equation.
32 -32 -2x = -8 -32
Combine like terms: 32 -32 = 0
0 -2x = -8 -32
-2x = -8 -32
Combine like terms: -8 -32 = -40
-2x = -40
Divide each side by '-2'.
x = 20
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How to solve the variables
Heyyyyyyyy how u doing I. Doing good how abt yo self
Find the value of x.
2x-8
6
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent.
[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]
Sunnyvale School is having their
annual lobster race. A team
consists of five lobsters. The
team score is the average of the five finishing place positions. His sister sally’s team has consistently finished behind his team, however, an unusual pattern has been noticed. For example, Sally’s first lobster finished right behind Peter’s first lobster. Her second lobster finished 2 places behind peter’s second lobster. Her third lobster finished 3 places behind peter’s third, her fourth was 4 places behind his fourth and her fifth was 5 places behind his fifth.
What is Sally's team score?
Sally's team score is 6.
We can determine Sally's team score by calculating the average of her team's finishing place positions.
From the information given, we know that:
Sally's first lobster finished one place behind Peter's first lobster.Sally's second lobster finished 2 places behind Peter's second lobster.Sally's third lobster finished 3 places behind Peter's third lobster.Sally's fourth lobster finished 4 places behind Peter's fourth lobster.Sally's fifth lobster finished 5 places behind Peter's fifth lobster.If we assume that Peter's team finished in 1st, 2nd, 3rd, 4th and 5th places, then we can calculate Sally's team score as follows:
Sally's first lobster finished in 2nd placeSally's second lobster finished in 4th placeSally's third lobster finished in 6th placeSally's fourth lobster finished in 8th placeSally's fifth lobster finished in 10th placeTo find the average of the five finishing place positions, we add up all the places and divide by 5:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
So, Sally's team score is 6.
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Isabel is shopping for her new car. She identified six models she likes at a local dealership. The table lists
the down payment she would need to make on each car to keep the monthly payment within her budget.
Assume that she's using only the money accumulated in her savings account to make the down payment.
Use this information and the appropriate time value of money formula e to select all the cars that are
within Isabel's budget.
5
choice 1
choice 2
choice 3
down payment: $8,500 down payment: $6,200 down payment: $5,100
choice 4
choice 5
choice 6
down payment: $7,250 down payment: $7. 750 down payment: $7,500
The value of Isabel's account after three years can be calculated using the future value of the annuity formula.
Isabelle's budget car is:
Choice 2Choice 3Choice 4Reason:
Monthly savings, PMT = $200
Account compound interest, r = 1.7%
t = Account value after 3 years is displayed as increase.
We know that:
[tex]FV =PMT * \frac{[(1+i)^n -1]}{i}[/tex] --------------------- (1)
Where;
i = r/12
⇒ n = 12 × t
From the above equation(1), we get:
[tex]FV =200 * \frac{[(1+\frac{1.7}{2} )^{12*3} -1]}{\frac{1.7}{12} }[/tex]
≈ 7381.4
Therefore,
The budget cars she can buy, those that require a down payment of less than $7,381.4, which are:
The required down payment of choice 02 is $6200.
The required down payment of choice 03 is $5100.
The required down payment of choice 04 is $7250.
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Find the mean, median, and mode of the data. Choose the measure that best represents the data. Explain your reasoning. 2. 55,65,49,22,56,65,61,57. 4. 20.1, 13.4, 9.8, 21.3, 20.8, 19.1, 68.1, 22.6
Answer:
2. mean: 53.75; median: 56.5; mode: 65; median is best
4. mean: 24.4; median: 20.45; no mode; median is best
Step-by-step explanation:
You want the mean, median, mode, and best representation of the data for data sets ...
2. — 55,65,49,22,56,65,61,57
4. — 20.1, 13.4, 9.8, 21.3, 20.8, 19.1, 68.1, 22.6
Mean
The mean of the data is the sum of the data values, divided by the number of data values.
MedianThe median data value is the middle of the sorted list, or the average of the two middle values. Here, there are an even number of data values in each list, so the median is the average of the middle two.
ModeThe mode of the data set is the value that is repeated most often. A data set may have multiple modes. Here, where one of the datasets has no repeated values, we describe it as having "no mode."
Data set 2The first attachment shows the descriptive statistics are ...
mean: 53.75median: 56.5mode: 65The data is skewed to the left, with the value 22 being an outlier. This value reduces the mean. The mode is the maximum value in the data set, so it does not fairly represent the data, either.
The median best represents the data.
Data set 4The second attachment shows the descriptive statistics are ...
mean: 24.4 median: 20.45mode: none (no repeated values)The data is skewed to the right, with the value 68.1 being an outlier. This tends to raise the mean above what it would otherwise be. There is no mode.
The median is best represents the data.
<95141404393>
Which statement correctly describes this picture?
Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. In how many week will he have enough money to the bike?Use the bar diagram to solve arithmetically. Then use an equatuio to slove algebraically.
Answer:
It will take him 9 weeks to be able to buy the bike.
Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.
What were the steps to lead us to this answer?So, we have:
- Cost of the bike = $189
- Money saved = $99
- Money saving each week = $10
We are trying to find how many weeks will he have enough money to the bike.
So, we are going to multiply and add the numbers to find are answer:
→ (n × $ 10) + $ 99 = $ 189
→ n × $ 10 = $ 90 n = $ 90 $ 10 n=9 weeks.
Therefore, Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. The correct answer is 9 weeks.
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If m/KLH = 134°, solve for x.
19=134+2
H
25°
N
(4x + 9)°
L
K
Step-by-step explanation:
KLH is a triangle, and the sum of all angles in a triangle is 180°.
now, we know the angle at L = 134°.
because of the symmetry of the angles in such a regular parallelogram, the upper angle at H is 25°, and the lower angle at H (one of the angles in our triangle) is (4x + 9)°.
and the upper angle at K is (4x + 9)°, and the lower angle at K is 25°.
so, we have
180 = 134 + 25 + (4x + 9) = 159 + 4x + 9 = 168 + 4x
12 = 4x
x = 12/4 = 3
What is an example of an absolute value equation?
The absolute value of a given number is said to be the positive version of that number. For example, the absolute value of -5 is + 5, which can be written as: − I5 | = 5. Other examples of absolute values of numbers: |−9| = 9, |0| = 0, − |−12| = −12, etc.
Absolute Value Equation:
An absolute value function is an algebraic function whose variables lie within the absolute value bar. This function is also called the modulus function, and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. In general, the absolute value function can be expressed as f(x) = a |x - h| + k, where a represents how much the graph stretches vertically, h represents the horizontal shift, and k represents the vertical shift of the graph for f(x) = |x|. represents If the value of 'a' is negative, the chart opens downwards, if positive, the chart opens upwards.
Now that we understand the meaning of the absolute value function, we understand the meaning of the absolute value equation f(x) = a |x - h|. + k and how the values of a, h, and k affect the value of the function.
'a' value determines how the graph of f(x) is stretched vertically.'h' value specifies horizontal displacement'k' value specifies the vertical displacementThe vertex (x) = a |x - h| + k of the absolute expression f is given by (h, k). You can also use the vertices of f(x) = a |x - h| Find + k using the formula (x - h) = 0 . When determining the value of x, substitute that value into the formula to find the value of k.
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solve for x and graph the solution on the number line below 7+x<16
Step-by-step explanation:
x<16-7x<11.....................
What is the slope of this line? (5 points)
Show all work.
Slope of the line AB is 7/6.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given graph the coordinates of A are (4, 3) and B is (-2, -4)
Slope AB=-4-3/-2-4
=-7/-6
Slope=7/6
Hence, slope of the line AB is 7/6.
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what is -2/5 plus 4/3
The required solution to the given statement is 14/15.
What is the Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers. For example, the LCM of 4 and 5 is 20; 20 is the smallest number that is both a multiple of 4 and a multiple of 5
The statement is given in the question below as:
-2/5 plus 4/3
Here "plus" represents the addition sign (+)
So, the algebraic form of the above statement will be as:
⇒ -2/5 + 4/3
Take the LCM between the fractions, we get
⇒ ( -6 + 20)/15
⇒ 14/15
This means 14/15 is obtained from -2/5 plus 4/3.
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Please solve area of figure
Formula and radius of figure in the picture
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
How can you calculate area using pi and radius?A circle's area is equal to pi times the radius squared (A = r2).
Pi times the radius r squared equals the area of a circle.
π ⋅ ( r a d i u s)2
In the formula for the area of a circle, substitute the value of the radius r =3. 3.14 is about how big a number pi is.
pi * 3^2
Raise 3 to the power of 2 to arrive at 9.
pi * 9
9 must be moved to the left of. 9 pi ( x y ^3 )^3.
Area of circle and formula and radius of circle is 9 pi ( x y ^3 )^3.
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What is the secret calculator app?
The secret calculator app is used to protect confidential Photos, Videos, Documents, Passwords, Notes, Contacts and To Dos.
The term calculator is referred as a device that performs arithmetic operations on numbers and it does the basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.
Here we need to find definition and the usage of secret calculator app.
As per the definition of calculator here we know that the app is used to acts like a photo vault to store all password protected files, and can only be viewed inside the app.
As the user who is unaware of this app you will never expect a simple calculator looking app is used to hide files.
Here if you want to access this you will need the password to open the photos from your child.
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