So, on solving the provided question, we can say that equation of diagonal WY is 13.03 units
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
by d=√((x2 – x1)² + (y2 – y1)²).
Coordinates of W = (-4,5) and Y = (3,-6)
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
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Dr. And Mrs. Tutt are married, lives in Burleson and file a joint return. The Tutts cannot
be claimed as dependents on anyone else's tax return. Their daughter, Lavender, is 19
years old, single and a full-time student away at college. Lavender earned $4,500
during the year, but her parents provided more than half of her support. Which of the
following statements is true?
The real earning of her could be less than $2250 during the year where their parents supported more than half.
What is linear equation ?
linear equation can be defined as the equation in which the highest degree of the exponent is one.
Given
The Tutts cannot be claimed as dependents on anyone else's tax return. Their daughter, Lavender, is 19years old,
single and a full-time student away at college.
Lavender earned $4,500 during the year
The real earning of Lavender could be
as her parents supported more than half.
so,
her real earning could be less than $2250
Hence , the real earning of her could be less than $2250 .
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True or False? A rectangle's area is found by adding the length of the sides and its perimeter is found by multiplying the base by the height.
Answer: The Answer is false!
Step-by-step explanation:
The area of a rectangle is found by multiplying the length by the width.
Suppose $PABCD$ is a right square pyramid with apex $P$ and base $ABCD$. If $PBD$ is an equilateral triangle with side length 6, then what is the volume of $PABCD$
The volume of a right square pyramid PABCD is 50.91 cubic units
Let l be the side length of right squared pyramid and h be the height.
We know that the formula for the volume of the right squared pyramid.
V = a²h / 3
And the formula for the height of right squared pyramid.
h = (1/√2)a
Here, the side length (a) = 6 units
So, using above formula of height,
h = (1/√2) × 6
h = 6/√2
h = 3√2 units
Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,
V = (6² × 3√2) / 3
V = 6² × √2
V = 36√2
V = 50.91 cubic units
Therefore, the volume of PABCD is 50.91 cubic units
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Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)
The value would be [tex]34^{-1} \pmod{47}=30[/tex]
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.
In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.
We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]
We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.
Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:
[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]
Now we can substitute the right side of the equation:
[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]
And now we can substitute the left side of the equation:
[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]
And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.
Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]
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The value would be 13.
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
We can use the property of modular inverse that
[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]
So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]
[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]
Hence, The value would be 13.
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What is the degree of the polynomial of 5x²y 8xy² 9?
The polynomial is a mathematical expression containing variables and coefficients and can be written as a sum of terms of various degrees. In this case, the polynomial is composed of three terms of varying degrees: 5x²y, 8xy² and 9. The degree of this polynomial is the highest degree of the terms, which is 4.
1. Identify the terms of the polynomial: 5x²y, 8xy² and 9
2. Identify the degree of each term: 5x²y has degree 3, 8xy² has degree 4 and 9 has degree 0
3. Determine the highest degree among the terms: The highest degree is 4
4. The degree of the polynomial is then the highest degree among the terms, which is 4.
A polynomial is a mathematical expression consisting of variables and coefficients and can be written as a sum of terms of varying degrees. In this case, the polynomial consists of three terms: 5x²y, 8xy² and 9. To determine the degree of the polynomial, we must first identify the degree of each term. The term 5x²y has degree 3, the term 8xy² has degree 4 and the term 9 has degree 0. The degree of the polynomial is then the highest degree among the terms, which is 4. This means that the polynomial has a degree of 4, as the highest degree among its terms is 4. The degree of a polynomial is an important factor in solving equations and other mathematical problems, as it can determine the complexity of the equation.
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x:(x+3) = 2:3
work out the value of x
Answer:
x = 6
Step-by-step explanation:
x:(x + 3) = 2:3
[tex] \frac{ \\ x}{x + 3} = \frac{2}{3} [/tex]
cross multiply
3x = 2(x + 3)
3x = 2x + 6
subtract (2x) from both sides
3x – 2x = 2x – 2x + 6
x = +6
x = 6
How do you write log in e form?
Log to exponential form is very useful to easily perform complicated numeric calculations. The logarithmic form
loga N=x
can be easily transformed into the exponential form as:
ax=N
Normally, large astronomical and scientific calculations are written in exponential form, and here we can use the log to exponential form of transformation.
Logarithms are occasionally transformed using antilog tables to normal form, rather than transforming into exponential form.
Log to exponential form required specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction.
And exponentials help in working across numbers with different bases and different powers.
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Translate each sentence into an equation!!!
1)Seven more than six times a number is 17.
2)Four less than five times a number is 11.
3)Six times the quantity, x-2, is 24.
4)Three less than six times a number is five more than twice the number.
5)Two more than the product of -3 and a number is 11.
Answers:
1. 6x + 7 = 17
2. 5x - 4 = 11
3. 6(x - 2) = 24
4. 6x - 3 = 2x + 5
5. (-3x) + 2 = 11
Step-by-step explanation:
Since your only translating the sentence and not actually solving, we don't need to determine a specific number. So in that case, whenever the question says "a number," use a variable such as x.
1. Seven more would mean +7, so your adding 7 to x. X is multiplied by 6, so your answer is 6x + 7 = 17.
2. X is being multiplied by 5, and 4 less means -4 so you get 5x - 4 = 11
3. X-2 is being multiplied by 6, so indicate that in parenthesis. You should then get 6(x - 2) = 24
4. This one is a little different, since it doesn't equal a direct number. X is being multiplied by 6, and 3 is getting subtracted from it so the first part is 6x - 3 and it equals X multiplied by 2 plus 5. Put it all together and you get 6x - 3 = 2x + 5
5. The word product means multiplication so you know that -3 is being multiplied with X. Again, indicate this in parenthesis. You should get (-3x) + 2 = 11
I hope this helps you! Have a good day/night! :)
HELPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPLEASEEEEEE
Answer: $49
Step-by-step explanation:
2.5% of 40 = 1, 9x1= 9, 40+9 = $49
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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Given: 3ab = 7ad and 3ac = 7ae prove: δabc ~ δade triangles a b c and a e d are connected at point a. complete the steps of the proof. ♣: ♦:
The given problem has been proved below using the rules of Congruence.
The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.
Given that,
3AB=7AD
3AC=7AE
So, by re-arranging them we get the same ratio that is,
AB/AD=7/3
AC/AE=7/3
Hence, we can conclude that,
AB/AD=AC/AE
Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.
But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.
So, SAS property ∆ABC~∆ADE is proved in the end.
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Kate loves to read. She wants to read all 70 books in her bookcase and has already finished 2. Write an equation to represent the time it will take for Kate to read all 70 books if she can read 3 books per month.
Answer:
simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month
Step-by-step explanation:
An ice cream factory makes 310 quarts of ice cream in 10 hours how many quarts could be made in 48 hours what was the ate per day
The factory can make 744 quarts of ice cream per day.
To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:
310 quarts / 10 hours = x quarts / 48 hours
To solve for x, we can cross multiply:
310 quarts * 48 hours = 10 hours * x quarts
x = (310 quarts * 48 hours) / 10 hours = 1480 quarts
So the factory could make 1480 quarts of ice cream in 48 hours.
To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:
rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day
So the factory can make 744 quarts of ice cream per day.
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Multiply (x-3)(4x+2) using the FOIL method. Select the answer choice showing the FOIL method products
The result of (x-3)(4x+2) using FOIL method is 4x^2 -6x +2x -6.
The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and follows these steps:
First: Multiply the first term of the first binomial by the first term of the second binomial
Outer: Multiply the first term of the first binomial by the second term of the second binomial
Inner: Multiply the second term of the first binomial by the first term of the second binomial
Last: Multiply the second term of the first binomial by the second term of the second binomial
Applying FOIL method to (x-3)(4x+2) we get:
First: 4x * x = 4x^2
Outer: 4x * -3 = -12x
Inner: -3 * 4x = -12x
Last: -3 * 2 = -6
So the result of (x-3)(4x+2) is 4x^2 -12x -12x -6 = 4x^2 -24x -6.
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how many even numbers of 3 digits can be formed of the digits 1,2,3,4,5,6 when repitition of digits is allowed
Answer:
To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed, we can use the formula for permutations:
Step-by-step explanation:
Number of permutations = (number of choices for the first digit) x (number of choices for the second digit) x (number of choices for the third digit)
In this case, we have 6 choices for each digit, since we are allowed to repeat the digits. Using the formula, we get:
Number of permutations = 6 x 6 x 6 = 216
Therefore, there are a total of 216 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6, with repetition allowed.
However, not all of these will be even. For a number to be even, the last digit must be even, so the last digit can only be 2, 4, or 6. This means that there are 3 choices for the last digit.
Therefore, the total number of even 3-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 is 366=108.
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028)
the cost to insure jewellery is a fixed amount plus a percentage of the value of the jewellery. it costs 32$ to insure 1000$ worth of jewellery or 44.5$ to insure 3500$ worth of jewellry.what is the fixed amount to insure jewellery?
i wrote jewellery so much it isnt a word anymore send help ( explanatio ) asap!
Answer:
The fixed cost to insure jewellery is $0.602.
Step-by-step explanation:
We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:
1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)
3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)
We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.
From equation (1)
y = (32 - 1000x) / 1000
then substitute this in equation (2)
3500x + 3500((32-1000x) / 1000) = 44.5
3500x + 32 - 3500x =44.5 - (1000x)
-20x = -12.05
x = 0.602 $
So, the fixed cost to insure jewellery is $0.602.
That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.
Select the correct answer from each drop-down menu. A picture frame with an area of 60 square inches has a width, w, and a height that is 4 inches greater than the width. Write an equation to represent the area, and solve to find the width. Equation: Of the two solutions, only a width of inches makes sense in the context of the problem. Reset Next
The width of the picture frame with the given area would be = 3.9in
What is a frame?A frame is a structure that can be a rectangle or a square shape which is used to display a picture.
The area of the frame = 60in²
The width of the frame = x
The height of the frame = 4x
The area of a rectangle = length×width
That is ; 60 = X × 4x
60 = 4x²
make X the subject of formula;
X = √60/4
X = √15
X = 3.9 in.
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What word is used to remember the 3 trigonometric ratios?
The word used to remember the 3 trigonometric ratios sine, cosine, and tangent is SOH-CAH-TOA
We know that in right triangle for an angle θ, the trigonmetric ratios are:
sin(θ) = opposite side of θ/ hypotenuse
cos(θ) = adjacent side of θ / hypotenuse
tan(θ) = opposide side of θ / adjacent side of θ
cot(θ) = 1/tan(θ)
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
The word 'SOH-CAH-TOA' is used to remember the sine, cosine, and tangent ratios in a right triangle.
SOH means, Sine = Opposite side / Hypotenuse.
CAH means, Cosine = Adjacent side / Hypotenuse.
TOA means, Tangent = Opposite side / Adjacent side
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50 POINTS! Calculate the expression in the most efficient way possible. Show steps.
5^1125 * 0.2^1123
Answer:
25
Step-by-step explanation:
Given expression:
[tex]5^{1125} \times 0.2^{1123}[/tex]
Rewrite 0.2 as a fraction:
[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]
Simplify the numerator by applying the exponent rule a¹ = a:
[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]
[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]
[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 5^{1125-1123}[/tex]
Simplify the exponent:
[tex]\implies 5^{2}[/tex]
Simplify:
[tex]\implies 5 \cdot 5[/tex]
[tex]\implies 25[/tex]
if i drank x ounces of juice and someone drank 1/3 more than that what is your equation.
Answer:
y = x + 1/3
Step-by-step explanation:
We know
You drank x ounces of juice and someone drank 1/3 more than what you think
Let's y represent the total, we have the equation
y = x + 1/3
Answer: 4/3x (or 1/3 + x, since your wording's pretty odd)
Step-by-step explanation:
i can't tell if the one-third you're referring to is a third of how many ounces of juice you drank (meaning it will change if you drank 1, 2, 3 oz of juice and so on) or if it's always going to be a third of an ounce more than the amount of oz of juice you drank (in which case it'd be 1/3 + x). anyway just choose whichever answer you're looking for :3
The areas of the squares adjacent to two sides of a right triangle are 29.2529.2529, point, 25 units^2 2 squared and 131313 units^2 2 squared. 13\text{ units}^213 units 2 29.25\text{ units}^229.25 units 2 xx Find the length, xxx, of the third side of the triangle.
Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The data given is -
Assume a, b and c are sides of right-angled triangle.
Then, two adjacent sides of right-angled triangle are -
a^2=29.25 squared units
b^2=13 squared units
The unknown side c is taken to be x.
Find the length of c using Pythagoras Theorem -
c^2=a^2+b^2
where, c is the hypotenuse, a is the perpendicular and b is the base.
Plugging the values in the equation -
x^2=29.25+13
x=√(29.25+13)
x=√42.25
x=6.5
Therefore, the third side measures x=6.5 units.
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What is the slope of the line that contains the points (-3, -7/2) and (2, -4)
Answer: m = -1/10
Step-by-step explanation:
Use the slope formula to find the slope m.
m = −1/10
Is Avogadro's number the same for all elements?
The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.
What is an atom?
Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.
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Find the value of x in the following equation:
3.5(5x + 4) = 17.5x + 14
No solution
Infinite solutions
x = 0
x = 1.3
The system of equations .5(5x + 4) = 17.5x + 14 have Infinite solutions.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, A system of equation 3.5(5x + 4) = 17.5x + 14.
17.5x + 14 = 17.5x + 14.
As the LSH and RHS are equal the equation of the two lines is the same and hence they coincide and have an infinite number of solutions.
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15 points...................................
Answer: D
Step-by-step explanation:
The statement says that the angles GIH and QRS must be the same measurement. To show that on diagrams, we use markings : if angles have the same markings, then it means they have the same measurement.
That way, we just need to see which diagram has the right measurements.
First, the angles GIH and QRS are the angles we see named by the letter in the center : then GIH and QRS.
So it must be the angles with letters of I and R that have the same markings.
A : doesn't work for I and R
B : doesn't work for I and R
C : doesn't work for I and R
D : works for I and R
it should be the D, of course if I didn't see well don't hesitate to make sure it's correct with what I said before :)
Answer:
the answer would be D
Step-by-step explanation:
the answer is D because of the person above me
13. Solve:* 3b⁴ x 6b² =
Answer:
18b^6
Step-by-step explanation:
3b⁴ x 6b²
which system of inequalities is represented on this graph? NEED THIS ASAP picture below
Complete the equation of the line who’s y intercept is (0,-1) and slope is 4
Y=4x-1
The equation of a line is:
Y=mx+c
We are told that the slope is 4 which is also gradient, meaning that M=4
Now we are left with:
Y=4x+c
There are two ways to get C:
1. We know that C represents the y-intercept so immediately we can conclude that C=-1
2. You can work it out by substituting the coordinate for the X and Y value:
-1=4(0)+c
-1=C
So in conclusion, the equation of the line is:
Y=4x-1
Hexagon K is a scaled copy of Hexagon J
The scale factor 5/2 takes hexagon J to hexagon K.
What is Hexagon?A hexagon or sexagon in geometry is a six-sided polygon or 6-gon that forms the shape of a cube. Any basic hexagon has 720° in total internal angles. No matter the type of hexagon, all of them have six sides. As a result, all types of hexagons—regular, asymmetrical, concave, and convex—have six sides. The hexagon, which has six sides mathematically, is particularly intriguing because it covers a plane with units of equal size and leaves no empty space. Because of its 120-degree angles, hexagonal packing also reduces a given area's perimeter.Hexagon AB, a leader in virtual reality hardware and software, was founded in 1992 and is a publicly traded, multinational information technology business with its headquarters in Stockholm, Sweden. Hexagon's B share is listed among the top firms by the Stockholm Stock Exchange.From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.
The scale factor = the ratio of edges
Scale factor = 20/8 = 30/12 = 5/2
Hence, the scale factor 5/2 takes hexagon J to hexagon K.
Complete question:
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what is 60 to the power of 3/2? not sure how to calculate it
Answer: 108000
Step-by-step explanation: Here's how I got my answer:
So, first, we need to know something. Whenever there's a fraction, you need to do this. I'll show you the numbers for this problem:
(60^3) / 2
So, the numerator goes in parentheses, and the denominator is what we are dividing by. So, 60^3 is the same as 60 x 60 x 60. You'd get 216000. Then, divide by 2 to get 108000. I hope this helps!
TIP: do NOT turn 3/2 into an improper fraction; 1 1/2. You would get a completely different answer.