The answer is 102.93174866
The Karatsuba set of rules becomes the primary multiplication set of rules asymptotically quicker than the quadratic "grade faculty" algorithm. The Toom–cook algorithm (1963) is a faster generalization of Karatsuba's technique, and the Schönhage–Strassen algorithm (1971) is even quicker, for sufficiently big n.
Multiplication is the main device for lots of forms of maths which include algebra, calculus, equations, and greater. The capacity to rehearse and understand multiplications up to and such as 12 by means of the final yr of number one college will permit your toddler to with a bit of luck and skillfully address greater complex mathematical topics.
Familiarity and skillability with the primary timetables are essential building blocks in math. It opens the door to multi-digit multiplication and demystifies tactics like long department and simplifying fractions. It lays the foundation for algebra.
Multiply 10 by
10.100+10(−√3)+√6⋅10+√6(-√3)
Multiply −1 by 10.100-10√3+√6⋅10+√6(−√3)
Move 10 to the left of
√6.100-10√3+10.√6+√6(−√3)
Multiply √6(−√3).
Combine using the product rule for radicals.
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{6.3}[/tex]
Multiply 6 by
3.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{18}[/tex]
Rewrite 18 as 32⋅2.
Factor 9 out of
18.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{9}[/tex](2)
Rewrite 9 as
32.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{32.2}[/tex]
Pull terms out from under the radical.
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−(3[tex]\sqrt{2}[/tex])
Multiply 3 by −1.100−10[tex]\sqrt{3}[/tex]10[tex]\sqrt{6\\}[/tex]−3[tex]\sqrt{2}[/tex]
The result can be shown in multiple forms.
Exact Form:
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6\\}[/tex]−3[tex]\sqrt{2}[/tex]
Decimal Form:
102.93174866
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96 multiplyed by 12 multyplied by 6
Answer: 6912
Step-by-step explanation:
96x12=1,152
1,152x6=6912
James and his friend both started a part -time job at the swimming hole earning $6 per hour.James worked 10 1/2 hours his first week .James agreed to pay his friend 1/10 of his salary for gas. How much did James pay his friend for gas ?
Answer: 6.30
Step-by-step explanation:
Brainliest and 40 points! Hurry!
Answer: 6
Step-by-step explanation:
Using the scale:
1/4 in = 2 ft, what would be the real-life measurement of an object that measures 4 inches on a scale drawing?
An object that appears to be 4 inches on a scale illustration actually measures 32 feet.
What is drawing to scale?A representation of a real thing with correct sizes that has been scaled back or blown up slightly (called the scale).
The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.
A measurement of 150 mm on the picture would be 1500 mm on the actual horse since this drawing has a scale of "1:10," meaning that everything represented with a size of "1" would have an the actual world, a size of "1" corresponds to a size of "10."
based on the facts provided;
4 in =1/4 in 2ft
= 16*2 ft
= 32 ft
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2. Write and simplify an expression showing how many times farther Neptune is from the Sun
than Mercury. Write the result in scientific notation. (2 points)
The sun is [(1.974) * (10^1)] times farther from Neptune, than Mercury, mentioned in scientific notation.
As per the question statement, there is no information provided about the actual distance of the sun from Neptune, or from Mercury. Hence, let us consider that the actual distance of the sun from Neptune is [4.5 * (10^9)] kilometers, while that from Mercury is [2.28 * (10^8)] kilometers.
We are required to calculate the number of times, which the sun is times farther from Neptune, than Mercury, and express our desired answer in proper scientific notation.
Considering that, the sun is "x" times farther from Neptune, than Mercury, we can state that,
[{2.28 * (10^8)} * x] = {4.5 * (10^9)}
or, x = [{4.5 * (10^9)}/{2.28 * (10^8)}]
or, x = [{4.5 * 10 * (10^8)}/{2.28 * (10^8)}]
or, x = [{45 * (10^8)}/{2.28 * (10^8)}]
or, x = (45/2.28)
or, x = 19.7368
or, x = 19.74
or, x = [(1.974) * (10^1)]
Scientific Notation: In Mathematics, Scientific Notation is an efficient method of expressing a number, which is too large or too small, by using the form of power of (10).To learn more about Scientific Notation, click on the link below.
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Scott borrowed $985 for a new TV and game system. He made 6 monthly payments to repay the loan. He paid $155 interest. What is his simple interest rate?
Based on the amount that Scott borrowed for the new TV and game system, and the interest paid, the simple interest rate is 15.7%
What is the simple interest rate?The simple interest rate can be found by the formula:
= Interest paid by Scott on the loan / Amount Scott borrowed x 100%
Solving for the simple interest rate gives:
= 155 / 985 x 100%
= 0.1573604060913705583756345177665 x 100%
= 0.157 x 100%
= 15.7%
This means that Scott paid 15.7% on the loan he borrowed.
In conclusion, Scott's simple interest rate is 15.7%.
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One endpoint of a segment is located at (14,21) find the coordinates of the other ep if the midpoints coordinates are (41,50)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{14}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +14}{2}~~~ ,~~~ \cfrac{ y +21}{2} \right) ~~ = ~~\stackrel{midpoint}{(41~~,~~50)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +14}{2}=41\implies x+14=82\implies \boxed{x=68} \\\\\\ \cfrac{ y +21}{2}=50\implies y+21=100\implies \boxed{y=79}[/tex]
Find value of x.
3x + 6 - 6 = 248
Answer:
The value of x is 82.67Step-by-step explanation:
Q. 3x + 6 - 6 = 248= 3 x = 248= x = 248 / 3 = 82.67∴ The value of x is 82.67
Answer:
x=82.7
Step-by-step explanation:
3x+6-6=248
3x=248
x=82.7
Please Help! Determine the range of the following graph:
the range of the function in the graph is:
-4 ≤ y ≤ 2
How to determine the range of a given graph?For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.
Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.
If we look at the graph, we can see that the minimum value of y is:
y = -4
And we can see that the maximum value of y is:
y = 2
Then the range of the function in the graph is:
-4 ≤ y ≤ 2
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A man travelled a distance of 8km in an hour. How long
will it take him to cover a distance of 12km, travelling at
the same speed?
Answer:1 hour 30 minutes
Step-by-step explanation:8 kilometres are compete in an hour, plus another 4 kilometres (to make 12 total) is half of that, so adds another half an hour
The time it will take the man 1.5 hours to cover a distance of 12 km, travelling at the same speed.
What is the relation of speed and distance?
Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.
The speed formula is speed = distance / time.
We are given that;
Distance = 12 km
Speed = 8 km/h
Now,
Plugging these values into the formula for time, you get:
time = 12 / 8
time = 1.5 hours
Therefore, by the given speed the answer will be 1.5 hours.
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f(x)= x; translation 2 units right followed by a horizontal stretch by a factor of 2
Answer: f(x) = | x |
Step-by-step explanation:
when transforming and translating a function, you use the form a | x - h | + k
a= vertical shrink/stretch factor
h = horizontal movement ( right or left)
k = vertical movement ( up or down )
So a = 1/2 h = 0 and k =2
g(x) = 1/2 | x-0 | + 2
g(x) = 1/2 | x | + 2 [which means vert shrink of 1/2 and up 2 units ]
In this figure, AB∥CD and m∠6=75° . What is m∠3 ?
115°
75°
15°
105°
The measure of angle <3 is 105 degrees
How to use the diagram to find the measure of angle 3?The diagram that completes the question is added as an attachment
The angle is given as
<6 = 75
From the diagram, we have
<3 + <6 = 180 degrees
The above is true by the sum of internal angles between parallel lines
So, we have
<3 + 75 = 180
Subtract 75 from both sides of the equation
So, we have
<3 + 75 - 75 = 180 - 75
Evaluate the like terms
So, we have
<3 = 105
Hence, the measure of angle <3 is 105 degrees
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Solve each equation. Check your answers.
ln (t-1)²=3
t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In ln ( t -1 )² = 3, by property of logarithm ( [tex]log_b(a)^m=m(log_b(a))[/tex]),
=> 2 ( ln (t -1) ) = 3
=> ln (t - 1) = [tex]\frac{3}{2}[/tex]
=> t - 1 = [tex]e^\frac{3}{2}[/tex]
=> t = [tex]e^\frac{3}{2}[/tex] + 1 = 4.48 + 1 = 5.48
Hence, t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
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Find the sum of (7.3 × 106) and (4.6 × 105). write the final answer in scientific notation. 11.9 × 1011 1.19 × 1010 7.76 × 106 7.76 × 105
The sum in scientific notation will give:
7.76*10⁶
How to find the sum in scientific notation?
Here we want to find the sum between the numbers (7.3*10⁶) and (4.6*10⁵).
To sum these numbers, we need to have the same exponent in the "10", then we can rewrite:
7.3*10⁶ = 73*10⁵
Now the sum will be:
73*10⁵ + 4.6*10⁵
Taking a common factor we get:
73*10⁵ + 4.6*10⁵ = (73 + 4.6)*10⁵ = 77.6*10⁵
Now we want to go back to scientific notation, so we need to move the decimal point one time to the left, we will get:
77.6*10⁵ = 7.76*10⁶
That is the outcome of the sum.
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Simplify each expression.
27¹/₃
The questions tests on indices. Write 27 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 27 = 3×3×3
27 = 3^3
(27^3)^(1/3) = 3^(3×1/3) = 3
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A holiday company offer a 12% discount if you book before 31st March. How much
would you pay today for a holiday to France if the full price is £1,245?
Simplify and write each expression
Fully. Show
(a) (3x²y-¹)(2³x³y).
The simplified form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).
What is an algebraic expression?An algebraic expression (or variable expression) is a term that has been combined with operations like addition, subtraction, multiplication, and division.
To simplify an algebraic expression, we simply combine like terms. As a result, variables that are similar will be combined. The same abilities will now be combined from the similar variables.
The given expression is (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y).
As we know [tex]x^{a}[/tex] + [tex]x^{b}[/tex] = [tex]x^{a+b}[/tex]
So, (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (3×[tex]2^{3}[/tex])([tex]x^{2}[/tex]×[tex]x^{3}[/tex])([tex]y^{-1}[/tex]×y)
(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])([tex]y^{0}[/tex])
(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])
As a result, the abbreviated form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).
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i need help with this
Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.
How to illustrate the information?It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.
In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.
Therefore, it should be noted that 8.33 will be:
= 8 + 1/3
It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...
Therefore, the appropriate fraction for 8.33 will be 8 1/3.
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Over the summer, Gabriela read 10 times as
many pages as Salima. Altogether, they read
12,078 pages. How many pages did each girl
read?
Answer:
i’m pretty sure it’s 6,039
Step-by-step explanation:
12,078 divided by 2
help- have to finish today
4 9/10
explanation:
1: Simplify both sides of the equation.
x+−2/5=9/2
2: Add 2/5 to both sides.
x+−2/5+2/5=9/2+2/5
x=4 9/10
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=1/√-2 x
Answer to this question is:
Domain of given function is (-∞,0),{x|x<0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is -1/2x²
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(-∞,0)
Set-Builder Notation:{x|x<0}
The set of all valid y values constitutes the range.
Interval Notation:(0,∞)
Set-Builder Notation:{y|y>0}
For calculation of inverse:
Interchange the variables x=1/√-2ySolve for yy=-1/2x²Replace y with f^-1(x)f^-1(x)=-1/2x²∴Domain of given function is (-∞,0),{x|x<0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is -1/2x²
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Can ya'll help me with this please?
Answer: C.
Step-by-step explanation:
Please help! What is the range of the function shown in the graph below?
Step-by-step explanation:
the range of a function is the interval or set of all valid y (function result) values.
so, what values is this function creating ?
we see that y never gets larger than -4.
but it will clearly go and go and go ... further down without any limit.
so, the range is
-infinity < y <= -4
An elephant charged 13.3 meters in 15 seconds. At this rate, how far would the elephant move if it could charge for one minute? (15 seconds = 1\3 minute)
The elephant can move 53.2 meters if it is charged for 1 minute.
Given,
The time that the elephant charged = 15 seconds
The distance that the elephant can travel by this charge = 13.3 meters
We have to find the distance moved by the elephant if it is charged for 1 minute:
That is,
15 seconds = 13.3 meters
Then,
1 minute (60 seconds) = x
Therefore;
15 × x = 13.3 × 60
x = (13.3 x 60) / 15
x = 798 / 15
x = 53.2
That is, the elephant can move 53.2 meters if it is charged for 1 minute.
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What is the highest common factor of 39375 and 779625?
Answer:
To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:
39375: 3 3 5 5 5 5 7
779625: 3 3 3 3 5 5 5 7 11
GCF: 3 3 5 5 5 7
The Greates Common Factor (GCF) is: 3 x 3 x 5 x 5 x 5 x 7 = 7875
Step-by-step explanation:
check attached images
Dan's has a current credit card statement of $785. his credit card apr is 24.42%. what would be his finance charge if he does not pay the balance in full?
A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.
If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.
Current Balanced Owned =$785
APR = 24.42%
Let’s suppose the billing cycle is 30 days, then
Finance charge = $15.76
The new balance you owe = $800.76.
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Multiply if possible. Then simplify. √2 . √8
The simplest form of the expression is 4 .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by academic degree operator in between.Simplifying expressions mean rewriting an analogous math expression with no like terms and through a compact manner.To change expressions, we have a tendency to tend to combine all type terms and solve all the given brackets, if any, then inside the simplified expression, we have a tendency to are aiming to be exclusively left with not like terms that cannot be reduced any.We have given an expression √2 . √8 .
On multiplying , we get
√2 . √8 = √16
On simplifying , we get
√16 = √ 4 × 4
= 4
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Suppose J is between H and K. Use the segment Addition Postulate to solve for x. Then find the length of the segment.
HJ=4x+9, Jk=3x+3, HK=33
The length of the segment when J is between H and K will be HJ = 21 and JK = 12.
How to illustrate the information?From the information given, J is between H and K and we want to use the segment addition Postulate to solve for x.
It should be noted that:
HJ=4x+9,
Jk=3x+3,
HK=33
Therefore, we will equate the values. This will be:
4x + 9 + 3x + 3 = 33
7x + 12 = 33
Collect like terms
7x = 33 - 12
7x = 21
Divide
x = 21 / 7
x = 3
HJ=4x+9, = 4(3) + 9 = 21
Jk=3x+3 = 3(3) + 3 = 12
Therefore, the length of the segment when J is between H and K will be HJ = 21 and JK = 12.
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Amir has 3 jars of sweets
Jar a contains 205 sweets
Jar c contains 175 sweets
Jar a has the most sweets and Jar c has the least of sweets how many sweets could be in jar b explain how you know this
The sweets in jar B in the box with Amir will be 190 sweats.
How to calculate the number?From the information, Jar A contains 205 sweets. Jar c contains 175 sweet. Also, jar a has the most sweets and Jar c has the least of sweets.
The deets in jar B will be:
= (205 + 175) / 2
= 380 / 2
= 190
Therefore, the sweets in jar B in the box with Amir will be 190 sweats.
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