The logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10 but ahs a base e.
In mathematics, the common logarithm is the logarithm with base 10.
It is also known as the decadic logarithm and as the decimal logarithm function.
Here, we have the logarithm function as:
( log 64 )
Now, we can see that:
It does not have a base.
So, we will take the base as e.
So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.
Therefore, we get that, the logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10.
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Solve each equation. Check your answers.
3 log x=1.5
3 log (x) = 1.5 => x = 3.162, 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.Given: 3 log (x) = 1.5
=> log x = [tex]\frac{1}{2}[/tex] = 0.5
Raising both sides by 10, in order to remove the logarithm:
=> [tex]10^{log_{10}x} = 10^{0.5}[/tex]
=> x = 3.162 (as [tex]a^{log_a(x)} = x[/tex])
Hence, 3 log (x) = 1.5 => x = 3.162, by properties of logarithm.
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I need help to find each product for the blank first one and the bottom one simplify each expression
Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
The term repeating decimals refers to non-terminating decimals that repeat. If the digits after the decimal point end, the number has a terminating decimal expansion.
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating
5- terminating
6- repeating
7- terminating
8-teminating
9-terminating
10-terminating
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A rectangular carpet measures 10 m by 6 m
Part of the carpet is covered by a square rug of length 2m
What fraction of the carpet is
covered by the rug?
Give your answer in its simplest form.
Optional working
Answer:
Answer:
Step-by-step explanation:
A rectangular carpet measures 8 m by 6 mPart of the carpet is covered by a square rug of length 2 m
Roxana fue de compras con 12000. ella gasto el 12% del dinero en carne, 25%en vegetales y guardo el resto ¿cuanto dinero guardo?
The amount that Roxana has left is $7560.
How to calculate the value?Total Amount = $12000
She spent 12% on meat and 25% on vegetables.
Therefore, the amount left will be:
= (100 - 12% - 25%) × 12000
= 63% × 12000
= 63/100 × 12000
= 0.63 × 12000
= $7560
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Hullan is 5 years older than Thomas. The sum of their ages is 69. What is Thomas's age?
Answer:
29
Step-by-step explanation:
69/2
The sun of a number and 14 written as an algebraic exspression?
Answer:
[tex]\mathrm{a + 14 = b}[/tex]
I need help with these problems.
Answer:
1. 4
2. 65
3. 4
4. 53
5. 14
Answer:
1.: 4 songs
2.: 65 dollars
3.: 4 cookies
4.: 53 cards
5.: 14 degrees
Step-by-step explanation:
1.: Split 40 songs evenly between 10 days. 40 divided by 10 equals 4.
2.: 160, the needed amount, minus 95, the amount already had, equals 65. 95+65=160.
3.: Split 32 cookies evenly between 8 people. 32 divided by 8 is 4.
4.: 200-147=53, so 147+53=200.
5.: -11-14=-25. Subtracting from a negative increases its absolute value, but it remains negative.
# 12
EE.2
A health food store was charging $5.26 for a small salad but raised the price 20%. The new price after the increase is $6.31.
Enter an expression to show how the new price was calculated.
Answer:
Step-by-step explanation:
20% can be written as a fraction
20% = 20/100
20/100 = 1/5
5.26 x 1/5
1 x 5.26/ 5
5.26/5
1.052 = 1.05
Old price : $5.26
New price : $6.31
Increase : $1.05
the quotient of a number,x, and five is half the difference of a number and four write an equation that represents the statement
The equation that represents the quotient of a number x, and five is half the difference of a number and four is [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
Given,
The number = x
When you divide a number with another number the result is called the quotient
The quotient of a number x and five = [tex]\frac{x}{5}[/tex]
Difference of a number and four = x-4
Half the difference of a number and four = [tex]\frac{1}{2}(x-4)[/tex]
Here the quotient of a number x and five is half the difference of a number and four, the equation will be
[tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
Hence, the equation that represents the quotient of a number x, and five is half the difference of a number and four is [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]
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Margo mixed 24 ounces of blue paint and 16 ounces of red paint to create a new purple color. In order to create 72 more ounces of this exact purple color, how many ounces of red paint would she need?
Answer:
Step-by-step explanation:
Well, since 24+16 is 40, this would mean we get 40 ounces of purple paint. There is also a 150% difference between 24 and 16, so 2/3 times 24 = 16.
2/3 of the mixture is blue paint, while 1/3 of the mixture is red paint, so 1/3 of 72 is 24.
Thus, the answer is 24 ounces of red paint.
Evaluate
-3 (2) (-1) (4)
64854755555557427382675
Sakura's house is at an elevation between 113 m and 120 m above sea level. Her friend Ted lives about 15 m below her.
Answer: he is 115 metters above sea level
Step-by-step explanation:
which is the oppisite of -12
The opposite of the number -12 is 12
How to determine the opposite of -12?The number is given as
Number = -12
As a general rule, the opposite of a number x is
Opposite = -x
This means that the opposite of -12 is 12
Hence, the opposite of -12 is 12
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the stock market fell 60 points over a period of 4 days. what was the average change in the stock market each day?
The average change in the stock market is 15 points each day.
Average is calculated by dividing the total number of values in a given set by the arithmetic mean of the sum of all the values. For groups of values that are nearly identical, an average is calculated. The numerical value that represents a lot of data is referred to as the average.
The stock market fell by 60 points
No. of days stock market fell = 4 days
The formula for average is given by:
Average = Sum of observations/Total no. of observations
= 60/4
= 15 points
Therefore, the stock market fell by 15 points each day
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Write an equation for 37.
Answer:
Can you please explain more about what do you mean about write a equation for 37.
Step-by-step explanation:
pls solve this fraction by steps
Answer:
-30
Step-by-step explanation:
-5/2 × 12
= -5/2 x 12/1
= (-5 × 12)/(2 × 1)
= -60/2
= -30
Answer:
-30 if this equation is multiplication!
Step-by-step explanation:
-5/2 times 12 (OG equation)
-5/2 times 12/1 (Convert)
-5 times 12/ 2.1 (Fraction Rule)
-5 times 12/2 (Multiply)
-5 times 6 (divide 12 by 2)
-30 (Simplify)
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a) what is the value of the 8 in the number 24.387?
Gve your answer as a fraction. ???
Answer:8/100
Step-by-step explanation: you would count the placement value of the numbers after the decimal point
A square has
has an area of
25 cm². show that the Perimeter of the square is
is 20 CM.
Step-by-step explanation:
[tex]l {25}^{2} [/tex]
L=5
5×4=20
An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
Answer:
if 312four + 52p = 96 find the value of p
The sum of the first six prime numbers is ?
Answer:
41
Step-by-step explanation:
A prime number is a whole number (bigger than 1) that is divisible only by itself and 1.
The first 6 prime numbers are 2, 3, 5, 7, 11 and 13.
2 + 3 + 5 + 7 + 11 + 13 = 41.
Answer: 41
Step-by-step explanation: We know that the first 6 prime numbers are 2, 3, 5, 7, 11, 13. We add them all and get 41!
Which of the following relations is not a function?
A) (-7,4)
(4,3)
(-5, 1)
(6,2)
B) (-5,4)
(4,2)
(6,1)
(-7,5)
C) (6,4)
(-5,2)
(4,1)
(-7,2)
D (4,4)
(-5,2)
(4,1)
(-7,2)
Part (D) is not a function as he element 4 has two images in y that is 4 and 1.
We are given some relations.
We need to tell which of the following is not a function.
A relation is a function when every element of x has only one mapping on the every element of y.
That is when we put one value of x, there should not be 2 values for y.
For part (A),
It is a function as it satisfies the condition.
For part (B),
It is also a function as it also satisfies the condition.
For part (C)
It is also a function as it also satisfies the condition.
Fort part (D),
It is not a function as the element 4 has two images in y that is 4 and 1.
Therefore, part (D) is not a function as he element 4 has two images in y that is 4 and 1.
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An ant can walk 8 feet in 1 minute.
Write an equation which describes how many minutes, t, it takes for an ant to walk d feet.
Answer:
8=t/d
Step-by-step explanation:
Barbara is in charge of the award medals for a sporting event. She has
31 medals to present to various individuals on 6 competing teams. She asserts that at least one
team will end up with more than 5 medals. Do you believe her
assertion? Justify your argument.
It should be noted that Barbara asserts that at least one team will end up with more than 5 medals. In this case,she's correct as a team will have 6 medals.
How to illustrate the information?From the information, Barbara is in charge of the award medals for a sporting event and she has 31 medals to present to various individuals on 6 competing teams.
It should be noted that each team will get:
= 31 / 6
= 5 remainder 1
Therefore, she asserts that at least one
team will end up with more than 5 medals. In this case, she's correct.
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How many feet of the parking lot are presented by 1 centimeter on the scale drawing?
The number of feet of the parking lot thay are presented by 1 centimeter on the scale drawing is 12 feet.
How to calculate the feet?The width of 48 feet is represented by 12.8cm; the length represented by 1cm is 48/12.8 = 15/4 = 3.75 feet.
The length on the drawing is 3.2cm, which is exactly 1/4 of the width of 12.8cm.
It should be noted that therefore the length of the actual parking lot is 48/4 = 12 feet.
In conclusion, it is 12 feet.
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The width of the parking lot is 48 feet. How many feet of the parking lot are represented by 1 centimeter. Based on the scale drawing, what is the length, in feet, of the actual parking lot? On the drawing, they have the width of 12.8 cm and a length is 3.2 cm.
F = G
G
(m₁m₂)
d²
where F is the force between two objects of masses
m₁ and m₂, G is the gravitational constant, and dis
the distance between the two objects. Solve the
formula for m₁.
Answer:
The formula for mass m1 will be as M1 = Fr²/GM2.
What is Newton law of gravitation ?
According to newton's law , force between mass m₁ and m₂ at distance x is given by the following expression is;
F = G m₁m₂ / x²
Where F is the force between two masses m1 and m2 G is the gravitational constant and x is the distance between the two objects.
For Solving for M1 in terms of Fg, G, M2 and r yields;
M1 = Fr²/GM2
To solve for M1 in terms of F, G, M2 and r;
We are required to make M1 the subject of the formula as follows:
F = (G M1M2)/r²
By cross product;
Fr² = G M1M2
by dividing through by G M2; we have;
M1 = Fr²/GM2
The formula for mass m1 will be as M1 = Fr²/GM2.
Evaluate the expression -7x -1/6y +2z-xy+28 when x = 2, y=12 and z =9
SHOW WORK FOR BRAINLIST.
Answer: 12
Step-by-step explanation:
x = 2, y=12 and z =9
-7x -1/6y +2z-xy+28=
-7(2) -1/6(12) +2(9)-(2)(9)+28=
-14-12/6+18-18+28=
-14-2+28=
-(14+2)+28=
-16+28=
28-16=12
Simplify. 3√63 +√28
The value of the expression 3√63 +√28 is 5√7 or 13.228.
A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.
A square root is a factor of a number that yields the original number when multiplied by itself.
Consider the expression 3√63 +√28,
Let's assume x = 3√63 +√28
Now,
63 = 3 × 21 = 3 × 3 × 7
28 = 2 × 14 = 2 × 2 × 7
Therefore,
x = 3√63 +√28
x = √ [ 3 × 3 × 7 ] + √ [ 2 × 2 × 7 ]
x = ( √ 3² ) × ( √7 ) + ( √2² ) × √7
x = 3√7 + 2√7
x = ( √7 ) × [ 3 + 2 ]
x = ( √7 ) × 5
x = 5√7
x = 5 × 2.6457
x = 13.228
Hence, the value of 3√63 +√28 is equal to 13.228.
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vector v is 448 M long and a 224 direction. Ha W is 336 M long in a 75.9 directions find the magnitude of their Vector sum
The magnitude of the sum of vectors is 240.8 M
How to find the magnitude of the vector sum?We know that vector V has a magnitude of 448 meters and a direction of 224°, then the components are:
x-component = 448m*cos(224°) = -322.3my-component = 448m*sin(224°) = -311.2 mThe other vector W has a magnitude of 336 meters and a direction of 75.9°, then the components are:
x-component = 336m*cos(75.9°) = 81.9my-component = 336m*sin(75.9°)= 325.9mNow if we add these two vectors, the coordinates of the sum are:
< -322.3m + 81.9m, -311.2 m + 325.9m> = <-240.4 , 14.7>
Then the magnitude is:
M = √( (-240.4)^2 + ( 14.7)^2) = 240.8
The magnitude of the sum of vectors is 240.8 M
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Suppose that a function pairs elements from set A with elements from set B . Recall that a function is called onto if every element in B is paired with at least one element in A .
b. What are the domain and range of the function?
The domain of the function will be the elements present in Set A and the range will be the elements present in Set B.
Domain of a function:
The domain of a function refers to the set of all possible inputs for the function. For example, we get that the domain of f(x) = x² is all real numbers, and the domain of g (x) = 1 / x is all real numbers except for x = 0( as it will make the function indefinite.) Some special functions can also be defined whose domain are limited.
Domain here will be = Set A
Range of a function:
The range of a function refers to the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
Range of the function here will be = Set B.
Therefore, we get that, the domain of the function will be the elements present in Set A and the range will be the elements present in Set B.
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Consider the system of linear
equations below. Choose nonzero values for a, b.
and c so the system satisfies the given condition.
Explain your reasoning.
x+y+z=2
ax + by + cz= 10
X- 2y+z=4
a. The system has no solution.
b. The system has exactly one solution.
c. The system has infinitely many solutions.
For no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.
We have the system of equations:
x + y + z = 2 …(1)
a x + b y + c z = 10 …(2)
x - 2 y + z = 4 …(3)
a. The system has no solution.
Put a = b = c = -1 in (2)
We get:
- x - y - z = 10
Now add (1) and (2)
0 = 12
which is not possible.
So, no solution.
b. The system has exactly one solution.
a = 1 and b = c = 0
We have the equations as:
x + y + z = 2 …(1)
x = 10 …(2)
x - 2 y + z = 4 …(3)
c. The system has infinitely many solutions.
a = b = c = 5
We will have the equations:
x + y + z = 2 …(1)
5 x + 5 y + 5 z = 10 …(2)
x - 2 y + z = 4 …(3)
Therefore, we get that, for no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.
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