After evaluating the logarithm log₂ 2⁵, we get the result as 5.
The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.
For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output. The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.
For example, the natural logarithm of 78 is written as ln 78. The natural logarithm determines how much we need to multiply "e" to get the required output.
We need to evaluate log₂ 2⁵Using the property logₐ (mⁿ) = n logₐ m log₂ 2⁵ can be written as
log₂ 2⁵ = 5 log₂ 2
We know that logₐ a = 15 log₂ 2= 5
Therefore, after evaluating the logarithm log₂ 2⁵, we get the result as 5.
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dana said that 0.6 divided by 30 = 0.02. is she correct? explain.
Answer:
It can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
Step-by-step explanation:
It is given that we need to rectify whether 0.6 divided by 30 = 0.02 or not.
Firstly, let us understand how does simplification work;
In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.
Now, let us understand what exactly is arithmetic;
According to the assertions, it deals with a number of operations in mathematics. Addition, subtraction, multiplication, and division are the four main arithmetic operators.
Now, let us equate the given condition that is;
=> 0.6 can also be expressed as 6/10
Now, let us divide the above numbers with each other as given in the question;
=> (6/10) ÷ 30
=> 6/300
On dividing both the numbers with each other we get;
=> 0.02 which can be expressed as 2/100
Therefore, it can be said that Dana is correct when she says that 0.6 divided by 30 gives 0.02 as a reminder.
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Answer:
Step-by-step explanation:
3 identical circles inside a rectangle each circle touches the other two circles and sides of a rectangle
the radius of each circle is 2mmworkout the exact area of the rectangle
give your answer in the form a√ 3+b
where a and b are integers
The area of the rectangle having three identical circles inside is calculated as: (16√3 + 32) mm².
What is the Area of a Rectangle?Area of rectangle = (length)(width)
The image of the three identical circles in the rectangle has been labelled as shown in the diagram attached below.
We need to find the measure of the length and width of the rectangle.
Radius = AB = BD = DF = FG = CD = HI = 2 mm
Length of the rectangle = AB + BD + DF + FG = 2 + 2 + 2 + 2
Length of the rectangle = 8 mm
Width of the rectangle = CD + DH + HI
CD = 2 mm
HI = 2 mm
Use the Pythagorean theorem to find the measure of DH
DH = √(FH² - DF²)
FH = 2 + 2 = 4 mm
DF = 2 mm
Substitute
DH = √(4² - 2²)
DH = √(16 - 4)
DH = √12 = 2√3 mm
Width of the rectangle = CD + DH + HI = 2 + 2√3 + 2
Width of the rectangle = 2√3 + 4
Area = (2√3 + 4)(8)
Area = (16√3 + 32) mm²
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Simplify each expression.
√11(4√11)
The expression given tests on indices. The expression can be written in index form as a^m. Thus, b√a = a^(1/b) From the power rule of indices, a^m x a^n = a^(m+n).
√11(4√11)
11^1/2 ( 11^1/4)
11 ^(1/2+1/4)
11^3/4
4√11^3
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The product of any integer and –1 is always
x+2−0.5x=1+.0.5x+1 solve for x
Answer:
x = 0
Step-by-step explanation:
x + 2 - 0.5x = 1 + 0.5x +1
2 - 0.5x = 2 + 0.5x
-0.5 - 0.5x = 2 - 2
-1x = 0
-1x/-1 = 0/-1
x = 0
Answer:
Step-by-step explanation:
Solve X + 2 - 0.5 x = 1 + 0.5 x + 1 : The answer is: X = 2X
work out value please
Answer:
270
Step-by-step explanation:
(∛9)³ × (√30)²
9 × 30 = 270
I hope this helps!
Answer:
Answer:
270
Step-by-step explanation:
(∛9)³ × (√30)²
9 × 30 = 270
Step-by-step explanation:
Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₅140
The value of logarithm as the quotient of two common logarithms is [tex]\frac{Log 140}{Log5}[/tex]. Because [tex]Log_{a}(b)=Log\frac{b}{a}[/tex]
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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solve the equation -27=3/4w
Answer: w = -32
Step-by-step explanation:
Start isolating the variable by getting rid of 3/4. You can do this by multiplying by its reciprocal.
That leaves us with 3/4 times -27
The product is -32.
Hope this helps!
rearrange x=3g+2 make g the subject
Answer:
3g=x-2
Step-by-step explanation:
3g+2=x then, move 2 to the other side(nb*change to negative) then it will be 3g=x-2 finally divide both sides by 3 then it will be g=x-2
3
A box of chocolates costs 9.49. Rita bought 4 boxes. How much did she spend?
Answer:
$37.96
Step-by-step explanation:
$9.49 x 4 = $37.96
P
=
2
L
+
2
W
to find the length of a rectangle when the width is
4 1/2
inches and the perimeter is
29 2/5
inches.
Answer:
10 2/5 inches
Step-by-step explanation:
Since P=2L+2W, we can flip it to find the length. For example, we could minus 2L from both sides to get P-2L=2W.
We already know that W is 4.5, and P is 29.4.
Plugging that in, we get 29.4-2L=9. Again we can flip the perimeter, and -29.4 on both sides. This would make -2L=-20.4.
For our last flip, we divide the -2 from both sides to finally get L=10.2 (or 10 1/5 if you want) inches.
Find all the real square roots of each number. 0.49
The real square root of the number 0.49 is 0.7
0.49 can also be presented as, 49* [tex]10^{-4}[/tex]
The square root of 49* [tex]10^{-2}[/tex]
= [tex]\sqrt{49}[/tex] * [tex]\sqrt{10} ^{-2}[/tex]
= 7 * [tex]10^{-2}[/tex]
=0.7
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The graph of y = f(X) is shown.
b) Find the roots of f(X) = 0
c) Find f(0)
A) The roots of the graph f(x) are; x = -2 and x = -1
B) The value of the function at f(0) is; 2
How to find the roots of a quadratic graph?
a) We want to find f(0) of the graph.
Now, f(0) simply refers to the y-values when x = 0.
This is the point at which the graph crosses the y-axis
From the graph we can see that the value here is 2. Thus;
f(0) = 2
b) To find the roots of f(x) , we simply find the points at which the plot crosses the x-axis.
From the graph, the roots are at x = -2 and x = -1
Thus, the roots of the equation are x = -2 and x = -1
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Use the properties of logarithms to evaluate each expression.
1/2 log₅15 - log₅√75
Using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
According to the question the expression that we have been given is
= [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75}[/tex]
Now solving it step by step using the properties of logarithm which are
[tex]log a^{m} = m*loga[/tex] , [tex]log \frac{x}{y} = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
As √75 is also equal to [tex](75)^{1/2}[/tex]. Thus equating in the equation we get
Therefore ,
[tex]= \frac{1}{2}log_{5} 15 - log_{5} 75^{\frac{1}{2} } \\= \frac{1}{2}log_{5} 15 - \frac{1}{2} log_{5}{75} \\[/tex]
As we can see that 1/2 is common in both the terms we will take out 1/2 common from both terms, by which we get
[tex]= \frac{1}{2} [log_{5} 15 - log_{5}{75} ] \\= \frac{1}{2} [log_{5} \frac{15}{75} ] \\\= \frac{1}{2} [log_{5} \frac{1}{5} ] \\= \frac{1}{2} [log_{5} 1 - log_{5}{5} ]\\= \frac{1}{2} [0 - 1]\\= -\frac{1}{2}[/tex]
Hence using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
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Find the real and imaginary solutions of each equation.
x⁴-14 x²+49=0
The given 4th order polynomial equation only has real solutions, x = √7 and x = –√7
The given equation is x⁴-14 x²+49 = 0.
This is a 4th degree polynomial equation.
Let p = x².
Then we can write x⁴-14 x²+49 = 0 as:
p²- 14p +49 = 0
This is a quadratic equation.
There are three ways to find the solutions of a quadratic equation:
By factoringBy completing the squareBy applying the quadratic formulaNotice that p²- 14p +49 = 0 can be written as a perfect square:
(p - 7)² = 0
Hence, it has only single real solution:
p - 7 = 0
p = 7
Substitute p = 7 into p = x², we get:
x² = 7
x = ± √7
The solutions are, therefore, x = √7 and x = –√7
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Write the equation of a line parallel to the line: y = − x − 1 that goes through the point (-2, -8).
The equation of the required line parallel to the given line is y = -x - 10.
What is slope ?Slope can be defined as the rate of change.
According to the given question we have to write an equation of a line parallel to the line y = - x - 1 that goes through the point (-2,-8).
We know that lines are parallel because of the same slope they have.
So, the required line also have a slope(m) = -1.
∴ The equation of the required line in slope intercept form can be written as y = mx + b.
Putting the value of given points (-2, -8) in (x,y) t evaluate y intercept b.
So, - 8 = (-1)(-2) + b.
- 8 = 2 + b.
b = -10.
∴The equation of the required line in slope intercept form is y = -x -10.
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3. Every conditional has two parts. The part following if is the
Ohypothesis
O conclusion
O inverse
O converse
(1 point)
Every conditional has two parts they are hypothesis and conclusion.
What are hypothesis and conclusion ?The hypothesis is the first part of a conditional statement 'if' and conclusion is the last part of a conditional statement 'then'
According to the given statement every conditional has two parts a hypothesis and a conclusion.
Conditional starts with if and ends with then.It is used to express possible situations.
For example-: if the two angles are complementary then their sum is 90°.
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can someone help me really quick
Answer:
2 2/4 because i just know the answer
What are the domain and points of discontinuity of the rational function? Are the points of discontinuity removable or non-removable? What are the x - and y -intercepts of the rational function?
c. y=x+1/x²+3 x+2}
The domain of given points are :
IR x ≠ -1 , -2
Points of discontinuity - x = -2 ( non removable / asymptote )
x = -1 ( removable / hole)
x - intercept = -1 , y - intercept = 1/2
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=x+1/x²+3 x+2
= x+1/x²+2x+x+2
= x+1/(x+2)(x+1)
The domain of given points are :
IR x ≠ -1,-2
Points of discontinuity - x = -2 ( non removable / asymptote)
x = -1 ( removable / hole)
x-intercept :
0 = x + 1
x = -1
y - intercept :
0+1 / (0+1)(0+2) = 1/2
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Each ordered pair is from an inverse variation. Find the constant of variation. (6,3)
The value of constant variation is 18.
Constant is what?A key integer with a stable value determined by a clear specification is referred to as a mathematical constant.
Inverse variation: what is it?connection in mathematics between two variables that may be described by an equation in which the sum of their products equals a constant
Inverse variation is y = k. 1/x
given y = 3
x = 6
So, 3 = k. 1/6
So, the value of k = 18.
We can conclude that the value of constant variation is 18.
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Given: m<4 + m<7 = 180 degrees
Prove: c || d
1) m∠4 + m∠7 = 180° (given)
2) ∠4 is congruent to ∠6 (vertical angles)
3) m∠4 = m∠6 (definition of congruent angles)
4) m∠6 + m∠7 = 180° (substitution)
5) c is parallel to d (converse of same side interior angles theorem)
An athlete trains for 105 min each day for as many days as possible write an equation that relates the number of days d that the athlete spends training when the athlete trains for 630 min
Grapes are selling for $0.26 a pound. Ashley spent $3.77 on grapes. How many pounds of grapes did Ashley buy?
the sum of a number and two thirds the number is the same as 4 less than twice the number
12
Step-by-step explanation:
n + (2/3)n = 2n - 4
(5/3)n = 2n - 4
(5/3)n - 2n = -4
(-1/3)n = -4
n = 12
Solve. Check for extraneous solutions. (x-2)¹/₂ -(28-2 x)¹/₄=0
-4 is an extraneous solution.
The equation is
[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0
To know whether the given equation has an extraneous solution or not we need to find the value of x.
[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]
Multiply both sides with the power of 4, and we get
[tex](x- 2)^{2}[/tex] = 28-2x
[tex]x^{2}[/tex] - 4x + 4 = 28-2x
[tex]x^{2}[/tex] - 2x - 24= 0
[tex]x^{2}[/tex]- 6x + 4x -24=0
x(x-6) +4(x-6)=0
(x-6)(x+4) = 0
x = 6 , -4
Now put both the value of x in the equation
x=6
[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0
[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0
2-2=0
0=0
Now
x = -4
[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0
[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0
[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0
Which is not possible and a negative integer is not present in the square root.
Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.
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What is the final version of this supposed to look like?
The graph of the inequality expressions is added as an attachment
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the graph of the inequality expression?The inequality expressions are given as
y ≥ 2
x + y ≤ 4
y ≤ 2x + 2
Next, we interpret each inequality expression
First expression: y ≥ 2
The inequality symbol in the above inequality expression is ≥
This implies that the inequality expression is a greater than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the upper part is shaded
Second expression: x + y ≤ 4
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the bottom part is shaded
Third expression: y ≤ 2x + 2
The inequality symbol in the above inequality expression is ≤
This implies that the inequality expression is a less than or equal to and the inequality symbol implies that the bottom part is shaded
See attachment for the graph of the inequality expressions
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The local gym holds two 45-minute workout sessions and four 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
Answer:
170 minutes
Step-by-step explanation:
So if there was two 45 min work outs in a week and she left those 10 mins early that was two 35 min work outs and then there was 4, 30min work outs and she left those 5 mins early so 4, 25min workouts so its 35+35+25+25+25+25.
The product of 3 and a number x is 23.
What is the value of x?
x=7/3
x=2/9
x=2
x=2 1/3
Answer:
D.
Step-by-step explanation:
x=2 1/3
That is the answer
A football team has a win to loss of 5:8. What is the ratio of losses to total games played
What inscribed polygon is being constructed? Explain how you know.
With an equilateral triangle, only two circles are formed.
In geometry, what is an inscribed polygon?An inscribed polygon is one whose vertices are circle points. "In" denotes "in" and "scribed" denotes "written." Connect the points in a straight line with segments.What kind of polygon is carved into the circle?
A cyclic polygon is one that is inscribed in a circle, and the circle is its circumscribed circle or circumcircle.So, according to the given figure, we know that an equilateral triangle and only two circles are formed.Therefore, with an equilateral triangle, only two circles are formed.
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