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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Tickets to a sporting event cost $125 each. What's a reasonable domain and range.
The domain and the range of a function is the set of input and output values of the function.
The domain is the set of all whole numbers.
The range is the set of all whole numbers.
Let the number of tickets be x, and the revenue be y.
So, the revenue function will be:
y = 125
The number of tickets cannot be less than 0.
So, the domain of the revenue function is
domain=0,∞
The above means that, the domain is the set of all whole numbers
Similarly, the revenue cannot be less than 0.
So, the range of the revenue function is
range = 0,∞
The above means that, the range is also the set of all whole numbers (in multiples of 125).
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If the point (x, y) is in Quadrant III, which of the following must be true?
x < 0 and y>0
x < 0 andy<0
Submit
x > 0 and y>0
x > 0 and y < 0
Answer: x < 0 and y < 0
Step-by-step explanation:
quadrant three is here
|
II | I
|
--------------------|-------------------
|
III | IV
|
here /\
so, the x is to the left which is negative, and the y is down which is negative. x is less than zero, and y is less than zero
Given f(x) = 3x + 3, write a new function if the y-intercept is increased by two units.
Answer:
f(x) = 3x + 5
Step-by-step explanation:
Because if the y-intercept is increased by two units in the slope formula where b is the y-intercept, then the answer is 3x + 5.
help plss
1. Solve for x:
1/3x = -26
Which translation takes y=|x| to y=|x+3|-1 ?
(A) 3 units right, 1 unit down (C) 3 units left, 1 unit down
(B) 3 units right, 1 unit up (D) 3 units left, 1 unit up
The translation is given by option (C)3 units left ,1 unit down.
A translation occurs when you a graph is moved either horizontally or vertically. That is to say, each point on the parent graph gets translated in one of four directions: left, right, up, or down. There is usually addition or subtraction involved in translation.
Let us consider the function y=|x+3|-1 which is translated from the parent function of y=|x|.
The following steps are followed for the translation of the function:
There is an horizontal shift to the left of the parent function about 3 units .There is a vertical shift downwards of 1 unit.The translation can be seen in the attached graphical representation of the two functions.
The blue line represents the translated function while the red line represents the parent function.
Therefore the translation required for the function y=|x+3|-1 from y=|x| is 3 units left and one unit down .
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Use the Change of Base Formula. What is the value of each expression?
b. log₄18
The value of the given expression that is log₄ 18 = 2.084
A logarithm operation can be rewritten as a fraction of logarithms with a new base using the change of base formula.
Example: logₐ b = (logₓ b) / logₓ a)
Therefore, log₄ 18 = (log₁₀ 18) / (log₁₀ 4).....eq(i)
We know, log₁₀ 4 = 0.602
We can write log₁₀ 18 as log₁₀(2x9).
Using the product rule of logarithms, log₁₀ 18 = log₁₀2 + log₁₀9log₁₀ 18 = 0.301 + 0.954log₁₀ 18 = 1.255
Substituting the value of log₁₀ 18 = 1.255 in eq(i) we get,
log₄ 18 = 1.255/0.602log₄ 18 = 2.084
The final answer to the question is log₄18 = 2.084 using the change of base formula.
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Which expression is NOT equivalent to ⁶√16 ²?
(A) (16 r²)¹/₆ (B) 4 r¹/₃ (C) (4 r)¹/₃ (D) ∛4 r}
The correct option is (B) [tex]4 r^\frac{1}{3}[/tex]
The exponential expression [tex]4 r^\frac{1}{3}[/tex] is not equivalent to ⁶√16r².
What is exponential expression ?In, mathematics a exponential function or exponential expression is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as [tex]a^x[/tex] .Or we can say that there is always has something power something rule in case of exponents.
where, a is the base expression of function
x = exponent of expression
According to question,
the expression,[tex]\sqrt[6]{16r^2}[/tex] can be written in following ways:
Case 1 : if we simplify the expression using fractional method ,
then, [tex]\sqrt[6]{16r^2}[/tex] = [tex]({16r^2})^{\frac{1}{6}} = (4r)^\frac{2}{6 } = (4r)^\frac{1}{3 }[/tex]
i.e. option (A) and (C) are satisfying the expression
Case 2 : if we simplify the equation exponentially ,
then, [tex]\sqrt[6]{16r^2} = 3\sqrt{4r}[/tex]
i.e. option (D) is satisfying the expression
Hence, the expression is not equivalent to ⁶√16r² is option B.
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If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies directly with x and inversely with y .
z = 20 x/y is the variation of equation.
How to write the function that models the relationship?A relationship between a set of values for one variable and a set of values for other variables is known as a variation.
One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.
given that
z=30 when x=3 and y=2
z varies directly with x that means z is directly proportional to x.
z = kx .................(1)
z varies inversely with y means z is inversely proportional to y.
z = k 1/y ................(2)
both equation 1 and 2
z = k x/y
k = zy/x
now, find the value of k using given information.
k = 30(2)/3
k = 60/3
k = 20
now,
z = k x/y
z = 20 x/y
This is the variation of equation.
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John calculates an arc length involving a circle with a radius of 9 inches. The associated central angle has a measure of radians. John's work is shown
Answer:
Step 3, computed the radius multiply by the center angle
Step-by-step explanation:
{arc-length: a * r}
arc-lenght= 3\pi * 9 = 27pi inches. John made his first error in sept 3, he listes the correct equations, but he should have computed the radius by the center angle
Answer:
Step-by-step explanation:
Please help!!
Solve for a:
b(a + f) = M
Kaylee deposits $500 into a savings account with a 3% intrest rate what will her balance be in 3 years
Answer: $576.99 in 3 years
Step-by-step explanation:
Answer:
546.36
Step-by-step explanation:
Interest rate calculator
DIG DEEPER A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180+58.5p) dollars. Write an expression that represents the cost of one kit.
Answer:
Step-by-step explanation:
mdcmmmm
Pleas look at screenshot
What are the solution(s) of 2(x+3)²/₃=8 ?
The solution is 5
Rewriting the expression -
2(x+3)²/₃=8
Divide Left Hand Side and Right Hand Side of the equation -
(2(x+3)²/₃)÷2 = 8÷2
Performing division to find the solution
(x+3)²/₃ = 4
Taking cube on both sides of the equation
((x+3)²/₃)³ = 4³
The exponent on Left Hand Side will be multiplied cancelling 3, as it is common in both numerator and denominator
(x + 3)² = 64
Now, taking square root on both sides of equation
√(x + 3)² = √64
Solving the square root on both sides of equation
x + 3 = 8
Shifting 3 to Right Hand Side of the equation
x = 8 - 3
Performing subtraction
x = 5
Hence, the solution of equation is 5
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Identify the like terms in the list.
16y ^6, 2y^ 5, 4y ^2, 10y, 16y^ 2
Answer:
4y^2
16y^2
Step-by-step explanation:
16 y^6 matches nothing. The powers on the letter must be the same to have like terms.
2y^5 has the same comment.
4y^2 and 16y^2 are similar terms. Both have y^2
10y matches nothing
8 over 3 / 3 simplified
Answer:
8
Step-by-step explanation:
if you mean 8/ (3/3), Then you get 8 because 3/3 = 1 and 8/1 is 8. Also if you put that equation into a calculator then you get 8
mr. fullingham has 75 geese and 125 turkeys. what is the ratio of te number of geese to the total number of birds in simplest terms
How much will a person pay for 5.5 pounds of bananas at a price of $1.66 per pound?
...
The person pay $9.13 for 5.5 pounds of bananas .
The unit method is a method of finding the value of one unit and then finding the value of the required number of units."It's a way to get a single unit value from a multiple unit value and a multiple unit value from a single unit value." or should find a lesser value. To do this, you must first find the value of one thing by division, and then find the value of more or less by multiplication. For simplicity, we always write the computed side on the right and the known side on the left.It is given that $1.66 per pound of bananas .
1 pound of banana cost = $1.66
5.5 pounds of banana cost will be [tex]=5.5\times1.66[/tex]
[tex]=\$9.13[/tex]
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can someone please tell me what 383.0 divided by 90 is?????????
Sure!!!
The answer is 4.25555!
Hope this helps! Have a great day! :D :)
Answer:
The answer is 4.2555555556
Pls help! Slope Question
The slope between points C and D is 12/7 = 1.71
How to find the slope between points C and D?
We know that the slope between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by:
s = (y₂ - y₁)/(x₂ - x₁)
In this case, the coordinates of point C are (0, 0)
The coordinates of point D are (7, 12)
Then the slope on that interval is:
s = (12 - 0)/(7 - 0) = 1.71
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Calculate (7.15 x 10^9) - (4.56 x 10^8).
2.59 x 10^1
2.59 x 10^9
6.694 x 10^8
6.694 x 10^9
Answer:
D. 6.694 * 10^9
Step-by-step explanation:
The exponent is 9 because the result of the first equation had 9 digits. It is positive because the decimal moves to the right.
Which table represents a linear function?
Are the lines paraellel, perpendicular, or neither? b) line 1 : y+1/3x=4 line 2 y=3x-2
Notes:
For semiannual premiums, use 51% of the annual rate.
For quarterly premiums, use 26% of the annual rate.
For monthly premiums, use 9% of the annual rate.
For females, use the age of a male three years younger.
Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value of $50,000. What will his annual premium be, if his age for insurance purposes is thirty-one?
(Use a thousands comma where applicable.)
The annual insurance premium that Will C. Lowe will be paying is $ 766.5
What is insurance premium?Insurance premium is annual, quarterly, semi annual or monthly payments that has to be paid accordingly to keep our insurance policy active.
Annual insurance premium can be calculated by multiplying the face value per $1000 of the policy by the rate of the insurance of policy.
Given is that Will C. Lowe is 31 year old male who wants to buy a ordinary whole life insurance policy with a face value of $50,000.
From the table we can see that rate of insurance for a 31 year old male for a ordinary whole life insurance policy is 15.33
Then annual premium = (face value per $1000)*(rate of insurance)
= $ (50,000/1000)*(15.33) = $766.5
Therefore, the annual insurance premium that Will C. Lowe will be paying is $766.5
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3xy+5x+2+3y+x+4 answer
The equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x + 3y + 6
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3xy + 5x + 2 + 3y + x + 4
Collect the like terms in the above expression
So, we have
3xy + 5x + 2 + 3y + x + 4 = 3xy + 5x + x + 3y + 4+ 2
Evaluate the like terms in the above expression
So, we have
3xy + 5x + 2 + 3y + x + 4 = 3xy + 6x + 3y + 6
Hence, the equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x + 3y + 6
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Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP
?hours
The mean lifetime of a bulb is 31. 57
What is mean?Mean can be defined as the average of a given set of values or elements.
The formula for the mean of a given set of values is expressed as;
Mean = sum of the occurrence of the values/ number of values
Or
Mean = sum of terms/number of terms
From the information given, the frequency of the lifetime of the bulbs were given as;
34, 31, 94, 40 , 0 , 17, 5
The sum of the terms is given as:
= 34 + 31 + 94 + 40 + 0 + 17 + 5
= 221
The number of terms = 7
Substitute into the formula
Mean = 221/ 7
Mean = 31. 571
In 2 decimal place
Mean = 31. 57
Thus, the mean lifetime of a bulb is 31. 57
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c rounded to the nearest 10 is 640.
d rounded to the nearest 10 is 420.
what are the lower and upper bounds of c + d?
The bounds of C is 635 - 644
The bounds of D is 415 - 424
The lower bounds of C + D can be found by adding 635 + 415, which is 1050
The upper bounds of C + D can be found by adding 644 + 424, which is 1068
So, the lower bounds of C + D is 1050 and the upper bounds is 1068
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
The upper bound is 1068 and the lower bound is 1050
What is the upper bound and lower bound of a number?The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value.
Given here, c rounded to the nearest 10 is 640 and d rounded to the nearest 10 is 420. Then we have the minimum and maximum value as
Min C = 635 and Max C = 644 & Min D=415 and Max D = 424
Therefore the upper bound for c+d = 644+424
= 1068
And the lower bound for c+d = 635+415
=1050
Hence The upper bound is 1068 and the lower bound is 1050
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The blue dot is at what value on the number line -16 to -10
Michael is doing an underwater handstand. His feet are sticking up 0.5 meters above the surface
hands are 1.8 meters directly below his feet.
of the water. Michael's
What is the position of Michael's hands relative to the surface of the water?
Answer:
Step-by-step explanation:
Answer:
michael is doing an underwater handstand . His feet are sticking up 0.5 meter above the surface handsare 1.8 meters directly below his feet of the water
michael handsrelative to the surface of the water
Step-by-step explanation: