Answers
We are given Logarithmic equations.
We need to find the equation which illustrates the product rule.
We know, the product rule of Logarithms is:
[tex]log_b (mn) = log_b(m) + log_b(n)[/tex].
According to the product rule of Logarithms, we need to separate logs by plus sign.
In the given options only 4th option logs are separated by plus sign.
[tex]log_2(4x) = log_2\ 4+log_2\ x[/tex].
Therefore, correct option is 4th option.Answer:
Its D
Step-by-step explanation:
Took test
Related Questions
The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?
Answers
The answer is convenience sampling.
Step-by-step explanation:
As per the given scenario, the president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip and she surveys only the twelfth-grade members of the math club.
This is convenience sampling as here the samples are the closest people available. Convenience sampling is a method where the samples are taken who are close to hand.
Here also the math club president is asking the math club students only. This is why it is convenience sampling.
Find all the points where the tangent plane to this ellipsoid is parallel to the plane y-8x-4z = 0
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the product of nine and x is greater than six more than the product of three and x...?
Answers
6x>6
It doesn't tell my to graph anything so I went ahead and just simplified.
Hope this helps!
The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length. Which of the following expressions represents the area of the rectangle, in square units?
Answers
l = x - 2
The width is 4 more than this length:
w = l + 4 = (x - 2) + 4 = x + 2
Now, given that we have the length and width and are looking for the area, we need to multiply these expressions together.
One way to write this would simply be (x + 2)(x - 2). If we wanted to find a different way of writing the area, we could use FOIL to find all terms and get x^2 - 4.
A probability experiment consists of rolling a a 6 6-sided die. find the probability of the event below. rolling a number with exactly 2 not necessarily unique prime factors number with exactly 2 not necessarily unique prime factors
Answers
The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.
The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:
4 has two prime factors: 2 and 2 (2 squared).6 has two prime factors: 2 and 3.The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.
Thus, the probability of rolling a number with exactly two prime factors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6 = 1 / 3
Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).
Find the sum of each row in the table. Explain why these sums make sense.
Table:
Food | Rent | Transportation
1/4 6/10 3/20
25%. 60%. 15%
0.25 0.60 0.15
Answers
1/4 6/10 3/20 1
25%. 60%. 15% 100%
0.25 0.60 0.15 1
Answer:
The sum of each row in the table makes sense because we are writing the same amount in three different ways.
Therefore, the result is the same.
Final answer:
The sums of each row in the table represent allocations of a whole expressed in different formats (fractions, percentages, and decimals), and they all add up to 1 or 100%, signifying a full allocation of resources.
Explanation:
To find the sum of each row in the provided table, we add the numbers given within that row. Since the table is arranged with fractions, percentages, and decimals that all represent proportions of a whole, the sum of each row should theoretically be equal if converted into the same format. For instance, we should expect each row to total 1 or 100% if we are discussing a full allocation of resources like a budget.
For the first row, we need to add the fractions: 1/4 + 6/10 + 3/20. To do this, we'd need a common denominator, which is 20. So we get (5/20) + (12/20) + (3/20) = 20/20, which simplifies to 1.
The second row represents percentages and they need to total 100%: 25% + 60% + 15% = 100%
Finally, the third row lists decimals which should sum up to 1: 0.25 + 0.60 + 0.15 = 1.00
All three rows make sense because they represent different ways of expressing the whole, which is split into portions allocated to Food, Rent, and Transportation.
Keller boat travels 24mph. find the rate of the river if she can travel 6 mi upstream. in the same amount of time she can go 10 mi downstream.
Answers
time=(distance)/(speed)
time taken to travel upstream is:
(24+x)/10
Time taken to travel downstream is:
(24-x)/6
given that the time taken to travel upstream and downstream is the same then:
(24+x)/10=(24-x)/6
6(24+x)=10(24-x)
144+6x=240-10x
6x+10x=240-144
16x=96
x=96/16
x=6 mph
6 mph.
Explanation:
We will use the formula d = rt for this, where d is distance, r is rate, and t is time.
We know that the time for both distances is the same; this means we want to isolate t in our formula. To do this, we will cancel r by dividing both sides:
d/r = rt/r
d/r = t
We will write an expression for the time upstream, an expression for the time downstream, and set them equal.
For the time upstream, the distance is 6 and the rate is 24-x; this gives us
[tex]\frac{6}{24-x}[/tex]
For the time downstream, the distance is 10 and the rate is 24+x; this gives us
[tex]\frac{10}{24+x}[/tex]
Together, these give us the equation
[tex]\frac{6}{24-x}=\frac{10}{24+x}[/tex]
We cross-multiply to solve this:
6(24+x) = 10(24-x)
Using the distributive property, we have
6*24 + 6*x = 10*24 - 10*x
144+6x = 240-10x
Adding 10x to each side,
144+6x+10x = 240-10x+10x
144+16x = 240
Subtract 144 from each side:
144+16x-144 = 240-144
16x = 96
Divide both sides by 16:
16x/16 = 96/16
x = 6
Lars deposited $50 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 29 years?
Answers
Suppose the account used was using compound interest. Thus to determine his future value we shall use the formula:
FV=P(1+r)^n
where:
FV is future value
p=principle
r=rate
n=periods
from the information given
FV=$100
p=$50
n=29 years
we are required to find r
thus
100=50(1+r)^29
100/50=(1+r)^29
2=(1+r)^29
2^(1/29)=1+r
1.02419=1+r
hence:
r=0.02419~2.419%
Answer:
Step-by-step explanation:
The answer is 2.5%
find x intercepts of y=-3^× + 2
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Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value of the house after 10 years
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square root of -72 written in terms of i
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Work:
√-72 --> √36 * √-2 (36 is the perfect square needed to solve this problem)
6√-2 ---> 6i√2
Answer: 6i√2
Hope this helps!
Clayton wants to make a cylindrical case that will fit a bass drum with a height of 14 inches and a diameter of 24 inches. With is the surface area of the case? Use 3.14 \pi[tex] \pi [/tex]
Answers
A=2πr²+2πrh
"A" is the surface area of the cylinder.
"r" is the radius.
"h" is the height of the cylinder (h=14 inches).
2. You need to calculate the radius. So, you have:
r=Diameter/2
r=24 inches/2
r=12 inches.
3. You already have the height and the radius, so you can substitute these values into the formula (A=2πr²+2πrh) for calculate the surface area of the case:
A=2πr²+2πrh
A=2(3.14)(12 inches)²+2(3.14)(12 inches)(14 inches)
A=904.32 inches²+1055.04 inches²
A=1959.36 inches²
What would happen to a monthly payment if the interest rate increased
Answers
If the interest rate increases it is expected the monthly payment also increases.
What is the interest rate?This is usually a low percentage of money paid to the bank or a similar institution for borrowing money. The interest rate is established when the loan is approved and it is proportional to the amount of money that needs to be paid.
What would happen if the interest rate increased?As both the payment and the interest rate are directly related if the interest rate increases, the amount of money to be paid would also increase.
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Which of the points listed is the same distance from the x-axis as the point (7, 8.75)?
Answers
we know that
The distance of the point (7, 8.75) to the x-axis (the horizontal line) is 8.75
then
case A) (-7, 5.25)---------> is not correct ( the distance to the x-axis is 5.25)
case B) (8.75, 6)---------> is not correct ( the distance to the x-axis is 6)
case C) (6, -8.75)---------> is correct ( the distance to the x-axis is 8.75)
the answer is the option C) (6, -8.75)
Answer:
(7,-3.25)
Step-by-step explanation:
If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answers
3 square unit(s)
Explanation
The question is testing the concept of substitution.
A=12s^2
If s=1/2 , what is the value of A?
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. The is not fraction in the answer.
the answer is three square units
Ben has b dollars. Cam has 7 fewer dollars than Ben. How many dollars does Cam have? Write your answer as an expression.
Answers
B is the number of dollars Ben has and Cam has 7 less so you just subtract 7 from b
Answer:
Cam has [tex]b-7[/tex] dollars.
Step-by-step explanation:
Here b represents the number of dollars Ben has,
Given,
Cam has 7 fewer dollars than Ben,
So, the number of dollars cam has = The number of Ben's dollar - 7
[tex]=b-7[/tex]
Hence, the expression that represents cam's dollar is,
[tex]' b-7 '[/tex]
Classify each pair of labeled angles as complementary, supplementary, or neither. Drag and drop the choices into the boxes to correctly complete the table. Each pair of angles may belong to more than one category. complementary supplementary neither Two angles, on the left a fifty three degree angle and on the right a one hundred twenty seven degree angleTwo angles, on the top a thirty four degree angle and on the bottom a fifty six degree angleTwo lines intersect with an angle on the top left labeled sixty seven degrees and on the bottom right sixty seven degrees
Answers
supplementary angles have the sum of 180 degrees
1-
[tex]53 + 127 = 180[/tex]
so its supplementary
2-
[tex]34 + 56 = 90[/tex]
it's complementary
3-
[tex]67 + 67 = 134[/tex]
it's none of them
hope it helps
Answer:
Step-by-step explanation:
Since it is given that when two lines intersect, the angle on the top left is 53° and 127°, thus they both form supplementary angles as the sum of both angles that is 53+127=180°.
Also, from the given information, the angle on the top is 34° and on the bottom is 56°, they both form a complementary angle pair, a sthe sum of both the two angles is 90° as 56+34=90°.
Also, the angle on the top left is =67° and the angle on the bottom right =67°, they both form vertical pair angles as both the angles are vertically opposite to each other.
Finley's pumpkin had a mass of 6.5 kilograms before he carved it. After carving it, the pumpkin had a mass of 3.9 k.g.
What was the percent decrease in the mass of the pumpkin?
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when derek planted a tree it was 36 inches tall. the tree grew 1 1/4 inches per year the tree is now 44 3/4 inches tall. how many years ago did derek lant the tree?
Answers
inverse of f(x)=5x+4
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Switch x and y
Solve for y
Combine like terms to simplify the expression below 5y-8x-y+12x
Answers
Hope this helps!
If the graph of the function h defined by h(x)=-3x^2+3 is translated vertically upward by 3 units , it becomes the graph of a function g. Find the expression for g(x)
Answers
g(x) = (-3x² +3) +3
g(x) = -3x² +6 . . . . . . . . . the desired expression for g(x)
A video game club has 42 members. The number of high school members is six less than twice the number of middle school members. Which expression represents the number of high school members in the club?
Answers
x= # middle school members
2x-6= # high school members
Two times the number of middle school students is 2 times x. 6 less means to subtract 6 from 2x.
ANSWER: 2x-6 is an expression representing the number of high school members.
Hope this helps! :)
Answer:
2x-6
Step-by-step explanation:
You buy a house for $130,000. It appreciate 1.6% per year. identify the initial amount, growth rate and growth factor for the situation above. Then great an equation that will model it.
Answers
Greg drew a pair of parallel lines and a line segment next to each other on a chalkboard. Which of these statements best compares the pair of parallel lines and the line segment? (1 point) Parallel lines and the line segment have no dimensions of measurement. The parallel lines and the line segment always meet at a common endpoint which is called the vertex. Parallel lines and a line segment cannot lie on the same plane at the same time because they do not overlap. The parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Answers
Answer: If drew drew a pair of lines and draw the segment between them, in a way that the segment is delimited by both lines, then:
If two lines are parallel, then they will never overlap each other, and if you draw a segment between them, then the segment will have two endpoints (one at each intersection with the lines)
So the correct answer is that the parallel lines extend infinitely in both directions, and the line segment has two endpoints.
Earth's diameter at the equator is 7,926 miles. Find the distance around Earth at it's equator to the nearest tenth.
Answers
what is the discount on shirts if shirts cost $24 and there is a discount 25%
Answers
Step-by-step explanation:
25% × $24 = $6
Subtract the discount from the original
24 - 6 = $18.00
How would the domain and range of the function y= 1/4x-6 be determined
Answers
Answer: Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers
Simplify the sum 4/m+9+5/m^2-81
A. 9/(m-9)(m+9)
B. 4m+41/(m-9)(m+9)
C.9/m2+m-72
D.4m-31/(m-9)(m+9)
Answers
4/ ( m+9) +5 / ( m-9)(m+9)=
4(m-9)/(m+9)(m-9)+ 5 / (m+9)(m-9)=
(4m-36+5)/(m+9)(m-9)=
4m-31/ (m+9)(m-9)
the answer is D
D
Explanation:
1- The given expression is:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{m^2 - 81} [/tex]
2- Factorize the denominator of the second term:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{(m+9)(m-9)} [/tex]
3- Get the common denominator for both terms. In this case, the common denominator would be (m+9)(m-9):
[tex] \frac{4(m-9)}{(m-9)(m+9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
This will give:
[tex] \frac{4m-36}{(m+9)(m-9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
4- Add the numerators normally since the two terms have common denominator:
[tex] \frac{4m-36+5}{(m-9)(m+9)} [/tex] = [tex] \frac{4m-31}{(m-9)(m+9)} [/tex]
Comparing the calculated result with the given options, we will find that the correct option is the last one
Hope this helps :)
Find the radius and the circumference to the nearest hundredth when d ≈ 3.8 in. Use 3.14 for π.
Answers
radius r=d/2=1.9
C, circumference
C=2*3.14*r or C=d*3.14
C=3.08*3.14=11.932
C=11.93
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
We have,
If we let d be the diameter of a circle, then the radius of the circle, r, is half of the diameter.
Therefore, we can find the radius of the circle by dividing the diameter by 2:
r = d/2
In this problem,
d ≈ 3.8 in, so we have:
r = 3.8/2 = 1.9 in
To find the circumference of the circle, we can use the formula:
C = 2πr
where π is approximately equal to 3.14 and r is the radius we just found. Substituting in the values, we get:
C = 2 x 3.14 x 1.9 ≈ 11.94 in
Therefore,
The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.
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