Answers
Note:
log_a c=b can be written as:
aᵇ=c
hence:
1. log₄ 16=2
will be written in exponential as:
4²=16
2. 25^(1/2)=5
will be written in logarithmic form as:
log₂₅5=1/2
3. Which function represents exponential growth?
#N/B For an exponential function:
y=a(b)^x
when b>1 it exponential growth
when b<1 it is an exponential decay
F: y=1/20(4)ˣ
b=4>1
exponential growth
G: y=16(0.4)ˣ
b=0.4<1
exponential decay
H: 20(1/8)ˣ
b=1/8<1
exponential decay
I. y=8x³
The above function does not have a growth factor, thus
it is a polynomial function not an exponential function.
4. Solve log₄3+log₄x=log₄18
when we add log functions we can multiply them as follows:
log₄(3*x)=log₄18
the log₄ will cancel and we shall remain with:
3x=18
solving for x we get:
(3x)/3=18/3
thus
x=6
5. Solve log₇36x-log₇2=log₇9
Dividing log functions is like subtracting them, thus we shall have:
log₇(36x/2)=log₇9
simplifying this we get:
log₇ 18x=log₇9
log₇ will cancel because of the same base and we shall have:
18x=9
thus
x=9/18
x=1/2
Expand the following:
Remember:
Multiplying logs is the same as adding them
Subtracting logs is the same as dividing them
thus
6. log₃ 4xy
expanding the above give us:
log₃4+log₃x+log₃y
Answer: log₃4+log₃x+log₃y
7. log₅ (xy²)/3
expanding this gives us:
log₅x+log₅y²-log₅3
Answer: log₅x+log₅y²-log₅3
Condense the following logarithms:
Using the concept from 6 and 7 we shall have:
8. log₈2+log₈7-log₈x
condensing this will give us:
log₈[(2*7)/x]
simplifying gives us:
log₈(14/x)
9. log₇9+3log₇y-4log₇2
Condensing the above gives us:
log₇9+3log₇y-4log₇2
=log₇9+log₇y³-4log₇2
=log₇(9*y³)/2
=log₇(9y³/2)
Related Questions
John's dog weighted 7 pounds when we got him. The dog's weight tripled each year for two years. How many ounces does John's dog now weigh?
Answers
7 pounds x 3(tripled) = 21 pounds
7*3*3=63 pounds and converting pounds to ounces, 63 pounds is 1,008 ounces.
If the height of your he sailboat is 3 centimeters, what is the height in meters, of the actual boat
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Describe the effect on the SURFACE AREA of multiplying the dimensions by 1/5.
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I don’t know I need help fast
Answers
The function rule for the following graph is y = 2x + 2. What is the value of y in the ordered pair (2, y)? 24 4 10 6
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Answer:
The correct answer is 6.
Step-by-step explanation:
I just did this question as well and 6 was the correct answer. Hope this helped :)
Part a) What do you know that will help you set up the equation to solve this problem?
Part b) Write the equation that allows you to solve for the height.
Part c) What is the height of the trapezoid (including units)
Answers
A = (1/2)(b₁ +b₂)×h
B) You are given the area and the lengths of the two bases. Substituting the given numbers into the formula will give you an equation for h.
280 cm² = (1/2)(8 cm +20 cm)×h
C) Solving the equation of part B, we have
280 cm² = (14 cm)×h
280 cm²/(14 cm) = h . . . . . . . . divide by the coefficient of h
20 cm = h . . . . . . . . . . . . . . . .. evaluate
The height of the trapezoid is 20 cm.
Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3
Answers
A(-2,-4) B(8,1)
let
M-------> the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3
we know that
A--------------M----------------------B
2 3
distance AM is equal to (2/5) AB
distance MB is equal to (3/5) AB
so
step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
Mx=-2+(2/5)*10-----> Mx=2
step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2
the coordinates of point M is (2,-2)
see the attached figure
Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. π , √5 ,√8 ,2√5
(a)Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
(b)Order the ribbon sizes from least to greatest. Use the original numbers given.
Answers
[tex] \pi = \frac{12.5}{2(2)} [/tex]
[tex] \pi = \frac{12.5}{4} [/tex]
[tex] \pi =3.125[/tex]
And to the nearest tenth:
[tex] \pi =3.1[/tex]
To approximate [tex] \sqrt{2} [/tex], we are going to use the Babylonian method:
Step 1. We are going to make a guess. Our guess is 2 because [tex] \sqrt{4} =2[/tex], so [tex] \sqrt{5} [/tex] must be close to 2.
Step 2. We are going to divide 5 by 2:
[tex] \frac{5}{2} =2.5[/tex]
Step 3. We are going to find the average between our initial guest and the result of our previous calculation:
[tex] \frac{2+2.5}{2} = \frac{4.5}{2} =2.25[/tex]
And to the nearest tenth: [tex] \sqrt{5} =2.2[/tex]
To approximate [tex] \sqrt{8} [/tex], we are going to use the Babylonian method one more time:
Step 1. Our guess is 3 because [tex] \sqrt{9} =3[/tex], so [tex] \sqrt{8} [/tex] must be close to 3.
Step 2. We are going to divide 8 by 3:
[tex] \frac{8}{3} =2.6[/tex]
Step 3. We are going to find the average between our initial guest and the result of our previous calculation:
[tex] \frac{3+2.6}{2} = \frac{5.6}{2} =2.8[/tex]
[tex] \sqrt{8} =2.8[/tex]
To approximate [tex]2 \sqrt{5} [/tex] we are going to multiply our approximation of [tex] \sqrt{5} [/tex] and multiply it by 2:
[tex]2 \sqrt{5} =2*2.2[/tex]
[tex]2 \sqrt{5}=4.4[/tex]
(b) Since we have our irrational numbers expressed as decimal approximations, we can compare them to arrange them form least to greatest:
2.2,2.8,3.1,4.4
Now, we just need to replace the decimal approximations with the original numbers:
[tex] \sqrt{5} [/tex],[tex] \sqrt{8} [/tex],[tex] \pi [/tex],[tex]2 \sqrt{5} [/tex]
We can conclude that ordering the ribbon sizes from least to greatest we get:
[tex] \sqrt{5} [/tex],[tex] \sqrt{8} [/tex],[tex] \pi [/tex],[tex]2 \sqrt{5} [/tex]
Factor completely; 100-9x^2
Answers
Answer:
(10 - 3x)(10 + 3x)
Explanation:
This type of question yields what is called a difference of squares, which is recognizable because of the subtraction (-) operation between the two terms of the binomial. When questions like this are seen, the formula for difference of squares can be implemented. This formula is:
(a² - b²) = (a - b)(a + b)
With this, we can square root both terms of the original binomial and plug our variables for a and b into the formula.
Let 100 = a², let 9x² = b²
√(100) = 10
√(9x²) = 3x
Those values are now a and b, respectively, so when we place them in their spots in the formula, the completed factoring is: (10 - 3x)(10 + 3x)
To check this answer for accuracy, we can use the FOIL method and combine like terms to see if it gives us the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing us which terms should be multiplied together so:
Firsts: 10(10) = 100
Outsides: 10(3x) = 30x
Insides: -3x(10) = -30x
Lasts: -3x(3x) = -9x²
We place them in the same equation and combine like terms:
100 + 30x - 30x - 9x²
100 + 0 - 9x²
100 - 9x²
We are back to our original equation so the answer of (10 - 3x)(10 + 3x) is accurate.
can anyone help me please
Answers
What is 98765+009225=
Answers
Short answer: 107990
Why?
One red flag I see here is two zeroes as the first to digits of the second number, so we can take that away. So we can write it as 9225. Set it up into an equation. Add straight down.
1 1
98765
+ 9225
**********
107990
Hope this helped you! ♥
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x^2 to the number of x-intercepts in the graph of g(x)=-x^2. Be sure to include the transformations that occurred between tye parent function f(x) and its image g(x)
Answers
shari has 1 1/2 gallons of orange juice. She wants to serve the orange juice equally among her 12 friends. How many ounces of juice will each friend receive
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So half a gallon would have 64 ounces
Now it says Shari has 1 1/2 which means we would add 128 ounces and 64 ounces together to get 192 ounces.
1 1/2 gallons = 192 ounces
Now we take the 192 ounces and divide it into 12 because she has 12 friends to share with.
192/12 = 16 ounces
Each friend with get 16 ounces of orange juice.
At a local used car lot, one out of every three cars is red. If the car lot had 54 cars on it, how many cars are red SHOW WORK PLZ
Answers
Number of red cars = 1/3 x 54 = 18
Answer: There are 18 red cars
To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3. The calculation is: Number of red cars = 54 * (1/3) = 18 cars.
Explanation:To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3.
To calculate how many cars out of 54 are red, we can multiply the total number of cars by the probability of a car being red:
Number of red cars = 54 * (1/3) = 18 cars
Therefore, there are 18 cars that are red in the lot.
A recent poll taken by the movie theatre industry shows that 28% of the population attends a movie in a theater at least once a month. A sample of 300 people shows that only 12% of people attends a movie in a theater at least once a month. To determine whether this sample supports the population proportion of 0.28, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.12. The minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28. What is the margin of error of the population proportion using half the range?
Answers
Answer:
The margin of error for this population proportion using half the range = ±0.09
Step-by-step explanation:
Confidence Interval is basically an interval of range of values where the true proportion can be found with a certain level of confidence.
Margin of Error is the width of the confidence interval about the central proportion.
For this question, the minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28, hence, the confidence interval for the question is (0.10, 0.28).
The width of this confidence interval = (Upper limit of the interval) - (Lower limit of the interval) = 0.28 - 0.10 = 0.18.
Hence, the margin of error for this population proportion using half the range, is 0.18/2 = 0.09.
Written appropriately as ±0.09.
Hope this Helps!!!
A small submarine starts at –1,260 feet in relation to sea level. Then it descends 5 feet per minute for 12 minutes. What is the new position of the submarine in relation to sea level? –1,260 + (–5)(12) = –1,260 + 60 = –1,200
Answers
It descends 5 ft/min for 12 min.
12 min * 5 ft/min = 60 ft.
It descended 60 ft, so you must subtract 60 ft from -1260 ft.
-1260 ft + (-5)(12) ft = -1260 ft - 60 ft = -1320 ft
The error in the last line in the problem is that (-5)(12) = -60, not 60.
The correct line is:
-1260 + (-5)(12) = -1260 - 60 = -1320
The new position of the submarine in relation to sea level is -1,200 feet.
Your calculation is correct. To find the new position of the submarine in relation to sea level after descending at a rate of 5 feet per minute for 12 minutes, you can use the formula:
New position = Initial position - (Rate of descent * Time)
In this case:
New position = -1,260 feet - (5 feet/minute * 12 minutes)
= -1,260 feet - 60 feet
= -1,200 feet
So, the new position of the submarine in relation to sea level is -1,200 feet.
To know more about submarine:
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Y = 4x + 2 y = x + 5 on a graph
Answers
What is the smallest 9 digit number ni the form, aaa,aaa,aaa such that is divisible by 9??
Plz help!!
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The smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9 is 111,111,111 because the sum of its digits is 9, which follows the divisibility rule for 9.
To find the smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9, we need to use the divisibility rule for 9. A number is divisible by 9 if the sum of its digits is also divisible by 9. Since we are looking for the smallest such number, we start with the smallest non-zero digit, which is 1.
The smallest 9-digit number where all digits are the same would be 111,111,111. Adding all the digits together, 1+1+1+1+1+1+1+1+1 equals 9, which is divisible by 9. Therefore, 111,111,111 is the smallest 9-digit number of the form aaa,aaa,aaa that is divisible by 9.
(2-9i)+(-2+7i) complex numbers simplify
Answers
[tex] (2-9i)+(-2+7i)=-2i [/tex]
Adam is making a rectangular frame. The frame is 24.2 feet long and 16.25 feet wide.
The formula for the area of a rectangle is A=bh.
What is the area of the frame?
Enter your answer as a decimal in the box.
(__ ft2
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b-----> the length of the base of the rectangle
h-----> the length of the width of the rectangle
we know that
Area of the rectangle=b*h
in this problem
b=24.2 ft
h=16.25 ft
so
area=24.2*16.25-----> area=393.25 ft²
the answer is
the area of the frame is
393.25 ft²
The price for a parakeet at Lydia's Pet World is $9.99. If you buy a cage and birdseed, the price decreases to $4.25. About what is the percent decrease in price if you buy a cage and birdseed?
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$5.74 represents ? %
9.99-4.25= 5.74 was discaunted
?= (5.74 •100)/9.99
Answer is about 57.46%
what is the square root of 50 to the nearest tenth
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Which one is bigger 11 g or 10,800 mg
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Can someone help with this please??
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7. semi circle is half a circle, there re 4 arcs smaller then half
they are DB, DC, AC and AB
last choice is correct
you are about take an 8 question multiple choice test .each of these questions has 4 answers (A,B,C,D). how many ways can you answer the test if you leave an answer for each question
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[tex] 4^8=65536 [/tex]
4^8 = 65536 answer is correct
Which word is an antonym for the word thrive?
Jasper knew we was going to thrive in his new school
A) fail
B) learn
C) worry
D) be busy
Answers
The antonym for the word thrive would be A. Fail Hope this helps :)
The required antonym for the word thrive is fall. Option A is correct.
The word "thrive" means to prosper, succeed, or flourish. Therefore, the antonym for "thrive" would be a word that represents the opposite, such as "fail." When someone fails, they do not achieve success or prosper in their endeavors. In the given sentence, Jasper is confident that he will thrive in his new school, indicating that he expects to do well and succeed. Choosing the word "fail" as the antonym creates a clear contrast, as it represents the opposite outcome of not being able to thrive or achieve success.
Thus, the requried antonym for the word thrive is fall. Option A is correct.
Learn more about antonyms here:
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8182÷k=1363.6666667
A- 9
B-2
C-6
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2 would be around 4000, and 9 would be less than 1000, so C is the only one
Hope this helps!
PLEASE MARK BRAINLIEST!
I NEED HELP I WILL GIVE BRAINLEST!!!!!!!!!!!
Answers
9^2 * 9^0
We know that anything to the zero power is one, so we are left with
9^2 which equals 81
–3x + 1 + 10x = x + 4
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1+7x=x+4
6x=3
x=.5
First, let's combine like terms.
-3x + 1 + 10x = x + 4
7x + 1 = x + 4
Now, subtract the one from the left. (we do this to combine terms)
7x + 1 = x+ 4
7x = x + 3
Now subtract the x from the right. (this is also to combine terms)
7x = x + 3
6x = 3
Finally, divide by 6 on both sides.
6x = 3
x = 1/2 or 0.5
Hope this helps!
please help the temperature in degrees fahrenheit can be estimated by counting the number of times a cricket chirps in one minute write an algebraic expression for the following written expression
the number of chirps divided by 4 added to 37