express as a single logarithm 3 loga (2x+1) - 2 loga (2x-1) +2
Answer:
Step-by-step explanation:
[tex]3 \log_{a} (2x+1)=\log_{a}(2x+1)^{3}[/tex]
[tex]2 \log_{a}(2x-1)=\log_{a}(2x-1)^{2}[/tex]
[tex]2=\log_{a}(a^{2})[/tex]
So the expression can be expressed as a single logarithm as follows:
[tex]3\log_{a}(2x+1)-2\log_{a}(2x-1)+2=\log_{a}(2x+1)^{3}-\log_{a}(2x-1)^{2}+\log_{a}a^{2}[/tex]
[tex]3\log_{a}(2x+1)-2\log_{a}(2x-1)+2=\log_{a}\left(\frac{(2x+1)^{3}a^{2}}{(2x-1)^{2}}\right)[/tex]
determine the y- intercept of 3x+2y=9
Answer:
The y intercept is (0,4.5)
Step-by-step explanation:
Because the y-intercept occurs at x = 0, we can substitute this into our equation and solve for y.
3(0) +2y = 9
2y = 9
y=4.5
Answer:
[tex]\boxed{(0 , 4.5)}[/tex]
Step-by-step explanation:
→ Rearrange into y = mx + c format
2y = - 3x + 9
→ Divide everything by 2
y = -1.5x + 4.5
→ Substitute x = 0
y = 0 + 4.5 ⇒ 4.5
here is a list 31 29 33 37 43 38 33 40 find the mode in number of list and work out on mean
Answer: Mode = 33, Mean = 35.5
Step-by-step explanation: The mode is whatever number appears the most.
To find the mode, first put the numbers in order from least to greatest.
29, 31, 33, 33, 37, 38, 40, 43
In this case, 33 appears the most, so the mode is 33.
The mean is the average of all of the numbers.
Firstly, add up all of the numbers:
29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284
Now that you have all of them added up, divide the final sum by the number of numbers you have in the list. In this case, you have 8 numbers.
284/8 = 35.5
Your mean is 35.5
Answer:
Mode = 33
Mean = 35.5
The mode is whatever number appears the most.
to find the mean:
add all the numbers:
29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284
divide that by the number of numbers you have in the list.
284/8 = 35.5
mean = 35.5
Find the difference: 3 4/6 - 1/6
Answer:
7/2 but as a mixed number 3 1/2
Step-by-step explanation:
Answer:
3 1/2 or 3 3/6
Step-by-step explanation:
radius of a cylideical water tank is 5ft, and it's height is 9ft. What is the exact volume of the tank in terms of π
Answer:
225 pi
Step-by-step explanation:
Take note.
V= volume
r = radius
h = height
Formula for Volume of Cylinder
[tex]V=\pi r^{2}h[/tex]
[tex]V=\pi* 5^{2}*9[/tex]
[tex]V=706.85835[/tex]
Now in terms of pi.
[tex]\frac{706.85835}{\pi } =225[/tex]
225 pi
PLEASE HELP PLEASE HELP
Answer:
x = 80
Step-by-step explanation:
the total of interior angles in a quadrilateral (any shape with only 4 sides) is 360
add the angles you're given
105 + 100 + 75 = 280
subtract that number from the total interior angles (360)
360 - 280 = 80
therefore, x = 80
hope this helps! have a lovely day!!
The women’s heptathlon in the Olympics consists of seven track and field events: the 200-m and 800-m runs, 100-m high hurdles, shot put, javelin, high jump, and long jump. In the 2000 Olympics, the best 800-m time, run by Gertrud Bacher of Italy, was 8 seconds faster than the mean. The winning long jump by the Russian Yelena Prokhorova was 60 centimeters longer than the mean. Bacher’s winning 800-m time of 129 seconds was 8 seconds faster than the mean qualifying time of 137 seconds (the standard deviation of the qualifying times was 5 seconds). Prokhorova’s winning long jump was 60cm longer than the average 6-m jump (Note: the standard deviation of the long jumps was 30 cm). Which performance is more outstanding (and hence deserves more points when computing their overall score)? Explain.
Answer: Prokhorova is more outstanding.
Step-by-step explanation: To compare scores from different distributions, first standardize it:
z-score = [tex]\frac{x-\mu}{\sigma}[/tex]
where
x is the individual mean you want to compare
μ is the mean of the population
σ is standard deviation
For Gertrud Bacher:
z-score = [tex]\frac{129-137}{5}[/tex]
z-score = [tex]-1.6[/tex] (s)
The negative sign indicates Bacher's mean is less than the mean
For Yelena Prokhorova:
z-score = [tex]\frac{660-600}{30}[/tex]
z-score = 2 (cm)
The positive sign indicates Prokhorova's mean is more than the mean.
Using z-score table, you determine the percentiles are:
For Bacher: Percentile = 5.5%
For Prokhorova: Percentile = 97.7%
Bacher's percentile means she is above 5.5% of the participants, while Prokhorova is 97.7% above the other competitors, which means Prokhorova have a better performance and deserves more points.
need more points ??? solve this .....only first part for 50 points .....and follow me also!
Answer:
see below
Step-by-step explanation:
i.
= √(3 + 4i)
= 2 + i
ii.
= √(-8 + 6i)
= √2(-4 + 3i)
iii.
= √(-40 - 42i)
= √-2(20 + 21i)
iv.
= √i
= √i
v.
= [tex]\sqrt{\frac{2 + 3i}{5 - 4i} } +\sqrt{\frac{2-3i}{5+4i} }[/tex]
= [tex]\sqrt{\frac{-2+23i}{41} } +\sqrt{\frac{2-3i}{46} }[/tex]
Answer:
ok iam follow
Step-by-step explanation:
Mark as brainleist answer
If 10 is decreased to 5, the decrease is what percent of the original number?
Answer:
50
Step-by-step explanation: love uuuuuu
A stadium has 45,000 seats. Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,168,200 from each sold-out event. How many seats does section A hold?
Answer:
should be 90 seats each section hope that helped
PLS HELP I WILL AWARD BRAINLY
If f(x)=1−x² and g(x)=x²−1, then for which of the following values of b does
f(3b)+8=g(3b)−8?
A) 1
B)√8
C) 8
D) √3
E) 0
Answer:
A
Step-by-step explanation:
We have the two functions: [tex]f(x)=1-x^2[/tex] and [tex]g(x)=x^2-1[/tex].
And we want to find the value of b such that [tex]f(3b)+8=g(3b)-8[/tex] is true.
Notice that we can multiply f(x) by -1. This yields:
[tex]-f(x)=x^2-1[/tex]
Notice that this is the same as g(x). Therefore:
[tex]-f(x)=g(x)[/tex]
If we substitute 3b for x:
[tex]-f(3b)=g(3b)[/tex]
So, we can go back to our equation. We have:
[tex]f(3b)+8=g(3b)-8[/tex]
Substitute -f(3b) for g(3b):
[tex]f(3b)+8=-f(3b)-8[/tex]
Solve. Subtract 8 from both sides and add f(3b) to both sides:
[tex]2f(3b)=-16[/tex]
Divide both sides by 2:
[tex]f(3b)=-8[/tex]
Now, we can use the function of f(x). Substitute 3b into f(x). So:
[tex]1-(3b)^2=-8[/tex]
Subtract 1 from both sides:
[tex]-(3b)^2=-9[/tex]
Divide both sides by -1:
[tex](3b)^2=9[/tex]
Take the square root of both sides:
[tex]3b=\pm 3[/tex]
Divide both sides by 3. So, the value of b can be:
[tex]b=-1, 1[/tex]
Therefore, our answer is A.
And we're done!
Answer:
A.1
Step-by-step explanation:
f(x) = 1 - x² ⇒ f(3b) = 1 - (3b)² = 1 - 9b²
g(x) = x² - 1 ⇒ g(3b) = (3b)² - 1 = 9b² - 1
f(3b) + 8 = g(3b) - 8 ⇒ (1 - 9b²) + 8 = (9b² - 1) - 8
⇔ 9 - 9b² = 9b² - 9
⇔ 9 + 9 = 9b² + 9b²
⇔ 18 = 18b²
⇔ b² = 1
⇒ b = 1; - 1
Susie has a bag with 10 hair pins, 6 pencils, 3 snacks, and 4 books. What is the ratio of books to pencils? (This question made my teacher heart sad)
Question 1 options:
A.64
B.46
C.106
D.410
Answer:
B. 4/6
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Which of the following is equivalent to 5x + 7 = 6y?
А
5z+6 = 7
B
5z+6y = -7
C
5X- 6y =7
D
5x - y = -7
Answer:
c
Step-by-step explanation:
Will give brainliest to first answer !! What is 2 to the power of 44 multiplied by 84
if negative y = 0, what would positive y be?
Answer:
positive y would be also 0
Step-by-step explanation:
y = 0
PLEASE ANSWER BUT TAKE YOUR TIME.
Write an equation for a polynomial with all the following features:
a. The degree is 5.
b. The polynomial has 4 terms.
c. The graph of the polynomial crosses the vertical axis at Y = 12 .
Identify the approximate input values of any relative maximums and minimums of this 5th degree polynomial.
Answer:
Step-by-step explanation:
(x-1)^5 = x^5 - 5x^4 + 15x^3 - 15x^2 + 5x - 1
That has 6 terms, so let's get rid of the two middle ones.
f(x) = (x-1)^5 - 15x^2(x-1)
Now, f(0) = 1, but we want f(0) = 12
So, let
f(x) = 12((x-1)^5 - 15x^2(x-1)) = 12x^5 - 60x^4 + 60x - 12
As for the graph, it looks like
y = (x+4)(x+2)(x-1)^2(x-6)
The extrema appear to be at about (-3,1), (-1,-1), (1,0), (4,-9)
The relative maximums and minimums of this 5th-degree polynomial appear to be at about (-3,1), (-1,-1), (1,0), (4,-9)
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The degree of the polynomial is 5.
The polynomial has 4 terms
So (x-1)⁵ = x⁵ - 5x⁴ + 15x³ - 15x² + 5x - 1
Let's eliminate the two middle terms from it, which has six.
f(x) = (x-1)⁵ - 15x²(x-1)
Given that the graph of the polynomial crosses the vertical axis at Y = 12
So, substitute f(0) = 1, but we determine f(0) = 12
So, let f(x) = 12((x-1)⁵ - 15x²(x-1)) = 12x⁵ - 60x⁴ + 60x - 12
As for the graph, it looks like
So the approximate input values of relative maximums and minimums of this 5th-degree polynomial :
y = (x+4)(x+2)(x-1)²(x-6)
The relative maximums and minimums of this 5th-degree polynomial appear to be at about (-3,1), (-1,-1), (1,0), (4,-9)
Learn more about the polynomial here:
brainly.com/question/11536910
#SPJ2
PLEASE HELPPPPP ASAPPPPP
Try this and if it doesn't help you I will give you the answer straight to you
The formulas for calculating changes in the money supply are as follows. Firstly, Money Multiplier = 1 / Reserve Ratio. Finally, to calculate the maximum change in the money supply, use the formula Change in Money Supply = Change in Reserves * Money Multiplier.
Person A can paint the neighbor's house 3 times as fast as Person B. The year A and B worked together, it took them 10 days. How long would it take each to paint the house?
Bro I don't know if I'm dumb or not but I literally can't figure this out. Please help my struggling self wcdfvrd
Answer:
A: 13 1/3 daysB: 40 daysStep-by-step explanation:
If person A can paint the house in 'a' days, then person B takes 3a days. Each day, the total amount of house painted when they work together is ...
1/a + 1/(3a) = 1/10
4/(3a) = 1/10 . . . combine terms
40 = 3a . . . . . . . cross multiply
a = 40/3 = 13 1/3 . . . . . divide by 3
A can paint the house in 13 1/3 days.
B can paint the house in 40 days.
Solve 2y−18x=−26 for y.
how do you write this in slope intercept form i don’t know
Answer: y = [tex]-\frac{2}{1.5}[/tex]x + 15
Step-by-step explanation:
Slope intercept form is written as y = mx + b, where m is the slope and b is the y- intercept.
2.00x + 1.50y = 15
1.50y = -2.00x + 15
y = [tex]\frac{-2}{1.5}[/tex]x + 15
Please help pre Algebra question
Answer:
4=No
-3=No
2=Yes
0=No
Step-by-step explanation:
enter enter all the factors into the equation and see which one equals -28 on both sides at the end.
I just need the answer please n thank u<3
Answer:
C. [tex]x=-9 \textsf{ and }x=1[/tex]
Step-by-step explanation:
[tex](x+4)^2=25[/tex]
[tex](x+4)(x+4)=25[/tex]
expand the brackets:
[tex]x^2+8x+16=25[/tex]
subtract 25 from both sides:
[tex]x^2+8x-9=0[/tex]
factor:
[tex]x^2+9x-x-9=0[/tex]
[tex]x(x+9)-1(x+9)=0[/tex]
[tex](x-1)(x+9)=0[/tex]
solve for x:
[tex]x-1=0 \implies x=1[/tex]
[tex]x+9=0 \implies x=-9[/tex]
9 + 1.25x > 14 + 0.75x
Answer:
X>10
Step-by-step explanation:
9+1.25x>14+0.75x
Answer:
x>10
Step-by-step explanation:
What is 24 times 2 equal to?
Answer:
The answer is 48 :)
On the number line, which two numbers are a distance.20 away from the number 5
Answer:
4.8 and 5.2
Step-by-step explanation:
5+.2=5.2 5-.2=4.8
Hopes this helps!
For me i got the awnser -15 and 25
(a+4)-[12-(a+2)-(a+2)
Answer:
a=4/3
Step-by-step explanation:
Opening the brackets,
a+4-12+a+2+a+2
3a=4
∴a=4/3
This graph shows the number of tickets for a new movie sold at a theater
during the first 8 weeks of the movie's release.
The company determined that the equation y = 7,500 - 850x modele
data fairly well. What is the meaning of the slope of the linear model?
Ticket Sales
(A)
the number of tickets sold each week
(B) the weekly change in the number of tickets sold
.
Tickets Sold
8,000
7,000
6,000
5,000
4,000
23,000
2,000
1,000
©
the smallest number of tickets sold in a week
0
the number of tickets sold on the first day the movie was
released
1 2 3 4 5 6 7 8
Week
Using linear function concepts, it is found that the meaning of the slope is given by:
(B) the weekly change in the number of tickets sold.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.From this, we have that the slope represents a rate of change, hence, option B is correct.
More can be learned about linear function concepts at https://brainly.com/question/24808124
Examine this multiplication problem. 3 2 5 × 1 2 Which are equal to the product? Check all that apply.
Answer:
17/10, 1 and 7/10
Step-by-step explanation:
Find the quotient: 60 ÷ 30 =
Answer:
2!!!!!
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
do 6/3 easy as pie! (not pi)
Which equation represents this sentence?
Four times the sum of a number x and a number y is equal to 20.
4xy = 20
4x + y = 20
O 4(x + y) = 20
4 + x + y = 20
Answer:
4(x+y)=20
Step-by-step explanation: