We are given the equation:
log₂(x-3) + log₂x - log₂(x+2) = 2
When is it defined:
in this equation, log₂(x-3) and log₂(x+2) can only be defined when
x-3 >0 and x+2 > 0
solving for the values of x, we get:
x > 3 and x > -2
which basically means x > 3
Because we are looking for an inequality which is true for both x>-2 and x>3
Hence, x will have a value greater than 3
Solving for x:
using the product rule [logₐb + logₐc = logₐ(bc)]
log₂[(x-3)(x)] - log₂(x+2) = 2
using the quotient rule [logₐb - logₐc = logₐ(b/c)]
log₂[(x-3)(x) / (x+2)] = 2
from the property [ aˣ = b ⇒ logₐb = x]
(x² - 3x) / (x+2) = 2²
x² - 3x = 4x + 8
x² - 7x - 8 = 0
x² + x - 8x - 8 = 0
x(x+1) - 8(x+1) = 0
(x-8)(x+1) = 0
(x-8) = 0 OR (x+1) = 0
x = 8 OR x = -1
We know that the equation is defined only for x > 3
We can see that x = 8 satisfies that inequality
Therefore, x = 8
Find the product. Enter your final answer as a simplified fraction.
1/4•4/5•5/6=
Answer:
I am sorry if I'm wrong, but I got 600 or 36000/60
Step-by-step explanation:
First I looked for the least common denominator,(LCM) it was 60. Then I multiplied the numerator by the number that was multiplied by the denominator to find the new numerator for each fraction.(Example: The denominator was 60, so I looked for what 60 divided by four was, because that was the denominator. It ended up being 15. now I multiplied the numerator, which was 1 by 15 to create the new numerator. Then I did that with the other two fractions.) After all the fractions have the same denominator, you can multiply them. To multiply fractions you multiply all the numerators together and leave the denominator the same. Then I just simplified it. From 36000/60 to 600. Hope this helped :)
What is the answer for number 5
Step-by-step explanation:
3x - 7 = 11
3x = 11 + 7
3x = 18
x = 18/3
= 6
To find the product of
3
7
×
5
9
, Cameron simplified
3
7
to
1
7
and then multiplied the fractions
1
7
and
5
9
to find the product
5
63
. What is Cameron's error?
Cameron divided a factor in one of the numerators by the GCF but did not divide a factor in one of the denominators by the GCF. He should have simplified
5
9
to and multiplied
1
7
and to find the product .
please i need help.
Answer:
.........................
The sum of three consecutive numbers is 84. What is the largest of these numbers?
26
27
28
29
Step-by-step explanation:
set 3 no is ,x _ I ,x,x+1
X-1 + x + x + I = 84
3 X = 84
X= 84/ 3
X= 2 8
largest no is 29
Carlos is blowing air into a spherical soap bubble at the rate of 5 cm3/sec.
How fast is the radius of the bubble changing when the radius is 10 cm? (Round your answer to four decimal places.)
How fast is the surface area of the bubble changing at that time? (Round your answer to one decimal places.)
Answer:
The answer is below
Step-by-step explanation:
a) dV/dt = 5 cm³/s
The volume (V) of the bubble is:
[tex]V=\frac{4}{3} \pi r^3\\\\Differentiating\ with\ respect\ to \ time(t)\\\\\frac{d}{dt}(V)=4\pi r^2 \frac{dr}{dt} \\\\Substituting\ \frac{d}{dt}(V)=5\ cm^3/s \ and\ r = 10\ cm\\\\5 = 4\pi *10^2*\frac{dr}{dt}\\\\5=400\pi *\frac{dr}{dt}\\\\\frac{dr}{dt}=0.004\ cm/s[/tex]
b) The surface area of the sphere (A) is:
[tex]A=4\pi r^2\\\\Differentiating\ w.r.t.\ t:\\\\\frac{dA}{dt}= 8\pi r\frac{dr}{dt} \\\\r=10, dr/dt=0.004\\\\\frac{dA}{dt}= 8\pi *10*0.004\\\\\frac{dA}{dt}=1\ cm^2/s[/tex]
The rate at which the radius of the bubble is changing at that time is [tex]0.0125 \pi cm^2/s[/tex]
The rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
The formula for calculating the volume of a sphere is expressed as;
[tex]V =\frac{4}{3} \pi r^3[/tex]
r is the radius of the sphere
Differentiating the volume with respect to time;
[tex]\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt} \\\frac{dV}{dt} = 4 \pi r^2\frac{dr}{dt}[/tex]
Given the following parameters
dV/dt = 5 cm^3/sec.
r = 10 cm
Substitute into the formula to get dr/dt
[tex]\frac{dV}{dt} = 4 \pi (10)^2 \times \frac{dr}{dt}\\5 = 400 \pi \times \frac{dr}{dt}\\ \frac{dr}{dt}=0.0125 \pi cm/s\\[/tex]
The surface area of the bubble is expressed as:
[tex]S = 4 \pi r^2\\\frac{dS}{dt} = \frac{dS}{dr}\times \frac{dr}{dt}\\ \frac{dS}{dt} =8 \pi r \times 0.0125 \pi\\ \frac{dS}{dt} =\pi ^2 cm^2/s[/tex]
Hence the rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
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1) 3 is 50% of what?
Answer: 6
Step-by-step explanation:
Which of these shows the following expression factored completely? 6x2 – 13x +5
Answer:
B
Step-by-step explanation:
That's my guess.
Answer:
C
Step-by-step explanation:
ANSWER THE QUESTION PLEASE I NEED 100%
Answer:
B 8 +(-5)
Step-by-step explanation:
It was at 8 degrees then dropped 5.
So 5 was subtracted from 8.
Hope this helps!!
Understand the question explain and u will be brainiest
Find the slope of the following line: y=6x+1
Answer:
m=6 x-intercept = ( ---- ----1,0,6) y-intercept =(0,1)
Step-by-step explanation:
Slope= rise and run Since 6 is essentially 6-1 we know that the slope goes up to 6 units and right 1 unit on a graph.
Make sure to brainliest
what is 2.898989... as a mixed number?
Answer:
2 89/100
Step-by-step explanation:
its 289/100 as an improper fraction
Keep in mind that 0.89 means 89/100.
Now apply the whole number 2.
We get 2_(89/100).
Emily went to the fair with $22.50. She spent $2.25 on food and wanted to spend the rest on rides which were $0.75. What is the maximum number of rides Emily can purchase?
Answer:
19
Step-by-step explanation:
2.25 + 0.75 = 3.00
22.50 - 3.00 = 19.50
Hope I helped!
Mr. Johnson listed each class’s average on a quiz in fraction form. Based on the chart, Which shows the classes ordered from the highest average to the lowest average?
A. C,D,A,B
B. C,A,D,B
C. B,D,A,C
D. B.A,D,C
Answer:
C
Step-by-step explanation:
I'm not sure if my picture made since because I'm not the best at drawing but that's how I'd explain it
The table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.
Answer:
Answer is C
Step-by-step explanation:
There is not enough samples.
Answer:
Yes, the variation of the sample means is small.
Step-by-step explanation:
How do you do this question?
Step-by-step explanation:
Start with the series representation for eˣ.
eˣ = ∑ₙ₌₀°° xⁿ / n!
Substitute -x².
e^(-x²) = ∑ₙ₌₀°° (-x²)ⁿ / n!
e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!
Multiply by x².
x² e^(-x²) = x² ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!
x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺²) / n!
Integrate both sides (use power rule).
∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺³) / ((2n + 3) n!)
Evaluate between x=0 and x=0.5.
∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (0.5²ⁿ⁺³) / ((2n + 3) n!)
This is an alternating series, so use alternating series estimation.
(0.5²⁽ⁿ⁺¹⁾⁺³) / ((2(n+1) + 3) (n+1)!) ≤ 0.001
(0.5²ⁿ⁺⁵) / ((2n + 5) (n+1)!) ≤ 0.001
n ≥ 1
So the estimate of the integral is the sum of the first two terms (n=0 and n=1).
I = (-1)⁰ (0.5³) / ((3) 0!) + (-1)¹ (0.5²⁺³) / ((2 + 3) 1!)
I = (0.5³) / 3 − (0.5⁵) / 5
I = 1/24 − 1/160
I = 17/480
I = 0.0354
Simplify: 5^ -3 • 5^ 5
25^ 8
25^ -15
5^ -3
5^ 2
5^2
Step-by-step explanation:
You just add the exponents
-3 +5 =2
Answer:
5^2 .............................
Step-by-step explanation:
-3 + 5 = 2
on Tuesday the Madison Avenue Hotel had 5 occupied rooms for every 2 unoccupied rooms. If there were 80 rooms occupied on Tuesday how many total rooms are there in the Madison Avenue Hotel?
Answer:
32
Step-by-step explanation:
if there are 5 occupied rooms for every 2 unoccupied, you just have to (80/5)x2
(16)x2
32
A dog has three puppies. Spot weighs 12 ounces. Rascal weighs 9.5 ounces. Socks weighs 10.2 ounces. What is the total weight of the litter expressed to the correct number of significant figures?
a. 31.7 ounces
b. 31 ounces
c. 32 ounces
d. 30 ounces
e. 31.70 ounces
Answer:
c. 32 ounces
Step-by-step explanation:
Given that:
The weight of the Spot = 12 ounces
The weight of Rascal = 9.5 ounces; &
The weight of Socks = 10.2 ounces.
To find the litters' total weight, we will sum all the given number of the puppies.
i.e. Total weight of the litter = (12 + 9.5 + 10.2) ounces
Total weight of the litter = 31.7 ounces
Total weight of the litter [tex]\simeq[/tex] 32 ounces to the correct number of significant figures.
you have a bill of $100. find a 10% tip?
Answer:
10 bucks
Step-by-step explanation:
Answer:
$10
Step-by-step explanation:
10%=0.1
100*0.1=10
$10
The table below shows the number of miles Josh drives and the number of hours it takes to get there. What is the constant of proportionality in the table?
Answer:
B. 50
Step-by-step explanation:
2×50=100
3×50=150
4×50=200
5×50=250
x squared - 7x-34=10 solve
The solution is: solve of the equation x²- 7x-34=10 is: x = 11 or, x = -4.
Here, we have,
given that,
the equation is: x squared - 7x-34=10
now, we have to solve this.
so, we have,
x squared - 7x-34=10
or, x²- 7x-34=10
or, x²- 7x - 44 = 0
or, x²- 11x + 4x - 44 = 0
or, x(x-11) + 4(x-11)
or, (x-11) (x + 4) = 0
so, we get,
either , x = 11 or, x = -4
Hence, The solution is: solve of the equation x²- 7x-34=10 is: x = 11 or,
x = -4.
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I WILL GIVE BRAINLIST
Zaire keeps track of the number of frisbee golf holes on which he makes par or better. The
table shows the number of holes Zaire has played during his round so far. If the ratio of holes
with par or better to total holes played is equal to 0.8, on how many of the holes has Zaire
made par or better?
Answer:
1.80
Step-by-step explanation:
Zaire has made par or better on 12 holes out of 15 that he has played.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
If the ratio of holes with par or better to total holes played is equal to 0.8, it means that Zaire has made par or better on 80% of the holes he has played.
Let's set up an equation to solve for the number of holes with par or better:
N/15 = 0.8
To solve for N, we can cross-multiply:
N = 15 x 0.8
N = 12
Therefore, Zaire has made par or better on 12 holes out of 15 that he has played.
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Which one is the slope and which one is the y-intercept? Thank you for answering whoever answers.
Answer:
2.50 is the y-intercept, and 0.30 is the slope.
Step-by-step explanation:
y = 0.3x + 2.5
Answer:
Y intercept is the intercept that goes up and down on a graph. (x,y) Rise/run is the slope. Rise is how many y units one point is from the other and run is how many x units is away from one point to another on a graph. Hope this helped at all.
What is 0.87 is 10 times as much as?
Answer:
0.087
Step-by-step explanation:
So the equation would be:
x × 10 = 0.87
So you need to find what x is
An easy way to do this is to just to:
Move the decimal point twice to the left to get 0.087
Hope this helps!
One pound of candies costs $3.50.
How many pound of candies can be bought for $10.50?
Answer:
2
Step-by-step explanation:
10.5/3.5=2
Solve for k. simplify the answer
Answer:
c=5/2k+ −45/2
Step-by-step explanation:
Answer:
K= 9 + 2/5C
Step-by-step explanation:
1. Remove the parentheses
C= 5/2 x (k-9)
2. Multiply both sides
C= 5/2k- 45/2
3. Move the terms
2C= 5k- 45
4. Divide both sides
-5k= -45- 2C
5. Write in parametric form
k=9 + 2/5C
An object moving in a straight line passes through the points (3, 0) and (2, 2). The object also passes through the point (0, a).
Calculate the value of a.
Answer:
colinear pts (meaning gradient is same throughout)
Step-by-step explanation:
since grad is same,
(2-0)/(2-3) = (a-0)/(0-3)
-2 = a/-3
6 = a (multiply both sides by -3)
The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of
the larger number is 6. If x is the smaller number and y is the larger number, which two equations
represent the sum and difference of the numbers?
O x - y = 77 and 1/2 x + 1/3 y = 6
O x + y = 77 and 1/2 x - 1/3 y = 6
Ox-y=6 and 1/2 x + 1/3 y = 77
Answer:
so x+y=77
1/2x-1/3y=6
Can someone help me plz
Answer:
i think the answer is 7
What is 15.23 rounded to the nearest hundredth
Answer:
15.20
Step-by-step explanation:
