Answers
Answer:
Step-by-step explanation:
I'll just write log for log base 10. The important rules about logarithms we need to know are:
[tex] a \log b = \log( b^a) [/tex]
[tex] \log a + \log b = \log( ab) [/tex]
and at the end we'll need something like
[tex]\log a = \log b \implies a=b[/tex]
Suitably armed we can begin,
[tex] \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) [/tex]
First rule,
[tex] \log 3^{ 1 + 1/2x} + \log 2 = \log (27 - 3^{1/x}) [/tex]
Second rule,
[tex] \log 2(3^{ 1 + 1/2x}) = \log (27 - 3^{1/x}) [/tex]
Third rule,
[tex] 2(3^{ 1 + 1/2x}) = 27 - 3^{1/x} [/tex]
We can rewrite this to be a quadratic equation in [tex]y=3^{1/2x}[/tex].
[tex] 6 (3^{1/2x}) = 27 - (3^{1/2x})^2 [/tex]
[tex]y^2 +6y - 27 =0[/tex]
[tex](y - 3)(y+9)=0[/tex]
[tex]y=3 \textrm{ or } y=-9[/tex]
First solution:
[tex]3^{1/2x} = 3 = 3^{1}[/tex]
[tex]1/2x = 1[/tex]
[tex]1=2x[/tex]
[tex]x = 1/2[/tex]
Second solution,
[tex]3^{1/2x} = -9[/tex]
No real powers of 3 will be negative, no solution here.
Answer: x=1/2
Check:
1 + 1/2x = 2 so the left side is log 2(3²) = log 18
Right side, log(27-3^2) = log 18 √
Related Questions
Mr. Norris buys a boat for $125,000. He has to pay a 5% tax on his purchase of the boat. How much money is the tax?
Answers
6250 is 5% of 125000
please find Area of triangle
Answers
Answer:
60
Step-by-step explanation:
Side A would end up being 15 and then to find the area you would use your formula 1/2 × base × height.
Which expression results in the smallest difference?
A.
B.
C.
12.5 - 3.1
12.5 -0.31
12.5 -0.031
D.
12.5 -0.0031
Answers
Factorize: (a+b)^2 + 4 (a+b)+ 4
Answers
Explain how the vertical line test can be used to determine if a graph
is a function.
Answers
Answer:
Step-by-step explanation:
If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
Example:
Answer:
Step-by-step explanation:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
The rectangle below has an area of x2 - 16 square meters and a width of x + 4 meters.
What expression represents the length of the rectangle?
x +4
Length
x2 - 16
Length
meters
Answers
Answer:
Length = x - 4 meters
Step-by-step explanation:
Area of a rectangle = length × width
Area of a rectangle = x² - 16
width of the rectangle = x + 4 meters.
Length of the rectangle = ?
Recall:
Difference of two perfect square x² - 16 = (x + 4)(x - 4)
Area of a rectangle = length × width
(x + 4)(x - 4) = length * x + 4
Length = (x + 4)(x - 4) ÷ x + 4
Length = x - 4 meters
Find the measure of the arc DC
Answers
Answer:
The measure of arc DC is 50°. Circle O is shown. Line segments A C and E B are diameters. Line segment O D is a radii. Point D is between points E and C. Angle B O D is 90 degrees. What is the measure of Arc E B C? 40° 90° 140° 220°
Step-by-step explanation:
3)
How many solutions are there to the following equation?
3x-2(1 + x) + 2 = x
A. O
B. 1
C. Infinitely many
Answers
Answer:
letter B.1
ayan po sagot sa number 3
Step-by-step explanation:
3x-2(1 + x) + 2 = x
3x-2-2x+2=x
x-x=0
infinitely many
Name a pair of adjacent angles and a pair of vertical angles in the figure
Answers
Answer:
Adjacent: <ABC and <CBD
Vertical: <ABC and <EBD
Step-by-step explanation:
Adjacent angles: Angles that share one ray.
Vertical Angles: Opposite angles created by the intersection of two lines.
Hope this helps!!
If f(x) = 28+x + 7, what is the value of f(-9), to the nearest
hundredth (if necessary)?
Answers
Answer:
26
Step-by-step explanation:
Problem: f(x) = 28 + x + 7
Plug in f(-9)
New equation: f(-9) = 28 + (-9) + 7
Simplify: f(-9) = 26
Answer: f(-9) = 26
reverse percentage problem
Answers
answer: you're missing the problem
Seventy weather balloons were sent up. Twenty-eight were found. What percent wer ound? 17
Answers
Step-by-step explanation:
let the percent of found balloons be x
given,
total number of balloons= 70
number of found balloons= 28
according to the question,
x% of 70= 28
x/100 × 70 = 28
x=40
hence 40% of the balloons were found
Two angles of a triangle are 120° and 6° What is the measure of the third angle?
Answers
Answer: 54
The angles of a triangle add up to equal 180.
Since we already know two angles, we can just use simple math to find the third.
120 + 6 = 126
180 - 126 = 54
Answer:
54°
Step-by-step explanation:
A triangle ALWAYS measure a 180° Angle in total so if the first and second angle is 120° and 6°, just add it together and will form a 126° Angle so subtract it to 180° Angle and it will result in a 54° Angle
Thank you and please mark me as brainliest ^^
Put these Set of Numbers in ascending order.
3
-1
[tex] \sqrt{5} [/tex]
13
-11
Answers
Step-by-step explanation:
i think may be
3 ,13 ,-1 ,-11 , root under 5
Can someone help me out
Answers
Answer:
4 (100-250 words with a 100-word minimum)
3, 6, 12,
The common ratio is
Answers
Answer:
The common ratio is 2.
Step-by-step explanation:
3 : 6 : 12
1 : 2 : 4
Estelle hosted a banquet for her extended family that cost $480.93. Estelle paid 9.25% sales tax and left an 18% tip on $480.93. What was the total cost?
Answers
Answer:
$563.89: total cost of the banquet
Step-by-step explanation:
Here we can to find the total cost, including tax and tip, by adding 9.25% and 18% together first. We obtain 17.25%, which translates into the decimal fraction 0.1725 and results in the amount added to the original cost, $480.93. The result is added to $480.93:
1.0000($480.93) + 0.1725($480.93) = $563.89
A shortcut would be to find the total cost, including the original $480.93 and the additional 17.25%, by multiplying $480.93 by 1.1725:
1.1725($480.93) = $563.89: total cost of the banquet
Describe the main parts of a proof? ..
Answers
Answer:
Answer Expert Verified
Given; prove; statements; and reasons. Explanation: The given is important information we are given at the beginning of the proof that we will use in constructing the proof. The "prove" is the statement we are trying to prove
Answer:
Sample Response: Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.
Step-by-step explanation:
Have the day you deserve :)
What is the probability of student liking music given they already like
Answers
Answer:
So so so easy its 1 because all of them like music
if a dog drinks 8 quart of water a day, how many gallons does the dog drink in 3 days
Answers
Answer:
6 gallons
Step-by-step explanation:
There are 4 quarts in gallons, so the dog drinks 2 gallons a day.
When we multiply 2 and 3, we would get 6.
So the dog drinks 6 gallons in 3 days (I don't know about you, but that's a lot of water)
---------------------------------------------------------------------------------------------------------------
Have a great summer :)
Answer:
The dog will drink 6 gallons.
Step-by-step explanation:
Every 8 quarts is 2 gallons.
Multiply 2 by 3, you'll get 6.
that's how much gallons a dog drinks in 3 days.
HELPPP ME PLEASE WILL MARK BRAINLIEST IF YOU GIVE ME THE CORRECT ANSWER
Answers
Answer:
Option (3)
Step-by-step explanation:
Properties for the vertical stretch or shrink of a function,
If a function is f(x) = k|x|
1). Function will be vertically stretched if k > 1
2). Function will have a vertical shrink if 0 < k < 1
To fit the given data graph of f(x) = |x| will vertically shrink without any translation along x or y-axis.
And the value of k will be, 0 < k < 1.
Therefore, g(x) = [tex]\frac{1}{3}f(x)[/tex] will be the transformed graph.
Therefore, Option (3) will be the correct option.
please help with number 53!!!!
pretty please
Answers
Answer:
The sequence would be arithmetic. This is because an arithmetic sequence has a common number multiplying, adding, subtracting etc. The common rule for this set of numbers was x5. 9x5=45, 45x5=225 etc. We simply used this method with negative numbers, but the rule was still multiplying.
Happy learning!
--Applepi101 :)
Answer:
Arithmetic
Step-by-step explanation:
It has a constant difference between each number whilst Geometric usually has the same difference between each number
HELPPP PLEASEEEEEEE!!
Answers
Answer:
We would use the explicit formula since the explicit formula is used for finding the nth term in a sequence. The reason why it's not the recursive is because the recursive formula helps you find the next terms using a formula of the preceding term or term before the next term.
What is the relationship between the values tand s plotted on the number line
below?
S
A. t= s
B. t>s
O c. tcs
Answers
Answer:
The answer should be t > s. (B) is the answer.
Solve
4(-5)(-2)(-3)
show your work<3
no links
Answers
Answer:
-120Step-by-step explanation:
4(-5)(-2)(-3)
= -20 × 6
= -120 (Ans)
Answer:
-120
Step-by-step explanation:
lots of approaches here
suggest saying that there are 3 (odd) number of negative signs
so the answer is negative (-)
5*4 = 20
20*2 = 40
40*3 = 120
we determined that the answer has to be negative
-120
Which relationship has a zero slope?
Answers
a²+b²=c²
5²+9²=c²
25²+81²=c²
106=c²10.2
5
A dealer paid $7,000 for a car at an auction. At the dealership, a salesperson sold the car for 30% more than the auction price. The salesperson received a commission of 25% of the difference between auction price and the dealership price. What was the sales person’s commission?
Answers
25% of $2100 is $525
Use the perfect square trinomial identity to write this expression in factored form:
x2 + 10x + 25.
Answers
(X + 5)^2
Answer:
[tex] {x}^{2} + 10x + 25 \\ = ( {x}^{2} + 10x + {5}^{2} ) + (25 - {5}^{2} ) \\ = {(x + 5)}^{2} [/tex]
STATEMENT OF THALES THEORM NEED URGENTLY
HAVE A NICE DAY GOOD MORNING
Answers
Answer:
The Thales theorem states that: If three points A, B, and C lie on the circumference of a circle, whereby the line AC is the diameter of the circle, then the angle ∠ABC is a right angle (90°).
Maria has $120. She plans to purchase a shirt for herself and gifts for 6 of her
friends. She plans to spend the same amount for each gift. Which of the
following inequalities best represents the maximum amount Maria can spend on
each gift? *
DONT say the answer is on some link that’s annoying.
Answers
on edge
