First note that any solution must belong to all of the intervals
x + 2 > 0 ⇒ x > -2
x > 0
2x - 1 > 0 ⇒ x > 1/2
3x - 12 > 0 ⇒ x > 4
so x must be larger than 4.
Recall that log(a) - log(b) = log(a/b). So we can rewrite
log(x + 2) - log(x) = log(2x - 1) - log(3x - 12)
log((x + 2)/x) = log((2x - 1)/(3x - 12))
Take the antilogarithm/exponential of both sides (note that the base of the logarithm doesn't matter here):
exp[log((x + 2)/x)] = exp[log((2x - 1)/(3x - 12))]
(x + 2)/x = (2x - 1)/(3x - 12)
Eliminate the fractions:
x (3x - 12) • (x + 2)/x = x (3x - 12) • (2x - 1)/(3x - 12)
(3x - 12) (x + 2) = x (2x - 1)
Expand both sides, collect terms and factorize to solve for x :
3x² - 6x - 24 = 2x² - x
x² - 5x - 24 = 0
(x - 8) (x + 3) = 0
x - 8 = 0 or x + 3 = 0
x = 8 or x = -3
What is the volume of the cylinder below? 5 4 6 O A. 60 units 3 B. 967 units 3 O C. 80 units 3 D. 120 units 23
Answer:
B. 967 units is the answer
Answer:
C
Step-by-step explanation:
Solve the equation using the method of completing the square.
3x2 + 24x – 24 = 0
Answer:
Logical first step: divide everything by
3
Explanation:
→
x
2
−
8
x
+
8
=
0
Completing the square would mean: taking half of the
x
-coefficient and squaring that:
x
2
−
8
x
+
(
−
4
)
2
=
x
2
−
8
x
+
16
=
(
x
−
4
)
2
But we still have to balance the
16
with the
8
we had:
→
x
2
−
8
x
+
16
→(x−4)2−8=0→(x−4)2=8
So
x-4=√8=2√2→x=4+2√2
Or
x−4=−√8=−2√2→x=4−2√2
Often written as x1,2=4±2√2
The solution of the given quadratic equation by completing the square method are [tex]2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex].
What is completing the square method?Completing the square method is factorizing a quadratic equation, and henceforth finding the roots or zeros of a quadratic polynomial or a quadratic equation.
According to the given question.
We have a quadratic equation
[tex]3x^{2} + 24x - 24 = 0[/tex]
The above quadratic equation can be written as
[tex]3(x^{2} + 8x - 8) = 0[/tex]
[tex]\implies x^{2} + 8x -8= 0[/tex]
Now, we will solve the above equation by completing the square method.
[tex]x^{2} +8x - 8= 0[/tex]
[tex]\implies x^{2} + 2(4x) +(4)^{2} -(4)^{2} -8 = 0[/tex]
[tex]\implies x^{2} + 2(4x) + 16 - 16 -8 = 0[/tex]
[tex]\implies (x+4)^{2} - 24=0[/tex]
[tex]\implies (x+4)^{2} = 24[/tex]
[tex]\implies (x+4)^{2} = 24[/tex]
[tex]\implies (x+4) = \sqrt{24}[/tex]
[tex]\implies x+ 4 = \pm 2\sqrt{6}[/tex]
[tex]\implies x = 2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex]
Hence, the solution of the given quadratic equation by completing the square method are [tex]2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex].
Find out more information about completing the square method here:
https://brainly.com/question/26107616
#SPJ2
A researcher wants to compare the mean score on the Achenbach Youth Self Report form for a sample of youth displaced by a
hurricane to the population mean of 50 and a population standard deviation of 10. The researchers report a sample mean of 48 for their
sample of 36 youth. What is the standard error (aka standard error of the mean) for this sample? Round each step to two decimal
places.
Using the Central Limit Theorem, it is found that the standard error for this sample is of 1.67.
What does the Central Limit Theorem state?It states that for a population of standard deviation [tex]\sigma[/tex], the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that [tex]\sigma = 10, n = 36[/tex], hence the standard error is given by:
[tex]s = \frac{10}{\sqrt{36}} = 1.67[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Please solve the missing parts
Answer:
34 28 37 56 34 37 28 20 43 15
The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.
Find the base and the height of the triangle.
Step-by-step explanation:
h=b-4
A=30ft^2
A=1/2bh
30=1/2b(b-h)
Cross Multiply
60=b(b-4)
60=b^2-4b
b^2-4b-60=0
Factorise the equation
(b^2+6) (-10b-60)
b(b+6)-10(b+6)
(b-10) (b+6)
b-10=0 or b+6=0
b=10 or b=-6
base =10 (since measurement can not be negative)
h=b-4
Sub the value of b
h = 10-4
h=6
So the height is 6ft and base is 10ft
I will give Brainliest!!! :D
Match each situation to an equation.
(You can just write the color of the equation card and the fraction in the situation, ex. Green card to 2/5) :)
Answer:
Purple to 1/4
red to 13/10
blue to 2/5
green to 1/5
Step-by-step explanation:
I think that is correct, butttt I am not postive
The hours students reported practicing their instruments last grading quarter were 29, 20, 36, 44, 30, 32, and 40.
The mean hours students reported practicing their instruments is
.
The mean absolute deviation for the data is
.
Answer:
The mean is 33 and the MAD is 6.
Step-by-step explanation:
I took it on edge and got it right. Sorry I don't have a better explanation.
The person above me is correct.
Step-by-step explanation:
The scatter plot shows the number of visitors to a beach and the high temperature for 25 days. To understand the trend of the data, does it make sense to connect all of the data points? What could you do to the graph to represent the general trend of the data? Why?
Answer:
Yes it does.
Step-by-step explanation:
I gives an estimate of what the weather is.
At a concession stand, three hot dog(s) and four hamburger(s) cost $12.00; four hot dog(s) and three hamburger(s) cost $10.75. Find the cost of one hot dog and the cost of one hamburger.
Answer:
hotdog is $1.25
hamburger is 1.75
Step-by-step explanation:
Given the recursive formula shown, what are the first 4 terms of the sequence?
Step-by-step explanation:
Answer is option A
f(1)=3
f(2)=f(2-1)+4=f(1)+4=3+4=7
... So on
Hence the series would be 3,7,11,15,..
The required first four terms are 3,7,11,15
I hope it helped you
Answer: the answer is a
3,7,11,15 (+4 each time )
Step-by-step explanation: we are adding 4 each time .Hope it helps .
3x+4/5=7-2x what is the solution to the equation?
Solve the equation for x.
X-5 = 11
Enter the number that belongs in the green box.
x = [?]
Enter
Jella rode on the bike trail one afternoon. She biked 12 miles in 1 hour and 24 miles in 2 hours
INn FOUR hours Jennifer will travel 12 m/h x4 = 48 miles
it will take Thomas 48 miles / 4 m/hr = 12 hours to reach the bike in the meantime Jennifer has EIGHT hours of walking 3 m/hr x 8 = 24 miles form the bike Thomas now sets out at 10 m/h this is 10 - 3 = 7 m/h faster than Jennifer is walking he will close the 24 miles and catch Jennifer in 7 m/hr *x = 24 m
24/7hours
So Thomas walks for 12 hours then bikes for 24/7 hr = 15 3/7 hrs = ~ 15 hr 26 min
Please answer this as soon as possible!!
Answer:
Step-by-step explanation:Given
-3+(-5)
-3+(-5)=-3-5=-8
Observing option A.) -3+-(-5)=-3+5=2
Observing option B.)-3+5=2
Observing option C.)-5-(-3)=-5+3-2
Observing option D.)-5-(-3)=-5+3=-2
It doesn’t seem that any option is correct maybe ask your teacher show them this or something
Two lines are perpendicular. If one line has a slope of 1/2, what is the slope the other line?
The slope of the perpendicular line would be the negative reciprocal of the other line.
negative reciprocal of 1/2 = -2
answer: -2
Raymond caught the football 28 out of 35 times at practice. Predict the number of times he will catch the football during the game if it is thrown to him 20 times.
Answer:
16 times
Step-by-step explanation:
This problem is solved by ratio. Since the ratio of 28 out of 25 times is 4:5, he has to catch the ball 4:5 or 4 of 5 times. You multiply both 5 and 4 by 4, because that's how many times he's gonna catch it. 4 x 4 = 16, so the answer is 16 times.
Answer:
(4/5)^20
Step-by-step explanation:
1) First, write the numbers of times Raymond caught the football out of 35 attempts. This is a necessary step in order to obtain an appropriate operand.
28
35
2) Reduce the fraction to lowest terms. This is an optional step but it simplifies the problem.
28 / 4
35 4
= 4
5
3) Raise the fraction to the 20th power. If the ball is thrown at him 20 times, the probability of him successfully catching the ball must be (4/5)^20.
= (4)^2
(5)
6 divided by 7215 and i need help its to hard????
Answer:
If you mean 6 / 7215 it is 0.00083
but if you meant 7215 / 6 it is 1202.5
Step-by-step explanation:
how many tiles of 16 cm² is needed to cover a floor dimension 8 cm by 50 cm?
A 45
B 25
C 28
D 30
(NO LINKS)
Answer:
C 28
Step-by-step explanation:
16 tiles is enough for 28 i think cuz i can't use links
Answer:
it is C 28
Step-by-step explanation:
Which real-world scenario involves a right triangle?
Answer:
Step-by-step explanation:
Medical treatments that involve laser beams.
We can measure how far we put perpendicular the laser beam to a patient skin and we can calculate using right triangles how wide the beams go to only target certain cells (like cancer cells.)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
can you send a better picture of the question so it can be clearer
Step-by-step explanation:
In which number does the digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691?
360,281
486,732
573,674
678,832
HELP PLEASE!!!!!!!!!
Answer:
The answer is 486,732
an amusment park sold 9.728$ worth of admission tickets for a seciak roller coaster at night expirement each ticket cost 38$ how many tickets were sold for the special event show your work
Answer:
256
Step-by-step explanation:
The revenue from the sale of n tickets at $38 each is given as ...
38n = 9728 . . . . total sales from special event tickets
Dividing by the coefficient of n gives the number of tickets:
n = 9728/38 = 256
256 tickets were sold for the special event.
Calculate: a) of 36 =
Answer: 9
Step-by-step explanation:
=> 1/4 of 36
=> 'of' always refers to multiplication:
=> 1/4 × 36
=> By cross cancellation of 4 and 36 we get:
=> 1 × 9
=> 9 Answer...
hope that helps...
does (-1, 2), (1, 1),( 1 -1), (2,1), (4,2) represent y as a function
No. A function maps one input to exactly one output. The given relation maps 1 to both 1 and -1, as indicated by the pairs (1, 1) and (1, -1).
please help!!!!!!!!!!
Answer:
false true false false
|x+3| if x=2 please help i have rsm
Answer:
5
Step-by-step explanation:
|x+3| =
|2+3| =
|5| =
5 =
Answer: 5
Step-by-step explanation:
If x = 2, the numbers in the brackets should now be 2 and 3.
2+3 = 5.
Because having numbers in brackets like these | | means absolute value, the number you get is always a positive number.
Find the both term of the arithmetic sequence –27, -24, -21, ...
Answer:
-18 is the ans you can calculate it
Which of the following can we use to determine if a data set represents a function? There may be more than one answer.
A. Vertical line test
B. Make sure “y” values do not repeat
C. Make sure there is one and only one input for each output
D. Make sure each x-value has more than one y-value
E. Make a table to determine the numbers in the domain appear only once.
Answer:
A, B,C, and E. I hope this helps.
Step-by-step explanation:
factor the expression 14x+13-8x-1
Answer:
2(11x+6)
Simplify to 22x + 12
Greatest common factor is 2
2x11x = 22
2x6 = 12
Find the perimeter of the figure.