Answers
Recall the following property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]
Now, notice that 6² = 36 and 6³ = 216, which means that
[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]
Recall another property of (real) exponents:
[tex](a^b)^c=a^{bc}[/tex]
[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]
So we have
[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]
Since both sides are equal powers of 6, that must mean that the exponents must be equal, so
[tex]-15k=4k-2[/tex]
Solve for k :
[tex]-15k-4k=(4k-4k)-2[/tex]
[tex]-19k=-2[/tex]
[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]
Related Questions
Solve the following system of equations.
(15 Points)
5x + 10 = -5y & x + y = -2
Answers
Answer:
x = -2-y
Step-by-step explanation:
What is 938,492,948,934,895*929,038,292,839,283,892,948,394,839
Answers
Answer:
8.7189589e+41
Step-by-step explanation:
Calculator
Answer:
i do not understand the question
explain
Step-by-step explanation:
A container holds 13 pencils, 5 black pens, and 3 blue pens. What is the ratio, in fraction form, of pens to all writing tools?
Answers
Answer:
8/21
Step-by-step explanation:
In Mrs. Bishop’s closet, there are 10 shirts and 15 skirts.
(a) Find the simplified ratio of shirts to skirts.
(b) If the ratio of shirts to skirts doesn’t change, but now the closet has 75 items in it. How many skirts will there be?
Answers
Answer:
(a) 2/3
(b) 45
Step-by-step explanation:
(a)
The "ratio of shirts to skirts" means "the number of shirts divided by number of skirts."
10 shirts
15 skirts
shirts : skirts = 10/15 = 2/3
Answer: 2/3
(b)
In the simplified ratio, there are 2 shirts for every 3 skirts.
Add 2 + 3 = 5.
The ratio of skirts to total number of items of clothing is 3:5.
There are 3 skirts to each 5 items of clothing.
Set up a proportion.
3/5 = x/75
5x = 3 * 75
x = 3 * 15
x = 45
Answer: 45
Speedie ran the 200 meter race in 25.5 seconds. How much of an hour did it take Speedie to run
the race? 1.0 hour = 3600.0 seconds
Answers
Answer:
Speedie ran the race in 0.708(3)% of an hour, the 3 in the parentheses means the 3 repeats forever
Step-by-step explanation:
We have 25.5/3600, and when we convert it to a decimal, we have 0.00708(3), the 3 in the parentheses means the 3 repeats forever. To convert it to percentage, we multiply it by 100, to get 0.708(3). Hope it helps!
What is 3/4 of a dollar forgot will mark Brainliest if right
Answers
Answer:
0.75 U.S. dollars
Step-by-step explanation:
If you're talking U.S dollar. It's 0.75 cents.
This doesn't seem like college work.
Write 0.6 as a percentage.
Answers
Answer:
60%
Step-by-step explanation:
all you need to do is multiply this by 100 (move two decimal places to the right).
0.6--> 60
60 percent
Answer: 60%
Explanation: .6 x 100 = 60
Shawna wants to purchase some shorts and a few pairs of socks. The shorts cost $10 and a pair of socks cost three dollars. Shawna can spend them no more than $45.
Let’s see represent the number of shorts purchased and Kay represent the number of pairs of socks purchased.
Which in quality represents the situation?
Answers
Answer:
The answer - C
Step-by-step explanation:
c- number of shorts
k - number of socks
10 shorts and 3 socks
10c+3k
no more than $45
no more than is a characteristic of less than or equal to.
10c+3k ≤ 45
And obviously, that isn't an answer choice so you have to switch the sign so it looks like this:
45≥10c+3k
7 What is the unit rate of miles to gallons?
Answers
Hope this helps!
What is the equation of the line that passes through the point (-2,5) and has a slope of -6
Answers
Answer:
y = -6x - 7
Step-by-step explanation:
y = mx + b
5 = -6(-2) + b
5 = 12 + b
b = -7
y = -6x - 7
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HEEEEEEELLLLLLPPPPPPPP!!!
THIS IS DUUEEEE TTTOOOODDDAAAYYYYY.
Question 1:
-|7-2x|+11= -8
Question 2:
9-7|-x-3|= -61
Question 3:
13|-2x+1|-10=159
Answers
Answer:
-|7-2x|+11= -8
x=-6 0r x=13
9-7|-x-3|= -61
x=-13 or x=7
13|-2x+1|-10=159
x=-6 or x=7
Step-by-step explanation:
-|7-2x|+11= -8
-|7-2x|=-8-11
either :
7-2x=-19
-2x=-19-7
x=-26/2
x=13
Or: 7-2x=19
-2x=19-7
-2x=12
x=-12/2
x= - 6
9-7|-x-3|= -619−7(|−x−3|)=−61
−7(|−x−3|)=−61-9
−7(|−x−3|)=−70
|-x-3|=-70/-7
|-x-3|=10
either :
-x-3=10 or -x-3=-10
-x=13 -x=-7
x=-13 x=7
13|-2x+1|-10=15913|-2x+1|=159+10
13|-2x+1|=169
|-2x+1|=169/13
|-2x+1|=13
either or
-2x+1=-13 -2x+1=13
-2x=-14 -2x=12
x=-14/-2 x=12/-2
x=7 x=-6
solve for brainliest A keem measured the capacity of a glass as
2 7 0 mL and the capacity of a Th e rm o s® a s
1 L. He said that the ratio 270 :1 compare s
the capacity of the glass with the cap a c i t y
of the Th e rm o s®. Is his reasoning corre c t ?
E x p l a i n .
Answers
Answer:
[tex]his \: reasoning \: is \: correct.[/tex]
Step-by-step explanation:
[tex]since \: the \: ratio \: of \: the \: glass \: to \:that \\ \: of \: the \: thermos \: is \: in \: the \: fraction : \\ \frac{2 7 0 mL }{1mL} \: which \: is \:270 mL : 1mL \\ then \: the \: keem \: is \: right.[/tex]
Point G(-3,2) is translated using the rule (x+10, y-6). What is the x-coordinate of G'?
Enter your answer in the box.
Answers
Answer:
the anser is 7 :)
Step-by-step explanation:
Which polynomial is in standard form?
2x-3x+ 10x
-16x2-9x+12
15x-6x2+3
-7x?+ 9x9 - 11x
Answers
Answer:
[tex]-16x^2-9x+12[/tex]
Step-by-step explanation:
[tex]2x-3x+ 10x[/tex]
[tex]-16x^2-9x+12[/tex]
[tex]15x-6x^2+3[/tex]
[tex]-7x+ 9x^9 - 11x[/tex]
Standard form is when the polynomial's terms's degrees go down so the highest power is the first and the lowest is the last.
We see that the first expression can be more simplified so that isn't right.
We see that the second expression is in standard form so that might be right.
We see that the third expression has the highest power as the second term so that is wrong
We see that last expression is the same as the third one so that is also wrong.
We can conclude that [tex]-16x^2-9x+12[/tex] is the correct one or in standard form.
What is the slope of this graph
Answers
Answer:
-7/8
Step-by-step explanation: If you use RISE/RUN, then you will see that they RISE is 7 and the RUN is 8 so therefroe,you would get 7/8. The graph is pointing down so, it is negative. Overall, your answer should be -7/8.
The group of points {(0, 1), (0,5), (2, 6), (3, 3)}
is not a function, but the group of points {(1, 4),
(2, 7), (3, 1), (5, 7)} is a function. What do you
notice about the two groups of points? What do
you think it means to be a function?
Answers
Answer:
each x point should be mapped to a y point
Step-by-step explanation:
find the value of x in the figure shown.
(Hint: the sum of angle measures in any triangle is 180
2x-10
(4x-80)
4x-10
Answers
Answer:
28
Step-by-step explanation:
2x +4x +4x-10 -80-10
10x-100=180
10x=180+100
10x=280
10x/10=280/10
x=28
If = and x > 0 what is the value of x ?
Answers
O valor de x é 45º
Explicação:Confia no pai
Help ! I’ll mark you brainly
Answers
Answer:
There you go :)
Hope this helped you
<3
Red
(5a^2 + 3) (4a^2 + 3)
Answers
Answer:
204+272+9
Step-by-step explanation:
y = 6 sin(x) y = 6 cos(x) 0 ≤ x ≤ π/4 about y = −1
Answers
are you speaking another language
На сколько процентов уменьшится объем прямоугольного параллелепипеда, если его длину уменьшить на 25%, а ширину и высоту на 20%?
Answers
Answer:
I dunno what your saying.
Step-by-step explanation:
Please us English
An example of multistage samples
Answers
Answer:
Multistage sampling divides large populations into stages to make the sampling process more practical.
Step-by-step explanation:
Let’s say you wanted to find out which subjects U.S. school children preferred. A population list a list of all U.S. school children would be nearimpossible to come by, so you cannot take a sample of the population.
An example of multistage samples is the Gallup poll.
What is the multistage sample?In this, we have to drawn the sample that should arise from the population that used the smaller and smaller group at every stage. It is applied for collecting the data from the large, and the group of people in national surveys.
The Gallup poll used multistage sampling. Like it randomly select a particular no of area codes after this randomly sample a no of phone numbers from within each area code.
Learn more about sample here: https://brainly.com/question/9555918
How many 5/16 are in. 1. 9/16
Answers
Answer:
The answer is 1.8.
Step-by-step explanation:
Can someone help
Please
Answers
Answer:
Step-by-step explanation:
.
please help me with this Geo question
Answers
Answer:
x = 31
Step-by-step explanation:
4x + 38 = 2x + 10 + 90
2x = 62
x = 31
Derik earns $10.00 per hour. He works 35 hours per week. How much will he earn in two weeks? If he spends $50, how much will Derik have left?
Answers
Answer:
650
Step-by-step explanation:
so the way I did this was by adding how much he works per week which is 35 per week. so he works 70 hours in 2 weeks. he earns 10 dollars per hour. so 10 times 70 you get 700 but he spends 50. so 700 minus 50. you get 650. he has 650 dollars left.
Find the extreme values of f on the region described by the inequality.
f(x, y) = e−xy; x2 + 4y2 ≤ 1
Answers
Answer:f(x, y) = e
−xy. For the interior of the region, we find the critical points:
fx = −ye−xy
, fy = −xe−xy, so the only critical point is (0, 0), and f(0, 0) = 1.
For the boundary, we use Lagrange multipliers.
g(x, y) = x
2 + 4y
2 = 1 ⇒ λ∇g = h2λx, 8λyi, so setting ∇f = λ∇g we get
−ye−xy = 2λx and −xe−xy = 8λy. The first of these gives e
−xy = −2λx/y,
and then the second gives −x(−2λx/y) = 8λy ⇒ x
2 = 4y
2
. Solving this
last equation with the constraint x
2 + 4y
2 = 1 gives x = ± √
1
2
and y = ±
1
2
√
2
.
Now f
± √
1
2
, ∓
1
2
√
2
= e
1/4 ≈ 1.284 and f
± √
1
2
, ±
1
2
√
2
= e
−1/4 ≈ 0.779.
The former are the maxima on the region and the latter are the minima.
Step-by-step explanation:
Ming li spent $15 at the movies. She then earned $30 babysitting. She spent $12 at the bookstor. She now has $18 left. How much money did ming li have to begin woth
Answers
Answer:
$15
Step-by-step explanation:
30 - (12+15)
30-27=3
18-3=15
Hope this helps ;)
Earned total 30
Left 18
15 + 30 = 45
45 - 27 = 18
She started off with 15
The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. x 1 2 4 8 16 p(x) 0.05 0.15 0.25 0.30 0.25 (a) Compute E(X) (in GB). (Enter your answer to two decimal places.) GB (b) Compute V(X) (in GB2) directly from the definition. (Enter your answer to four decimal places.) GB2 (c) Compute the standard deviation of X (in GB). (Round your answer to three decimal places.) GB (d) Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.) GB2
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
x: ____ 1____ 2____ 4____ 8____ 16
p(x): _0.05_ 0.15__ 0.25__0.30__ 0.25
E(X) : Σ[(X). P(X)]
Σ(1*0.05) + (2*0.15) + (4*0.25) + (8*0.30) + (16 * 0.25)
= 7.75
B)
E(x) = u = 7.75
Var(X) = E[(x - u)²*p(x)] = (1 - 7.75)^2 * 0.05 + (2 - 7.75)^2 * 0.15 + (4 - 7.75)^2 * 0.25 + (8 - 7.75)^2 * 0.30 + (16 - 7.75)^2 * 0.25 = 27.7875
C)
Standard deviation (s)
s = √Var(x)
s= √27.7875
s = 5.271
D)
VAR(X) = E(X²) - (E(X))²
E(X²) = Σx²*p(x)
E(X²) = Σ(1^2 * 0.05 + 2^2 * 0.15 + 4^2 * 0.25 + 8^2 * 0.30 + 16^2 * 0.25) = 87.85
V(X) = E(X^2) - (E(X))^2 = 87.85 - 7.75^2 = 27.7875
