(1/2)^x=16^2
Could you please help me with the step-by step? This problem is giving me trouble.
Answers
Write both sides as powers of 2. First,
1/2 = 2⁻¹
16 = 2⁴
so the equation can be rewritten as
(1/2)ˣ = 16²
(2⁻¹)ˣ = (2⁴)²
Recall that [tex](a^b)^c=a^{bc}[/tex], so that
2⁻ˣ = 2⁸
The bases are the same, so the exponents must be equal:
-x = 8
x = -8
Related Questions
A 960-square-foot apartment in New York City costs $540,000. What is the price per square foot? $
Answers
Answer:
The price per square foot is $468.75
Step-by-step explanation:
You would take the price and divide it by the square footage.
540,000
------------- = 468.75
960
A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters),
after m months is given by the following function.
H (m) - 51+ m
What is the plant's height after 27 months?
Answers
Answer:
78 becayse u take 51 and add 27
Answer:
78
Step-by-step explanation:
just add them to get it it might sound hard but it's pretty easy
Help ASAP!!!!!!! It’s to confusing
Answers
Answer:
every one equals 32
Step-by-step explanation:
Every hour equals 32 tickets sold
Answer:
32
Step-by-step explanation:
all equal 32
Which TWO representations show the same function
(picture included)
Answers
Why couldn’t you live without your tv 5 sentences!!!!
Answers
Answer:
because would die of boredom .and i wouldn't have Netflix or Hulu.and i would have nothing to look forward. to when i come home from school i would have to just go and do homework. and without TV you would not have a news channel so you wouldn't know things to are important to life.
Step-by-step explanation:
write and equation to solve for x.
what is the value of x?
Answers
90=2x+3x+5
85=5x
17=x
and to find the angles, just plug in x which is 17
Who can help me out with this please??
Answers
Answer:
i can't sorry
Step-by-step explanation:
The population of rabbits on an island is growing exponentially. In the year 1992, the population of rabbits was 8300, and by 2000 the population had grown to 21500. Predict the population of rabbits in the year 2009, to the nearest whole number.
Answers
Answer:
36350
Step-by-step explanation:
1992 : 8300
2000 : 21500
1992/2000 = 8300/21500
Each year, population grow around 1650 rabbits
In 2009: 21500+(1650*9) = 36350
Find the quotient: 23 ½ ÷ ¼ =
Answers:
23 2/6
23
23 1/8
94
Answers
Answer:
The answer is d: 94
Step-by-step explanation:
find x and y in
(i) 23x- 29y= 98 and 29x -23y =110
(ii) 99x +101y =499 and 101x +99y =501
Answers
Answer:
23 x-29y=98.......(1)
29 x-23y=110.......(2)
adding (1) and (2)we get
52 x-52y=208
52(x+y)=208
x-y=4...(3)[we get four by dividing 208 with 52]
subtract (2) from (1) we get
-6 x-6y=-12
x-y=2.....(4)
adding (3) and (4) we get
2x=6
therefore x=3
now from (4) we get
x-y=2 [we substitute xfor 3]
3-y=2
y=2-3
y=-1( that is the answer for your first question)
Step-by-step explanation:
99x+101y=499.....(1)
101x+99y=501.....(2)
add (1) and (2)
(99+101)x+(101+99)=(499+501)
200x+200y=1000
200(x+ y)=1000
x+y=5.....(3)
subtract (2)from(1) we get
2x-2y=2
2(x-y)=2
x+y=1.......(4)
x+y=5
x-y=1(add them together)
2x=6
x=3
substitute x equal to 3 in equation (3)
x+y=5
3+y=5
y=2
y equal to 2 and x equal to 3
hope is not too lateOriginal price of an SUV: $42,000.00
Tax: 3%
Answers
Answer:15
Step-by-step explanation:
Can someone tell me the answer, please?
Answers
Answer:
Rose bouquets
Step-by-step explanation:
Please mark me branliest?!?!
If tan(A + B) = √3 and tan(A - B) = 1/√3; 0° < A + B ≤ 90° ; A > B, find A and B.
Pls answer it correctly..
Answers
Sol➜
We have, tan(A + B) = √3
⇒ tan(A + B) = tan60°
∴ A + B = 60° -----[i]
Again, tan(A - B) = 1/√3
⇒ tan(A - B) = tan30°
∴ A - B = 30° -----[ii]
Now, Adding [i] and [ii], we get
A + B + A - B = 60° + 30°
2A = 90° ⇒ A = 45°
Putting the value of A in [i], we have
45° + B = 60°
∴ B = 60° - 45° = 15°
Hence, A = 45° and B = 15°.
Answer:
[tex] \displaystyle A = {45}^{ \circ} \\ B = {15}^{ \circ}[/tex]
Step-by-step explanation:
we are given two equation and condition
[tex]\displaystyle \begin{cases}\tan(A+B)=\sqrt{3} \\ \tan(A - B) = \dfrac{1}{ \sqrt{3} } \end{cases}( {0}^{ \circ} < A+B < {90}^{ \circ} ) \: \text{and} \: A > B[/tex]
let's work with first equation
recall unit circle so A and B should be in Q:I
[tex] \displaystyle \: A+B = \arctan( \sqrt{3} )[/tex]
[tex] \displaystyle \: A+B = {60}^{ \circ} \cdots \: \text{I}[/tex]
let's work with second equation:
[tex] \displaystyle \: \tan(A - B) = \frac{1}{ \sqrt{3} } [/tex]
[tex] \displaystyle \: A - B = \arctan(\frac{1}{ \sqrt{3} } )[/tex]
[tex] \displaystyle \: A - B = {30}^{ \circ} \cdots \: \text{II}[/tex]
now let's use elimination method to figure out A and B
to do so combine equation I and II
[tex] \displaystyle \underline{\begin{array}{c c c}A+B = {60}^{ \circ} \\ A - B = {30}^{ \circ} \end{array}} \\ 2A = {90}^{ \circ} [/tex]
divide both sides by 2:
[tex] \displaystyle \: \frac{2 A}{2} = \frac{ {90}^{ \circ} }{2} \\ A = {45}^{ \circ} [/tex]
substitute the value of A to the second equation:
[tex] \displaystyle \: {45}^{ \circ} - B = {30}^{ \circ} [/tex]
cancel 60° from both sides:
[tex] \displaystyle \: - B = { - 15}^{ \circ} [/tex]
divide both sides by -1
[tex] \displaystyle \: B = {15 }^{ \circ} [/tex]
hence,
[tex] \displaystyle \: A = {45}^{ \circ} \\ B = {15}^{ \circ} [/tex]
please find the median!!!
will give brainliest!!!
Answers
Answer:
8, 10, 15, 16, 17, 17, 22
16 is the median
Step-by-step explanation:
Answer:
median is 16
Step-by-step explanation:
PLEASE HELP
What is the area of this trapezoid?
Enter your answer in the box.
Answers
Answer:
it would be 44
Step-by-step explanation:
because you do base ×hight ×base
Does any one know how to do determining the GFC
Answers
Answer:
Yes, GCF stands for (greatest common factor)
so to find it do this:
List the prime factors of each number.
Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.
Multiply all the circled numbers. The result is the GCF.
Step-by-step explanation:
help agin please number 8
Answers
Answer:
G
Step-by-step explanation:
5 + 7 > 9
12 > 9
5 + 9 > 7
14 > 7
7 + 9 > 5
16 > 5
Answer:
G as
5+7 more than 9
5+9 more than 7
7+9 more than 5
Complete the sentences to describe the function f (x) = StartFraction 2 x squared + 16 x Over 16 x cubed minus x EndFraction.
The function is discontinuous at x =
.
To create the extended function, add f(x)=
.
Answers
Answer:
0 & -16,x=0
Step-by-step explanation:
The function is discontinuous at x = 0, x = 1/4 and x = -1/4.
To create the extended function, add f(x) = 0.
What does it mean when a function is discontinuous?A function is discontinuous when the f(x) cannot be defined.
What is an extended function?An extended function aims to make the function continuous at some values of the variable.
It is given that:
[tex]f(x)=\frac{2x^{2}+16x}{16x^{3}-x}[/tex]
StepsStep 1 of 2:The function becomes discontinuous when the denominator becomes zero.
∴ 16x³ - x = 0
⇒ x(16x² - 1) = 0
⇒ x = 0 and 16x² -1 = 0
This is further simplified:
16x² -1 = 0
x² = 1/16
x = ±1/4
This means that the function is discontinuous at x = 0, x = 1/4 and x = -1/4.
Step 2 of 2:The function can be extended as follows:
[tex]f(x)=\frac{2x^{2}+16x}{16x^{3}-x}\\f(x)= \lim_{x \to 0} \frac{2x^{2}+16x}{16x^{3}-x}\\= \lim_{x \to 0} \frac{x(2x+16)}{x(16x^{2}-1)}\\= \lim_{x \to 0} \frac{2x+16}{16x^{2}-1}\\[/tex]
We do not have to add anything to f(x) to extend it. Hence zero can be added to it.
Therefore, we have found that the function is discontinuous at x = 0, x = 1/4 and x = -1/4, and that we can create the extended function by adding 0.
Learn more about discontinuity here: https://brainly.com/question/1417220
#SPJ2
The symbol used in the statement that relates the sides or angles looks like what?
Answers
Where can parentheses be placed in the expression so that it has a value of 500?
6+23−4 ⋅ 3
Answers
Answer:
(6 + 2)³ - 4 x 3
Step-by-step explanation:
Find the value of x.
Answers
Answer:
X = 9
okay If I'm wrong sry what's 9x3 it's 45 right ( me not using a caluctalter ) ( I didn't even spell that Right lol ) but anyways it's X=9
which of the following situations has a straight line doesn't pass through the origin?
a) X and Y are in a proportional relationship
b) y= 10 + 250
c) David and $15 to his savings account each month
d) every five t-shirts cost $12
Answers
Answer:
a or c
Step-by-step explanation:
hope i helped sorry if not?! have a wonderful day! :)
a class has 10 students how many choices for a president and a vice president are possible?
Answers
Answer:
for president there are 10, and in vice president there are 9
A grocery store sells three different quantities of sugar. A 1-pound bag costs $1.08, a 2-pound bag costs
$1.86, and a 3-pound bag costs $2.76. Enter the unit cost in price per pound for each. Complete the
description about how the unit cost changes as the quantity of sugar increases.
Answers
Answer:
for every pound is x + 10. x is originally 80
John belongs to a boating club that rents sailboats for $60 for the first hour and $20 for each additional hour. After renting a boat one day, he owed the boating club a fee of $140.
Write and solve an equation to find how many hours he kept the boat.
Answers
Answer:
4 Hours
Step-by-step explanation:
The original boating fee is $60 then you add $20 per hour so 20 x 4 = 80
80+60=140 $140
Answer: 140=60+20x. He kept the boat for 4 hours
Step-by-step explanation:
x=hours
y=final cost and the final cost is $140
to find x you would use the equation: 140=60+20x
you would first subtract 60 from both sides and you would get:
80=20x
Now you would divide 20 from both sides
So x is 4
The system shown is
• Inconsistent
• equivalent
© consistent
Answers
Answer:
Consistent
Step-by-step explanation:
3y - 21 = 12x
Help please
Answers
3Y+-21=12X
Re-order the terms
-21+3Y=12X
(Solving for Y variable)
Move all terms containing y to the left, all other terms to the right.
Add 21 to each side of the equation
-21+21+3Y=21+12X
Combine like terms: -21+21=0
0+3Y=21+12X
3Y=21+12X
Divide each side by 3
Y=7+4X
Simplifying
Y=7+4x
I hope this helps!! :)
Which expression is equivalent to
(r-7)6?
Answers
Answer:
Step-by-step explanation:
The expression equivalent to
[tex]( r^{-7})^{6} \\is\\\frac{1}{r^{42} }[/tex]
Hope it helps :)
Answer for brainliest.
Answers
Answer:
2880 in^3
Step-by-step explanation:
since 6 times 2 is 12 then you multiply 1440 times 2 as well :)
Mark me brainlyiest pls :)
Answer: [tex]720^{3}[/tex]
Step-by-step explanation: plz mark me brainliest
Help........Betty wants to bake the perfect cookie. She wants to determine the ideal temperature at which to bake the cookies. She has enough batter to make 60 cookies. She decides to randomly assign 15 cookies to be baked at 300°, 15 at 325°, 15 at 350°, and 15 at 375°. The baking time for each batch is 12 minutes. Which statement about the randomization for the completely randomized design is correct? Betty should place the first 15 balls of cookie dough that she scoops from the batter on a tray, and those will be baked at 300°. The next 15 will be placed onto a second tray to be baked at 325°. She should continue in this manner until all 60 cookies have been placed on trays. Betty should scoop a ball of cookie dough from the batter, and then roll a die. Numbers 1–4 would indicate at which temperature the cookies will be baked, and 5–6 would indicate that she should roll again. She should repeat this process until all 60 cookies have been allocated. Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated. Betty should place the first cookie on a tray to be baked at 300°. The second cookie will go on a tray to be baked at 325°, the third will go on a tray to be baked at 350°, and the fourth will go on a tray to be baked at 375°. She will continue placing the cookies in this pattern until all 60 cookies are on trays to be baked.
Answers
Answer: Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.
Step-by-step explanation: I just got it correct on Edge :)
The true option about the randomized design is (c) Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.
The given parameters are:
[tex]\mathbf{n = 60}[/tex]
[tex]\mathbf{Batches = 4}[/tex]
[tex]\mathbf{Cookies= 15}[/tex] ---- the number of cookies in each batch
[tex]\mathbf{Temperature= 300,325,350,375}[/tex]
To randomly assign the cookies to the given temperatures, all cookies have to be subjected to the same conditions (except the difference in the temperature).
This means that, she can bake all the cookies at once at different temperatures, while noting down the cookies with a given number.
Hence, the true option is (c)
Read more about randomization at:
https://brainly.com/question/20046524