Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.
(-2)
1.
1-21-10
32
2. 21.24
-32
3.
32
1
4.
2-
Answers
Answer:
1) [tex]\frac{(-2)^{-5}}{(-2)^{-10}}=-32[/tex]
2) [tex]2^{-1}.2^{-4} = \frac{1}{32}[/tex]
3) [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}[/tex]
4) [tex]\frac{2}{2^{-4}} = 32[/tex]
Step-by-step explanation:
1) [tex]\frac{(-2)^{-5}}{(-2)^{-10}}[/tex]
Solving using exponent rule: [tex]a^{-m}=\frac{1}{a^m}[/tex]
[tex]\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32[/tex]
So, [tex]\frac{(-2)^{-5}}{(-2)^{-10}}=-32[/tex]
2) [tex]2^{-1}.2^{-4}[/tex]
Using the exponent rule: [tex]a^m.a^n=a^{m+n}[/tex]
We have:
[tex]2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}[/tex]
We also know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]
Using this rule:
[tex]2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}[/tex]
So, [tex]2^{-1}.2^{-4} = \frac{1}{32}[/tex]
3) [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2[/tex]
Solving:
[tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}[/tex]
So, [tex](-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}[/tex]
4) [tex]\frac{2}{2^{-4}}[/tex]
We know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]
[tex]\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32[/tex]
So, [tex]\frac{2}{2^{-4}} = 32[/tex]
Related Questions
Figure ABCD is a kite. Find the
value of x.
Answers
Answer:
x=5
Step-by-step explanation:
i think you posted this question twice, but here it is:
in order for this figure to truly be a kite, AD and AB have to be equal.
So:
4x=x+15
now we must solve the equation:
3x=15
x=5
The weight of body is 420 N. Calculate is mass
0.34 m 11.67,000 g 1,72.800 s 1 day
LOSSARY
the ratio of mass and volume
the rate of change of velo
the rate of displacement of be
Answers
Answer:
42.857 kg
Step-by-step explanation:
Given that :
Weight of body = 420N
Recall : Weight (W) = mass(m) * acceleration due to gravity(g)
Thus ;
Mass, m = Weight, W / acceleration due to gravity
Acceleration due to gravity is a constant, g =, 9.8 m/s²
Mass = 420N / 9.8m/s²
Mass = 42.857142kg
The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for each flower. The October price was a 20% increase of the September price. Part A: What was the price of the flowers in September? Part B: The seventh-grade class earned 40% of the selling price of each flower. In September, they sold 900 flowers. In October, they sold 700 flowers. Did they earn more money in September or October? How much more?
Answers
120/100 * x = $1.50
1.2x = $1.50
x = $1.50/1.2 = $1.25
The price of flowers in September is $1.25
Total money realised in September = $1.25 x 900 = $1,125
40% earned = 0.4 x $1,125 = $450
Total money realised in October = $1.50 x 700 = $1,050
40% earned = 0.4 x $1,050 = $420
The class earned more money in September and they earned $30 more than in October.
Joey makes 20 less dollars than Jeremy. If they make a total of $72, how much does
Joey make? You must write two let statements and an equation to solve this problem.
Answers
Answer:
Joey makes 52 dollars
Step-by-step explanation:
solve;
i) X+10%of X =22
ii)x+20%of X=rs60
iii)X+25%ofx=rs120
iv)X=rs200+50%of X
v)X=180+10%of x
question from equation and inequality
Answers
Answer:
i) 20
ii) 50
iii) 96
iv) 400
v) 200
Step-by-step explanation:
Given equations, for which we have to solve for the variable.
i)
[tex]X+$10\% of X $=22\\\Rightarrow X + \dfrac{10}{100}X =22\\\Rightarrow \dfrac{11}{10}X=22\\\Rightarrow X = 20[/tex]
ii)
[tex]x+$20\% of x = Rs.\ 60 $\\\Rightarrow x+\dfrac{20}{100}x =60\\\Rightarrow \dfrac{6}{5}x = 60\\\Rightarrow x = 50[/tex]
iii)
[tex]x+$25\% of x = Rs. 120$\\\Rightarrow x + \dfrac{25}{100}x = 120\\\Rightarrow \dfrac{5}{4}x = 120\\\Rightarrow x = 96[/tex]
iv)
[tex]X= $ Rs. 200+50\% of X$\\\Rightarrow \dfrac{50}{100}X = 200\\\Rightarrow X = 400[/tex]
v)
[tex]X=180+$10\% of X$\\\Rightarrow X - \dfrac{10}{100}X = 180\\\Rightarrow \dfrac{9}{10}X = 180\\\Rightarrow X = 200[/tex]
An aquarium holds 12 liters of water.
How many aquariums can we fill with 48 liters of water?
Include fractions of aquariums, if applicable.
Answers
Answer:
4 aquariums
Step-by-step explanation:
because each aquarium can hold 12 liters and if there is 48 liters total you divide 48 by 12 and get a total of 4 aquariums
2,704 rounded to the nearest thousand
Answers
Answer:
3000,
Step-by-step explanation:
5 or above round up, 4 and below keep it the same
There are 9 times as many cubes in the black bag as in the green bag. The green bag has 12 cubes. How many cubes are in the black bag?
Answers
Answer:
108 cubes
Step-by-step explanation: 9 times 12 equals 108
9 • 12 = 108 cubes
Answer:
108
Step-by-step explanation:
9×12=108
That's it!
Can someone help me with this please
Answers
Answer: 19
Step-by-step explanation:
[tex]a-4b\\\\=7-4(-3)\\\\=7-(-12)\\\\=7+12\\\\=19[/tex]
In a large population, 61 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated
Answers
Answer:
0.94
Step-by-step explanation:
Computation for what is the probability that AT LEAST ONE of them has been vaccinated
Based on the information given this is a binomial Distribution therefore Let;
Number of people represent n= 3 people
Population represent p = .61
Using this formula
Probability(AT LEAST ONE vaccinated) = 1 - [ 1*(1-Population vaccinated^People randomly selected)]
Let plug in the formula
Probability(AT LEAST ONE vaccinated) = 1 -[1*(1-.61^3)]
Probability(AT LEAST ONE vaccinated) = 1 - [1×(1-.61^3)]
Probability(AT LEAST ONE vaccinated) = 1 - (1×.39^3)
Probability(AT LEAST ONE vaccinated) = 1 - 0.059319
Probability(AT LEAST ONE vaccinated) = 0.940681
Probability(AT LEAST ONE vaccinated) = 0.94
Therefore the probability that AT LEAST ONE of them has been vaccinated is 0.94
HELP PLEASEEE !!! 50 POINTS
Answers
Answer:
haha
Step-by-step explanation:
first off thats not 50 points
Answer:
Step-by-step explanation For the first on 5 and -4 all u do is divide y over x so it wpuld be -4/5 which would be -0.8
just keep doing the process of dividing y over x
the second 1 would be 0/3 which is 0
just keep doing this process
plzzzzzzz help help help. A sum of money put out at compund interest in increased by Rs.180 at the end of first year and by Rs. 188.10 at the end of second year. find out the sum and rate of interest . plzzzzz help
Answers
Answer:
This is the answer. Do it fast. All the best
The price of some Beats by Dre were reduced from $125 to $100. By what percentage was the price of the Beats reduced?
Answers
Answer:
10% of 100=10
20%of 100=20
5% of 100=5
50%=50
125
55/(4+1)+3-three cubed
Answers
Answer:38
Step-by-step explanation:
Answer: 14
Step-by-step explanation:
First you have to do 4+1=5, then you do 55/5 and get 11, once you do that you do 11+3=14.
I hope that this helps!!!
9) A 5 inch by 7 inch picture has a frame surrounding
it on all four sides of width w. The total area of the
picture frame and picture is 80 square inches.
a) Using the diagram and information, write an
expression for the total length, including the
frame, and with an expression for the total
width, including the frame.
Length expression:
Width expression:
b) Using the expressions for total length and width, write an equation for the total
area of the rectangular picture and frame (Hint: Area = l × w).
c) Using your knowledge of factoring, solve the equation from (b) for the width of
the frame surrounding the picture.
Answers
Answer:
w = 3/2
Step-by-step explanation:
Area of a Rectangle
The 5-inch by 7-inch picture has a frame of width w surrounding all four sides.
a)
The total length of the framed picture is 7 + 2w
The total width of the framed picture is 5 + 2w
b)
The total area of the framed picture is:
At = (7 + 2w)(5 + 2w)
c) We know the total area is 80 square inches, thus:
(7 + 2w)(5 + 2w) = 80
Operating:
[tex]35 + 14w + 10w + 4w^2=80[/tex]
Simplifying:
[tex]4w^2 + 24w -45 =0[/tex]
We now write:
[tex]4w^2 + 30w - 6w -45 =0[/tex]
Factor out 2w from the first two terms and -3 from the last two terms:
[tex]2w(2w + 15) - 3(2w + 15) =0[/tex]
Factor out 2w+15
(2w + 15)(2w - 3)=0
The solutions are:
w = -15/2
w = 3/2
The only feasible solution is the positive value, thus
w = 3/2
La serie de el 2 12 32 62 al 1902
Answers
Answer:
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Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers,
Express in exponential form.
logo0.001 =3
Answers
In order to write log10(0.001) = -3 in index form, we have [tex]10^{-3} = 0.001[/tex].
Exponential form of logarithmThe logarithm of a number refers to the power to which a given base is raised to give the number. In this case, the base is 10 and the index is 3. Our task is to write log10(0.001) = -3 in index form.
Recall that;
[tex]a^{x}[/tex] = PHence, to write log10(0.001) = -3 in index form we have to write, [tex]10^{-3} = 0.001[/tex]
Learn more about logarithm: https://brainly.com/question/7302008
Write down in terms of n the expression for the nth term of the following sequences : 12,10,8,6,4
Answers
Answer:
n-2
because 12-2=10
who wants brainlest?
what is 5 + 5
(hardest question in the galaxy)
what is the name of that oger in shrek?
(very hard)
what is the name of the most popular web browser?
hint: not internet explorer
(starts with a g)
bonus question:
(heart)
who is the 2nd most popular robl0x yt channel
(pls sub to him)
and pewds
if you want to compete in the next brainlest competition, you could friend me or, follow my questions to keep yourself updated...........
Answers
Answer:
10
shrek
g00gle
denis or flamingo?
Step-by-step explanation:
determine the value of x for which r parallels s. then find measure of angles one and two
measure of angle one= 30-4x
measure of angle two= 50-44x
the value for which r parallels s is .....
measure of angle one.....
measure of angle two ......
Answers
Answer:
[tex] m\angle 1 = 28\degree
m\angle 2 = 28\degree [/tex]
Step-by-step explanation:
[tex]\because line\: r || line\: s\\
m\angle 1 = m\angle 2\\(corresponding \: \angle s) \\
\therefore 30 - 4x = 50 - 44x\\
\therefore 44x - 4x = 50 - 30\\
\therefore 40x = 20\\
\therefore x = \frac{40}{20}\\
\therefore x = 0.5\\
m\angle 1 = 30 - 4x = 30 - 4(0.5) = 30 - 2 \\
m\angle 1 = 28\degree \\
\implies m\angle 2 = 28\degree [/tex]
WILL MARK BRAINLIEST ONLY HAVE 30 MINUTES
Answers
Answer:
Step-by-step explanation:
the answer is 21
Answer:
its 21
Step-by-step explanation:
you add 9 +12= 21 inches
Suppose a small cannonball weighing 16 lb is shot vertically upward with an initial velocity
v_0 = 300v 0 =300 ft/s.(a) Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by d^2s/dt^2 = -gd 2 s/dt 2 =−g.Since ds/dt = v(t)ds/dt=v(t) the last differential equation is the same as dv/dt = -gdv/dt=−g, where we take g = 32g=32 ft/s^2 2 . Find the velocity v(t)v(t) of the cannonball at time tt.(b) Use the result obtained in part (a) to determine the height s(t)s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.
Answers
Answer:
a) v(t)=-32t+300
b) s(t)=-16t^{2}+300t
[tex]s_{max} =\frac{5625}{4}ft=1406.25 ft[/tex]
Step-by-step explanation:
A good way to start solving this problem out is to draw a diagram of the situation (see attached picture).
a)
For part a, we need to find an equation for the velocity of the cannon ball. We have an equation of its acceleration:
[tex]a=\frac{dv}{dt}=\frac{d^{2}s}{dt^{2}}=-g[/tex]
we know that:
[tex]g=32 ft/s^{2}[/tex]
so we got the following differential equation:
[tex]\frac{dv}{dt} =-32[/tex]
we can find the function for velocity by integrating, so we get:
[tex]v =\int\limits {-32} \, dt[/tex]
which yields:
v(t)=-32t+C
we need to find the value of C. The problem tells us that v(0)=300 ft/s so we can use this to find c:
300=-32(0)+C
so
C=300
therefore the equation for velocity is:
v(t)=-32t+300
b)
For part b) we need to find an equation for the height of the cannonball. We know that:
[tex]v=\frac{ds}{dt}[/tex]
so:
[tex]\frac{ds}{dt}=-32t+300[/tex]
so we can integrate this equation to find the function for height of the ball, so we get:
[tex]s=\int\limits {-32t+300} \, dt[/tex]
which yields:
[tex]s(t)=-\frac{32t^{2}}{2}+300t+C[/tex]
which can be simplified to:
[tex]s(t) =-16t^{2}+300t+C[/tex]
We know the height is measured from the ground level, this means that s(0)=0 so we can find C with this information:
[tex]0=-16(0)^{2}+300(0)+C[/tex]
so C=0, therefore our equation is:
[tex]s(t)=-16t^{2}+300t[/tex]
in order to find the maximum height attained by the cannonball, we can set the velocity function equal to zero and solve for t, so we get:
0=-32t+300
-32t=-300
[tex]t=\frac{300}{32}[/tex]
[tex]t=\frac{75}{8} s[/tex]
and substitute it into our position function so we get:
[tex]s(\frac{75}{8})=-16(\frac{75}{8})^{2}+300(\frac{75}{8})[/tex]
which yields:
[tex]s_{max} =\frac{5625}{4}ft=1406.25 ft[/tex]
what is the value of 8^4/12
Answers
Answer:
1024/3
Step-by-step explanation:
First we want to do 8^4 which is 4096/12. Now, we can factor this equation by factoring out 4: 4(1024)/12. Cancel the common factors to get 1024/3. This can also be written as 341. 3 (the decimal 3 has a line over it) or 341 1/3
Answer:
1024/3
Step-by-step explanation:
Weston used the steps below to determine the percent equivalent to StartFraction 1 Over 40 EndFraction
Step 2: StartFraction 1 Over 40 EndFraction = StartFraction question mark Over 100 EndFraction. StartFraction 1 Over 40 EndFraction = StartFraction question mark Over 100 EndFraction. Multiply both sides by 2.5.
Step 3: 1 times 2.5 = 2.5
Step 4: StartFraction 2.5 Over 100 EndFraction = 25%
What was Weston’s ethe second fraction should have been out of a multiple of 40.
Answers
Weston's second fraction should have been 0.25.
How do we convert 1/40 to a percentage?Percentage can be described as a fraction out of an amount expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to denote percentages is %.
1/40 x 100 = 2.5%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
5. If a = -6 and b = 7, then 4a(3b+5)+2b=?
A. 638
B. -485
C. 850
D.-610
Answers
Answer:
D.-610
Step-by-step explanation:
-6 ×4 =-24
7 times 3 =21
The temperature on the moon vary from -173*C to 127C find the difference between the maximum and minimum temperatures
Answers
Answer:
300°
Step-by-step explanation:
Difference means to subtract:
127 - (-173) = 300
Therefore, the temperatures have a difference of 300°.
Answer: 300
Step-by-step explanation:
The max temp is 127C
The min temp is -173C
The difference between the maximum and minimum temperatures = max temp - min temp= 127-(-173) = 127+173=300
given that y varies inversely with x, and y = 100 when x + 3, find x if y = 60
Answers
Step-by-step explanation:
xy = k, where k is a real constant.
y = 100 when x = 3, therefore (3)(100) = k.
=> k = 300.
Hence when y = 60, x(60) = (300), x = 5.
Answer:
cchhgfhhfhçhuyffffffcghhhh
Ştiind că a . b = 2 019 şi a c= 2019, calculați a. (b-c)
Answers
Answer: a × ba × c = a (bc) = 0
a × ba × c = 2019-2019 = 0
Step-by-step explanation:
PLS Help! This is DUE! 50 Points
[tex]log_{6}(2x-7)=4[/tex]
Answers
Answer: x = 651.5
Step-by-step explanation:
First, we can re-write the equation as = 2x - 7.
Now, we simplify 6^4 = 1296.
1296 = 2x - 7
1303 = 2x
x = 651.5
Buddy and Michael get into a
snow fight with some boys on the
way home from school. It seems
as though Buddy can throw 4
times as many snowballs as the
boys can. If Buddy throws 1200
snowballs, how many did the boys
throw? Write an equation and
solve.
Answers
Answer:
1500
Step-by-step explanation:
1200/4=300
1200+300=1500
Answer:
This means the boys throw 300 snowballs while Buddy throws 1200 snowballs
Step-by-step explanation:
Equations
Let's call
x = number of snowballs the other boys throw.
4x = number of snowballs Buddy throws.
We know Buddy throws 1200 snowballs, thus
4x = 1200
Divide by 4:
x = 1200/4
x = 300
This means the boys throw 300 snowballs while Buddy throws 1200 snowballs