Answer:
a^6b^4
Step-by-step explanation:
(a³b²)²
a^6b^4
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Answer:
a⁶b⁴
Step-by-step explanation:
The relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
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These let us simplify the expression as follows:
[tex](a^3b^2)^2=(a^3)^2(b^2)^2=a^{3\cdot2}b^{2\cdot2}=\boxed{a^6b^4}[/tex]
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Additional comment
It might be helpful to remember that an exponent signifies repeated multiplication.
a·a·a = a³ . . . . . . 'a' is a factor 3 times, so the exponent is 3.
Similarly, ...
(a³)² = (a³)·(a³) = (a·a·a)·(a·a·a) = a⁶
Given the triangle below, find the angle θ in radians. Round to four decimal places.
Answer:
θ = 0.9626
Step-by-step explanation:
Hi there!
We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:
[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Plug in the given information
[tex]\displaystyle cos\theta=\frac{4}{7}[/tex]
Use the inverse cosine ratio
[tex]\displaystyle \theta=cos^-^1(\frac{4}{7})[/tex]
Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)
[tex]\displaystyle \theta=0.9626[/tex]
Therefore, θ = 0.9626 when rounded to four decimal places.
I hope this helps!
Answer:
theta = 0.9626 radians
Step-by-step explanation:
cos theta = a/h
cos theta = 4/7 = 0.5714
so, the angle theta = arc cos 0.5714 =
55.1520 °
in radians => 55.1520 × π / 180°
= 0.9626 radians
The manager at a computer recycling plant says it takes workers a minimum of 120 seconds to break down a computer monitor. The exact amount of time depends on the number of screws in the computer that must be removed. It takes 10 seconds to remove each screw, and then an additional 30 seconds to sort the computer parts into their appropriate containers for recycling. Write an inequality that determines the minimum number of screws that are in each computer monitor.
Answer: 120 + 10s + 30
Step-by-step explanation:
120 + 10s + 30
let "s" be the amount of screws
Evaluate the expression 4x + 6 -y^2 when x=-3 and y=4
The expression 4x + 6 -y^2 when evaluated has a value of -22
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
4x + 6 -y^2
Also, we have
x=-3 and y=4
Substitute the known values in the above equation, so, we have the following representation
4x + 6 -y^2 = 4 * -3 + 6 - 4^2
Evaluate
4x + 6 -y^2 = -22
Hence, the solution is -22
Read more about expression at
https://brainly.com/question/30492964
#SPJ6
The graph of the reciprocal parent function, f(x) = ), is shifted 9 units
down and 11 units to the right to create the graph of g(x). What function is
g(x)?
Answer:
g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice
Step-by-step explanation:
I. If move right is +x and move down is -y
then f(x) = [tex]\frac{1}{x}[/tex]
+x = 11, -y = -9
so g(x) = [tex]\frac{1}{x+11}-9[/tex]
Hope that help :D
The median speed at which Dave drove to work was __________. 63 miles per hour 62 miles per hour 58.89 miles per hour 59 miles per hour
Step-by-step explanation:
Dave run with was 63 miles
Someone please help me with 13 and 14 I’m really struggling
Answer:
Step-by-step explanation:
Derrek wants to find another way to show 6 thousands. Which value is equal to 6 thousands?
Answer:
6,000
Step-by-step explanation:
60 hundreds.
600 tens.
Which describes the relationship between the distance and the difference?\
Answer:
The distance is always the opposite of the difference.The distance is the absolute value of the difference.
Hope it helps you.Have a nice day!!Answer:
The distance is the absolute value of the difference
Step-by-step explanation:
Sum is the when 2 or more numbers are added . Difference is the quantity at which 2 numbers differ i.e difference between 9 and 7 is 2. If you are talking about distance in reference to segment the distance ishow far apart two points are.
Help I'll mark you as brainiest
Answer:
It is a function and 0to^2 shows your function dt.c and 4c-3 shows your function is wrong and the answer is 0 and 31/4 to the power of 25 and shows that the function is 8.
Step-by-step explanation:
During a science lab, four-fifths of the class completed the lab and earned a grade of 100. What percent of the class didnt earn a grade of 100?
F. 60%
G. 80%
H. 20%
J.45%
Answer: H. 20%
Step-by-step explanation: if 4/5 got 100 then 80% got 100 so the other 20% did not get a 100
The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7. Find the probability of observing exactly three accidents on this stretch of road next month.
Select one:
A. 18.147387
B. 2.846161
C. 0.332381
D. 0.052129
Answer:
D
Step-by-step explanation:
hhgxhsbjxkxjebdibfhejx
Find the value of x if
Answer:
C. 4
Step-by-step explanation:
We have the equation [tex]\sqrt[x]{81} =3[/tex] and are asked to find the value of x.
To find x, we need to find how many times 3 can go into 81 but as an exponent, instead of saying 3 * x it would be [tex]3^x[/tex].
So find the value of each exponent by replacing it with each answer choice :
[tex]3^8 = 6561[/tex]
[tex]3^{27} = 7.6255975e+12[/tex]
[tex]3^4 = 81[/tex]
[tex]3^2 = 9[/tex]
Since to the power of 4 equals the cube root in the original equation, therefore B. is the answer.
A CD with a diameter of 120 millimeters rotates a rate of 45 revolutions per minute. Find the linear speed of the CD in millimeters per minute. And find the angular speed of the CD in radians per minute
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Answer:
16,965 mm/min90π ≈ 282.7 radians/minStep-by-step explanation:
The circumference of the CD is ...
C = πd
C = π(120 mm) ≈ 376.99 mm
This is the distance a point on the edge of the CD will travel when making one revolution. It will travel 45 times this far when making 45 revolutions:
(376.99 mm/rev)(45 rev/min) ≈ 16,965 mm/min
__
There are 2π radians in each revolution, so the angular speed is ...
(2π rad/rev)(45 rev/min) = 90π rad/min ≈ 282.7 rad/min
5 times some number added to 8 amounts to 10 added to the product of 3 and the number
How do you solve this
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Answer:
the number is 1
Step-by-step explanation:
First of all, you need to know what you're solving. Here, we assume you're trying to find "the number."
__
Let n represent "some number." The given relation can be written using math symbols as ...
5n +8 = 10 +3n
Subtract 3n +8 from both sides to separate the variable and the constant terms.
2n = 2
n = 1 . . . . . . . divide by 2
The number is 1.
__
Check
5 times 1, added to 8 is 13. This amounts to the same thing as 10 added to the product of 3 and 1.
2. What is the distance between points A and B?
A. -6 units
B. -1 unit
C. 5 units
D. 6 units
Answer:
5 units
Subtract -6 and -1, and you get -5. -5 can't be the answer since we are asked to find the distance, so it is the absolute value of -5, 5.
Answer:
D) 6 units
Explanation:
Point A is 5 units away from 0 (the middle)
Point B is 1 unit away from 0
5 + 1 = 6
Distance between two points cannot be negative
Twenty is 12% of what number? Round to two decimal places if needed.
Answer:
166,67
Step-by-step explanation:
We want to find a number x which 12% is 20:
x * 0.12 = 20
x = 20 / 0.12
x = 166,67
Help please! What is the length of the highlighted side? (Show work)
Answer:
7
Step-by-step explanation:
15ft - 8ft
Ruben is driving along a highway that passes through Barstow. His distance d, in miles, from Barstow is given by the equation
d = |210 − 60t|,
where t is the time, in hours, since the start of his trip and
0 ≤ t ≤ 5.
When will Ruben be exactly 90 miles from Barstow? (Enter your answers as a comma-separated list.)
The absolute value of a number returns the positive value of the given number. Ruben will be at exactly 90 miles in 2 hours or 5 hours
Given that:
[tex]d = |210 - 60t|[/tex]
To calculate t when [tex]d = 90[/tex], we have:
[tex]90 = |210 - 60t|[/tex]
Rewrite as:
[tex]|210 - 60t| = 90[/tex]
Remove absolute bracket
[tex]210 - 60t = 90 \ or\ 210 - 60t = -90[/tex]
Collect like terms
[tex]- 60t = -210 + 90 \ or\ - 60t = -210 -90[/tex]
[tex]- 60t = -120 \ or\ - 60t = -300[/tex]
Divide through by -60
[tex]t = 2 \ or\ t = 5[/tex]
Hence, Ruben will be at exactly 90 miles in 2 hours or 5 hours
Read more about absolute values at:
https://brainly.com/question/1301718
Calculate the area of this section of floor in square feet.
Answer:
A total= 0.6703125 ft²
Step-by-step explanation:
A1= 3.9× 14.3= 55.77 in²
A2=1/2 × 14.3× ( 9.6-3.9)= 40.755 in²
A total= A1+ A2= 55.77+40.755=96.525 in²
1 ft= 12 in , 1ft²= 144 in²
Atotal= 96.525÷144= 0.6703125 ft²
what is the slope of a line containing 1,-2 and -1,5
Use the formula y2-y1/x2-x1
That gives you
5 - (-2) / -1 - 1 = -7/2
-7/2 should be your slope.
(Or it could be -3.5 in decimal form)
Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card or an Ace.
Choose the correct probability of drawing a face card or an Ace. Answer choices are in the form of a percentage, rounded to the nearest whole number.
31%
8%
4%
25%
Answer:
8%
Step-by-step explanation:
Ok, there is 52 cards per deck, 13 per suit ( club, diamond, heart, and spade)
if you multiply 13 by 4 ( 4 is dependent on the number of suit, and 4 will always be the number of suit )
The probability is 8%.
Why, because 25 would be pulling a random card and your saying you want the suit to be diamond the probability of you getting a random diamond card would be 25%. But were not doing that. So cross out 31% and 25%.
Also, 4% would be as your counting 100 cards. So that leaves me with 8%.
Plzzz helppppp!!!!!!! 20+PTS and brainliest!!!!!!!!!!!!!!!
Please show work!!!!!!!!!!!
Refer to the equation y=mx+c
Please Help Me Do This I cant understand it no matter how hard I try. (Problem in the image)
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Answer:
7.28
Step-by-step explanation:
Consider the attachment. There, we have identified a point C that makes ABC a right triangle with the right angle at C.
The Pythagorean theorem gives you the relationship between side lengths of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
AB² = AC² +BC²
We can count grid squares to find the lengths of AC and BC. They are 2 units and 7 units, respectively. This means ...
AB² = 2² +7²
AB² = 2·2 +7·7 = 4 +49 = 53
When we know the square, we can find what it is the square of by taking the square root. Generally, a calculator is required for this.
AB = √53 ≈ 7.2801099
When we round this number to two decimal places (the nearest hundredth), we get ...
AB ≈ 7.28 . . . units
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Additional comments
You will notice that the length AC in the diagram is the difference of the x-coordinates of points A and B. Similarly, the length BC in the diagram is the difference of y-coordinates. Then the square AB² is the sum of the squares of these differences. The length AB is the square root of that sum.
In general, this is how you find the length of a line segment from its end point coordinates.
__
A little magic, perhaps: You may find that repeating the 11-digit number on the first line several times a day for a few days will help to moderate your difficulty understanding this. The numbers convey an energy that is intended to counteract the brain block that often arises when seeing a math problem.
Write 7 hundred in standard form
Answer:
700
Step-by-step explanation:
Answer:
700
Step-by-step explanation:
7 hundred in standard form is 700.
Given log4(3) =0.7925 and log4(5) =1.1610, use log properties to find log4(300).
Answer:
4.1145
Step-by-step explanation:
You can use the following formula to solve this kind of problems,
[tex] log_{a}(b) + log_{a}(c) = log_{a}(bc) [/tex]
So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.
[tex] log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145[/tex]
the sum of 3 and a number
Answer:
the number will vary the answer
Step-by-step explanation:
3×1=3
3×2=6
x ^ 2 − 17x − 60
Which expression is equivalent to the expression above?
(Please explain in simple terms cause, it's usually hard for me to understand)
[tex] {x}^{2} - 17x - 60 \\ (x + 3)(x - 20)[/tex]
First we put parentheses and in each bracket we put (X) and then we put the signs x² is positive and the 17X before it is a negative q is positive with negative —> negative, and negative before 17X and negative before the 60 —> positive. And then the number that does not have (x) where did it come from, for example 60 came from 20 x 3 or 30 x 2...etc. We can verify this by multiplying the parentheses together and the same number comes out .
Or it can be checked by multiplying the first bracket 3 with x from the second parenthesis comes out 3X and negative 20 from the second parenthesis with X from the first parenthesis and subtract 3X from –20xcomes out –17X .
I hope I helped you^_^
I'm a little stuck on this, could I get some help? C:
How much would you need to deposit in an account each month in order to have $50,000 in the account in 10 years? Assume the account earns 5% annual interest compounded monthly.
Thank you, and I am eternally grateful.
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Answer:
$321.99
Step-by-step explanation:
Use the annuity formula and solve for P.
A = P(12/r)((1 +r/12)^(12t) -1) . . . . value of a series of deposits P earning rate r compounded monthly for t years.
50,000 = P(12/0.05)((1 +0.05/12)^(12·10) -1) = P(240)(0.64700950)
P = 50,000/155.282279 = 321.99
You would need to deposit $321.99 in the account each month to have $50,000 in 10 years.
Let f(x) = x - 3 and g(x) = x + 11 find f(x) times g(x)
What is the answer?
f(x) *g(x) = (x-3)(x+11) = x^2 +11x -3x -33 = x^2 +8x -33
Sorry if its wrong :(
Sarah, Bob and Nellie are cousins. Sarah is half the age of Bob. In three years time Nellie will be twice as old as Sarah. Their ages at the moment add to 38 years. Determine the ages of Sarah, Bob and Nellie
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Answer:
Sarah is 7Bob is 14Nellie is 17Step-by-step explanation:
Let s, b, n represent the current ages of Sarah, Bob, and Nellie, respectively.
s = b/2 . . . . . . Sarah is half Bob's age
2(s+3) = n+3 . . . . in 3 years, Nellie will be twice Sarah's age
s + b + n = 38 . . . . . their ages now add to 38
__
We can rearrange the first two equations to find Bob and Nellie's age in terms of Sarah's. Then we can substitute into the third equation to find Sarah's age.
b = 2s . . . . . . multiply the first equation by 2
2s +3 = n . . . . subtract 3 from the second equation and simplify
s +(2s) +(2s+3) = 38 . . . . substitute for b and n
5s = 35 . . . . . . . . . . . . subtract 3, collect terms
s = 7 . . . . . . . . . . . . divide by 5
b = 2(7) = 14
n = 2(7) +3 = 17
Sarah is 7, Bob is 14, and Nellie is 17.