how do we write repeated multiplication as powers and how do we evaluate powers
Answers
Answer:
\(5 { \\ }^{2} \)
Step-by-step explanation:
exponents are ways to write multiplication powers 5
\(5 {}^{2} \)
= 5×5 = 25
Answer:
the exponent signifies the number of times the base is a factorpowers can be evaluated by performing the multiplicationsStep-by-step explanation:
You want to know how multiplication and powers are related, and how powers can be evaluated.
Repeated additionYou may be familiar with the fact that a coefficient is used to signify repeated addition:
y + y + y + y = 4y
The coefficient of 4 in 4y signifies that y is in the sum that many times.
Repeated multiplicationAn exponent is used to signify repeated multiplication:
y × y × y × y = y⁴ . . . . y to the fourth power
The exponent of 4 signifies that y is a factor in the product that many times.
In typeset text, the exponent is rendered in a superscript font. In plain text, the exponent (power) is identified using a caret (^):
y⁴ = y^4
Rules of exponentsThe rules of exponents derive from the idea of exponents signifying repeated multiplication:
\((x\cdot x)=x^2\\(x\cdot x\cdot x)=x^3\\(x\cdot x)\cdot(x\cdot x\cdot x)=(x\cdot x\cdot x\cdot x\cdot x)\ \Longrightarrow\ x^2\cdot x^3=x^{2+3}=x^5\)
Division has a similar rule.
\(\dfrac{(x\cdot x\cdot x\cdot x\cdot x)}{(x\cdot x)}=(x\cdot x\cdot x)\ \Longrightarrow\ \dfrac{x^5}{x^2}=x^{5-2}=x^3\)
This supports the idea that a positive exponent in the denominator is the same as a negative exponent in the numerator, and vice versa.
Evaluating powersPowers can be evaluated in a straightforward way by carrying out the multiplications.
In general, the number of significant digits in the result will be the product of the exponent and the number of significant digits in the base.
For example, 9.2^5 could be expected to have 2×5 = 10 significant digits:
9.2^5 = 9.2×9.2×9.2×9.2×9.2 = 65,908.15232
Most calculators are limited to 12 digits or less, and most spreadsheets are limited to 16 digits or less. Some special-purpose calculators have "variable" precision, so are able to properly render higher powers of numbers with more than 1 or 2 significant digits.
A calculator may use any of several techniques for evaluating powers. Among them might be ...
logarithmsrepeated squaring.LogarithmsLogarithms turn a power problem into a multiplication problem:
log(9.2^5) = 5·log(9.2)
Of course, once the logarithm is found, the issue of evaluating powers comes back:
9.2^5 = 10^(5×log(9.2)) ≈ 10^(4.818939136727776)
Fortunately, there are methods of evaluating antilogs that simplify this part of raising to a power. The difficulty is that precision may be lost. Here, using the rounded value 10^(4.81893913673) gives the result 65,908.152320337..., which is in error after the 10th digit.
Repeated squaringAn integer power can be written as a sum of powers of 2. For example, ...
37 = 32 +4 +1 = (8 +1)4 +1
Then ...
9.2^37 = (((((9.2^2)^2)^2 · 9.2)^2)^2) · 9.2
This requires only 7 multiplications, not 36
__
Additional comment
Only the first token after the caret is considered to be the exponent:
y^4x = (y^4)(x) . . . . . the first token is 4
y^1/2 = (y^1)/2 = y/2 . . . . the first token is 1
If the exponent has multiple parts, they should be enclosed in parentheses:
\(y^{3x+1}\)
will be written in plain text as ...
y^(3x+1)
and ...
y^(1/2) = √y
You also need to be careful writing multiple exponents using the caret symbol. Parentheses are usually required. The Order of Operations has you evaluate multiple exponents right to left.
3^4^5 = 3^(4^5) = 3^1024
(3^4)^5 = 3^20
Related Questions
There are 7 red marbles, 5 blue marbles, and 11 green marbles in a bag. If John randomly pulls a marble from the bag, what is the probability that he selects a blue marble? Give your answer as a decimal to the nearest hundredth.
Answers
Answer:
0.23
Step-by-step explanation:
Find the next three terms in the sequence 4, 16, 36, 64, 100, ...
Answers
Answer:
144 196 256
. .............
You can walk 1/34 miles in 1/2 hour. What is your average speed?
Answers
4x+5(7x-3)=9(x-5)
x????
Answers
Answer:
x=-1
Step-by-step explanation:
4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1
Answer:
\( \sf \: x = - 1\)
Step-by-step explanation:
Given equation,
→ 4x + 5(7x - 3) = 9(x - 5)
Now the value of x will be,
→ 4x + 5(7x - 3) = 9(x - 5)
→ 4x + 35x - 15 = 9x - 45
→ 39x - 15 = 9x - 45
→ 39x - 9x = -45 + 15
→ 30x = -30
→ x = -30 ÷ 30
→ [ x = -1 ]
Hence, the value of x is -1.
Find the standard form of the equation
Answers
\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)
\(\qquad \tt \rightarrow \: y = x² +6x -16\)
____________________________________
\( \large \tt Solution \: : \)
The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.
So, the values of x, when y = 0 are the roots of the given quadratic function.
that is : x = -8 and x = 2
And it can be represented as :
\(\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0\)
[ h1 and h2 represents roots of the quadratic function ]
\(\qquad \tt \rightarrow \: (x -2)(x + 8) = 0\)
It can be further simplified as :
\(\qquad \tt \rightarrow \: {x}^{2} -2x +8x -16 = 0\)
\(\qquad \tt \rightarrow \: x {}^{2} +6x -16 = 0\)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Simplify 3(x+2) + 2x + 5
Answers
Answer:
\(5x+11\)
Step-by-step explanation:
Step 1: Distribute
\(3x+6+2x+5\)
Step 2: Add like terms
\(5x+11\) < your answer
Write an equation in general form (Ax+By+C =0) for the line that passes through A(2, 4) and B(11, 8).
Answers
Answer:
4x - 9y + 28 = 0------------------------
Find the slope of AB:
m(AB) = (8 - 4)/(11 - 2) = 4/9Use point-slope form and point A(2, 4) to determine the line:
y - 4 = (4/9)(x - 2)Multiply both sides by 9 to clear fraction:
9(y - 4) = 4(x - 2)Open parenthesis and convert the equation into ax + by + c = 0:
9y - 36 = 4x - 8 ⇒4x - 9y - 8 + 36 = 0 ⇒4x - 9y + 28 = 0x less then or equal to -1
Answers
Answer:
x ≤ -1
Step-by-step explanation:
I hope this helped!
Identify whether each function is linear or exponential.
Function A:
Function C
Function D:
You have $200 in
a savings
account that
earns 1% annual
interest
b. Which function has the greatest growth factor? Justify your response.
Answers
Answer:
A)
Function A: Exponential
Function B: Linear
Function C: Exponential
Function D: Exponential
B) Function A
Step-by-step explanation:
Function A: This is exponential because- (1, 3)(2,9)(3,27)
It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.
Function B: This is linear because- (1, 64)(1, 80)(1, 96)
It is going up by 16 each time, (a constant number) which means it is linear.
Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.
Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.
The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.
gabrielle wants to buy a new pair of jeans. if the jeans were originally $25.00, but are on sale with a $15 discount, how much will gabrielle have to pay for the jeans.
Answers
the same thing i did when my dad died in a motorcycle crash and my mom had a stroke in her arms when i got to work in a hospital
25-15=10
abubububuvuv
5/7−(−1/7) please answer fast I need iittt
Answers
Answer: \(\frac{6}{7}\)
Step-by-step explanation:
\(\frac{5}{7}-\left(-\frac{1}{7}\right)\)
Once you take off the parenthesis, your sign should change from negative to positive.
\(\frac{5}{7}-\left(-\frac{1}{7}\right)=\frac{5}{7}+\frac{1}{7}\\\\\frac{5}{7}+\frac{1}{7}\)
The fractions now both have the same denominator. Thus, we can add the numerators.
\(\frac{5+1}{7}\\\\5+1\\\\6=\frac{6}{7}\)
Therefore, \(\frac{5}{7}-\left(-\frac{1}{7}\right)=\frac{6}{7}\)
The storage capability of computers has been doubling every 5 years since the first computers were invented in the 1960s. If the first computer could store .5 megabytes, about how many megabytes can today's computers store? How long did it take for computers to store 100 megabytes?
Answers
It takes time of near about 35 year.
Given that,
Storage capability of computers has been doubling every 5 years
The date of 1st computer made = 1980
computer could store 5 megabytes,
Now,
We can use the following calculation to determine how long it took computers to store 100 megabytes:
Therefore,
Log₂ (final amount / beginning amount)
= Log₂ (100 / 0.5)
= log₂ (200)
= 7.64 is the number of doublings.
If each doubling takes five years, then it would take computers just over seven doublings or almost 35 years to store 100 megabytes.
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Find the rate of change between:
(-4, 0)
(-4, 2)
Answers
Answer:
Its increasing the y value by 2 everytime
Step-by-step explanation:
-4,0 + 0,2 = -4,2
-4,2 + 0,2 = -4,4
to understand the increasing value add 2.
QUESTION 4 of 10: It is estimated that 32 patrons will attend an event for every $100 spent in advertising. If tickets cost $75, how much can a
promoter expect to increase sales if he spends $25,000 in advertising?
Answers
Answer:
$575000Step-by-step explanation:
Spend on advertising = $25000
32 patrons per $100
Number of patrons:
25000/100×32 = 8000Sales amount:
8000×$75 = $600000Increase in sales excluding advertisement cost:
$600000 - $25000 = $575000Answer:
$600,000
Step-by-step explanation:
$25,000 / 100 then 250 x 32 then 8,000 x 75 to get $600,000
I NEED YOUR HELP!! I'LL. GIVE YOU BRAINLIEST
Answers
Answer: ∠16 and ∠11
Step-by-step explanation:
All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.
The correct corresponding angles are ∠16 and ∠11.
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
Answers
Answer:
the number of days when instructor do the work alone is 8 days
Step-by-step explanation:
Given that
The apprentice can do the work in 24 days
And, the apprentice and instructor together can do it in 6 days
We need to find out the number of days when instructor do the work alone
So,
\(= \frac{1}{6} - \frac{1}{24} \\\\= \frac{4 - 1}{24} \\\\= \frac{3}{24} \\\\= \frac{1}{8} \\\\= 8\)
hence, the number of days when instructor do the work alone is 8 days
Plz help (extra points)
Answers
Answer:
6/18 bags
Step-by-step explanation:
Answer:
8/12 OF A BAG IS THE RIGHT ANSWER
Harry coaches 25 children on Wednesday. On Saturday, he coaches 9 more children. How many children does he coach in all? How did you know to regroup to solve this problem?
Answers
Answer:
34
Step-by-step explanation:
25+9=34
We don't know if he did or how much he coached on other possible days so in total with the information given. He did 34
use the figure to solve for X.
I tried looking this one up and all i’m getting is 11/3 and it’s wrong. Please help
Answers
Answer:
x = -1
Step-by-step explanation:
\(5+2x+6=x+10\\2x+11=x+10\\x+11=10\\x=-1\)
The sum of two numbers is 3. One number is 15 more than the other one. Find the numbers.
Answers
Answer: The sum of two numbers is 7. Three times one of the numbers is 15 more than the other number. Find the numbers.
Let X and Y be the two numbers.
X + Y = 7 "The sum of two numbers is 7."
3X = Y + 15 "Three times one of the numbers is 15 more than the other number."
Taking the TOP EQUATION and solving for X:
X + Y = 7
X = 7 - Y Subtracting Y from both sides of the equation.
Plugging 7 - Y into the BOTTOM EQUATION for X:
3X = Y + 15
3(7 - Y) = Y + 15
21 - 3Y = Y + 15 Distribute 3 times (7 - Y)
-3Y = Y + 15 - 21 Subtracting 21 from both sides of the equation.
-3Y = Y - 6 15 - 21 = -6
-4Y = - 6 Subtracting Y from both sides of the equation.
Y = - 6/ - 4 Dividing both sides of the equation by - 4.
Y = 3/2 or 1.5
Plugging 3/2 into the TOP EQUATION for Y to solve for X:
X + Y = 7
X + 3/2 = 7
X = 7 - 3/2 Subtracting 3/2 from both sides of the equation.
X = 14/2 - 3/2 = 11/2 = 5.5
ANSWER: ONE NUMBER IS 1.5 AND THE OTHER NUMBER IS 5.5
CHECKING:
TOP EQUATION: X + Y = 7
5.5 + 1.5 = 7 Yes!
BOTTOM EQUATION: 3X = Y + 15
3(5.5) = 1.5 + 15
16.5 = 16.5 Yes!
Step-by-step explanation:
Please help. Will award brainliest
Answers
The dimension of the rectangular of a norman window will be 1.6803*3.3606.
What is the area of Rectangle?
In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.
Let r represents the radius, and b be the breadth.
Then, perimeter = 3.14*r+2r+2b = 12
For the dimension needed for the most light to enter we need to maximize the area.
Hence, area of the window : area of the semicircle + area of the rectangle
= \(\frac{3.14*r^2}{2} + 2rb\)
= \(12r - (\frac{3.14+4}{2}) r^2\)
A'(r) = 0
Therefore, \(r=\frac{12}{3.14+4}\) which is nearly equal to 1.6803m
From this value of r we can calculate the value of b to be;
b= 1.6803m
Thus, a= 3.606m
Thus the required dimension is : 1.6803*33606
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The stem and leaf plot here shows the current sale prices
for 60 houses in Horsham, PA, in thousands of dollars.
Note how the key helps communicate the prices.
Describe the distribution of housing prices.
Answers
Answer:
Symmetric
Step-by-step explanation:
In the stem and leaf plot above which represents the current sale prices of houses in dollars, we can observe the shape of the distribution seem like that of a bell shape. Most of the data values are concentrated towards the center compared to the concentration at both extremes.
This implies that most of the current sales price is centered close to the median price of roughly 49/50 dollars.
Therefore, the distribution of housing price can be described as roughly symmetric.
I just need to know the answer and some explanation please
Answers
Answer:
f(x)=(x+5)(x+3)(x-1)(x-3)(x-4)(x²+2)
Explanation:
Given that the polynomial must have zeros at -5, -3, 1, 3, and 4, some of the factors are:
\((x+5)(x+3)(x-1)(x-3)(x-4)\)Next, it must have a factor that produces a non-real zero:
\(\begin{gathered} x^2+2=0 \\ \implies x=\pm2i \end{gathered}\)One example of a factor that produces a non-real zero is x²+2.
Adding this factor to the previous ones, the polynomial becomes:
\(f(x)=(x+5)(x+3)(x-1)(x-3)(x-4)(x^2+2)\)The polynomial is of a degree of 7 as required.
The sketch of the polynomial is given below:
What is 17 + 8 x (2.7 ÷ 6) - 3
using
P
E
M
D
A
S
Answers
Answer:
17.6
Step-by-step explanation:
2.7÷6= 0.45
0.45×8= 3.6
17+3.6 - 3=17.6
True or False:
In the diagram, ∠1 and ∠2 are adjacent angles.
Explain your thinking.
Answers
Answer:
false
Step-by-step explanation:
adjacent angles should share a common arm and a common vertex. no arms are common and vertex of first angle is CAB whereas the vertex of second angle is DAE
Answer: false
Step-by-step explanation:
Adjacent angles are angles share the same vertex and the same common side. They are two angles that are right next to each other.
B:
The usual monthly expenses of midas family is 3500.00 for their electric and and with bill, 10,
000 for house and 5,000.00 for their food. The rest of their income will be their savings How much
will be their savings if the couple both earn 10,000.00each
Answers
Answer:
$1,500
Step-by-step explanation:
Income - Expenses = Savings
Income = 2 × 10,000 = $20,000
Expenses = 3,500 + 10,000 + 5,000 = $18,500
$20,000 - $18,500 = $1,500 left for Savings
This is just a question I had.
If Denny (random name) left to another country and he left the Tuesday of this week (June 20) and he left for a month, what day would he be back on? I though July 18 but I’m not sure. Pls help?
Answers
Answer:
Step-by-step explanation:
Well, since the length of a month can vary in the number of days, this answer can also vary.
For example, February is only 28 days long, while December is 31 days long.
That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back July 19th of July 20th.
I hope this helps!
In a lottery, the top cash prize was $642 million, going to three lucky winners. Players pick five different numbers from 1 to 56 and one number from 1 to 49.
Save
A player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 49). What is the probability of winning the minimum award?
The probability of winning the minimum award is
Answers
Total number of possible outcomes:
Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957
Number of ways to choose 1 number from 49: 49
Total number of possible outcomes = 22,957 * 49 = 1,128,593
Number of favorable outcomes:
Number of ways to choose 1 number from 49: 1
Number of favorable outcomes = 1
Probability of winning the minimum award:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%
Suppose you run 3 miles from your house to a friends house at a speed of 7 miles per hour when the time comes to return home you are tired and walk the same 3 miles home at 2 miles per hour
Answers
The amount of time you spent running to your friend's house was 3 / 7 hours
The amount of time you spend walking home was 1. 5 hours
How to find the time taken ?To find the time taken, when given distance and speed, the formula is:
= Distance / Speed
The time you spent running to your friend's house is therefore :
= Distance / Speed
= 3 / 7
= 3 / 7 hours
The time you spent walking back home was :
= 3 / 2 x 60
= 1. 5 hours
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The questions are:
a. How long did you spend running to your friend's house? hour(s)
b. How long did you spend walking home?
The model represents an equation. What value of x makes the equation true?
Answers
Answer:
I think i wanna say one of the fractions
Step-by-step explanation: