Indices Home Learning
Simplify the following, leaving your answers in index notation.
1. (39)
2. Zf x 9f
38
3. 124 x 1210
4. (6m)
5. 252-3
6. 42g? = 7g?
7. 39 x 36
35
8. 116 x 116
112 x 11
Solve the following.
9. 7-2
10. 3-3
Answers
Answer:
We know that,
[tex](a^{x}) ^{y} =a^{xy}[/tex]
[tex]a^{x} *a^{y} =a^{x+y}[/tex]
[tex]\frac{a^{x} }{a^{y} } =a^{x-y}[/tex]
Let's solve now.
1) [tex](3^{8})^{4} =3^{32}[/tex]
2) [tex]7f^{3} * 9f^{9} =63f^{12}[/tex]
3) [tex]12^{4} *12^{10} =12^{14}[/tex]
4) [tex](6m^{5} )^{3} =6m^{15}[/tex]
5) [tex]\frac{2^{5} }{2^{-3} } =2^{8}[/tex]
6) [tex]\frac{42g^{7} }{7g^{2} } =6g^{5}[/tex]
7) [tex]\frac{3^{9}*3^{6} }{3^{5} } =\frac{3^{15} }{3^{5} } =3^{10}[/tex]
8) [tex]\frac{11^{6}*11^6 }{11^2*11^3} =\frac{11^{12}}{11^5} =11^7[/tex]
9) [tex]7^{-2} =\frac{1}{7^2} =\frac{1}{49}[/tex]
10) [tex]3^{-3} =\frac{1}{3^3} =\frac{1}{27}[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Related Questions
What is the value of x?
A
3x - 5
Enter your answer in the box.
4x - 30
В
B
X=
2x + 20
Answers
Answer: x = 25
Step-by-step explanation:
This appears to be an equilateral triangle. All angles are shown to be the same. This means all 3 sides will have the same length:
3x-5
4x-30
2x+20
are all equal to each other.
3x-5 = 4x-30
x = 25
----
3x-5 = 70
4x-30 = 70
2x+20 = 70
Triangle ABC is similar to triangle EFD. What
scale factor is required to dilate triangle ABC
so that its image, A'B'C', is congruent to
triangle EFD?
Answers
Determine the solution and the reasoning that justifies the solution to the systems of equations.
O (2,7), because this point is true for both equations
O (4, -6), because this point lies only on one of the two lines
(4, -6), because this point makes both equations true
O (2,7), because the lines intersect the x-axis at these points
Answers
Answer:
A or CStep-by-step explanation:
The system is not given to give exact answer.
Possible solution is:
A. (2,7), because this point is true for both equations
Yes, same point lies on both lines, it is their intersectionB. (4, -6), because this point lies only on one of the two lines
No, this is not a solution to both equationsC. (4, -6), because this point makes both equations true
Yes, same point lies on both lines, it is their intersectionD. (2,7), because the lines intersect the x-axis at these points
No, this is not confirming any solutionSelect the correct answer. The probability that Ashley drives faster than the speed limit (event A) is 0. 34, and the probability that he gets a speeding ticket (event B) is 0. 22. The probability that he drives faster than the speed limit, given that he has gotten a speeding ticket, is 1. Are events A and B dependent or independent? A. Dependent B. Independent C. Insufficient data D. Depends on the other events in the sample space.
Answers
Answer:
Depends on other factors, although I'm not certain, so to speak.
Step-by-step explanation:
We don't know the probability of Ashley getting a speeding ticket when he is not speeding. [It happens].
Otherwise, event B is dependent on event A. Speeding must occur to initiate event B.
If you take a sample of 9 pacemakers from the company, what is the probability that the mean lifetime of components in this sample will be longer than 99 months
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 9 years, hence, in months, [tex]\mu = 9(12) = 108[/tex]The standard deviation is of 1 year, hence, in months, [tex]\sigma = 12[/tex].Sample of 9 pacemakers, hence [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].The probability is 1 subtracted by the p-value of Z when X = 99, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{99 - 108}{4}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
1 - 0.0122 = 0.9878.
0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.
A similar problem is given at https://brainly.com/question/24663213
what percentage of this grid is shaded
how many more squares need to be shaded so that 60% of the grid is shaded?
Answers
Answer:
44%, and 4
Step-by-step explanation:
The grid has 5 rows and 5 columns so we have 5*5 = 25 squares.
25 squares represent 100 % of the grid
a) In the grid 11 of the 25 total squares are blue, so if
25 squares are 100%
11 squares will be x%
x= (11* 100) / 25 = 1100/ 25 = 44 %
b) we find the number of squares that gives us 60 %
25 squares are 100%
x squares will be 60%
x= (60*25)/ 100 = 15
The question is " How many more squares " so we have to compare with the 11 given ones in part a)
15 -11 = 4
4 more squares will give 60 % blue grid.
g/(g ^ 2 + 4g) - g/((g + 4) ^ 2) =?
Simplify.
Answers
Answer:
[tex] \frac{4}{(g + 4) ^{2} }[/tex]
Step-by-step explanation:
Factor the expressions that are not already factored in g/g² + 4g.[tex] \frac{g}{g(g + 4)} - \frac{g}{(g + 4) ^{2} } [/tex]
Cancel out g in both numerator and denominator.[tex] \frac{1}{g + 4} - \frac{g}{(g + 4) ^{2} } [/tex]
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of g+4 and (g+4)² is (g+4)². Multiply 1/g + 4 times g + 4/g + 4.[tex] \frac{g + 4}{(g + 4) ^{2} } - \frac{g}{(g + 4) ^{2} } [/tex]
Since g + 4/(g + 4)² and g/( g + 4)⁴ have the same denominator, subtract them by subtracting their numerators.[tex] \frac{g + 4 - g}{(g + 4) ^{2} } [/tex]
Combine like terms in g+4−g.[tex] \frac{4}{(g + 4) ^{2} } [/tex]
Expand (g + 4)².[tex] \frac{4}{g^{2} + 8g + 16 } [/tex]
Hope It's Help
A house is sold for 8% above its original price. If it was sold for £378000 then calculate its original price
Answers
Answer:
$350,000
Step-by-step explanation:
lets say the original price is x, then 378000=1.08x, divide by 1.08 to get 350000
help with this question
Answers
Answer:
B
Step-by-step explanation:
Solve the inequality *NUMBERS ONLY, NO WORDS*
n/4 - 1 ≥ 1
Answers
Answer:
[tex]n\geq 8[/tex]
Step-by-step explanation:
n/4-1[tex]\geq[/tex]4
n-4[tex]\geq[/tex]4 (move constant to right)
n[tex]\geq[/tex]4+4 (calculate)
n[tex]\geq 8[/tex]
Terry buys an orange for 39p.
He pays with a £1 coin.
How much change does he get?
Give your answer in pence.
Answers
Answer:
61p
Step-by-step explanation:
There are 100 pence in 1 pound, so subtract 39 from 100 to get the change.
A robot can complete 5 tasks in 34 hour.
Each task takes the same amount of time.
**Round to the hundredths place.
a. How long does it take the robot to
complete one task?
3/4 divided by 5 = 3/4, so it’s 3/4 hours per task
Answers
Answer:
6.8h
Step-by-step explanation:
5 tasks in 34h
So 1 task is taking 34/5 h
34/5 = 6.8h
1 task is taking 6.8h to complete
solve pls brainliest
Answers
Answer:
1)YES:This is a decimal neither terminates nor repeats
2)YES:Repeating decimal
3)NO: Terminating decimal
4)YES: this is a decimal neither terminates nor repeats.
Step-by-step explanation:
Hope it can help you lovelots
Solve the following system of equations graphically on the set of axes below.
y=x−2
y= - 1/5x-8
Answers
+1.5x
-8=2.5x-2
+2
-6=2.5x
Divided by 2.5
X=2.4
So put x in an equation
2.4-2=y
.4=y
3x+5y=-9
-6x-10y=18
elimantion substuion method
Answers
Answer:
Infinitely many solutions
Step-by-step explanation:
2(3x + 5y = -9)
6x + 10y = -18
-6x - 10y = 18
0 = 0
What is 4.06 increased by 17?
please help me
Answers
Answer:
21.06
Step-by-step explanation:
4.06 increased by 17
4.06 + 17
21.06
SUPER EASYYYYYYYYYYYYYYYY
Answers
Hello, hope you are having a nice day.
t^3*t^9
When we multiply numbers with the same base, we add the powers.
t^12
That's the answer. Hope it helps
Ask me if you have any queries.
[tex]MagicalNature[/tex]
Good luck.
On his bike, Jason can travel 8 miles in 50 minutes.
At this rate, how far can Jason travel in 150 minutes.
Answers
Answer:
24 miles
Step-by-step explanation:
50 minutes = 8 miles
100 miles = 16 miles
150 minutes = 24 miles
Answer:
Jason can travel 24 miles in 150 minutes.
Step-by-step explanation:
8= miles. 50&150= mins
8=50.
Your trying to find how many miles Jason can travel in 150 mins. So your going to divide the new amount of minutes to the old amount.
150÷50= 3.
So since 50 can go into 150 3 full times that means you will multiply the original amount of miles by 3 to get your new amount.
3×8= 24
So, if Jason can travel 8 miles in 50 mins (8=50) Then, he can travel 24 miles in 150 mins (24=150)
Hope this wasn't too confusing,
Hope this helps!
In the circle below, suppose m STQ = 102° and mZTSR=56º. Find the following.
Answers
Answer:
q
Step-by-step explanation:
What is the equation in slope-intercept form of the line that passes through the point (5, 0) and is parallel to the line represented by =2.2+1.2
y
=
2.2
x
+
1.2
.
Group of answer choices
=−2.2+11
y
=
−
2.2
x
+
11
=2.2−11
y
=
2.2
x
−
11
=−2.2−5
y
=
−
2.2
x
−
5
=2.2+5
Answers
what is the improper fraction 2 7/8what is the improper fraction 8 2/3
Answers
Answer:
1. 23/8
2.26/3
Step-by-step explanation:
PLEASEEEEEEE HELP ME GUYS!!
Answers
will give brainliest no files will report.
Answers
You have a $50 gift card to go shopping for school supplies. You buy 2 packs of pencils, 5 notebooks. 6 folders, 1 pack of pens, 3 packs of paper, 1 pack of highlighters, and 2 binders.
pens: $1.57
pencils: $1.98
folder: $0.75
highlighter: $3.45
notebooks: $2.95
binders: $3.55
paper: $0.69
What value represents the change in value of the gift card after buying your school supplies ?
Answers
The value of the gift card declined by $37.40.
The total cost of all the items purchased has to be determined.
Total cost of pens = $1.57 x 1 = $1.57Total cost of pencils = $1.98 x 2 = $3.96Total cost of folders = $0.75 x 6 = $4.50 Total cost of highlighter: $3.45 x 1 = $3.45Total cost of notebooks: $2.95 x 5 = $14.75Total cost of binders: $3.55 x 2 = $7.10Total cost of paper: $0.69 x 3 = $2.07The sum of these items is $37.40
Change in value = value of the gift card - cost of items
$50 - $37.40 = $12.60
A similar question was answered here: https://brainly.com/question/19891026
Answer:
Total cost of pens = $1.57 x 1 = $1.57
Total cost of pencils = $1.98 x 2 = $3.96
Total cost of folders = $0.75 x 6 = $4.50
Total cost of highlighter: $3.45 x 1 = $3.45
Total cost of notebooks: $2.95 x 5 = $14.75
Total cost of binders: $3.55 x 2 = $7.10
Total cost of paper: $0.69 x 3 = $2.07
The sum of these items is $37.40
Change in value = value of the gift card - cost of items
$50 - $37.40 = $12.60
Step-by-step explanation:
Are the ratios 17:10 and 2:1 equivalent?
Answers
Answer:
No, they don't have the same valueStep-by-step explanation:
Are the ratios 17:10 and 2:1 equivalent?
17 : 10 = 1.7
2:1 = 2
Does anyone know this?
Answers
Answer:
△RED~△TAN
Step-by-step explanation:
Both triangles are similar, even if they have different sizes. They still retain the same degrees.
Proof: Angle RED
180 - 110 - 28 to find m∠E.
m∠E = 42
m∠A = 42
m∠E = m∠A
please help I will give 30 points but I need this answer please.
Answers
whats the question???
also it says 5 points-
If d varies directly as t and d=20.5 when t =12 find the value of constant
Answers
Answer:
12÷20.5= 0.5953658537
A savings account increases from 150$ to 153$. What is the percent increase of the savings account?
Answers
Answer:
The correct answer would be 2.00%
PLEASE HELP
What is the slope of the line?
Answers
Step-by-step explanation:
you know what the slope of the line is ? it is the inclination of the line. how strongly is it going up or down, or is it maybe flat ?
in the formulas the slope is always the factor of x. the slope is excised as ratio of y coordinate change / x coordinate change when going from one point to another.
we see here 2 clear points in my opinion :
(0, -3) and (3, 0)
that is where the line crosses the y and the coordinate axis.
so, going from (0, -3) to (3, 0) :
x changes by +3 (from 0 to 3)
y changes by +3 (from -3 to 0).
so, the slope is
+3/+3 = 1