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
if i can get 3 snapple Iced tea. and its 3 for $6 How would it be if i get 2 snapple Iced tea?
explain
Answers
Answer:
4 dollars for 2 drinks (2 dollars for 1 drink)
Step-by-step explanation:
Okay, so you can get 3 snapple drinks from 6 dollars. and you want to know the cost of 2 snapple drinks.
3 ÷ 6 = 2
So 1 drink is 2 dollars, if you wanted to buy 2 drinks the cost would be 4 dollars! Have a great day friend! :D
Answer:
$4
Step-by-step explanation:
If 3 Snapple Iced teas cost $6, we can divide 6 by 3 to find the cost for one.
6/3 is 2 and 2 * 2 is 4, so 2 Snapple Iced teas would cost $4.
please help me:((( i need help!
Answers
Answer:
Step-by-step explanation:
96 for 1st triangle and 128 for he 2nd triangle....hope this helps!
Yall i need help asap! please help
Answers
Sorry, couldn't help in Q. 10
The question seems undefined or I haven't seen this question before.
If answered correct you will be MARKED BRAINLIEST
Answers
Answer:
a^18
Step-by-step explanation:
(a^2 x a^2 x a^2)^3
first, calculate the product inside the parentheses
(a^6)^3
simplify the expression
a^18
Answer number eight please
Answers
Answer:
Obtuse triangleStep-by-step explanation:
#8If the square of one side is greater than the sum of squares of other sides, the angle opposite to this side is greater than 90°.
It means the triangle has an obtuse angle, so the triangle is an obtuse triangle.
Which table shows the values that would result from using the function machine?
Answers
Answer:
A
Step-by-step explanation:
Evaluate f(2). This gives you 2^2 + 1, which is 5. That eliminates C and D.
f(3) = 3^2 + 1 = 10. This must mean that A is the answer.
What is the value of y?
Answers
Answer:
40°
Step-by-step explanation:
We know that a triangle is equal to 180°
Since one angle is 50° we can figure out that the rest of the angles are equal to 130° (180° - 50°)
If we use 40° then 2·(40°) = 80°
and the second angle is 40° + 10° = 50°
if we add all the angles (80° + 50° + 50°) we get 180° which is correct.
Help pls
Which statement correctly describes the picture?
Answers
Answer:
D
Step-by-step explanation: The line GH has an arrow, so is designated as GH with an arrow over it. The line EF has no direction (no arrow), so it is represented simply as EF with a line, with no arrow. The point P is, well, just point P.
What is the y-intercept of the graph of the equation y =(2x−3)^2+7
Answers
Answer:
(0,16)
Step-by-step explanation:
Hi there!
The y intercept is the value in which the parabola passes through the y axis
Therefore, the value of x at the y intercept is 0
So to find the value of the y intercept, substitute x as 0 in the equation.
y=(2x-3)^2 + 7
If x=0, then:
y=(2(0)-3)^2 + 7
Multiply
y=(0-3)^2 + 7
Subtract 3 from 0
y=(-3)^2 + 7
Raise -3 to the second power
y= 9 + 7
Add 9 and 7 together
y = 16
So the y intercept is the point (0,16)
Hope this helps!
multiply 4 (-52/3) in simplest form
Answers
Answer:
Should be -69 1/3
Step-by-step explanation:
Let X equal the decimal number
Equation 1:
X=69.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
With 10 digits in the repeating decimal group,
create a second equation by multiplying
both sides by 1010 = 10000000000
Equation 2:
10000000000X=693333333333.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Subtract equation (1) from equation (2)
10000000000XX9999999999X===693333333333.3333333333...69.3333333333...693333333264
We get
9999999999X=693333333264
Solve for X
X=6933333332649999999999
Find the Greatest Common Factor (GCF) of 693333333264 and 9999999999, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 3333333333,
693333333264÷33333333339999999999÷3333333333=2083
Simplify the improper fraction,
=6913
In conclusion,
−69.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯=−6913
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the inverse of the line provided on the graph.
Drawing Tools
Click on a tool to begin drawing.
Answers
The inverse function will have x intercept additive inverse of this.
Inverse of the line's interceptsx-intercept=-(-5)=5y intercept=1Now
equation of line in intercept form
[tex]\\ \sf\longmapsto \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{x}{5}+\dfrac{y}{1}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{x+5y}{5}=1[/tex]
[tex]\\ \sf\longmapsto x+5y=5[/tex]
Graph attached
The Graph of the inverse of the function is given below.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
From the given graph,
x intercept=-5
y intercept=1
The inverse function will have x intercept additive inverse of this.
The inverse of the line's intercepts
x-intercept = 1
y-intercept = -5
Now
equation of a line in intercept form
x/a + y/b = 1
x/1 +y/-5 = 1
5x - y = 5
Learn more about function here:
https://brainly.com/question/29633660
#SPJ7
Please find x and y... I will mark you brainliest
Answers
Answer:
Step-by-step explanation:
Dodoodo
Step-by-step explanation:
x=30 and y=30. I have solve it. See the picture that I have attached.
whT is the largest interger less then or equal to 30?
Answers
Answer:
30
Step-by-step explanation:
since it can be equal to 30 that means the answer is 30
Answer:
30
Step-by-step explanation:
if the interger can be equal to 30, it can be 30
a car travels at a constant speed for 2 hours. what is that speed miles per hour
Answers
Answer:
Distance/2 hours
Step-by-step explanation:
Distance=Speed times Time, and since the time is 2 hours, we can say Distance=Speed times 2 hours.
Now we divide both sides by 2 hours, resulting in Distance/2 Hours= Speed.
DUBS
Please consider a brainliest!
how many teaspoons are in 15 milliliters? 1 tsp = 5 mL
Answers
Answer:
The number of teaspoons in 15 ml is 3 tsp.
Step-by-step explanation:
All you have to do is divide 15 by 5 and get 3. This is because for every 5 ml there is 1 tsp. So for the 15 ml, there is 3 tsp.
the distance between town A and town B is 123 km. Two buses begin their journey and move directly toward each other. From town A, the bus is moving at a speed of 45 km/hr and from town B, the bus is moving at a speed of 67 km/hr. Assuming the buses started at the same time, find how far is their meeting point from town A?
Answers
Answer:
Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Step-by-step explanation:
Let speed of first bus be x mph
Then speed of second bus = x+10 mph.
Let A and B have a distance d.
Then given that faster bus reached in 3.5 hours.
i.e. ... i
THe other bus was away from B by 1/6 times d.
Distance travelled by slower bus = 1-1/6 = 5d/6
Time taken = 3.5 hours
i.e. ... ii
Divide i by ii to eliminate d.
ie Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Use ii equation
miles
answer and please show work.
Answers
Slope is equal to the change in y over the change of x, or rise over run.m=change in y / change in x
The change in x
is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
m= y2-y1/x2-x1.
Substitute in the values of x and y into the equation to find the slope.
m =-4 -(7)/ -6 -(-4)
Simplify.
m=11/2.
A machine paints 340 toy boats in 45 minutes. Which expression equals the unit rate per minute?
Answers
Answer:
7.55556 toy boats per minute
or
340 = 45x
Step-by-step explanation:
340 = 45x
340/45 = 45x/45
7.55556 = x
7.55556 toy boats per minute
(6x + 4) - (3x - 2) simplify
Answers
Answer:
9x -2
Step-by-step explanation:
6x + 4 - 3x - 2
6x + 3x +4 - 2
9x -2
Answer:
3x + 4Step-by-step explanation:
(6x + 4) - (3x - 2) simplify
(6x + 4) - (3x - 2)=
6x + 4 - 3x + 2
3x + 6
Can some one help me
Answers
Answer:
Step-by-step explanation:
Line A:
Mark two points in line A.
(1,3) & ( 2 , 5)
[tex]Gradient =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{5-3}{2-1}=\dfrac{2}{1}\\\\\\= 2[/tex]
Line B:
(0,5) ; (5,0)
[tex]Gradient = \dfrac{0-5}{5-0}=\dfrac{-5}{5}=-1[/tex]
At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold.
The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold.
2x + 3y = 1240
x = 2y – 10
How many of each type of ticket were sold?
180 food tickets and 293 ride tickets
180 food tickets and 350 ride tickets
293 food tickets and 180 ride tickets
350 food tickets and 180 ride tickets
Answers
Answer:
180 food tickets and 350 ride tickets
Step-by-step explanation:
The number of food tickets sold is 180 and ride tickets is 350.
In order to determine how many of each type of ticket was sold, the two equations given have to be solved simultaneously using the substitution method.
2x + 3y = 1240 equation 1
x = 2y – 10 equation 2
Substitute for x in equation 1
2(2y -10) + 3y = 1240
4y - 20 + 3y = 1240
Combine similar terms
7y = 1240 + 20
7y = 1260
Divide both sides of the equation by 7
y = 1260 / 7
y = 180
Substitute for y in equation 1
2x + 3(180) = 1240
2x + 540 = 1240
2x = 1240 - 540
2x = 700
x = 700 / 2
x = 350
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Write the following phrase as an algebraic expression. Use k for the unknown.
"The product of 20 and a number"
Answers
Answer: 20k
Step-by-step explanation: product means to multiply. Use k for the unknown number. 20 times k can be written as 20k.
PLS HELPP!! The table shows the progress of Carson and Jayden as they each read books. Carson Jayden Pages Minutes Pages Minutes 8 6 6 97 16 11.5 12 18 20 20 30 What TWO statements are TRUE?
Answers
Answer:
Step-by-step explanation:
If , a = x + 2y and b = x - 2y , find ( 2a + b ) - ( a - 2b ) , in terms of x and y .
don't give unwanted ans to get the points ~
stay away if u don't know the ans ( no spams and plagiarism )
well explained ans needed ~
Thanks !! ~
Answers
question ;
if , a = x + 2y and b = x - 2y , find ( 2a + b ) - ( a - 2b ) , in terms of x and y .
answer with explanation ;
by substituting the value of a and b 2a + b = 2 ( x + 2y ) + ( x - 2y ) = 2x + 4y + 1x - 2y = 2x + 1x + 4y - 2y = 3x + 2y a - 2b = ( x + 2y ) - 2 ( x - 2y ) = x + 2y - 2x + 4y = -1 + 6yi hope my answer helps !!
Answer:
4x - 4yStep-by-step explanation:
Simplify the expression:
( 2a + b ) - ( a - 2b ) =2a + b - a + 2b = a + 3bSubstitute values:
a + 3b = x + 2y + 3(x - 2y) = x + 2y + 3x - 6y = 4x - 4yAndrea has 473 scented stickers in her sticker book. How many tens of stickers does Andrea have?
7
40
47
70
Answers
Answer:
Andrea has 70
Step-by-step explanation:
7 is the tens place that would make it 70
Answer:
47
Step-by-step explanation:
Given:
473 scented stickers
To Find:
How many tens of stickers does Andrea have?
Solution:
To find the answer divided 473 by 10 = 47.3
That mean Andrea have 47 tens of stickers.
Therefore the answer is 47
plss help ill give brainlest
Answers
What is an equation of the line that passes through the points (-6, -5) and (-3, 0)?
Answers
Answer:
Y=5
Step-by-step explanation:
For each table, write the equation that represents the price per ticket.
Answers
Answer:
x=7.5y
Step-by-step explanation:
I took the test
Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3
Answers
Answer:
-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
The higher the negative number the lower it really is.
Answer:
-4.5, -.5, .3, .7,2.3
Step-by-step explanation:
Help me pls I don't get it
Answers
Answer:
maybe A
Step-by-step explanation: