for any numbers x,y [x=0 in(4) and y = 0 in (5)] and any positive integers m,n, the following holds:x^m · x^n=x^m+nProve number 1
![For Any Numbers X,y [x=0 In(4) And Y = 0 In (5)] And Any Positive Integers M,n, The Following Holds:x^m](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/CeELNI4jga7xcl33QzyhQ2njgvYSHTiu.png)
Answers
Proved
Explanation:
To prove x^m · x^n=x^m+n, let's assign numbers to x, m and n
let x = 2
m = 3, n = 4
x^m · x^n = 2^3 . 2^4
x^m+n = 2^(3+4)
Solve each of the above seperately and comparew the answer:
[tex]\begin{gathered} x^m\times x^n=2^3\times2^4 \\ =\text{ (2}\times2\times2)\times(2\times2\times2\times2) \\ =\text{ 8}\times16 \\ =\text{ }128 \end{gathered}[/tex][tex]\begin{gathered} x^{m+n}=2^{3+4} \\ =2^7\text{ = 2}\times2\times2\times2\times2\times2\times2 \\ =\text{ 128} \end{gathered}[/tex][tex]\begin{gathered} sincex^m\times x^n\text{ = 128} \\ \text{and x}^{m+n}\text{ = 128} \\ \text{Therefore, }x^m\times x^n\text{ = x}^{m+n} \end{gathered}[/tex]This expression x^m · x^n=x^m+n has been proved to be equal
Related Questions
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Answers
Answer:
See below.
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Transitive Property of Equality
If a=b and c=b, then a=c.
Proof that ∠1=∠2
∠3 is equal to ∠4 (Vertical Angle Theorem).As BC intersects the set of parallel lines AB and CD (given), ∠3 is equal to ∠2 (Alternate Interior Angles Theorem).If ∠3=∠4 and ∠3=∠2 then ∠2=∠4 (Transitive Property of Equality).Given that ∠1=∠4 and ∠2=∠4 then ∠1=∠2 (Transitive Property of Equality).[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}[/tex]
A 56-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
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A 56-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. The length of all the three pieces are : 7, 21, 18.
LengthThere are 3 pieces:
Length of first piece = x
Length of second piece = 3x
Length of third piece = 4x
Total length = 8x
Now, 8x = 56
Divide both side by 8x
x = 56 /8
x = 7
Length of second piece = 3x where x = 7
3x = 3 ( 7)
= 21
Length of third piece = 4x where x = 7'
4x = 4 ( 7)
= 28
Therefore we can conclude that the length are : 7, 21, 18.
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The access code for a gym locker consists of three digits. Each digit can be any number from 1 through 6, and each digit can be repeated. Complete parts (a) through (c).(a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?
Answers
A.The number of the possible access codes:
[tex]6\cdot6\cdot6=216[/tex]B. The probability of randomly select the correct access code on the first try:
[tex]P=\frac{1}{216}[/tex]C. The probability of not selecting the correct access code on the first try :
[tex]P=\frac{99}{216}[/tex]
00:00 Jayden evaluated the expression a = (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement Choose... Jayden's solution is incorrect. Choose... Jayden added in the parentheses before dividing. Choose... Jayden substituted the wrong value for a. Choose... Jayden divided 14 by 2 and added 1.5.
Answers
Explanation:
Let's see what's the value of the expression if we substitute a = 14:
[tex]14\colon(2+1.5)=14\colon3.5=4[/tex]So definetly Jayden's solution is not correct.
Let's check the second statement: that's what we just did - add the parentheses before dividing. If Jayden would've done that he would have arrieved at the same solution we did, so definetly this statement is false
The third statement could be true. Let's see which value of a gives 8.5 as a result:
[tex]\begin{gathered} a\colon(2+1.5)=8.5 \\ a\colon3.5=8.5 \\ a=8.5\times3.5 \\ a=29.75 \end{gathered}[/tex]If 'a' were 29.75, Jayden would be correct.
Let's see what happens if we divide 14 by 2 and then add 1.5:
[tex](14\colon2)+1.5=7+1.5=8.5[/tex]This is the result Jayden got, so definetly this is one option for what he did wrong.
Answer:
• Jayden's solution is incorrect: ,true
,• Jayden added in the parentheses before dividing:, ,false
,• Jayden substituted the wrong value for a: ,true
,• Jayden divided 14 by 2 and then added 1.5: ,true
A basketball player had scored 879 points in 34 games. a) At this rate, how many games will it take him to score 1500 points? b) There are 82 games in an entire season. At this rate, how many points would he score in the entire season? a) It will take him approximately games to score 1500 points . (Round up to the next whole number of games.) b) At this rate, he would score approximately (Round to the nearest one if necessary.) points in the entire season. Enter your answer in each of the answer boxes.
Answers
We know that he scored 879 points in 34 games, so we can calculate the average rate as:
[tex]r=\frac{879\text{ points}}{34\text{ games}}=25.85\text{ points/game}\approx26\text{ points/game}[/tex]At this rate, we can calculate the total points P by multiplying the rate r by the number of games n:
[tex]P=r\cdot n=25.85\cdot n[/tex]We can calculate how many games are needed for P=1500 as:
[tex]\begin{gathered} P=26\cdot n=1500 \\ n=\frac{1500}{25.85}\approx58.02\approx58\text{ games} \end{gathered}[/tex]For n=82 games, the expected number of points P is:
[tex]P=25.85\cdot n=25.85\cdot82=2119.7\approx2120\text{ points}[/tex]Answer:
a) It will take him approximately 58 games to score 1500 points.
b) At this rate, he would score approximately 2120 points in the the entire season.
at the pet store 25 bunnies were examined and 7 of them had blue eyes.
Answers
Given
[tex]\begin{gathered} 25\text{ }bunnies=7blue\text{ }eyes \\ 60\text{ }bunnies=xblue\text{ }eyes \\ \\ x=\frac{60\times7}{25} \\ \\ x=16.8 \\ \\ x\approx17 \end{gathered}[/tex]The final answer is 17 bunnies
a person weighs 140 pounds has 4 quarts if blood. estimate the number of quarts of blood in a person who weighs 120 pounds
Answers
The number of quarts of blood in a person who weighs 120 pounds is 3.4
How to calculate the number of quarts of blood ?The expression can be written as
W= kV
W represents the weight in pounds
V= number of quarts
k= 140/4
= 35
The number of quarts of blood in a person that weighs 120 pounds can be calculated as follows
= 120/35
= 3.4
Hence 3.4 quarts of blood is gotten from a person who weighs 120 pounds. This was done by dividing 120 by 35
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Enter your answer as an integer or as a reduced fraction in the form A/B.
Answers
From the given graph, let's find the slope of the line.
To find the slope of the line, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points on the line:
(x1, y1) ==> (-6, 4)
(x2, y2) ==> (3, -2)
To find the slope, we have:
[tex]\begin{gathered} m=\frac{-2-4}{3-(-6)} \\ \\ m=\frac{-6}{3+6} \\ \\ m=\frac{-6}{9} \\ \\ m=-\frac{2}{3} \end{gathered}[/tex]Therefore, the slope of the line is:
[tex]-\frac{2}{3}[/tex]
ANSWER:
[tex]-\frac{2}{3}[/tex]
I WILL MARK BRAINLIEST
Which method is best to solve this system?
y = -6x + 5
-2x + y = 5
Option 1: Guess and Check
Option 2: Elimination
Option 3: SUbstitution
Option 4: Graphing
Answers
Answer: I'm sure Option 4 Could help you find your answer.
Step-by-step explanation:
y=−6x+5−2x+y=5
Hope this helps.
4
An ice cream shop has a sign in the shape
of an ice cream cone. The sign is made
using a semicircle and a triangle, as
modeled below.
The base of the
triangle is the
6 in.
diameter of the
semicircle.
12 in.
Which is the best estimate of the area of
the sign in square inches?
F 150 in.2
F
G 14 in.2
H 36 in.2
J 50 in.2
Answers
In order to determine the total area of the sign, we need to calculate the area of the triangle, and the area of the semicircle. The expressions we need to use are described below:
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\cdot r^2}{2} \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \end{gathered}[/tex]We were given the diameter of the semicircle, it's radius is half of the diameter, therefore:
[tex]r=\frac{6}{2}=3\text{ in}[/tex]The base of the triangle is equal to the diameter of the semicircle. With this we can calculate both areas:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{6\cdot12}{2}=36\text{ square inches} \\ A_{\text{semicircle}}=\frac{\pi\cdot3^2}{2}=14.13\text{ square inches} \end{gathered}[/tex]The total area of the figure is the sum of the above, therefore:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{semicircle}} \\ A=36+14.13=50.13 \end{gathered}[/tex]The area is approximately 50 in². The correct option is J.
Two planes, which are 2505 2505 miles apart, fly toward each other. Their speeds differ by 85mph 85 mph . If they pass each other in 3 3 hours, what is the speed of each?
Answers
When two planes which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph
Their speeds differ by 85mph
Consider the speed of first plane = x mph
The speed of second plane = 90+x mph
The relative speed = sum of both speed
= x + x+90
= 2x+90 mph
The distance between the planes = 2505 miles
Time taken to pass each other = 3 hours
Therefore in 3 hours
3(2x+90) = 2505
6x+270 = 2505
6x = 2505-270
6x = 2235
x = 2235/6
x = 372.5 mph
The speed of second plane = 90+x
= 90+372.5
= 462.5 mph
Hence, when two planes which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph.
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Nancy is a high scorer on her basketball team. she made 24 free throws out of 32 free throws attempted. what was her percentage of free throw shots made?
Answers
32 ------------------ 100
24 -------------------- x
x = (24 x 100) / 32
x = 2400/32
x = 75%
To solve this problem use a rule of three
x 0 1 9
P(X = x) 0.14 0.35 0.51
Answers
Answer:
Step-by-step explanation:
k = 0.2
Use the formula n+1/2 to find the median in the list of numbers. 1, 2, 2, 3, 3, 3, 3, 5, 6, 8, 9, 10, 13, 18, 18, 19, 21
Answers
The median is 6 in the given list of numbers
The list of numbers is 1, 2, 2, 3, 3, 3, 3, 5, 6, 8, 9, 10, 13, 18, 18, 19, 21
Formula: (n+1)/2th term
Median: The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to evaluate the entire set of data for representation, and in these cases, the median is helpful.
where n is the number of items in the list of numbers
n = 17
Substituting the value in the formula we get:
(17+1)/2th term
= 9th term
9th term in the list is 6
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Jonah saw a news report that stated that 72% of children in his town played a sport last year. If there are 4,000 children in his town, how many children in his town played a sport last year?(1 point) children in his town played a sport last year.
Answers
Lucas is riding his rocket-powered big wheel. He rides at a constant speed. After riding for 5 hours, Lucashas travelled 46.5 miles. After 8 hours, he has travelled 74.4 miles.a. What is the dependent variable?b. What is the independent variable?c. What is Lucas' speed?d. If you were to graph Lucas' travel, what would the y-intercept be? Why?
Answers
a. Distance travelled
Given that he rides at a constant speed and after riding for 5 hours, he had travelled 46.5 miles. Per review, the distance travelled is dependent on time hence distance or miles covered is the dependent variable
The sides of a square are represented by 3x-9. If the perimeter is 216, what's the
value of X?
Answers
The value of X = 21 .
What is perimeter?The length of every closed shape's perimeter is its whole perimeter. This rectangular farm has two sides, with l being the bigger side and b being the smaller side. His farm's circumference may be calculated by adding the lengths of its four sides. Total distance = 2l + 2b (l + b + l + b). In light of this, a rectangle's perimeter is equal to 2 (l + b) units. The complete distance around a shape is referred to as its perimeter. It is any two-dimensional geometric shape's perimeter or outline length. Depending on the measurements, the perimeter of multiple figures may be equivalent. Consider a triangle that is constructed from an L-length wire as an example.
Permitter of square= 4(x)
y = side
y = 3x -9
4(3x -9) = 216
x = 21
Each side = 54
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A local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday. There were 68 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
Answers
The number of hamburger is 350 and the number of cheeseburger is 282.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
In this case, the local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday and there were 68 fewer cheeseburgers sold than hamburgers.
Let Cheeseburger = x
Hamburger = x + 68
This will be:
x + x + 68 = 632
2x + 68 = 632
2x = 632 - 68
2x = 564
x = 564/2
x = 282
Cheeseburger = 282
Hamburger = x + 68 = 282 + 68 = 350
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find the distance the points (-3,-5) and (9,-10). Enter the exact value of the answer.
Answers
x= -13 will this line be horizontal or vertical? based on this expression
Answers
EXPLANATION
The equation x=-13 represents a vertical line.
for each equation give for solution. Then, graph the solution set on the graph provided.
Answers
Given the equation x+2y=8
[tex]\begin{gathered} \text{When x=-4} \\ x+2y=8 \\ -4+2y=8 \\ 2y=8+4 \\ 2y=12 \\ y=6 \\ (-4,\text{ 6)} \end{gathered}[/tex]When x = -2
[tex]\begin{gathered} \\ x+2y=8 \\ -2+2y=8 \\ 2y=8+2 \\ 2y=10 \\ y=5 \\ (-2,\text{ 5)} \end{gathered}[/tex]When x=0
[tex]\begin{gathered} \\ x+2y=8 \\ 0+2y=8 \\ 2y=8 \\ y=4 \\ (0,\text{ 4)} \\ \end{gathered}[/tex]When x=2
[tex]\begin{gathered} \\ x+2y=8 \\ 2+2y=8 \\ 2y=8-2 \\ 2y=6 \\ (2,\text{ 3)} \end{gathered}[/tex]We then plot these points.
Henry is shipping a package that weighs 7 7/8 lbs. What is the weight of the package expressed as a decimal?
Answers
Answer:
7.875
Step-by-step explanation:
5 · 4 -3 + 10 ÷ 2 A. -65 B. -55 C. -35 D. -25
Answers
we have
5 · 4 · -3 + 10 ÷ 2
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
step 1
Multiplication
5.4.-3=-60
substitute
-60+10÷ 2
step 2
Division
10÷ 2=5
substitute
-60+5
step 3
Addition
-55
therefore
option BFactor differences of square m^4 - n^4
Answers
Remember that a difference of squares can be written as the product of two conjugate binomials:
[tex]a^2-b^2=(a+b)(a-b)[/tex]In the given expression, notice that m^4 and n^4 can be written as (m^2)^2 and (n^2)^2:
[tex]m^4-n^4=(m^2)^2-(n^2)^2[/tex]Once written as a difference of squares, we can factor the expression:
[tex](m^2)^2-(n^2)^2=(m^2+n^2)(m^2-n^2)[/tex]Therefore:
[tex]m^4-n^4=(m^2+n^2)(m^2-n^2)[/tex]The average teachers' salary in a certain state is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.What is the probability that a randomly selected teacher makes less than $50,000 per year?
Answers
Normal distribution of salaries
d = Standard dev = $7500 =
Correction factor= 0
Di
f(x) = (1/ d•√2π )• e ^- ((s- s')^2/2d^2)
Average value = u = 57337
Now calculate f(x)
Difference of salaries ,with respect to average
S^ 2= 57337 - 50000= = 7337
Now squared = (7337^2) = 53831569
d = 7500
2•d^2= 112500000
Then
S^2/ (2•d^2) = 53831569/112500000= 0.4785
Then now calculate
f(x) = (1/ d•√2π )•e^- (0.4785)
f(x)= 0.619/ (2•d^2)
Answer is
Probability of 61.9%
Write the quadratic function in standard form. g(x) = x2 − 10x
Answers
The quadratic function in standard form is g(x)= x²-10x+0
What is a quadratic function?Quadratic functions are polynomial functions of the second degree, meaning they contain at least one squared term.
Quadratic functions are another name called quadratics. The quadratic function has the following general form: f(x)=ax² + bx + c.
An quadratic function is given as g(x)= x²-10x
In the standard form of the quadratic equation, there should be three terms, terms with power two, one and a constant.
In the given equation, there is a constant term missing.
So, we add a zero to the end because it brings no change to the function quantitatively.
So, the standard form of the given quadratic function will be g(x)= x²-10x+0
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5 MATH QUESTIONS WILL MARK BRAINLIEST PLS HELP
Answers
The correct options regarding the functions are given as follows:
1. C. y = -2x - 7/9, m = -2, b = -7/9.
2. A. y = 1400x + 5000, 10,600 lbs.
3. A. t = 0.75m + 12, $23.25.
4. A. y = (x - 2) - 3.
5. B. 302.5 miles.
Item 1In slope-intercept formula, a linear function is given as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For this problem, the equation is:
-18x - 9y = 7.
Then:
9y = -18x - 7
y = -2x - 7/9, which slope -2 and intercept -7/9.
Thus option C is correct.
Item 2The table represents a linear function, in which:
The initial value is the intercept of b = 5000.Each week, the amount increases by 1400, hence the slope is of m = 1400.Thus the function is:
y = 1400x + 5000.
In four weeks, x = 4, hence the amount is of:
y = 1400(4) + 5000 = 10600.
Which means that option A is correct.
Item 3Also a linear function, in which:
The intercept is the flat fee of $12.The slope is the cost per mile of $0.75.Hence the function is:
t = 0.75m + 12.
For 15 miles, the cost is given as follows:
t = 0.75(15) + 12 = $23.25.
Which means that option A is correct.
Item 4In this graph, we have a concave up parabola with vertex at (2,-3), hence the rule is:
y = (x - 2) - 3.
Which means that option A is correct.
Item 5The distance function after t hours is given by:
d = 45t + 100.
Hence, after 4.5 hours, as 1/2 = 0.5, the distance is of:
d = 45(4.5) + 100 = 302.5 miles.
Which means that option B is correct.
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In ATUV, the measure of ZV=90°, VU = 7, UT = 25, and TV = 24. What ratiorepresents the sine of ZU?U25NVT24Answer:Submit Answer
Answers
1) Since the sine is the ratio between the opposite leg and the hypotenuse.
And the hypotenuse is always opposite to the right angle
Then we can write
2) The sine of ∠ U can be written as the following ratio
sine (∠U) = 24/25
sine(∠U)= 0.96
Ally has a square backyard with an area of 169 square feet. What is the length of one side of thebackyard?Sut
Answers
Ally has a square backyard with an area of 169 square feet.
Given a square of side length, s
[tex]\text{Area of a Square}=s^2[/tex]Therefore:
[tex]\begin{gathered} s^2=169\text{ square feet} \\ \text{Take the square root of both sides} \\ \sqrt{s^2}=\sqrt{169} \\ s=13\text{ feet} \end{gathered}[/tex]Therefore, the length of one side of the backyard is 13 feet.
What are two ordered pairs that the midpoints (4, -10)? Please show that your points work.
Answers
In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).
For example, let's choose p = q = 2, so we have:
[tex]\begin{gathered} midpoint\text{ \lparen4,-10\rparen}\\ \\ \\ \\ 1st\text{ endpoint:}\\ \\ (4+2,-10+2)=(6,-8)\\ \\ \\ \\ 2nd\text{ endpoint:}\\ \\ (4-2,-10-2)=(2,-12) \end{gathered}[/tex]Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).