Step-by-step explanation:
Question:-To simplify the expression Expression:-[tex] \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]Solution :-[tex] = \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In numerator we take 6^8 common][tex] = \frac{ {6}^{8} ( {6} + 1)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In denominator as we know, a^x × a^y = a^(x+y)][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8 + ( -9)} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{ - 1} )} [/tex]
[As we know, 1/a^-1 = a ][tex] = {6}^{8} \times 7 \times 6[/tex]
[On further multiplying of 6][tex] = {6}^{9} \times 7[/tex]
Result:-In exponential form:
[tex] = {6}^{9} \times {7}^{1} (ans)[/tex]
In numerical form:
70,543,872 (Ans)
[tex] \huge \: \bf \: Question:—[/tex]
[tex] \sf \longmapsto6^9+6^8)/(6^8 \times 6^{-9})[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex]\sf \longmapsto \: \dfrac{ {6}^{9} + {6}^{8} }{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696 + {6}^{8} } { {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696+1679616}{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \: \dfrac{11757312}{{6}^{8} \times {6}^{ - 9}} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616(6 {}^{ - 9} )} [/tex]
[tex] \boxed{\bf \: As \: a^{-n} = 1/a(n) \: ,}[/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616 \bigg(\dfrac{1}{10077696} \bigg )} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{ \dfrac{1}{6} } [/tex]
[tex]\sf \longmapsto \: \: 70543872[/tex]
[tex] \boxed{\bf \: \: \: Convert\: 70543872 \: to\: scientific \: notation}[/tex]
[tex] \sf \longmapsto \: 7.0543872 × 10 {}^{7} [/tex]
[tex]\boxed{ \bf \: \: Convert\: 70543872 \: to\: exponent}[/tex]
[tex]\sf\longmapsto {6}^{9} \times 7 [/tex]
_________________________________
[tex] \boxed{\bf \: Answer\: in\: Number}:—[/tex]
[tex] \boxed{\bf \: 70543872}[/tex]
[tex]\boxed{ \bf \: Answer\: in\: Exponent:—}[/tex]
[tex] \boxed{\bf \: {6}^{9} \times 7}[/tex]
[tex]\boxed{\bf Answer\: in\: Scientific\: Notation:—}[/tex]
[tex]\boxed{ \bf \: 7.0543872 × 10 {}^{7} }[/tex]
Select All equivalent expressions to 4( x + 2)
Answer:
3x 3-x and 3+x
Jose and Gavin are reading the same book. At the beginning of the month, Jose was
on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will
read 14 pages per day. Let J represent the page of the book that Jose is on at the end
oft days into the month, and let G represent the page of the book that Gavin is on at
the end oft days into the month. Write an equation for each situation, in terms of t,
and determine what page Jose and Gavin will be on on the day they are both on the
same page.
Using linear functions, it is found that:
Jose's equation is: [tex]J = 17x + 10[/tex].Gavin's equation is: [tex]G = 14x + 37[/tex].They will be on the same page on the 9th day.Linear function:A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.Jose:
Initially, he was on page 10, hence [tex]b = 10[/tex].He reads 17 pages per day, hence [tex]m = 17[/tex].Hence, Jose's equation is: [tex]J = 17x + 10[/tex].Gavin:
Initially, he was on page 37, hence [tex]b = 37[/tex].He reads 14 pages per day, hence [tex]m = 14[/tex].Hence, Gavin's equation is: [tex]G = 14x + 37[/tex].The day they will both be on the same page is x for which:
[tex]J = G[/tex]
Hence:
[tex]17x + 10 = 14x + 37[/tex]
[tex]3x = 27[/tex]
[tex]x = \frac{27}{3}[/tex]
[tex]x = 9[/tex]
They will be on the same page on the 9th day.
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evaluate the expression for h= -6.
Answer:
63-|-6| = 57
Step-by-step explanation:
63-|-6|
63-6
57
Answer:
57
Step-by-step explanation:
Substitute -6 for variable h.
[tex]63-|(-6)|\\63-6\\57[/tex]
Please help!!!
THE POPULATION OF NEW YORK STATE CAN BE MODELED BY:
==========================================================
Explanation:
We plug t = 220 into the given function. The 220 is from 2020-1800 = 220, i.e. we have a span of 220 years from 1800 to 2020.
[tex]P(t) = \frac{19.71}{1+61.22e^{-0.03513t}}\\\\P(220) = \frac{19.71}{1+61.22e^{-0.03513*220}}\\\\P(220) = \frac{19.71}{1+61.22e^{-7.7286}}\\\\P(220) \approx \frac{19.71}{1+61.22*0.00044005976972}\\\\P(220) \approx \frac{19.71}{1+0.02694045910226}\\\\P(220) \approx \frac{19.71}{1.02694045910226}\\\\P(220) \approx 19.192933558417\\\\P(220) \approx \boldsymbol{19.193}[/tex]
This indicates that the population of New York state in 2020 is roughly 19.193 million.
This converts to 19,193,000 which is 19 million, 193 thousand.
---------------
Extra info:
According to census data (census.gov), the more accurate population figure appears to be 20,201,249 which is a bit over 20.2 million. The given population function isn't too far off.
Mean for population data
Answer:
I need only 5 brainlisted please give me
Step-by-step explanation:
please understand my situation
Marshall wants to buy a picture frame. The original price is $15,
How much will Marshall pay if he buys it during the sale?
SALE
25% off
original price
Assume running consumes 93 calories per mile. If you run 8 - minute miles, what is your average power output, in watts?
Average power output, in watts = 0.8103 watts
What is average power?The average power represents the constant energy that has been used throughout the time of the journey at a constant rate.
It can be expressed by the following relation:
P=E/T
Given,
Energy consumed per mile = 93 calories
Time taken to cover 1 mile = 8 minutes
Energy consumed per minute = 93/8 calories
Average power = 93/8 = 11.625 calorie per minute
1 calorie per minute = 0.0697 watt
Average power output in watts = 11.625 × 0.0697
= 0.8103 watt
Hence, 0.8103 watt is the average power output in watt.
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Which inequality represents this statement?
The product of −6 and a number is no less than −12.
−6n≤−12
−6n>−12
−6n≥−12
−6n<−12
Answer:
−6n≥−12
Step-by-step explanation:
The correct inequality to show the given statement is,
⇒ - 6n ≥ - 12
Where, 'n' is any number.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The statement is,
''The product of - 6 and a number is no less than - 12.''
Now, Let a number = n
So, We can formulate the correct inequality is,
⇒ - 6n ≥ - 12
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Evaluate the expression 2-8 × 2-7=
Answer:
-21
Step-by-step explanation:
2-8 × 2-7 = 2-(8×2)-7
= 2-16-7
=-14-7
=-21
There are nine marbles in a group, and four of those marbles are red. What
fraction of the marbles are red?
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value?
You have to add.
Step-by-step explanation:
I'm trash at math.
I NEED HELP FOR MY FINALS PLS N TY!!!
1. Compute the length of a rectangle with a perimeter 40.2 in and width of 6.7 in.
Answer:
13.4
Step-by-step explanation:
You would take the width x 2 which is 13.4. Now you subtract the combined width from 40.2. From here you are left with 26.8. Since this is a rectangle the length would be the same on both sides. You divide 26.8 by 2 and you get 13.4.
Jesper can run 6 miles in 45 minutes. He is thinking about running in two different races, a 9-mile race and a 15-mile race. At his current rate, how many more minutes will it take Jesper to complete the 15-mile race than the 9-mile race?
Find minutes per mile by dividing time by distance:
45 minutes / 6 miles = 7.5 minutes per mile
Now multiply his speed by each distance:
7.5 x 9 = 67.5 minutes
7.5 x 15 = 112.5 minutes
Now subtract the two:
112.5 - 67.5 = 45 minutes more
It will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.
Jesper's running speed is 6 miles in 45 minutes.
To find out how long it will take him to complete the races, you can use the formula:
Time = Distance / Speed
Let's calculate the times for both races:
For the 9-mile race:
Time = 9 miles / (6 miles/45 minutes)
= 9 × (45/6)
= 67.5 minutes
For the 15-mile race:
Time = 15 miles / (6 miles/45 minutes)
= 15 × (45/6)
= 112.5 minutes
The difference in time between the 15-mile race and the 9-mile race will be:
Difference = Time for 15-mile race - Time for 9-mile race
= 112.5 minutes - 67.5 minutes
= 45 minutes
So, it will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.
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Select all statements that are true.
All points on the same plane are congruent.
All points on the same plane are congruent.
All segments on the same plane are congruent.
All segments on the same plane are congruent.
All angle on the same plane are congruent.
All angle on the same plane are congruent.
All triangles on the same plane are congruent.
Congruence means equivalence in comparison.
All points on the same plane are congruent. (True)
A point is an exact location .
It can be anywhere on the plane. It has one dimension. The point is always the same.All segments on the same plane are congruent. (False)
A line segment has two end points.It can be of different length.Two line segments are congruent only if they have the same length.Without knowing the lengths of different segments these cannot be termed as congruent.
All angle on the same plane are congruent. (False)
Two angles can only be the same if they have the same position with regard to parallel lines. Two angles can only be same if they have the same degree of measurement.All triangles on the same plane are congruent. (False)
Two triangles are congruent if they have
same lengths of their corresponding sidessame measurements of the three angles of both triangles.The triangles congruence can also be understood by
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The angles congruence can also be understood by
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The line segments congruency can also be understood by the following link
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Please hurry!! This assignment is almost due thank you!!
Answer:
x = 33
Step-by-step explanation:
(x-17)°+(5x-1)°=180°
6x-18 = 180
6x = 198
x = 33
Can you solve this? Please ( 15+ points)
Answer:
112+24x
Step-by-step explanation:
2(16+(10*4)+(x*12))
solve the inner bracket
2(16+40+12x)
solve this bracket
2(56+12x)
solve this now
112+24x
Answer:
[tex]24x+112[/tex]
Step-by-step explanation:
First of all we will start with the brackets inside the equation,
1. [tex]2[16+40+12x][/tex]
Now we can multiply 2 by all the values inside the parentheses
2. [tex]32+80+24x[/tex]
I just wanted to confirm that the big X is a variable?
Fact: Did you know that there are about 4 types of parenthese: ( ) - round brackets, [ ] - square brackets, { } - curly brackets, and < > - angle bracket.
Beatrice watched two films at the theatre. The first she watched was 2 1/6 hours long and the second film was 1 5/6 hours long . Calculate the total length of the two films
Answer:
4 Hours
Step-by-step explanation:
2 1/6 = 13/6
1 5/6 = 11/6
13/6+11/6= 24/6
Simplify 24/6 which will give you 4
Write an equation in point-stope form for the line through the given point with the given slope.
Answer:
y-3=6(x-8)
Step-by-step explanation:
given that the slope is 6 and the line passes through (8,3), we can use the formula y-y1=m(x-x1), where (x1, y1) is the ordered pair and m is the slope. we can plug the given values in from there. m=6, x1=8, and y1=3. hope this helps!
PLS SOMEONE HELP ME PLS WITH GEOMETRY
Answer:
They are congruent by SAS
Step-by-step explanation:
MQ=PN
The angles with markings also go together
The line right in the middle is the second side because of the reflexive property
Please help me on this!!! I would appreciate it so much!!!
Given that
P
=
x
−
y
.
Find
P
when:
x
=
15
and
y
=
20
Answer:
the answer would be -5
Step-by-step explanation:
p=15-20 p=-5
2 squared all divided by 4
please
Answer:
think answer is 0.5 each
Which of the following equations could be the equation to represent the given graph? Make sure you explain your answer thoroughly.
Unit 7 Algebra 2a sample work connections academy
The equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]
The graph is an exponential function, and it passes through the points:
[tex](x,y) = (1,1)\ (0,2)[/tex]
An exponential function is represented with:
[tex]y = ab^x[/tex]
At (0,2), we have:
[tex]ab^0 = 2[/tex]
This gives
[tex]a(1) = 2[/tex]
[tex]a = 2[/tex]
At (1,1), we have:
[tex]ab^1 = 1[/tex]
[tex]ab = 1[/tex]
Substitute 2 for (a)
[tex]2b = 1[/tex]
Divide both sides by 2
[tex]b = \frac 12[/tex]
Substitute values for a and b in [tex]y = ab^x[/tex]
[tex]y = 2(\frac 12)^x[/tex]
Hence, the equation that represents the function is [tex]y = 2(\frac 12)^x[/tex]
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WRITE THE FUNCTION RULE FOR F(X)=-6;X-AXIS
Answer:
-6 is Y
Step-by-step explanation:
When ever the number is outside of the f(x) it is = y.
Given x+2y=-6 solve for y
y= x-6/2
y= -x+6/2
y= -x-6/2
Answer:
y= -x-6/2
Step-by-step explanation:
Given,
x+2y=-6
or,2y=-x-6 (cross multiplication)
or,y= -x-6/2
factor x[tex]x^{2} -81[/tex]
Step-by-step explanation:
[tex]x^2-81=x^2-9^2=(x-9)(x+9)\\\\\text{Used}\\\\a^2-b^2=(a-b)(a+b)[/tex]
3/2x-5=-4/7x+1/5 please
The value of x in the equation is 364/145
The equation is given as:
[tex]\frac 32x - 5= -\frac 47x + \frac 15[/tex]
Collect the like terms
[tex]\frac 32x + \frac 47x= 5 + \frac 15[/tex]
Take the LCM
[tex]\frac{21x + 8x}{14} = \frac{25 + 1}{5}[/tex]
Evaluate the sum
[tex]\frac{29x}{14} = \frac{26}{5}[/tex]
Cross multiply
[tex]145x = 364[/tex]
Divide both sides by 145
[tex]x = \frac{364}{145}[/tex]
Hence, the value of x in the equation is 364/145
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What is f(3) for the function f(x) = 5x + 7?
What is the solution to the equation 8b+32=104?
Answer: the answer is b=9
Step-by-step explanation:
Step 1: Subtract 32 from both sides.
104-32= 72
Step 2: Divide both sides by 8.
72 divided by 8 is 9
therefor the answer is 9
There are 9 new books and 5 used books. What is the ratio of all the books on the shelf to the new books
Answer:
14 to 5
Step-by-step explanation:
9 + 5 = 14(total books)
new books = 5
so ratio of total books to new books is 14 to 5