Answers
Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
All the exponents inside the parenthesis are multiplied by the exponent outside the parenthesis.
Then
[tex]\frac{m^{-7}n^{14} }{m^{-25}n^{40} }[/tex] ÷ [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]
[ Using the rule [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] ]
= [tex]m^{(-7-14)}[/tex] [tex]n^{(14-(-28)}[/tex] ÷ [tex]m^{(-15-10)}[/tex] [tex]n^{(25-(-15)}[/tex]
= [tex]m^{-21}[/tex] [tex]n^{14+28}[/tex] ÷ [tex]m^{-25}[/tex] [tex]n^{25+15}[/tex]
= [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]
= [tex]m^{(-21-(-25))}[/tex] [tex]n^{(42-40)}[/tex]
= [tex]m^{(-21+25)}[/tex] n²
= [tex]m^{4}[/tex] n² = [tex]m^{x}[/tex] [tex]n^{y}[/tex] , so x = 4 and y = 2
Then
[tex]m^{x-2y}[/tex] = [tex]m^{4-2(2)}[/tex] = [tex]m^{4-4}[/tex] = [tex]m^{0}[/tex] = 1 ← as required
Related Questions
i reallyyy need help ! a p e x
Answers
Answer:
D
Step-by-step explanation:
Because the closed dot is connected to the one less than 1, we know that one of the equation is less than or equal to 1. So this eliminates A.
B makes no sense because it shows two equations for when x < 1. So this one can be ruled out immediately.
We also notice the shape of the functions, the one on the bottom looks like a cube, you can make out the beginning of the chair shape. So the one that is less than or equal to 1 is the cubic function. Which eliminates C.
This leaves D and you can plug in values of x and y to confirm this is correct.
Answer:
Step-by-step explanation: First you look at the left side of the graph. You can tell by the shape that it is an x^3 function. also the filled in circle means inclusive. so we know that when x <= (whatever number). It is impossible to tell for sure with this graph if it is on 1. for the first part. the only answer that has less then or equal to is the last one, D. So the answer is D. You can look at the right side that it is open circle. So we know it is >. So we can see the bottom part of D has that as well
A and B are partner in a business .A contribution RS 20000 and B rs 30000 a however acts as a manager the understanding being that of the profit should get 25% for his service as manager the remaining divided in the ratio of their contribution .If B ges Rs 1350 Ashish share what would A get
Answers
Answer:
Rs 1,650
Step-by-step explanation:
The given contribution are;
A contributes Rs 20,000, and B contributes Rs 30,000
The percentage of the profit A receives as manager = 25%
The amount of the profit divided in the ratio of their contribution = The remaining profit (75%)
The amount B gets = Rs1,350
The amount A gets = required
The ratio of their contribution at which the remaining profit is shared = 20,000:30,000 = 2:3
Where, out of 5 parts of 75% of the profits, B gets 3, while A gets 2
Let P represent the profit, we have;
B's share = 3/5× 0.75 × P = 1,350
∴ P = (5 × 1,350/3)/0.75 = 3,000
A gets 25% of the profits and 2/5 of the 75% remaining profit
∴ The amount A gets = 0.25×3000 + (2/5)×0.75×3000 = 1,650
Or simply put;
A gets the remainder of the profit which is Rs 3,000 - Rs 1,350 = Rs 1,650
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answers
Answer:
A linear equation in the standard form is written as:
y = a*x +b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
a = (d - b)/(c - a)
So we know that our line passes through the points (8, -1) and (2, -5)
then the slope will be:
a = (-5 - (-1) )/(2 - 8) = (-4/-6) = 2/3
Then our line is something like:
y = (2/3)*x + b
to find the value of b, we can use the fact that we know that our line passes through the point (2, -5)
this means that when x = 2, we must have y = -5
replacing these values in the equation we get:
-5 = (2/3)*2 + b
-5 = 4/3 + b
-5 - 4/3 = b
-15/3 - 4/3 = b
-19/3 = b
then the equation is:
y = (2/3)*x - 19/3
(in the question you wrote the point-slope form, but you can see that it does not work for the second point, so there may be a mistake there, as the slope is missing)
The actual equation in the point-slope form is:
y + 1 = (2/3)*(x - 8)
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
I Got It Right Instruction on edge
This frequency table represents the number of cars owned by each family on a street. What is the mean number of cars owned by each family?
A. 2.5
B. 3
C. 4
D. 5.5
Answers
Answer:
B
Step-by-step explanation:
={(1x4)+(2x3)+(3x4)+(4x7)+(5x2)}÷20
={4+6+12+28+10}÷20
={10+40+10}÷20
={60}÷20
=3
The rectangle is 200 feet long 85 feet wide.Ignoring the corner rounding what is the distance around a hockey rink?
Answers
Answer:
570 feet
2*200 + 2*85
400 + 170
570
Step-by-step explanation:
find the LCM and hcf of 72 and 162 , leaving the LCM in prime factors
Answers
=========================================================
Explanation:
Find the prime factorization of 72 and 162
72 = 8*9 = 2^3*3^2162 = 2*81 = 2*9^2 = 2*(3^2)^2 = 2*3^4Here's a simplified version of each
72 = 2^3*3^2162 = 2*3^4We have these unique primes: 2, 3
Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.
This means 2^3*3^4 is the LCM (lowest common multiple).
2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.
------------------------------
Now onto the HCF (highest common factor; aka GCF).
Looking at
72 = 2^3*3^2162 = 2*3^4We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.
Those common factors you circled are then multiplied.
Overall, the HCF is 2*3^2 = 2*9 = 18
-----------------------------
Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.
Answer:
LCM= 648
HCF= 18
Step-by-step explanation:
What are the fractions simplest form
Answers
Answer:
the first one 2/-1, hope it helps...
Please help I need this
Answers
Answer:
from side a _2,4.5
from side b _-4
5,-2.
hope this will be helpful for you.
Find the decay factor from the model y =4520(0.6)square 6
Answers
Answer:
Step-by-step explanation:
Which of the following is equivalent to (x+5)(2x^2 +8)?
A. (x+5)(2x^2)• (X+5)(8)
B. (x+5)(2x^2)+(x+5)(8)
C. (x+5)(2x)+(x+5)(8)
D. (x+5)(2x)• (x+5)(8)
Answers
Answer:
(x+5)(2x^2 +8)
Multiply (x+5) in both sides
(x+5)(2x^2) × (x+5)(8)
Answer is a
what is the significant figures for 0.045325
Answers
Answer:
There are 5 significant digits in 0.045325 and they are 4, 5, 3, 2, and 5.
Step-by-step explanation:
Significant digits rules:
All non-zero numbers count as significant digitsLeading zeroes (zeroes in front of any non-zero numbers) are never significant digitsZeroes in-between non-zero numbers count as a significant digitsTrailing zeroes (zeroes after all non-zero numbers) count only if there is a decimalIn 0.045325, the two zeroes are leading zeroes and therefore do not count. The rest of the digits, (4, 5, 3, 2, and 5) are all non-zero and therefore count. Thus, there are 5 significant digits in 0.045325.
what is 100^100 / 100^98 to be 100?
Answers
Answer:
100 ^2
10000
Step-by-step explanation:
100^100 / 100^98
We know that a^b / a^c = a^(b-c)
100 ^ (100-98)
100 ^2
10000
Answer:
100
Step-by-step explanation:
Pleaseeee helppppppp
Answers
Answer:
d = 8t
Step-by-step explanation:
5
Drag the tiles to the boxes to form correct pairs
Match each equation to its factorized version and solution
24x6 = 0
2x + 3) = 0
Solution X = 0.3
14x - 7x2 = 0
6x14x)=0
Solution 30 X34
2x26x0
x14 - x)=0
Solution: x = 0, x= 4
4XX=0
7x(2 - x)=0
Solution XEOX= 2
Answers
Answer:
1. 2x^2+6x=0 <--> 2x(x+3)=0
2.4x-x^2=0 <--> x(4-x)=0
3.14x-7x^2=0 <--> 7x(2-x)=0
4.24x-6x^2=0 <--> 6x(4-x)=0
Step-by-step explanation:
just try to expand the answer given for example when you look at no.1, 2x•x=2x^2 so look for the equation where there is a 2x^2 in it.
for finding the solution, for example when you look at no.1 again, you have 2x=0 so x=0/2=0 and you also have x+3=0 so x=-3
this applies to all the pther no.
HELP ASAP 10 POINTS AND BRAINLYEST AND 5 STAR AND THANKS BUT IF CORRECT
Answers
Answer:
D
Step-by-step explanation:
The opposite faces are congruent, that is the surface area (SA) is
SA = top/ bottom + 2 sides + front/ back
= (3 × 2) + (3 × 2) + (2 × 5) + (2 × 5)+ (3 × 5) + (3 × 5)
= 6 + 6 + 10 + 10 + 15 + 15
Mike, a Salvation Army bell ringer, has 20% as many quarters as nickels in his cup. If Mike has $6.00 in quarters and nickels, how many nickels does he have?
Answers
5.8 Nickels
Step-by-step explanation:
Let x rep no of Nickels in Mike's cup
Then x - 0.2 = Number of quarters in Mike's cup
0.2x = Amount of money that mike has from the nickels
1 ( x - 0.2) = Amount of money that Mike has from the quarter
Then,
0.2x + 1 (x - 0.2) = 6
Expand the bracket
0.2x + x - 0.2x = 6
x = 6
Recall
x - 0.2 = 0
6 - 0.2 = 5.8
Therefore, Mike has 5.8 nickels for the quarter
What does x stand for in the equation 1+x=2
Answers
x = 1
Step-by-step explanation:
1 + x = 2
x = 1
How many real solutions exist for this system of equations?
y=x^2+4
y= 4x
ОА. .
zero
OB.
one
Ос.
two
OD
infinite
Reset
Next
Answers
Answer:
One
Step-by-step explanation:
Set each equations equal to each other
[tex] {x}^{2} + 4 = 4x[/tex]
[tex] {x}^{2} - 4x + 4[/tex]
Find the discrimant.
[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]
This means there is one real solution. Since the discramnt equal 0.
Questlon 4 of 10
What is the midpoint of the segment shown below?
AE
101
O A. (10.)
(5.4)
O B. (5,1)
10
(5,-3)
O C. (5,-)
O D. (10,1)
SUBMIT
Answers
Answer:
c
Step-by-step explanation:
To find the midpoint the formulas
x=x1+x2/2 and y=y1+y2/2 are used
in this case x1 is 5,x2 is 5,y1 is 4 and y2 is -3
therefore
x=5+5/2.
=10/2
=5
y=4+(-3)/2
=1/2
The midpoint of a line segment divides the line into equal segments
The midpoint of the line segment is (5,1/2)
The endpoints of the line is given as:
(5,4) and (5,-3)
The midpoint of the line is calculated as:
(x,y) = 0.5(x1 + x2, y1 + y2)
So, we have:
(x,y) = 0.5(5 + 5, 4 - 3)
Evaluate the sum and difference
(x,y) = 0.5(10, 1)
Evaluate the product
(x,y) = (5, 1/2)
Hence, the midpoint of the line segment is (5,1/2)
Read more about midpoints at:
https://brainly.com/question/16828532
Please help me with this one ASAP
Answers
Answer:
114 in^2
Step-by-step explanation:
umm find the area of all the shapes and add them up...
20 points!!!!! Help!!!!A company manufactures car radiators. The cost of producing x car radiators is given by the function f(x) = 600x + 500.
The revenue which the company receives for selling x car radiators is given by the function g(x) = 700x + 100.
Determine the resulting profit function, h, of the company.
O
h(s)
f() - g(1) = -1001 + 400
h(s)
--
g(1) - |(1) = 1001 - 400
O
Ο Ο
h()
f(x) + g(x)
= 1,3001 + 600
Oh(x)
g(a) f(I) = (7000 + 100) (600x + 500)
Answers
Answer:
100x-400
B
Step-by-step explanation:
Profit= Revenue - cost
so just subtract the two equations
(700x+100)-(600x+500)
100x-400 which is answer choice B
Answer:
Step-by-step explanation:
so subtract the cost function from the revenue function
700x + 100
-(600x + 500)
profit(x) = 100x -400
2z^8- 32z^8
Help plz
Answers
Answer:
-30z^8
Step-by-step explanation:
[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]
Answer:
-30z^8
Step-by-step explanation:
2z^8- 32z^8
-30z^8
Divide round to the nearest tenth 0.197 divided by 3.0
Answers
Answer:
0.657 I think this is the answer or it's 0.065 hehe
Solve for the missing angle. Round to the nearest degree.
Answers
Step-by-step explanation:
here's the answer to your question
Can someone help me figure this out?
Answers
Answer:
See picture below.
Step-by-step explanation:
I had to write a new option for one of the lines.
Please helppppp!!!!!!!!
Answers
Answer:
128 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h
where b1 and b2 are the lengths of the bases and h is the height
A =1/2( 10+22) * 8
A = 1/2 (32)8
= 128
Answer:
A=128 cm²
Step-by-step explanation:
Hi there!
We are given a trapezoid and we want to find the area of it
The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height
The bases are the parallel sides
They are the sides marked as 10 cm and 22 cm in this case
The height is the distance between the bases
In this case, it is the side marked as 8 cm
We know everything needed for the area, let's just label everything to avoid any confusion
a=10
b=22
h=8
Now substitute into the formula
A=[tex]\frac{a+b}{2}h[/tex]
A=[tex]\frac{10+22}{2}*8[/tex]
add the numbers on the numerator together
A=[tex]\frac{32}{2}*8[/tex]
Divide 32 by 2
A=16*8
multiply
A=128 cm²
Hope this helps!
Which function is the inverse of f(x) = 2x + 3?
کا انM
f'-1(x) =-1/2x-3/2
f’-1(x) = 1 / 2X - 3/2
F'-1(x) = -2x+3
F’-1(x) = 2x+3
Answers
Answer:
a) 1/2 x - 3/2
Step-by-step explanation:
y = 2x +3
y-3 = 2x
x = (y - 3 )/2
x= 1/2 - 3/2
Pleasee help
The green line below *blank*. check all that apply
Answers
Answer:
C and D
Step-by-step explanation:
Answer:
C & D
Step-by-step explanation:
Correct,
C. The line goes through both x & y (since it is on zero)
D. The line crosses through the exact center which is also called the origin
Incorrect,
B. It is not parallel to any line
E. It does not cross the exact x-axis line
F. It does not cross the exact y-axis line
Not 100%,
A. Not too sure whether you consider that perpendicular, might wanna look it up
What is the measure of AC
Answers
Answer:
180°
Step-by-step explanation:
Well we know that AB is 90° and considering CB is the exact same I guess it's 90° too so 90+90=180°
Determine the number of roots the equation x^2+14x=-49 using the discriminant.
Answers
Answer:
[tex]\boxed {\boxed {\sf 1 \ real \ root}}[/tex]
Step-by-step explanation:
The quadratic formula is used to find the roots or zeroes of a quadratic equation. It is:
[tex]x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}[/tex]
The discriminant helps us find the number of roots. If the discriminant is...
Negative: there are no real roots Zero: there is one real root Positive: there are two real rootsIt is the expression under the square root symbol:
[tex]b^2-4ac[/tex]
First, we must put the given quadratic equation into standard form, which is:
[tex]ax^2+bx+c=0[/tex]
The equation given is [tex]x^2 +14x= -49[/tex]. We have to move the -49 to the left side. Since it is a negative number, we add 49 to both sides.
[tex]x^2+14x+49 = -49 +49 \\x^2+14x+49=0[/tex]
Now we can solve for the discriminant because we know that:
a= 1 b= 14 c= 49Substitute these values into the formula for the discriminant.
[tex](14)^2 -4 (1)(49)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Solve the exponent.
(14)²= 14 * 14= 196[tex]196- 4(1)(49)[/tex]
Multiply 4, 1, and 49.
[tex]196-196[/tex]
Subtract.
[tex]0[/tex]
The discriminant is zero, so the quadratic equation x²+ 14x = -49 has 1 real root.
