Answers
Answer:
[tex]a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Step-by-step explanation:
The question relates with rules of indices
(a) The give expression is presented as follows;
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}[/tex]
By expanding the expression, we get;
[tex]\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}[/tex]
Collecting like terms gives;
[tex]\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
(b) The given expression is presented as follows;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4[/tex]
Therefore, we get;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}[/tex]
Collecting like terms gives;
[tex]x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )[/tex]
[tex]x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Related Questions
(3 1/3) (6) What is the answer?
Answers
Answer:
20
Step-by-step explanation:
(6x3=18) (6x1/3=2) (18+2=20)
First things first!
Multiply 6 by 3 (18).
Mulitply 6 by 1/3 (2).
Add 18 and 2, and ... *drum roll*, the final answer is 20!
Hope this helps :)
Write the six step in division
Answers
Answer:
Divide the tens column dividend by the divisor. Multiply the divisor by the quotient in the tens place column. Subtract the product from the divisor
Step-by-step explanation:
I
7. The total cost to rent a truck is $100 and $0.20 per km.
a. Determine an algebraic model for the relationship between total cost and distance driven. Use C to
represent total cost (S) to rent the truck and d to represent distance driven (km).
Answers
Answer:
C= 100+ d*0.2
Step-by-step explanation:
Give data
Cost of rental = $100
Cost per km= $0.2
Total cost= C
Distance= d
Let us model the expression
Hence the expression is given as
C= 100+ d*0.2
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
V10
Answer: 2=
=
Submit Answer
Answers
Answer:
x=2*sqrt(5)
Step-by-step explanation:
Since the triangle is isosceles, the other side of the triangle is sqrt(10) too. By using Pythagoras theorem, we have 10+10=x^2, x=2*sqrt(5).
Q:1)A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?
Q:2)An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.
Answers
$\sf\underline\bold{Question:1-}$
A ball is thrown upwards and it goes to the height of 100meter and comes down. What is the net displacement?
$\sf\underline\bold{Solution}$
$\sf{According \: to\:the\: question,}$
Displacement for the above situation is 0. As we know, that displacement is the shortest path from the initial to the final point. Here, the initial and the final points are the same, and henceforth, it takes no time to travel. So the displacement is 0.
_________________________$\sf\underline\bold{Question:2-}$
An athlete completes one round of a circular track of diameter 200m in 30 seconds. Find the distance covered by the athlete at the end of 30 second.
$\sf\underline\bold{Solution:}$
$\sf\bold{Given\:parameters:}$
$\sf\small{☆The\:diameter\:of\:the\:circular\:track:200m}$
$\sf{Radius=}$ $\sf\dfrac{200}{2}$ → $\sf\underline{Radius = 100m}$
☆Time taken by an athlete to complete one round : 30 seconds.
$\space$
$\sf\bold{To\:find:}$
❍Distance travelled by an athlete in 30 seconds.
$\space$
❍ AND,Distance travelled by the athlete will be equal to the cumference of the circle.
$\space$
$\space$ $\space$ $\space$ $\space$ $\space$ $\space$ $\sf{So,}$
$\mapsto$ $\sf{Circumference\:of\:the\:circle: 2 πr}$
$\space$
$\mapsto$ $\sf{Circumference=2\times}$ $\sf\dfrac{22}{7}$ $\sf{\times 100}$
$\space$
$\mapsto$ Circumference of the circle : $\sf\dfrac{4400}{7}$
$\space$
[tex]\sf\underline\bold{∴Circumference = 628.57m}[/tex]
$\space$
||Therefore,The distance travelled in 30 seconds, by the athlete is 628.57m.||
______________________0 = 1st answer
628.57 m = Question 2 answer.
Write the phrase as a variable expression. Use x to represent "a number."
5) The quotient of a number and 9, decreased by 4
Answers
Answer:
a/9 - 4
Step-by-step explanation:
The expression will be (x/9) - 4.
It is given that a number x is the quotient of a number and 9 decreased by 4.
We have to find the variable expression for this.
What will be the expression for , 2 times of a number minus 4 ?
The expression will be 2x -4.
Quotient of a number and 9
= x / 9
Decrease this by 4 ; we get
= (x / 9 ) - 4
Thus , the expression will be (x/9) - 4.
To learn more about algebraic expression click here ;
https://brainly.com/question/2164351
#SPJ2
The set of whole numbers and their opposites are known as ?
Answers
need some help with this
Answers
Answer:
A horizontal line has a slope of zero
Step-by-step explanation:
Let’s start by some examples!
We’re going to use two points that identify that a horizontal line has a slope of zero
Two points will be: (7, 4) & (7, -6)
Then use the Slope-Formula to identify the slope
Slope = change in y/change in x
Slope = (y2 - y1)/(x2 - x1)
Slope = (-6 - 4)/(7 - 7)
Slope = -10/0
Slope = 0
Therefore, a horizontal line has a slope of zero
Answer:
Zero (0)Step-by-step explanation:
Horizontal lines have no steepness at all because any calculation the slope of line means dividing zero by another number to the answer is always zero
Josh has a aquarium 30 inch deep.it takes him 5 min to fill the bucket with 3 inch of water.he estimates that it will take him under an hour to fill the entire bucket with water.is he correct.explain why or why not
Answers
Answer:
No
Step-by-step explanation:
From the information provided, we can say that he is not correct. This is because the depth of the water is the only measurement that he is using to make his estimate. Comparing the depth of the aquarium and the bucket is one measurement, but both the aquarium and bucket are most likely of different shapes and sizes. Therefore, this equates to more buckets for the same amount of depth in the aquarium. To get a proper estimate on how long it will take he needs to calculate the volume of water in the bucket and compare it to the volume of water needed to fill the aquarium.
Find the value of x for which ABCD must be a parallelogram
a. 0
b. 25
c. 4
d. 7
Answers
Answer:
d. 7
Step-by-step explanation:
A parallelogram has equal opposite sides that are parallel to each other. Therefore, opposite interior angles would be congruent to each other.
Thus:
3x - 17 = 25 - 3x
Add 3x from each side
3x - 17 + 3x = 25 - 3x + 3x
6x - 17 = 25
Add 17 to both sides
6x - 17 + 17 = 25 + 17
6x = 42
Divide both sides by 6
6x/6 = 42/6
x = 7
f(x) = x2 – 12x – 29
f(3) = (x+ ?)+ ?
Answers
Answer:
-6 and - 65
Step-by-step explanation:
X-12x-29, by completing the square we get (x-6)^2-65
Square 1 has an area of 24 square units. If square 2 is half the size, what is the ratio of the area of square 1 to square 2.
Answers
Answer:
12
Step-by-step explanation:
I'm going to guess that 1/2 the size means the sides are 1/2 the size.
Square 1 has an area of 24. The sides are s, so the area is found by using s^2
The second square is made from sides that are 1/2 s
Area = 1/2 s * 1/2 s
Area = 1/4 s^2
Area 1 / area 2 = 24 / x^2 = s^2 / 1/4 s^2 = 1/0.25
A trapezoid is a polygon that has exactly one pair of parallel sides.
Select one:
True
False
Answers
false dsddsfsdfsfdfdsfdsdfsdfsdsfdfsfdsdfsdfsdfsfdsfd
jdksiifkekfkrjfi
Solve for y, given that b=22(Round your answer to 1 decimal place, if necessary.)
Answers
Answer:
37.7
Step-by-step explanation:
First, we have to divde 22/7 to find the scale factor. I chose 22 and 7 because those two sides are ocngruent. We get 3.14. We then have to multiply 12 by 3.14 beacuse that is the side that is congruent with the side y. When you multiply you should get 37.68. Since we have to round we get 37.7.
Maya just bought a refrigerator for $642. She paid $160.40 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answers
Answer:
120.40 per payment
Step-by-step explanation:
Subtract the down payment
642 - 160.40
481.60
Divide this by 4
481.60 / 4
120.40
what is it initial value
Answers
Can someone help me out
Answers
Answer:
82.8
Step-by-step explanation:
area of the parallelogram = base × height
= 13.8×6
= 82.8 in²
Answered by GAUTHMATH
In the first quadrant, you start at 2, 6 and move 2units rights and 3 units down what point will you end up on?
Answers
Answer:
[tex]End = (4, 9)[/tex]
Step-by-step explanation:
Given
[tex]Start = (2,6)[/tex]
Transformation: 2 units right and 3 units down
Required
The new point
First, we take the right translation;
When a point is translated right by 2 units, the rule is:
[tex](x,y) \to (x + 2, y)[/tex]
So, we have:
[tex](2,6) \to (2 + 2, 6)[/tex]
[tex](2,6) \to (4, 6)[/tex]
Next, we take the down translation;
When a point is translated down by 3 units, the rule is:
[tex](x,y) \to (x, y + 3)[/tex]
So, we have:
[tex](4,6) \to (4, 6+3)[/tex]
[tex](4,6) \to (4, 9)[/tex]
Hence, the endpoint is:
[tex]End = (4, 9)[/tex]
In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.
m 4 + m 5 + m 6 = 180.
1 and 4 are alternate interior angles.
m 5 = m 3 + m 2
. m 5 + m 1 = 180.
Answers
Answer:
all except the first
Step-by-step explanation:
do u really want an explanation
find the missing side.
Answers
Answer:
24.8
Step-by-step explanation:
sin75 = 24/x
x = 24/sin75 = 24.8466 = 24.8 (nearest tenth)
NEED HELP
A coin collection has 33 quarters and nickels. The number of nickels is 5 greater than
three times the number of quarters. How many coins of each type are there? Write a
system of equations and solve using substitution.
Answers
Answer:
7 quarters
26 nickels
Step-by-step explanation:
x = number of quarters
y = number of nickels
x + y = 33
y = 3x + 5
x + 3x + 5 = 33
4x = 28
x = 7
y = 3×7 + 5 = 26
Answer quick tyyyyyyyyyyyyyy
Answers
Answer:
5
Step-by-step explanation:
(x+5)(x-3)=20
x=5
√6 (√24-√6in class problem
Answers
Answer:
6
Step-by-step explanation:
√6 (√24-√6)
Distribute
sqrt(6) sqrt(24) - sqrt(6)sqrt(6)
sqrt(144) - sqrt(36)
12 - 6
6
What are the coefficients for the binomial expansion of (a + b)^3?
Answers
Answer:
coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively. (required coefficient)
Step-by-step explanation:
Coordinates of C and D are (-14 , 6) and (x , 13) respectively.Given x is a positive integer and the distance CD is 25 units.Find the value of x.
Answers
Answer:
10
Step-by-step explanation:
1) The vector CD is equal to (X-(-14); 13-6)= (x+14; 7)
2) The module of the vector CD is equal to diatance CD=25. It is equal to
sqrt ((x+14)(x+14)+7*7) from the formula of module (with coordinates).
25= sqrt ((x+14)(x+14)+7*7)
625= (x+14)*(x+14)+49
625= x^2+28x+196+49
X^2+28X-380=0
a=1 b=28 c=-380
D= b*b-4ac= 28*28-4*1*(-380)= 784+1520= 2304
sqrt D= sqrt2304=48
x1= (-28-48)/2= -38
x2= (-28+48)/2= 10
But x1<0 it is negative and it is not suitable, x2>0 it is positive, so answer is 10.
Find the place value of 3 in 3546.
Answers
Answer:
that is the thousands place value.
the place value of 3 in 3546.= 3000
SOMEONE HELP ME PLEASE
Answers
For the given question,
Total number of outcomes
= 6 (i.e. 1, 2, 3, 4, 5 and 6)
Number of favourable outcomes
= 4 (i.e. 3, 4, 5, 6)
So,
[tex]P = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes} \\ = > P= \frac{4}{6} \\ = > P = \frac{2}{3} \\ = > P = 0.6666......[/tex]
Find the length of x
. Assume the triangles are similar.
Answers
Answer:
x=2.24
Step-by-step explanation:
To do this problem, you must find the scale factor. Using two corresponding sides you can find it.
Using 2.4 and 3:
2.4 / 3 = 0.8
Scale factor: 0.8
Now find x:
2.8 × 0.8 = 2.24
x = 2.24
Hope this helped.
Someone plssss help me with this question!!
Answers
Answer:
There are 3 possible values for a.
Step-by-step explanation:
a/b=2/3
3a=2b
If b>5 and b<13
apply all possible values
b=6 -> 3a=12 ==> a=4 1st possibility
b=7 -> 3a=14 ==> a=4.something Not a possibility
b=8 -> 3a=16 ==> a=5.something Not a possibility
b=9 -> 3a=18 ==> a=6 2nd possibility
b=10 -> 3a=20 ==> a=6.something Not a possibility
b=11 -> 3a=22 ==> a=7.something Not a possibility
b=12 -> 3a=24 ==> a=8 3rd possibility
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
A
4y - 2
B
14 units
VX
0 38 units
3x - 1
44 units
2x + 2
49 units
D
2y + 6
С
Answers
Answer:
3rd option, 44 units
Step-by-step explanation:
3x-1 = 2x+2
or, x = 3
so each side, 3×3-1 = 8
4y-2 = 2y+6
or, y = 4
so each side, 4×4-2 = 14
so perimeter
= 2(8+14)
= 44 units
Answered by GAUTHMATH
