Answer:
The pairs are:
[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex] => [tex]\frac{p^2}{9q^2}[/tex]
[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex] => [tex]6pq^3[/tex]
[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex] => [tex]6p^2q^2[/tex]
[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex] => [tex]\frac{q}{3}[/tex]
Step-by-step explanation:
We are going to solve the questions one by one and then write the quotients with every question.
In order to calculate the division, the terms are multiplied then exponents are added or subtracted between numerator and denominator to get the simplest form of answer.
First Expression:
[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex]
When two fractions have to be divided the second fraction is reversed i.e. numerator becomes denominator and vice versa.
[tex]= \frac{4p^3q}{6p^2q^2} * \frac{2p^2q^2}{12pq^3}\\=\frac{p^5q^3}{9p^3q^5}\\=\frac{p^2}{9q^2}[/tex]
Second Expression:
[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex]
Removing the division symbol
[tex]=\frac{10p^3q^3}{2p^2q} * \frac{6pq^2}{5pq}\\=\frac{6p^4q^5}{p^3q^2}\\=6pq^3[/tex]
Third Expression:
[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex]
Removing the division symbol
[tex]=\frac{14p^2q^3}{2pq} * \frac{6p^3q^2}{7p^2q^2}\\= \frac{6p^5q^5}{p^3q^3}\\= 6p^2q^2[/tex]
Fourth Expression:
[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex]
Removing the division symbol
[tex]=\frac{16pq^3}{24p^2q^3} * \frac{p^3q^3}{2p^2q^2}\\=\frac{p^4q^6}{3p^4q^5}\\=\frac{q}{3}[/tex]
Hence,
The pairs are:
[tex]\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}[/tex] => [tex]\frac{p^2}{9q^2}[/tex]
[tex]\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}[/tex] => [tex]6pq^3[/tex]
[tex]\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}[/tex] => [tex]6p^2q^2[/tex]
[tex]\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}[/tex] => [tex]\frac{q}{3}[/tex]
12*PLEASEE ANSWER THIS FAST IT'S VERY URGENT IS IT LEFT OR RIGHT WHICH IS THE CORRECT ANSWER!!!
Answer:
Right
Step-by-step explanation:
20 boxes minus 9 boxes
I need help on my math.
Henry needs a 16 ft. table for his family dinner. He is going to put two tables together. He has an 8ft table. How long does the other need to be?
Answer:
The other table needs to be 8ft long as well.
Step-by-step explanation:
To get to 16ft, we need to subtract the 8ft that Henry already has.
16 - 8 equals 8.
So, the other table needs to be 8 feet.
#teamtrees #WAP (Water And Plant)
The sum of the ages of David and Morgan is 78 years. 7 years ago, David's age was 3 times Morgan's age. How old is David now?
Answer:
David is 55 years old
Morgan is 23 years old
__________________________________________________________
Step-by-step explanation:
Let the age of David = x years
Let the age of Morgan = y years
We are Given:
The sum of David and Morgan's age is 78
7 years ago, David's age was 3 times Morgan's age
__________________________________________________________
Making the equations:
from the first statement, the sum of their ages is 78
So, we can write it as:
x + y = 78
from the second statement,7 years ago, David's age was 3 times Morgan's age
David's age 7 years ago = (x - 7)
Morgan's age 7 years ago = (y-7)
So, we can write the equation as:
(x - 7) = 3(y - 7)
which can be simplified to:
x = 3y - 14
__________________________________________________________
Solving the equations:
We have the 2 equations:
x + y = 78x = 3y - 14from the first equation, we can say that:
x = 78 - y
Using this value in the second equation:
x = 3y - 14
78 - y= 3y - 14 [since x = 78 - y]
78 + 14 = 4y
4y = 92
y = 23
Using this value in the first equation:
x + y = 78
x + 23 = 78 [since y = 23]
x = 55
__________________________________________________________
The Age of David and Morgan:
Since we assigned x to the age of David:
David is 55 years old
We assigned y to the age of Morgan. So,
Morgan is 23 years old
An investor invested a total of $2,100 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If the investor’s total profit was $83, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 5% was $___.
The amount invested in the mutual fund that earned 3% was $___.
Answer:
The amount invested in the mutual fund that earned 5% was $1000.
The amount invested in the mutual fund that earned 3% was $1100.
Step-by-step explanation:
Let the amount invested in the mutual fund that was earned 5% be x and the amount invested in the mutual fund that earned 3% be y.
Statement 1: [tex]\frac{5}{100}[/tex]X+[tex]\frac{3}{100}[/tex]y = 83
Statement 2: x+y = 2100
I'll use the elimination method:
Statement 1 × 20: x+[tex]\frac{60}{100}[/tex]y = 1660
Minus Statement 1 × 20 from Statement 2: x+y-x-[tex]\frac{60}{100}[/tex]y = 2100-1660
[tex]\frac{40}{100}[/tex]y = 440
y = [tex]\frac{100}{40}[/tex]×440
= 1100
x = 2100-1100
= 1000
For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the disage at which it occurs.
B(x)= 395x^2- 2370x^3, 0 <= x <= 0.16
a. The maximum is obtained for a dosage of __________________.
b. The maximum blood pressure obtained is ______________.
Answer:
A) Maximum for dosage is 0.11
B) maximum blood pressure = 1.625
Step-by-step explanation:
We are given the function;
B(x) = 395x² - 2370x³
To find maximum, we will find the derivative of the function and equate to zero.
B'(x) = 790x - 7110x²
Equating to zero gives;
790x - 7110x² = 0
790x = 7110x²
Dividing both sides by x gives;
790 = 7110x
x = 790/7110
x = 0.11
This falls in between the range of 0 <= x <= 0.16 given to us.
Therefore x = 0.11 is a maximum
Plugging this into B(x) = 395x² - 2370x³ gives;
B(0.11) = 395(0.11)² - 2370(0.11)³
B(0.11) = 1.625
Thus;
Maximum dosage is 0.11
maximum blood pressure = 1.625
Find the slope of each line passing through the given points using the slope formula.
(-3, -10) and (-1, -1) URGENT Please answer
Slope (m)= y\x= 9/2 = 4.5
your equation for the line is
y=4.5x+3.5
4% as a fraction or mixed number in simplest form
Answer:
1 /25
Step-by-step explanation:
percent means
out of 100
⇒
4
%
=
4
100
as a fraction
To simplify the fraction we require to find a
common factor
to both 4 and 100 and reduce the fraction by dividing. The common factors are 2 and 4 . Choose the largest, that is 4
⇒
4
100
=
4
÷
4
100
÷
4
=
1
25
This calculation is usually set out using
cancelling
4
100
=
4
1
100
25
=
1
25
←
in simplest form
A fraction is in
simplest form
when no other factor but 1 will divide into the numerator/denominator.
What’s the answer to this multi step equation? -3(12x+9)=9
Answer: x=-1
Step-by-step explanation:
find the value of x if log3 (x+6) =2
Answer:
3(x+6) =2
3x+18 =2
3x=2-18
3x=16
x=16/3
x=5.33333333
Hey guys I have a hard time with these questions. Can someone explain it to me? :)
Answer:
Step-by-step explanation:
there are a couple ways to find slope
1. Rise over Run Method:
for this method, you use basic counting
to do this, you count the number of x spaces it takes the line to get from one y space to the next
for your line, the run is 3 because it takes 3 x spaces to get from one whole number to the next on the y spaces
you would say the rise is -1 because the line is going down, and it takes 3 x spaces to get the next pot that is on a y-axis increment
so we know the rise is -1 and the run is 3
if you put this into rise/run format, you get 1/-3
so -1/3 is you slope
2. Using the Coordinates
in this line, you see two points
the points are 1. (-1, -1), and 2. (2, -2)
using the coordinates means that you use a formula: [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
the y2 is the y value of the second coordinate (-2), the y1 is the y value of the first coordinate (-1)
the x2 is the x value of the second coordinate (2), the x1 is the x value of the first coordinate (-1)
if you plug these it you get: -2 - (-1) / 2 - (-1)
this can be simplified to -2 + 1 / 2 + 1
and simplified again to -1/3
Qhat ever method you use, you should get the same answer. Using both methods is a good way to check your work.
The diameter of Saturn at its equator is about 120,540,000 meters. What is 120,540,000 written in word form?
Answer:
Step-by-step explanation:
Onehundred twenty-million-fivehundred forty thousand
Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.
What is the sum of the factors?
What is the sum of 347+645=
Answer:
347 + 645 = 992
Step-by-step explanation:
347
+645
922
Eddie is reading a novel for English class. He has read 168 out of 480 pages. What percent of the book has he read?
Answer:
0.35%
Step-by-step explanation:
The polygons are similar. Find the value of X and Y
Answer:
X=8, Y=9
Step-by-step explanation:
9/6=1.5
12/1.5=8
6*1.5=9
PLS GIVE BRAINLIEST
10 .find the partial sum S10 of the arithmetic series with a1 = 4, d = 5.
Answer:
S10 = 320
Step-by-step explanation:
The formula for calculating the sum of the nth term of an AP is expressed as
Sn = n/2(2a+(n-1)d))
Given
a = 4
d = 5
n = 10
S10 =10/2{2(5)+(10-1)5}
S10 =5{10+9(6)}
S10 =5{10+54}
S10 = 5(64)
S10 = 320
Hence the sum of the first ten terms of the sequence is 320
PLEASE PLEASE PLEASE HELP
Answer:
some dumb mod deleted my answer because i didnt show work. Who cares about the work everyone just wants the answers.
55.) A.9 B. 29
57.) SAS
Step-by-step explanation:
Can someone please do this?
Solve the inequality 2 (x - 2) +8.6 < 14.
Answer:
x<4.7
Step-by-step explanation:
2(x-2)+8.6<14
2x-4+8.6<14
2x=4.6<14
2x<14-4.6
2x<9.4
_____
x<4.7
mom said its my turn to be brainliest answer ;0
also, help me on my math hw maybe ?
Answer: x < 4.7
Step-by-step explanation:
Hi. :) if you are a "Blink" what album should i get?
Answer:
Changes
Step-by-step explanation:
#teamtrees #WAP (Water And Plant)
Answer:
♡ let's kill this love! ♡
you should definitely get "the album."
it has a very good rating and its great ☆
stan blackpink for clear skin, have a great day!
-madi/madeline
✧・゚: *✧・゚:・゚✧*:・゚✧・゚: *✧・゚:・゚✧*:・゚✧
Step-by-step explanation:
arrangement the following in ascending order ; -5/7, -3/14, 4/7, -6/7
Answer:
-4/7-5/7-6/7-3/14 ascending order
Answer:
The sorted inputs in order from least to greatest is:
-6/7 < -5/7 < -3/14 < 4/7
Step-by-step explanation:
Given
-5/7, -3/14, 4/7, -6/7
The least common denominator (LCD) is: 14
Rewriting as equivalent fractions with the LCD:
-5/7 -3/14 4/7 -6/7
-10/14 -3/14 8/14 -12/14
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
-6/7 -5/7 -3/14 4/7
-12/14 < -10/14 < -3/14 < 8/14
Therefore, the sorted inputs in order from least to greatest is:
-6/7 < -5/7 < -3/14 < 4/7
I NEED HELP ASAP DUE MORNING AND REPORT CONFERENCE TMM
Answer:
A. Horizontal and slope is 0
B. Horizontal and slope is 0
C. Vertical and slope is undefined
D. Vertical and slope is undefined
Step-by-step explanation:
∠1 and ∠2 are vertical angles. If m∠2 = 124°, find the measure of the supplement of ∠1 plzzz i need help
Answer:
∠1 = 124 degrees
Step-by-step explanation:
Vertical angles are always congruent
So ∠1 = ∠2
Answer:
Supplement of m∠1 = 56°
Step-by-step explanation:
Since both angles are vertical, they both equal to each other.
m∠2 = m∠1
= 124°
To find the supplement of m∠1, we need to remember that supplementary angles add up to 180°.
Supplement of m∠1 = 180°-124°
= 56°
$120 less than half of d dollars
Answer:
[tex]\frac{d}{2} - 120[/tex]
Step-by-step explanation:
You work backwards:
Half of d dollars is d/2. Then you take 120 less than that, which means you are subtracting.
Answer:
1/2d-120
Step-by-step explanation:
Alright.
d=amount of money
1/2d=half of the amount of money
1/2d-120=half of the money minus 120
Twenty percent of the town's population is over the age of 65. If there are 320 residents over the age of 65, what is the town's total population?
Answer:
65
Step-by-step explanation:
I think. hope this hepls
Answer:
There are 1600 residents.
Step-by-step explanation:
0.2 times x = 320 divide by 0.2
x = 1600
Heidi has $4.55. She needs to buy bolts at the hardware store. Bolts cost $0.13 each.
What division equation and related multiplication equation could Heidi use to find how many bolts she can buy?
Answer
35
Step-by-step explanation:
4.55/.13=35. Also, Heidi could do 35x13. I hope this helps!
What percent is 8 out of 32?
Answer:
25%
Step-by-step explanation:
8/32= 25%
Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.Area: 49 square feet ft (smaller value) ft (larger value)
Answer:
Length = 7 ft
Breadth = 7 ft
Step-by-step explanation:
Let lenght of rectangle be x
and breadth be y
Area = [tex]49\ \text{ft}^2[/tex]
[tex]xy=49\\\Rightarrow x=\dfrac{49}{y}[/tex]
Permiter of a rectangle is given by
[tex]P=2(x+y)\\\Rightarrow P=2x+2y\\\Rightarrow P=2\times\dfrac{49}{y}+2y\\\Rightarrow P=\dfrac{98}{y}+2y[/tex]
Differentiating with respect to y we get
[tex]\dfrac{dP}{dy}=-\dfrac{98}{y^2}+2[/tex]
Equating with zero
[tex]0=-\dfrac{98}{y^2}+2\\\Rightarrow -2=-\dfrac{98}{y^2}\\\Rightarrow y^2=\dfrac{98}{2}\\\Rightarrow y^2=49\\\Rightarrow y=7[/tex]
Double derivative of the equation
[tex]\dfrac{d^2P}{dy^2}=2\dfrac{98}{y^3}\\\Rightarrow \dfrac{d^2P}{dy^2}=\dfrac{196}{y^3}>0[/tex]
So the value of y is minimum at 7.
[tex]x=\dfrac{49}{y}=\dfrac{49}{7}\\\Rightarrow x=7[/tex]
Hence, [tex]x=7,y=7[/tex]
The mimimum length and breadth of the rectangle is both 7 ft.
will someone plz do this question
Answer:
the answer is a your welcome