Answers
The simplified expression is as follows:
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]
How to simplify expression?The expression can be simplified as follows:
To simplify an expression means to write an equivalent expression which contains no similar terms.
This means that we will rewrite the expression with the fewest terms possible.
Therefore,
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } }[/tex]
The expression can be represented as follows:
3x⁶ / 14y⁹ ÷ 33x⁴ / 10y²
3x⁶ / 14y⁹ × 10y² / 33x⁴
Hence,
3x⁶ / 14y⁹ × 10y² / 33x⁴ = 30x⁶y² / 462x⁴y⁹
Therefore,
30x⁶y² / 462x⁴y⁹ = 10x² / 154y⁷ = 5x² / 77y⁷
Hence,
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]
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Related Questions
Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?
Answers
Okay, here we have this:
Considering the provided information we obtain the following:
a)
Replacing in the Compound Interest formula we obtain the following:
[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]b)
After 1 year (t=1):
[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]We obtain that after one year the balance is aproximately $17,161.06.
After 2 years (t=2):
[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]We obtain that after two years the balance is aproximately $18,331.90
After 5 years (t=5):
[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]We obtain that after five years the balance is aproximately $22,345.90.
After 10 years (t=10):
[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]We obtain that after ten years the balance is aproximately $31,082.44.
c)
In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:
[tex]32130=16065e^{0.066t}[/tex]Let's solve for t:
[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.
Select all the situations in which a proportional relationship is described.
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Robert spends $2 in the first 3 days of the week and $5 in the next 4 days.
Answers
Answer:
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Step-by-step explanation:
A proportional relationship is one that has a constant of proportionality.
In this case, the correct options are Mia, Piyoli, and Robert.
In shop, you make a table. The sides of the table measure 36" and 18". If the diagonal of the table measures 43", is the table "square"? (In construction, the term "square" just means the table has right angles at the corners.)
Answers
We are given the following information:
Table sides = 36 inches & 18 inches
Diagonal of table = 43 inches
We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:
[tex]\begin{gathered} \text{The Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ c=43in,b=36in,a=18in \\ \text{Substituting we have:} \\ 43^2=18^2+36^2 \\ 1849=324+1296 \\ 1849=1620 \\ \Rightarrow1849\ne1620 \\ \\ \therefore\text{ The table is not ''square''} \end{gathered}[/tex]Therefore, the table is not "square" (it does not have right angles at the corners)
For each ordered pair, determine whether it is a solution to 3x + 5y=-17. Is it a solution? X 6 ? No (-8,3) (-4, -1) (6, 7) (7,2)
Answers
Determine whether is a solution for:
[tex]\begin{gathered} 3x+5y=-17 \\ To\text{ determine if it's a solution, we can isolate y and see if the statement} \\ is\text{ true:} \\ 5y=-17-3x \\ y=-\frac{17}{5}-\frac{3}{5}x \end{gathered}[/tex]For, x=-8, y has to be 3:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-8) \\ y=\frac{7}{5}=1.4 \end{gathered}[/tex](-8, 3) is not a solution for the equation.
For x=-4, y has to be -1:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-4) \\ y=-1 \end{gathered}[/tex](-4, -1) is a solution for the equation.
For x=6, y has to be -7:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(6) \\ y=-7 \end{gathered}[/tex](6, -7) is a solution for the equation.
For x=7, y has to be 2
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(7) \\ y=-\frac{38}{5}=-7.6 \end{gathered}[/tex](7, 2) is not a solution for the equation.
there are 12 questionsI got 7 right what did I make?
Answers
there are 12 questions
I got 7 right
the easiest way to solve this is by using a rule of three
Step 1
Let
[tex]12\text{ questiones }\Rightarrow100\text{ percent}[/tex]then
[tex]7\text{ questions }\Rightarrow x\text{ percent}[/tex]Step 2
do the relation and solver for x
[tex]\begin{gathered} \frac{12}{100}=\frac{7}{x} \\ 12\cdot x=100\cdot7 \\ 12\cdot x=700 \\ x=\frac{700}{12} \\ x=58.33 \\ \end{gathered}[/tex]so, you did the 58.33 %
Julie is 6 feet tall if she stands 15 feet from the flagpole and holds a cardboard square the edges of the square light up with the top and bottom of the flagpole approximate the height of the flagpole
Answers
Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \frac{6}{15}=\frac{15}{x-6} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 6(x-6)=15^2 \\ 6x-36=225 \\ 6x=225+36 \\ 6x=261 \\ x=\frac{261}{6} \\ x=43.5ft \end{gathered}[/tex]How many offices are between 41 and 50 meters ?
Answers
Solution
For this case we want to find the number of offices between 41 and 50 m and the answer is:
2 meters
The graph of which function has a minimum located at (4,-3)
Answers
We need to obtain the first derivate
[tex]\begin{gathered} f\mleft(x\mright)=-\frac{1}{2}x^2+4x-11 \\ f^{\prime}(x)=-x+4 \end{gathered}[/tex][tex]\begin{gathered} f\mleft(x\mright)=-2x^2+16x-35 \\ f^{\prime}(x)=-4x+16 \end{gathered}[/tex][tex]\begin{gathered} \: f\mleft(x\mright)=\frac{1}{2}x^2-4x+5 \\ f^{\prime}(x)=x^{}-4 \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x^2-16x+5 \\ f^{\prime}(x)=4x-16 \end{gathered}[/tex]Answer: B on edge23
Step-by-step explanation:
f(x) = 1/2^x2–4x + 5
under normal conditions, 1.5 feet of snow will melt into 2 inches of water. after a recent snowstorm, there were 4 feet if snow. how many inches of water will there be when the snow MELTS? express your answer as a fraction reduced to lowest terms or decimal rounded correctly to two decimals places. Do not include units with this answer.
Answers
If 1.5 feet of snow melts into 2 inches of water, this implies that:
[tex]undefined[/tex]Given the equations and the table below, what is the first x-value when the y-value of equation 2 is greater than the y-value of equation 1 after the functions first intersect?Equation 1: f(x)=5x^3Equation 2: f(x)=2x+3
Answers
the first x value, when the y-value of the equation is greater than the y value of equation one, is x=15
Because the y-value of equation 2 with x=15 is 32771, while the y-value of equation 1 is 16875
Write the slope-intercept form of the equation. Put your answer in y = mx + b form.Passing through (-4, -8) and (-8, -13)
Answers
Answer:
[tex]y=\frac{5}{4}x-3[/tex]Step-by-step explanation:
Linear functions are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]The slope of a line is given as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex](-4,-8) and (-8,-13):
[tex]\begin{gathered} m=\frac{-8-(-13)}{-4-(-8)} \\ m=\frac{5}{4} \end{gathered}[/tex]Use the slope-point form of a line, to find the slope-intercept form:
[tex]\begin{gathered} y_{}-y_1=m(x_1-x_{}) \\ y+8=\frac{5}{4}(x+4) \\ y+8=1.25\mleft(x+4\mright) \\ y=\frac{5}{4}x-13 \\ y+8=\frac{5}{4}x+\frac{20}{4} \\ y=\frac{5}{4}x+5-8 \\ y=\frac{5}{4}x-3 \end{gathered}[/tex]Ramon has assets that sum up to $253,000. He has liabilities that sum up to $216,345. what is his net worth?
Answers
Net worth is equal to total assets minus total liabilities (debt).
So,
Total Assets = 253000
Total Liabilities = 216345
Hence,
Net Worth = 253000 - 216345 = $36,655
Solve the system you any method. State the final answer as an ordered pair. DO NOT include spaces or dollar signs in your answer.
Answers
To solve the problem, we notice that both of the equations are written with the y solved then we can equate the expressions of x and solve the resulting equation of x:
[tex]\begin{gathered} x-12=-3x+12 \\ x+3x=12+12 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Once we have the value of x we plug it on the first equation to find y:
[tex]\begin{gathered} y=6-12 \\ y=-6 \end{gathered}[/tex]Therefore, the solution of the system of equations is (6,-6)
Corky writes four equations to show each of the properties of equality. Which of Corky's equation is incorrect? Explainwill send image.
Answers
6 + m = 12
A. This IS equivalent
6 + m - m = 12 - m ==> 6 = 12 - m ==> 6 + m = 12
B. This IS NOT equivalent
6 + m - 6 = 12 - 12 ==> m = 0
C. This IS equivalent
6 + m + 2 = 12 + 2 ==> 6 + m = 12
D. This IS equivalent
6 + m - 6 = 12 - 6 ==> m = 6 ==> 6 + m = 12
Answer:
B is not equivalent
Consider the following expression:-27 x (-18)By the laws of signs, this is equivalent to27 x 18 this is equivalent to:27 x 18= 486we can conclude thatthe correct answer is:486I feel like that’s wrong, it’s not algebra can anyone help
Answers
The answer is actually CORRECT.
The correct procedure is when two negatives multiply each other, the answer is always a positive.
Therefore;
[tex]\begin{gathered} -27\times(-18)=27\times18 \\ 27\times18=486 \end{gathered}[/tex]We can conclude that the correct answer is 486
How many rays are in the next two terms in the sequence?
Answers
The sequnce is
2, 3, 5, 9, ....
this sequence follows the next formula:
[tex]a_n=2^{n-1}+1[/tex]where an is the nth term.
[tex]\begin{gathered} a_1=2^{1-1}+1=1 \\ a_2=2^{2-1}+1=3 \\ a_3=2^{3-1}+1=5 \\ a_4=2^{4-1}+1=9 \\ a_5=2^{5-1}+1=17 \\ a_6=2^{6-1}+1=33 \end{gathered}[/tex]The next two terms are 17 and 33
the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Answers
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
PMark for Review 1 Harold spent the summer working at a diner. He now pays for a monthly subscription to a magazine. The equation y -35x + 180 can be used to represent this situation, where y is the amount of money Harold has remaining after x months of paying for his monthly magazine subscription. Which statement best describes the amount of money Harold has, given this equation? - A) Harold started with $35 and he spends $180 per month on his magazine subscription. B) Harold started with $180 and he gets paid $35 per month. C) Harold started with owed $180 for magazines and he continues to spends $35 per month on his magazine subscription. D) Harold started with $180 and he spends $35 per month on his magazine subscription.
Answers
the option D is the correct answer
the equation is
y = 35x +180
that means he started with 180 $ and his monthly subscription is 35 $.
Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
Answers
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
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Solve for x: 4 open parentheses 2 x minus 1 close parentheses plus 8 minus 14 x equals negative 8 x plus 4 plus 2 x The solution is X = _________
Answers
Answer:
x = 1
Step-by-step explanation:
4(2x-1)+8-14= -8x+ 4+ 2x
12x÷4yif x=-8 and y=3
Answers
To solve 12x÷4y, first, let's evaluate the products on both sides of the ÷ symbol, we know that x = -8, then we have:
[tex]12\times(-8)=-96[/tex]We have -96 on the left side of the ÷ symbol.
We know that y = 3, then, on the right side, we have:
[tex]4\times3=12[/tex]Then, we have 12 on the right side of the ÷ symbol, now the expression looks like this:
-96 ÷ 12. what we have to do is to divide -96 by 12, then we get:
[tex]-96\text{ }\div12=\frac{-96}{12}=-8[/tex]Then, the answer is 8
Complete a triangulation calculation to measure the distance between actual objects in or near your home. include a well-labeled diagram.
Answers
Triangulation means the measuring of distances in surveys with triangles. If the distance of two objects and the angle between is knwon, the distance between these objects can be calculated.
Given the diagram we have:
So, the distance between both objects will be calculated by:
[tex]c=\sqrt{a^2+b^2-2ab\cdot\cos\theta}[/tex]Where:
Distance to the first object a = 6
Distance to the first object b = 6
Angle between both objects θ = 60°
Substitute the values, we have:
[tex]c=\sqrt{6^2+6^2-2(6)(6)\cdot\cos60}[/tex]Simplify:
[tex]c=\sqrt{36+36-72(0.5)}=\sqrt{72-36}=\sqrt{36}=6[/tex]So, the distance between both objects c = 6 inches
Quadrilateral MNOP is dilated by a scale factor of % to create quadrilateral M'N'O'P. The perimeter of quadrilateral MNOP is x units. What is the perimeter in units of quadrilateral M'N'O'P'? A. x units B. ( V2 x units COM X units D. 8/7 x units
Answers
If the perimeter of the quadrilateral MNOP is x
And a scale factor of a dilated image is
[tex]\frac{7}{8}[/tex]If the perimeter of M'N'O'P' = y
Then
[tex]\text{scale factor = }\frac{perimeter\text{ of y}}{perimeter\text{ of x}}\text{ = }\frac{7}{8}[/tex]Cross multiplying,
[tex]perimeterofy=M^{\prime}N^{\prime}O^{\prime}P^{\prime}=\frac{7}{8}\text{ x units}[/tex]The perimeter of M'N'O'P' = 7/8 x units
Option A is correct
What is 44 over 13 rounded to the nearest 10 tenths
Answers
we have that
44/13=3.38
rounded to the nearest tenths
3.38=3.4
the answer is 3.4Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answers
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
Compare A and B in three ways, where A = 51527 is the number of deaths due to a deadly disease in the United States in 2005 and B = 17241 is the number of deaths due to the same disease in the United States in 2009. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.
Answers
ANSWER
Ratio of A to B = 2.99 (to 2 decimal places)
Ratio of B to A = 0.33 (to 2 decimal places)
A is 299% of B (to nearest integer)
STEP BY STEP EXPLANATION
for ratio of A to B:
[tex]\begin{gathered} \frac{A}{B}\text{ = }\frac{51527}{17241}\text{ = }2.98863 \\ \text{ = 2.99 (to 2 decimal places)} \end{gathered}[/tex]for ratio of B to A:
[tex]\begin{gathered} \frac{B}{A}\text{ = }\frac{17241}{51527}\text{ = 0.33460 } \\ \text{ = 0.33 (to 2 decimal places)} \end{gathered}[/tex]A is x % of B:
[tex]\begin{gathered} A\text{ = }\frac{x}{100}\times B \\ x\text{ = }\frac{100\text{ }\times A}{B} \\ x\text{ = }\frac{100\text{ }\times\text{ 51527}}{17241}\text{ = 298.86} \\ x\text{ = 299\% (to nearest integer)} \end{gathered}[/tex]Hence, the ratio of A to B = 2.99 (to 2 decimal places), B to A = 0.33 (to 2 decimal places) and A is 299% of B (to nearest integer).
Please Help!!!!! NOT FOR QUIZ!!!!!!!!
Answers
The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation , the correct option is (c) .
In the question ,
it is given that
the equation of the line is y [tex]=[/tex] -3x + 4 ,
we have to plot the line in the coordinate plane .
we plot the line ,w e need at least two points .
for the first point ,
for x = 0 , we have
y = -3(0) + 4
y= 0 + 4
y = 4
the first point is (0,4)
for the second point
for y = 0 , we have
0 = -3x + 4
-3x = -4
x = 4/3
the second point is (4/3 , 0)
so , from the graph plotted below , we can see that the line y [tex]=[/tex] -3x+4 shows the set of all solutions to the equations .
Therefore , The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation .
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May I please get help with this math problem. I am so lost and confused
Answers
We are given three angles and we are asked to determine if the angles are the angles of a triangle. To do that we need to have into account that the measure of the angles of a triangle always adds up to 180, therefore, if we add up the angles and the result is 180, then these angles can be angles measures of a triangle. If the result is different from 180 the angles can't be the angle measures of a triangle. Taking the first set of three angles we get:
[tex]58+34+42=134[/tex]Since the result is different from 180 then these angles can't be the angle measure of a triangle.
The same procedure is used to determine the other sets of angles.
Need help asap !!!!!
Answers
The practical domain is 1 ≤ x ≤ 20 and the practical range is 13.61 ≤ C(x) ≤ 127.61
How to determine the practical domain?From the question, the given parameters are:
Charges = $7.61Reservation = $6Maximum number of windows = 20Total cost = CThe domain is dependent on the number of windows washed
Using the maximum as a guide, the minimum number of windows could be
Minimum = 1
The domain is then represented as
Minimum ≤ x ≤ Maximum
So, we have
1 ≤ x ≤ 20
How to determine the practical range?Using the given parameters in (a), we have
Total cost, C = Charges * Number of windows + Reservation
So, we have
C(x) = 7.61 + 6x
Where x is the number of windows
When x = 0, we have
C(1) = 7.61 + 6(1)
C(1) = 13.61
When x = 20, we have
C(20) = 7.61 + 6(20)
C(20) = 127.61
So, we have the range to be 13.61 ≤ C(x) ≤ 127.61
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A package of 5 pairs of insulated socks costs 27.95$. What is the unit price of the pairs of ?
Answers
Answer:
$5.59
Step-by-step explanation:
You want the unit price of a pair of socks, given that 5 pairs cost $27.95.
Unit priceThe unit price is found by dividing the price by the number of units.
$27.95/5 = $5.59
The unit price of a pair of socks is $5.59.