Simplify the complex rational expression. When typing your answer for the numerator and denominator be sure to type the term with the variable first with no spaces between characters. If an exponent is needed use the carrot key (^) by pressing shift and 6 at the same time.\frac{\left(\frac{2}{a}+\frac{7}{b}\right)}{b}The numerator is AnswerThe denominator is Answer
Answers
The given expression is
[tex]\frac{(\frac{2}{a}+\frac{7}{b})}{b}[/tex]To add 2 fractions we have to give them the same denominators
In the up part (numerator) we have 2 different denominators a and b
Then the common denominator of the 2 fractions must be the product of them
[tex]\frac{2}{a}+\frac{7}{b}=\frac{2b}{ab}+\frac{7a}{ab}=\frac{2b+7a}{ab}[/tex]Then the fraction will be
[tex]\frac{\frac{2b+7a}{ab}}{b}[/tex]Now, we will multiply the denominator of up by the denominator of the first fraction (ab x b)
[tex]\frac{\frac{2b+7a}{ab}}{b}=\frac{2b+7a}{b(ab)}[/tex]Multiply b by b to simplify, then
[tex]\frac{2b+7a}{b(ab)}=\frac{2b+7a}{ab^2}[/tex]The numerator is 2b + 7a
The denominator is ab^2
Related Questions
8.26×10^0 scientific notation or standarn form
Answers
The number 8.26 10^0 is shown in scientific notation.
Its standrad form is: 8.26 since we know that any base different from zero raised to the power "0" (zero) gives "1" (one).
I am having trouble with the last two questions. I worked through finding the slope and y-intercept with a previous tutor, before we got disconnected.6. Express this equation as a function D of P and find its domain.7. How many shirts per month will be demanded if the price is $27?
Answers
Data:
[tex]m=-\frac{203}{152}\approx-1.3355[/tex][tex]b=\frac{11227}{152}\approx73.862[/tex]Equation as a function of D of P
[tex]D(P)=-1.3355\cdot P+73.862[/tex]Answer (6):
• Domain
[tex](-\infty,+\infty)[/tex]To know how many shirts per month will be demanded if the price is $27, we have to use P = $27:
[tex]D(27)=-1.3355\cdot27+73.862\text{ }\approx37.80[/tex]Answer (7): $37.80
Farmer jones, and his wife, dr. jones, decide to build a fence in their field, to keep the sheep safe. since dr. jones is a mathematician, she suggests building fences described by y=11x^2and y=x^2+4. farmer jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. what is the area of the enclosed region?
Answers
Given:
The equation is:
[tex]\begin{gathered} y=11x^2 \\ y=x^2+4 \end{gathered}[/tex]Required:
Find the area enclosed by the region.
Explanation:
The given equation is:
[tex]\begin{gathered} y=11x^2 \\ y=x^2+4 \end{gathered}[/tex]Find the intersecting point of the curve.
[tex]\begin{gathered} 11x^2=x^2+4 \\ 10x^2=4 \\ x^2=\frac{4}{5} \\ x=\pm\sqrt{\frac{4}{5}} \\ x=\pm\frac{2}{\sqrt{5}} \end{gathered}[/tex]The enclosed area is:
[tex][/tex]Debbie's checkbook balance was $2,715.50. She wrote checks totaling $5,298.13 during the month of May. Deposits made during the month were $250.16 on May 1. On May 15, her payroll check was electronically processed for $2,980.66; on May 22, a check from the IRS was electronically processed for $2,550. On May 27, she recorded $534.10 for payments debited to her account for auto insurance and utilities. What is her checkbook balance?
Answers
Debbie's checkbook balance is $-3,297.23, which shows an overdraft.
When does an overdraft occur?An overdraft occurs when the money (deposits) in Debbie's account does not exceed her payments or withdrawals.
While Debbie had a positive beginning balance, the ending balance shows an overdraft of $-3,297.23.
By this overdraft, Debbie's bank is extending her some short-term credit, which she should pay back with interest.
Beginning balance on checkbook = $2,715.50
Checks for the month = $-5,298.13
Deposits for the month = $250.16
Payroll check = $-2,980.66
IRS check = $2,550
Auto insurance and utilities = $-534.10
Ending balance on checkbook = $-3,297.23
Thus, Debbie's ending checkbook balance will show an overdraft of $-3,297.23.
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16. A rectangular picture measures 6 inches by 8 inches. Simon wants to build a
wooden frame for the picture so that the framed picture takes up a maximum area
of 100 square inches on his wall. The pieces of wood that he uses to build the
frame all have the same width. Write an equation or inequality that could be used
to determine the maximum width of the pieces of wood for the frame Simon could
create.
Explain how your equation or inequality models the situation.
Solve the equation or inequality to determine the maximum width of the pieces of
wood used for the frame to the nearest tenth of an inch.
Answers
Answer:
[tex]w \leq 1.9[/tex]
Step-by-step explanation:
The picture itself measures 6" by 8". Therefore, the area is 6 * 8 = 48 square inches.
All of the pieces of wood have the same width, and we know that two of them will be 6 inches long and two will be 8 inches long.
Therefore, the combined area of the pieces of wood will be 2 * 6w and 2 * 8w. This gives us 12w + 16w.
Now we can set up an inequality:
48 (area of picture) + 12w + 16w <= 100 (maximum area).
Simplify the left side of the equation to give us this:
[tex]48+28w\leq 100.[/tex]
We can move the 48 over to the other side to get [tex]28w \leq 100 - 48[/tex], which simplifies to [tex]28w \leq 56[/tex]. Now, you just have to divide both sides by 28 to get [tex]w\leq 1.857[/tex].
Rounding to the nearest tenth of an inch gives us 1.9 as the maximum width of the pieces of wood.
can you solve 3 5/12 + 1 3/8 ?
Answers
Answer:
4 19/24
Explanation:
First, we need to convert the mixed numbers into a fraction, so:
[tex]\begin{gathered} 3\frac{5}{12}=\frac{3\times12+5}{12}=\frac{36+5}{12}=\frac{41}{12} \\ 1\frac{3}{8}=\frac{1\times8+3}{8}=\frac{8+3}{8}=\frac{11}{8} \end{gathered}[/tex]Then, we can add the fractions as follows:
[tex]\frac{41}{12}+\frac{11}{8}=\frac{41(8)+12(11)}{12(8)}=\frac{328+132}{96}=\frac{460}{96}[/tex]Finally, we can simplify the fraction and write the fraction as a mixed number as:
[tex]\frac{460}{96}=\frac{460\div4}{96\div4}=\frac{115}{24}[/tex][tex]\frac{115}{24}=4\frac{19}{24}[/tex]Because when we divide 115 by 24, we get 4 as a quotient and 19 as a remainder.
Therefore, the answer is: 4 19/24
The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020? Explain your answers.
Answers
Given the function of the rate of change of the population:
[tex]P(t)=200e^{0.02t}[/tex]The integral of this function will be the value of the population growth of the town from 1990 to 2010. This is because P(t) is the rate of change of population, its integral will be the antiderivative, that is the population of the town.
To calculate the change in population we have to find the integral from 5 to 10 of P(t):
[tex]\begin{gathered} \int_5^{10}200e^{0.02t}dt \\ 200\int_5^{10}e^{0.02t}dt \\ 200\cdot\frac{e^{0.02t}}{0.02} \\ 10000e^{0.02t} \\ (10000e^{0.02(10)})-(10000e^{0.02(5)}) \\ 1162.3 \end{gathered}[/tex]The change in population can not be a decimal number, so we can round it to 1162.
To calculate the population in 2020 we have to find the integral from 0 to 30 of P(t) and then add it to 10000 which was the initial population (we already know the integral so we're just going to evaluate it):
[tex]\begin{gathered} 10000e^{0.02(30)}-10000e^{0.02(0)} \\ 8221.2 \\ 10000+8221.2=18221.2 \end{gathered}[/tex]It means that the population in 2020 is 18221 (Remember that we round it because it is not possible to have a decimal value for the population of the town).
Graph the parabola.
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
Answers
The graph of the parabola is added as an attachment
The vertex is (0, 0)The points to the right are (1, 1) and (2, 4)The points to the left are (-1, 1) and (-2, 4)How to graph the parabola?From the complete question (added at the end of the solution), the equation of the parabola is given as
y = x²
When a parabola has the form of y = x², then the vertex of the parabola is
Vertex = (0, 0)
Set x > 0 to determine the points to the right
When x = 1
y = 1² = 1
When x = 2
y = 2² = 4
Set x > 0 to determine the points to the left
When x = -1
y = -1² = 1
When x = -2
y = -2² = 4
So, the points are
(1, 1), (2, 4), (-1, 1) and (-2, 4)
While the vertex is (0, 0)
Next, we plot the graph of the parabola using a graphing calculator
See attachment for the graph
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Complete question
Graph the parabola y = x²
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
Graph the solution of the following inequality and answer the questions below
Answers
We have the next inequality
[tex]11x+9<-11y+9[/tex]First we need to isolate the y
[tex]11y<-11x+9-9[/tex][tex]11y<-11x[/tex][tex]y<\frac{-11}{11}x[/tex][tex]y<-x[/tex]The boundary line need to be dashed because the sign is less than
Two points of the boundary line can be calculated using the next equality y=-x
x=0
y=0
Point (0,0)
x=-5
y=5
Point (-5,5)
The area will be the area below the boundary line because we have a sign less than
Find the solution to the system of equations represented by the matrix shownbelow.83-161E441371-63ХUse the operation buttons to start solving
Answers
The solution to the system of equations represented by the matrix is (x, y, z) = (6, 7, 6).
Maybe your matrix is ...
[tex]$\left[\begin{array}{ccc|c}3 & -1 & 7 & 53 \\ 1 & 7 & 1 & 61 \\ 9 & 1 & 1 & 67\end{array}\right]$[/tex]
A calculator can tell you the solution is ...
(x, y, z) = (6, 7, 6)
The third variable in systems of equations with more than two variables can be defined in terms of the other two (as for solution by substitution). This can be used to create two equations with two unknowns by substituting it into the remaining equations. The value of the third variable can then be determined using that answer. The use of this technology is demonstrated in the attached.
The last equation served as a definition, which was then applied to the first two equations. An algebraic solution can be solved using the same strategy.
The answer is (x, y, and z) = (6, 7, 6).
Complete question: Find the solution to the system of equations represented by the matrix shown below. 3 -1 7 53 1 7 1 61 9 1 1 67
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If f(x)=√x and g(x)= - 2x+3, find (f . g)(x) and (g . f)(x).
(f . g)(x)=_____
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Thee values of the functions are;
(f . g)(x) = √(-2x + 3)
(g . f)(x) = - 2√x + 3
What is a function?A function can simply be defined as a law, rule or expression showing the relationship between two variables in an equation or expression.
The two variables are given;
The dependent variableThe independent variableGiven the functions;
f(x)=√x g(x)= - 2x+3To determine the function (f . g)(x), substitute the value of x as g(x) in the function, we have;
(f . g)(x) = √(-2x + 3)
To determine the function (g . f)(x), substitute the values of x in the function g(x), we have;
(g . f)(x) = - 2√x + 3
Hence, the functions are √(-2x + 3) and - 2√x + 3
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Put the following rational numbers in ascending order. r 0.4, 7/10, 9/10
Answers
Answer:
Step-by-step explanation:
Ascending is least to greatest.
We can convert the fractions into decimals.
SO,
7/10 can be 0.7 and 9/10 can be 0.9
In least to greatest order, it would be:
0.4, 0.7, 0.9 ANSWER
What are the dimensions of the rectangle with Maximum area?
Answers
Let x be the length of the rectangle and y be the width of the rectangle, then we can set the following equations:
[tex]\begin{gathered} 2x+2y=40, \\ A=x\cdot y\text{.} \end{gathered}[/tex]Solving the first equation for x we get:
[tex]\begin{gathered} 2x=40-2y, \\ x=\frac{40}{2}-\frac{2y}{2}, \\ x=20-y\text{.} \end{gathered}[/tex]Substituting x=20-y in the second equation we get:
[tex]\begin{gathered} A=(20-y)\times y, \\ A=20y-y^2. \end{gathered}[/tex]Now, we will use the first and second derivative criteria to find the maximum.
The first and second derivatives are:
[tex]\begin{gathered} A^{\prime}(y)=20-2y. \\ A^{\prime\prime}(y)=-2. \end{gathered}[/tex]Since the second derivative is a negative number that means that A(y) reaches a maximum when A´(y)=0.
Solving A´(y)=0 for y we get:
[tex]\begin{gathered} 20-2y=0, \\ 20=2y, \\ 10=y\text{.} \end{gathered}[/tex]Now, substituting y=10 in x=20-y, we get:
[tex]x=20-10=10.[/tex]Answer:
Length 10 yards.
Width 10 yards.
Evaluate the following expression 8!
Answers
The value of the expression 8! is 40320.
What is an expression?It should be noted that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 8! will be:
= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 40320
This illustrates the concept of multiplication.
Therefore, it is 40320.
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how many grams are in a Kilogram?1,0000.0010.01100
Answers
Ok, so
The answer is that there's 1,000 grams in a Kilogram. That's the equivalence.
I need help with this question parts a - e
Answers
Given:
650 lb of coffee is sold when the price is $4 per pound,
400 lb of coffee is sold at $8 per pound.
To find:
A) List the data points
B) The slope of line joining the points
C) Interpretation of meaning of slope of line
D) linear equation of data using point slope form
E) Using the function we need to predict the number of consumers buying at $6 per pound
Step-by-step solution:
A) Data points of the given data:
Data points:
(4,650) and (8,400)
B) The slope of the line joining the points:
[tex]\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ Slope=\frac{400-650}{8-4} \\ \\ Slope\text{ =-62.5} \end{gathered}[/tex]C) Interpretation of meaning of slope of line:
Slope here means that:
When there is an increase in the price of coffee then the weight of coffee decreases.
Weight per dollar of coffee decreases at the rate of 62.5
D) linear equation of data using the point-slope form:
Applying point-slope form:
y - y1 = m(x - x1)
y - 650 = -62.5(x - 4)
y = -62.5x + 900
In function notation it can be represented as:
S(P) = -62.5P + 900
E) Using the function we need to predict the number of consumers buying at $6 per pound
To predict that, we will simply put the value of P equal to 6 in the given function:
S(P) = -62.5P + 900 At P = 6
S(P) = -62.5(6) + 900
S(P) = 525
Thus we can say that 525 customers will buy at $6 per pound.
Answer this please question in picture it’s geometry
Answers
The value of P is 1 and value of V is 5 .
In this addition, each letter represents a single digit.
Now, Given that
1 7 2
2 9 4
+ 7 V 6
= P 2 P 2
To find the value of P
To solve this addition:
1 7 2
2 9 4
+ 7 5 6
= 1 2 1 2
Hence, The value of P is 1 and value of V is 5 .
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bebe ené’eben’´´enz’bzva
Answers
Answer:
What?
Step-by-step explanation:
What?
which statement best describes the equation x + 5 imprint c squared + 4 (x + 5) + 12 equals 0
Answers
Given:
[tex](x+5)^2+4(x+5)+12=0[/tex]let u = x+5
so, the equation will become:
[tex]u^2+4u+12=0[/tex]so, the equation is quadratic in form because the substitution u = x+5
The answer is the first statement
Note:
the second statement is wrong, because when the equation expanded, it will be a second degree polynomials not fourth degree
Also, the last 2 statements are wrong, because it is quadratic equation.
Steve files head of household. In 2022, he received $23,000 in social security benefits, $10,000 in taxable retirement income, and $4,000 in interest and dividend income. Using the Social Security Benefits Worksheet - Line 6a and 6b, determine Steve's taxable social security benefits.
Answers
Steve's taxable social security benefits is zero.
Since Steve declares himself as the head of the home, his social security payments, which range from $25,000 to $34,000, will be subject to a 50% tax.
Retirement income, interest income, and dividend income are not considered social security benefits for determining the limit. Nevertheless, in the case at hand, the social security benefits total $23,000, which is less than the maximum of $25,000 and is thus not taxable.
As a result, Steve's Social Security benefits are not taxable.
Hence the taxable amount on Steve on social security benefits is Zero.
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4x^3 + 12x^2 + 3x + 9 factor completely
Answers
The factored expression of 4x^3 + 12x^2 + 3x + 9 is (4x^2 + 3)(x + 3)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to factor the expression completely?The expression is given as
4x^3 + 12x^2 + 3x + 9
Group the expression in 2's
So, we have
4x^3 + 12x^2 + 3x + 9 = (4x^3 + 12x^2) + (3x + 9)
Factor each group
So, we have
4x^3 + 12x^2 + 3x + 9 = 4x^2(x + 3) + 3(x + 3)
Rewrite as
4x^3 + 12x^2 + 3x + 9 = (4x^2 + 3)(x + 3)
Hence, the factored expression is (4x^2 + 3)(x + 3)
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Find the measure of the side labeled x. Round to two decimal places as needed.
Answers
The Solution:
Given:
We are asked to find the value of x.
By applying the Trigonometrical Ratio, we have:
[tex]\begin{gathered} \sin42.8=\frac{opp}{hypotenuse}=\frac{x}{20.9} \\ \\ \sin42.8=\frac{x}{20.9} \end{gathered}[/tex]Cross multiplying, we get
[tex]x=20.9\sin42.8=14.2003\approx14.20[/tex]Therefore, the correct answer is 14.20
Hi can you help me with this problem i dont understand itIll do anything if your correct
Answers
You can use multiplication to generate an equivalent ratio by multiplying both sides of the ratio by the same factor, this way:
[tex]\begin{gathered} 47\cdot2\colon3\cdot2 \\ 94\colon6 \end{gathered}[/tex]Please help!!!!!!!!!
Answers
Answer:
x and y is 59 degrees
Step-by-step explanation:
You can find the angle next to 121 which is 59 degrees considering linear pair. Then, you can figure out y by doing corresponding angles and so this means that y is also 59 degrees. To find x, we know that x is vertical to y and that they are the same value. So, this means that x is 59 degrees as well. Hope this helps!
Question 6Three times the sum of a number and four is equal to five timesthe number, decreased by two. If x represents the number, whichis a correct translation of the statement?A3(x + 4) = 5x - 23x + 4 = 5x - 2B3(x + 4) = 5(x - 2)D3x + 4 = 5(x - 2)
Answers
'the sum of a number and four' means
[tex](x+4)[/tex]And three times that is
[tex]3(x+4)[/tex]Then, that 'equals to five times a number'
[tex]5x[/tex]'decreased by two':
[tex]5x-2[/tex]So, the statement is translated into the equation:
[tex]3(x+4)=5x-2[/tex]The correct answer is option A
Is (-2,-6) a solution to the equation y = 3x?
Oyes
Ono
Answers
Answer:
yes
Step-by-step explanation:
if y = -6,
3x = -6
x = -2
Answer:
yes
Step-by-step explanation:
y = 3x?
Let x = -2 and y = -6
-6 = 3(-2)
-6 = -6
This is a true statement so (-2,-6) is a solution to the equation y = 3x
Kimberly wants to invest $3,000 in an account that earns 4% annual interest, and x dollars in an account that earns 7%, so that, on average, she earns 5.5% interest for both accounts. Select the equation to model the situation.A.0.04(3,000) + 0.07x = 0.55xB.0.055(3,000 + x) = 120 + 0.07xC.0.04x + 0.07x = 3,000D.0.055(3,000) = 0.04x + 0.07x
Answers
As given by the question
There are given that the total investment money is $3000 and earns 4% annual interest.
Now,
x dollars in an account that earns 7% and that earns 5.5% interest for both accounts.
Then, for the equation
Assuming that the money is invested at simple interest for one year,
We have:
[tex]\begin{gathered} 0.04(3000)+0.07x=0.055(3000+x) \\ 120+0.07x=0.055(3000+x) \end{gathered}[/tex]Hence, the correct option is B
Answer:
B- .0.055(3,000 + x) = 120 + 0.07x
Period Kuta Software - Infinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Sarandha cedules Date 220 21 1) n+1-3 or 4n
Answers
n+1< -3
n< -3 -1
n<-4
-4n< - 8
n>-8/-4
n > 2
so, the solution is,
n < - 4 or n > 2
find inverse of function f(x)=3/x+2
Answers
You need a common numerator in order to add or subract two fractions.
O True
O False
Answers
Answer: False
Step-by-step explanation:
You need a common denominator (the bottom number)