The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to
(y)/ (y +x).
As given in the question,
Given complex fraction is equal to [tex]\frac{1}{1+\frac{x}{y} }[/tex]
Simplify the given complex fraction by taking the least common multiple of the denominator,
[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]
Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to (y)/ (y +x).
Learn more about simplification here
brainly.com/question/2804192
#SPJ4
7/8 add 1/2 in fractions
Answer:
so first we should find LCM of the denominator.and then find the answer
[tex] \frac{7}{8} + (\frac{1}{2} \times 4) = \: \: \: \frac{7}{8 } + \frac{4}{8 } = \frac{11}{8} or1 \frac{3}{8} [/tex]
- 7 (4 - r) = 35 what's the correct answer?
Answer:
9
Step-by-step explanation:
- 7 (4 - r) = 35
First you need to do the parentheses
-7 times 4 is -28
-7 times -r is 7r
-28+7r=35
add 28 to both sides
7r=63
r=9
Answer:
r=9
Step-by-step explanation:
-28+7r=35, rearrange to put like terms together
7r=35+28, 7r=63, divide both sides by 7 to get r
r=63/7, r=9
mark me brainliest if it helped
write the equation of the perpendicular bisector of the line segment containing the points (2,-1) and (-4,3)
Answer: y = 3x/2 + 5/2
Step-by-step explanation:
Write the slope formula m = y2 - y1
x2 - X1
Substiue { x1 = 2
{ x2 = -4 Into m =3 - (-1)
{ y1 = -1 -4 - 2
{ y2 = - 3
Calculate and you get m = -2/3
Slope of the line that is perpendicular to m = -2/3 is m = 3/2
Substitute it: ( 2 - 4 -1 + 3 )
2 2
Calculate it 2 - 4
2
Simplify -2/2 and you get -1
Calculate -1 + 3
2
Simplify it 2/2 and you get 1
Rewrite solutions as coordinates: (-1 , 1)
Substitute { m = 3/2
{ x = -1
{y = 1
y = mx + b
Calculate 1 = 3/2 x (-1)= b and you get b = 5/2
Lastly Substitute { m = 3/2 into y = mx + b
{ b = 5/2
Answer: y +3x/2 + 5/2
Write the equation of the line in slope-intercept form.
y-5x=16
The equation of the line in slope-intercept form is y = 5x + 16 .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is y - 5x = 16 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
y - 5x = 16
On adding 5x on both sides in above equation, we will get
y = 5x + 16 equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 5
Intercept = c = 16
The equation of the line in slope-intercept form is y = 5x + 16 .
To know more about Slope Intercept Form refer to the link:
https://brainly.com/question/19440459
#SPJ4
A- x = 4, PQ = 8, QR = 13
B- x = 5, PQ = 10, QR = 11
C- x = 4, PQ = 12, QR = 9
D- x = 4, PQ = 10, QR = 11
The ratio of 12.9 is equal to the ratio of 1/3 to
A. 1/4
B. 1
C. 5/4
D. 2
E. 4
The ratio of 12:9 is equal to the ratio of 1/3 to 1/4.
As given in the question,
Given ratio is equal to 12:9
Simplify the given ratio by factorizing it :
12 : 9 = 12 / 9
⇒12 : 9 = ( 4 × 3 ) / ( 3 × 3)
⇒ 12 : 9 = 4 / 3
⇒ 12 : 9 = 1 / 3 × 4 / 1
⇒ 12 : 9 = 1 /3 to 1/ 4
Therefore, the ratio of 12 : 9 is equal to the ratio of 1/3 to 1/4.
The complete question is:
The ratio of 12:9 is equal to the ratio of 1/3 to
A. 1/4
B. 1
C. 5/4
D. 2
E. 4
Learn more about ratio here
brainly.com/question/13419413
#SPJ4
Which of the following equations have exactly one solution?
Choose all answers that apply:
-5x+12=5a-5
-5x+12= -12x - 12
-52125 12
or 12 Nữ 12
You might need: Calculator
Show Calculator
The following equations have exactly option (A) and option (B) and option (C) are correct answers.
option (A) ⇒ -5x + 12 = 5x - 5 ⇒ x = 17/10 is correct equation.
option (B) ⇒ -5x+12= -12x - 12 ⇒ x = -24/7 is correct equation.
option (C) ⇒ -5x+12= 5x + 12 ⇒ x = 0 is correct equation.
Based on given equations, formulate,
(A). -5x + 12 = 5x - 5
Calculate the expression,
-5x + 12 = 5x - 5
-5x - 5x = -5 - 12
We can sum or difference the values,
-10x = -17
x = -17/-10
We can divide the product,
x = 17/10
(B). -5x+12= -12x - 12
Calculate the expression,
-5x + 12 = -12x - 12
-5x + 12x = -12 - 12
We can sum or difference the values,
7x = -24
We can divide the product,
x = -24/7
(C). -5x+12= 5x + 12
Calculate the expression,
-5x + 12 = 5x + 12
-5x - 5x = 12 - 12
We can sum or difference the values,
-10x = 0
We can divide the product,
x = -0/10
x = 0
(D). -5x+12 = -5x - 12
Calculate the expression,
-5x+12 = -5x - 12
-5x + 5x = -12 - 12
12 = -12
Therefore,
The following equations have exactly option (A) and option (B) and option (C) are correct answers.
Hence,
option (A) ⇒ -5x + 12 = 5x - 5 is correct equation.
option (B) ⇒ -5x+12= -12x - 12 is correct equation.
option (C) ⇒ -5x+12= 5x + 12 is correct equation.
To learn more about visit Equation problems :
brainly.com/question/2292179
#SPJ1
Among a town’s registered voters, there are 34% Democrats and 25% Republicans. The rest are Independents. If there are 1517 registered Independent voters in this town, how many total registered voters are there?
The total number of registered voters is 3700.
What is the total number of registered voters?
Percentage can be described as the fraction of a number expressed as an amount out of 100. Percentage is a measure of frequency. The sign that is used to represent percentages is %.
The first step is to determine the percentage of independent voters.
Percentage of independent voters : 100 - (percent of democrats + percent of republicans)
100 - (34% + 25%)
100- 59% = 41%
Total number of voters = number of independent voters / percentage of independent voters
1517 / 41%
1517 / 0.41 = 3,700
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
Peter pays 6% interest on his $30,000 college loan and 7% interest on his $12,000 car loan.
What average interest rate does he pay on the total $42,000 he owes?
Round your answer to the nearest tenth of a percent.
Answer:
12,000 for college 7.5,000 in car whe he pays around 20k for that
Write algebraic expressions for two numbers with a sum of -13. Let one of the numbers be represented by x. If one number is represented by x, how would the other number be represented?
Answer:
If a sum of 2 numbers is -7 and one is x then you can write it down as X + Y = -7, or you can write it then ... Let one of the number be represented by x.
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Combining a coin toss and a roll of a die makes a simple event.
False , Combining a coin toss and a roll of a die makes a simple event.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.False , Combining a coin toss and a roll of a die makes a simple event.
A true statement is "For data at the interval level, you CAN calculate meaningful differences between data entries."
Learn more about probability
brainly.com/question/11234923
#SPJ4
Give an example of a sequence that is not an arithmetic sequence.
The sequence 2, 3, 5, 6..is example of the sequence which is not in arithmetic sequence AP.
What is the AP sequence (arithmetic progression)?In Arithmetic Progression (AP), the distinction between two arithmetical orders is a constant. It is also known as Arithmetic Sequence.
Then we'd run into some important words in AP, such as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be described using common distinctions, as shown below.
The following is the way to determine an AP's n-th term: an = a + (n − 1) × dThe formula for arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' is d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the question;
Consider any sequence. Let's say 2, 3, 5, 6..
Let's consider the first term is'a₁' = 2.
Let's consider 'a₂' = 3 is the second term.
Let's consider the third term is 'a₃' = 5.
Let's consider the fourth term be 'a₄' = 6
d₁ = a₂ - a₁
Substitute the values;
d₁ = 3 - 2 = 1 ........(equation 1)
Now take the other set;
d₂ = a₃ - a₂
d₂ = 5 - 3 = 2 .......(equation 2)
From the two equations 1 and 2. it is clear that the value of both common difference d₁ is not equal to d₂. Thus, the sequence considered is not in AP.
Therefore, the considered sequence 2, 3, 5, 6.. is not in AP.
To know more about the arithmetic progression, here
brainly.com/question/6561461
#SPJ4
Write an algebraic expression for the verbal phrase. The quotient of 5 times
a number and 3.
Answer:
(5x)/3
Step-by-step explanation:
5 times a number is 5x.
Quotient means to divide, so the answer is (5x)/3.
Mila buys cookies and oranges at the store.
She pays a total of $22.39.
She pays a total of $6.58 for the cookies.
She buys 3 bags of oranges that each cost the same amount.
Write and solve an equation which can be used to determine xx, how much each bag of oranges costs.
The equation that can be used to represent the cost of oranges and cookies is; 6.58 + 3x = 22.39. Thus, the cost of each bag of orange is x = $5.27
How to Solve Algebra Word Problems?We are given;
Total Amount paid by Mila = $22.39.
Amount Mila paid for cookies = $6.58
Now, we are told that she also buys three bags of oranges. Now, if we denote the cost of each bag of orange to be x, then it means that;
Cost of 3 bags of oranges = $3x
Thus, we can write the equation to represent the cost of oranges and cookies as;
6.58 + 3x = 22.39
Subtract 6.58 from both sides to get;
3x = 22.39 - 6.58
3x = 15.81
x = 15.81/3
x = 5.27
Thus, the cost of each bag of orange is x = $5.27
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
ALGEBRA Simplify 4(3 x-2)(2 x+4)+3x² + 5x-6
F 9x² + 3x - 14
H 27x² + 37x - 38
G 9x² + 13x - 14
J 27x² + 27x - 26
The simplified form of the given equation 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6 is [tex]27x^{2} + 37x - 38[/tex].
The branch of mathematics that deal with the study of mathematical symbols and the rules for manipulating those symbols is known as Algebra. Elementary Algebra, Abstract Algebra, Advanced Algebra, Linear Algebra, and Commutative Algebra are sub-branches of Algebra.
Algebra forms the basis for advanced studies in many fields, including science, mathematics, medicine, engineering, and economics.
The given equation is 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6. The step wise simplification of this algebraic equation is as follows :
4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6
= (12x - 8)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6
= [tex]24x^{2} - 16x + 48x - 32 + 3x^{2} + 5x -6[/tex]
= [tex]27x^{2} + 37x -38[/tex]
The simplified form of the given equation 4(3x-2)(2x+4) +[tex]3x^{2}[/tex] + 5x - 6 is [tex]27x^{2} + 37x - 38[/tex].
To know more about Algebraic Expressions refer to the link:
https://brainly.com/question/4344214
#SPJ4
How many days does it take Company C to produce the same number of radios as Company B produces in 6 days?
Answer:
I need a picture of the diagram to answer your question.
Step-by-step explanation:
Find the perimeter of the figure write your answer in simplest form
Answer:
7 1/8
Step-by-step explanation:
Convert 2 3/8 to improper fraction 19/8 and multiply by 3/1. Reduce to lowest terms.
Mr. vincent is setting up 4 obstacle courses at the brookfield middle school field day. each obstacle course has 2 jump rope stations and 2 pogo stick stations. mr. vincent needs x jump ropes at each jump rope station and y pogo sticks at each pogo stick station. pick all the expressions that represent how many jump ropes and pogo sticks mr. vincent needs in all.
Answer:
8x + 8y
Step-by-step explanation:
Each obstacle course has 2 jump rope stations and 2 pogo stick stations.
There are 4 obstacle courses
So total number of jump rope stations = 4 x 2 = 8
Each jump rope station requires x jump ropes
So total number of jump ropes needed = 8x
Each pogo stick stations. requires y pogo sticks
So total number of pogo sticks needed = 8y
Expression to represent how many jump ropes and pogo sticks Mr. Vincent needs in all is
8x + 8y
Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .
The sequence 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, ... is a geometric sequence with common ratio 2.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .
Notice that
a(2) : a(1) = 3/16 : 3/32 = 2
a(3) : a(2) = 3/8 : 3/16 = 2
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 2
Learn more about sequence here:
https://brainly.com/question/12006112
#SPJ4
Answer to part c please
Answer:
X=least=30
Y=greatest=40
(c) 759 TA 50% P to 67° SA Rx° R
Question in the image
Answer:
x = 56
Step-by-step explanation:
assuming you require to find the value of x
the sum of the exterior angles of a polygon = 360°
sum the 6 exterior angles and equate to 360
x + x + x + 67 + 50 + 75 = 360
3x + 192 = 360 ( subtract 192 from both sides )
3x = 168 ( divide both sides by 3 )
x = 56
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?
The function which represents the frog population after x years will be F(x) = [tex]1200 * (0.97)^{x}[/tex]
The population is decreasing at an average rate of 3% per year.
For decrease in population, if the rate is decreasing per year is r%, the initial population is P, after time x the equation to use would be:
net decrease = [tex]P * (\frac{100 - r}{100})^{x}[/tex]
r = Reduction
x = time duration
P = 1200
Reduction rate = 100 - 3 = 97%
Reduction rate will be 97% i.e. 0.97
Reduction after one year = 1200 * 0.97
Reduction after two years = 1200 * 0.97 *0.97
= 1200 * (0.97)²
Reduction rate after three years = 1200 * 0.97 * 0.97 * 0.97
= 1200 * (0.97)³
therefore,
Reduction rate after x years = [tex]1200 * (0.97)^{x}[/tex]
The function representing the frog population after x years is F(x) = [tex]1200 * (0.97)^{x}[/tex]
To know more about function,
https://brainly.com/question/793205
#SPJ1
pls help!!! what do i dooo
Answer:
Save and exit.
Step-by-step explanation:
Just save and exit
Answer: Click the links slowly read or look over the meterials and then make your file(s)
not sure if i helped -^-
Solve for x: 2/3 + 1/3=2x
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] = 2x ( combine fractions on left side )
1 = 2x ( divide both sides by 2 )
[tex]\frac{1}{2}[/tex] = x
Write each of the following functions in a piecewise format and sketch its graph. For each function, find the value(s) of x where one piece ends and another begins (There's 3 problems/ screenshots) (20 pts)
Using the definition of the absolute value function, we have that, for item b, the function and breaking points are given as follows:
y = -3x - 1, x < -0.5.y = x + 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that: (problem 59)
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
The graphs are given at the end of the answer.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
In general terms, we have that:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.Then, for item b, we have that:
|2x + 1| = 2x + 1, x ≥ -0.5.|2x + 1| = -2x - 1, x < -0.5.Then:
y = -3x - 1, x < -0.5.y = x - 1, x ≥ -0.5.The function breaks at x = -0.5.
For item c, we have that:
|2x - 1| = 2x - 1, x ≥ 0.5.|2x - 1| = -2x + 1, x < 0.5.|x + 3| = x + 3, x ≥ -3.|x + 3| = -x - 3, x < -3.Then:
y = -2x - 2, x < -3.y = 4, -3 ≤ x ≤ 0.5.y = 4x + 2, x > 0.5.The function breaks x = -3 and x = 0.5.
For item d, we have that:
|x + 1| = x + 1, x ≥ -1.|x + 1| = -x - 1, x < -1.Hence:
y = -2x - 2, x < -1.y = 2x + 2, x ≥ -1.The function breaks at x = -1.
More can be learned about the absolute value function at https://brainly.com/question/24734454
#SPJ1
Simplify the expression.
8-17 / 12-(-3)
The simplified expression is -3/5.
To simplify the given expression in question, we will solve it step wise. Firstly we will simplify the numerator by performing operation according to the sign. Similar approach will be repeated for the denominator. Then we will write it in fraction form to find the simplified form of expression.
Numerator -
Numerator = 8 - 17
Here subtraction of large number is required form small number, so the result will be subtracted value with negative sign
Numerator = -9
Denominator -
Denominator = 12 - (-3)
Here two negative signs are present, so, we will perform addition and the result will be with positive sign
Denominator = 12 + 3
Denominator = 15
Writing the fraction form -
Expression = -9/15
Dividing the expression by 3
Expression = -3/5
Hence, the simplified expression is -3/5.
Learn more about expression simplification -
https://brainly.com/question/1280754
#SPJ4
find the value of x if RS bisects AB and RS = 36
Answer:
18 + 2y + 6 = 36
2y = 12
y = 6
step explanation:
Since RS bisects AB,
25 - 3x = 2y + 5
25 - 3x = 2(6) + 5 = 12 + 5 = 17
3x = 25 - 17 = 8
x = 8/3
Subtract (4x2-x+6) from (3x² + 5x - 8).
O A. 7x² + 6x - 14
O B. x² + 4x + 2
O C. 7x² + 4x - 2
O D. x² + 6x - 14
Answer:
X^2 -6x+14
Step-by-step explanation:
y=2
How do I graph this
A horizontal line passing through A ( 0 , 2 )
13.a) sketch a graph of a function that has a set of integers as its domain and all integers less than 5 as its range. b) sketch a graph of a relation that is not a function and that has the set of real numbers les then or equal to 10 as its domain and all real numbers greater than -5 as its range
The required function that has a set of integers as its domain and all integers less than 5 as its range is y = -|x| + 5
Given that,
To draw a sketch of a graph of a function that has a set of integers as its domain and all integers less than 5 as its range.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
In order to draw the graph of a function that has a set of integers as its domain and all integers less than 5 as its range.
We add
y = -|x|
For the domain to be all integers
Now, adding 5
Y = -|x| + 5
Thus, the required function that has a set of integers as its domain and all integers less than 5 as its range is y = -|x| + 5.
Learn more about graphs here:
brainly.com/question/16608196
#SPJ1
