Answers
Answer:
1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0
Step-by-step explanation:
You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.
SimplificationThe expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.
[tex]\dfrac{1}{a^2+ab}+\dfrac{1}{ab+b^2}=\dfrac{1}{a^2+ab}\cdot\dfrac{b}{b}+\dfrac{1}{ab+b^2}\cdot\dfrac{a}{a}=\dfrac{b+a}{a^2b+ab^2}\\\\=\dfrac{a+b}{ab(a+b)}=\boxed{\dfrac{1}{ab}\quad a\ne0,b\ne0,(a+b)\ne0}[/tex]
The given conditions ensure the denominator(s) will not be zero.
Related Questions
What fraction of an inch is 1 millimeter? Show reasoning
Answers
The fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.
How to convert inch to millimeter?One inch is equivalent to 25.4 millimeters internationally.
Expressing this relationship as a formula is as follows.
1 inch = 25.4mm
This official, standardized measurement has been used in international records since 1959.
Both inches and millimeters are units of measurement. Inches belong to the British system of units, and millimeters belong to the metric system of units.
Inches are used in the United States, but it is often necessary to convert this unit of measurement to a metric unit of measurement, such as "millimeters." for scientific purposes. Conversely, there are 0.0393700787402 inches in millimeters.
Thus , the fraction of an inch in 1 millimeter is given by 1mm = 0.03937008 inches.
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Stats Determine the y-intercept and slope from the equation: y = 5.8 +2.5x
Answers
The slope is 2.5
The y-intercept is 5.8.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = 5.8 + 2.5x
This is in the form of y = mx + c
So,
m = 2.5
And,
The y-intercept is when x = 0.
So,
y = 5.8 + 2.5x
Substitute x = 0,
y = 5.8
Thus,
Slope is 2.5
The y-intercept is 5.8.
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You place one grain of rice on the first square of a chess board. You then put two on the second,
four on the third, eight on the fourth, and so on until you've reached the sixty-fourth square.
If Scrooge McDuck bought five-pound bags of enriched white rice from Walmart, could he afford
to buy all the rice needed for the previous paragraph?
Answers
Answer:
yes
Step-by-step explanation:
j is the midpoint of HI and GH. complete the proof that GHJ ≅ GIJ
Answers
4. Reflexive property
5. SSS
O REAL NUMBERS
Signed fraction multiplication: Basic
Multiply.
(-9) (-7/3)
Write your answer in simplest form.
Answers
Answer:
21
Step-by-step explanation:
(-9)([tex]-\frac{7}{3}[/tex]) = 63/3 = 21
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answers
Answer: 39%
Step-by-step explanation:
using calculator
1 seat = 0.058%
1700 - 1037 = 663 seats are taken.
0.058% x 663 seats = 39%
Can someone pls help me?
What is the initial value of the function?
Answers
The initial value of the function is 1.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
A relationship in which one input value exactly equals one output value is known as a function. A function's initial value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.
The line intersects the y-axis at (0,1).
The initial value of the function is 1.
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The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answers
Answer: Given the ratio of boys to girls at the park is 4 to 5, then there are 4 boys for every 5 girls. If there are 45 girls at the park, then there are 4 * 45 / 5 = 36 boys at the park.
So, the answer is B) 36.
Step-by-step explanation:
show that the following function are continuos and discontinuos
A.(f×)={×+1 ,for×less than or equai to 2
{ 2×–1 ,for 1<×<2
{×–1 ×<1
Answers
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = [tex]\lim_{x\to1^-}[/tex] f((h - 1)) = [tex]\lim_{h \to 0}[/tex] (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = [tex]\lim_{x\to1^+}[/tex] f(h + 1) = [tex]\lim_{h \to 0}[/tex] (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Solve x - 5 = 8 - 4x
Answers
Answer:
Step-by-step explanation:
x - 5 = 8 - 4x
rearrange
x - 5 = -4x + 8
x + 4x - 5 = -4x + 4x + 8
5x - 5 = 8
5x - 5 + 5 = 8 + 5
5x = 13
Divide by 5
5x/5 = 13/5
x = 13/5 or 2 [tex]\frac{3}{5}[/tex]
or 2.6 as a decimal
Area of composite shapes, There is a pair of parallel sides in the following shape.
What is the area of the shape?
Answers
The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².
What does mathematicians mean by area?Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.
The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.
So, 1/2 * ( 9+5) * 3
= 1/2 * 14 * 3
= 1/2 * 42
= 21 cm²
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If a seed is planted, it has a 95% chance of growing into a healthy plant.
If 7 seeds are planted, what is the probability that exactly 4 don't grow? Round answer to 4 decimal places.
Answers
The probability that exactly 4 out of 7 seeds planted do not grow is 0.0007 (approximately), given that each seed has a 95% chance of growing into a healthy plant.
Calculating the probability of a specific outcome using the binomial distribution formula.The probability that a seed doesn't grow is 1 - 0.95 = 0.05.
To calculate the probability that exactly 4 seeds don't grow out of 7, we need to use the binomial distribution formula, which is:
P(X=k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]
where:
X is the random variable representing the number of seeds that don't grow.
k is the specific number of seeds that don't grow (in this case, k=4)
n is the total number of seeds planted (n = 7)
p is the probability that a seed doesn't grow (p=0.05)
C(n,k) is the number of ways to choose k items out of n, also known as the binomial coefficient.
Plugging in the values, we get:
P(X=4) = C(7,4) * 0.05⁴ * 0.95³
= 35 * 0.00000625 * 0.857375
= 0.0006522
Rounding to four decimal places, the probability that exactly 4 seeds don't grow is 0.0007 (approximately).
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NEED HELP ASAP!!!!
Task EXPONENTIAL GROWTH AND DECAY
Question 1 Part A:
A consulting company wants to track the results of its new
marketing plan. The media manager recorded the number of views Weeks, x
for one of the company's online videos. The results from the first 4
weeks are shown in this table.
0
Write an equation to model the relationship between the number of weeks,
x, and the number of views, f(x).
Double click and enter the correct answer in the box by replacing the values
of a and b.
<||►
-f(x) = a(b)*
I
1
2
3
4
Views, f(x)
2,160
3,240
4,860
7,290
10,935. Question 1 Part B:
During this same time, the website manager tracked the number of visits to the website's homepage.
She found that before launching the new marketing plan, there were 6,400 visits.
Over the course of the next 4 weeks, the number of site visits increased by a factor of 1.25 each week.
Write an equation to model the relationship between the number of weeks, x, and the number
of site visits, f(x).
Double click and enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)*.
Question 1 Part C
During their team meeting both managers shared their findings. Complete the statement describing their combined results.
Double click and highlight the correct answers
• the initial number of video views was - fewer than, the same as, more than- the initial number of site visits
• The number of website visits grew by a - smaller factor than, larger factor than, the same factor as- the number of video views.
• The difference between the total number of website visits and video views after 4 weeks is - 10,935, 4,690, 8,726, 15,625
Answers
f(x) = a(b)*.
Question 1 Part C
During their team meeting both managers shared their findings. Complete the statement describing their combined results.
Double click and highlight the correct answers
• the initial number of video views was - fewer than, the same as, more than- the initial number of site visits
• The number of website visits grew by a - smaller factor than, larger factor than, the same factor as- the number of video views.
• The difference between the total number of website visits and video views after 4 weeks is - 10,935, 4,690, 8,726, 15,625
Answer:
10,935, 4,690, 8,726, 15,625
Step-by-step explanation:
On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.
Answers
The second telephone pole is 72 feet tall. Since the ratio of the height of the first telephone pole to the length of its shadow is 24/6 = 4.
We can use this ratio to find the height of the second telephone pole.
If the second telephone pole casts a shadow of 18 feet at the same time of day, we can set up the following proportion:
height of second pole / length of shadow of second pole = height of first pole / length of shadow of first pole
Letting x be the height of the second pole, we can plug in the values we know and solve for x:
x / 18 = 24 / 6
Multiplying both sides by 18, we get:
x = 72
Therefore, the second telephone pole is 72 feet tall.
The answer is (e) 72.
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Complete question:
On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.
a. 6
b. 12
c. 24
d. 36
e. 72
The height of two buildings is 34 m and 29 m respectively. If the distance between the two buildings is 12 m, find the distance between their tops.
Answers
Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.
Let's call the horizontal distance between the two buildings "d".
d^2 = 12^2 + (34 - 29)^2
d^2 = 144 + 25
d^2 = 169
d = 13
So, the horizontal distance between the two buildings is 13 meters.
To find the distance between their tops, we simply add the height of each building:
distance = 34 + 29 = 63 meters
So, the distance between the tops of the two buildings is 63 meters.
Step-by-step explanation:
The sum of one and six times a number is 151. What is the number?
Answers
This is a word problem and the value of the unknown number is equal to 25
Word problems in mathematicsWord problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.
Let us represent the unknown number with the letter x so that we derive the equation;
1 + 6x = 151
we subtract 1 from both sides of the equation
1 - 1 + 6x = 151 - 1
6x = 150
divide through by the coefficient of x which is 6
6x/6 = 150/6
x = 25
Therefore, the value of the unknown number for the word problem is equal to 25
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Is 2/3 equal or bigger than 1/2
Answers
Answer: 1/2 is
Step-by-step explanation:
In a fair out of 5 people 2 are men and 2 are women and the remaining are children there are 2500 people at the fair. what percentage of people are adult?
Answers
Answer:
Step-by-step explanation:
4 out of the 5 people are adults (since 2 women and 2 men) therefore 80% of people are adults.
Answer:
80%
Step-by-step explanation:
Its either too easy or too hard. 2+2=4 obviously, and 4/5=8/10. 8/10, 0.80, or 80% is the answer. If I got this right I don't know how lol.
please help with explanation
Answers
The answer to the question on the value of x in a triangle is x = 60 degrees.
What is the value of x ?The fact that all the angles are labeled as x means that this is an equilateral triangle which is a triangle where all the angles are equal.
Should this be the case, the value of x would be:
= Sum of interior angles of triangles / Number of sides in triangle
Sum of interior angles of triangles = 180 degrees
Number of sides = 3 sides
The value of x is:
= 180 / 3
= 60 degrees
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a triangle has ___ , ___ and ____ .
Use an appropriate modification of the law of cosines to find the angle in degrees. assign the result to q4.
Answers
A triangle has three sides, three angles, and three vertices (also known as corners).
What is a Triangle?A triangle is a geometric shape that consists of three line segments that connect three non-collinear points.
Each of these line segments is called a side of the triangle. The three points where these sides meet are called the vertices (singular: vertex) of the triangle.
The triangle also has three interior angles formed by its sides. These angles are located inside the triangle, and their sum is always equal to 180 degrees.
In summary, a triangle is defined by its three sides, three angles, and three vertices.
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A certain model car has a keypad with 5 numbers on the door. To open the door, 5 numbers must be entered in the correct order and no number can be used more than once. What is the probability that someone could guess the correct code?
Answers
Answer:
Step-by-step explanation:
The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.
To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.
So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.
What is the solution to the equation?
2(x + 7) 2/3 = 8
Answers
Answer: x = -1
Step-by-step explanation:
simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there
Find the magnitude and vector
-22.2m
12.6m
Answers
The magnitude of the vector is 25.5 metres.
How to find magnitude of a vector?The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
| N | = √22.2² + 12.6²
| N | = √492.84 + 158.76
| N | = √651.6
| N | = 25.5264568634
| N | = 25.5 metres
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In 2015, there were about 22 million teenagers (aged 13–17) in the United States. They each sent an average of 800 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation.
Answers
The number of text messages all of the teenagers in the United States send each month is 17600 million.
What are integers?In mathematics, an integer is a grouping comprising both positive and negative numbers. Integers are similar to whole numbers in that they do not include the fractional portion. Integers are thus numbers that can be positive, negative, or zero but not fractions. All mathematical operations, including addition, subtraction, multiplication, and division, can be carried out on integers.
Given that,
Number of teenagers = 22 million
Text sent on average = 800
Total messages sent = (22)(800) = 17600 million
Hence, the number of text messages all of the teenagers in the United States send each month is 17600 million.
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Help me find the area of the regular polygon!!
Answers
The area of the polygon is 6x√3 / 3 units².
How to find the area of a polygon?The polygon above is a triangle. The polygon has three sides. Therefore, the area of the polygon can be calculated as follows:
area of the polygon = 1 / 2 pa
where
a = apothemp = perimeter of the polygonTherefore, the perimeter of the polygon is the sum of the whole sides. The sides of the polygon is the same. Hence, the perimeter is 3x.
where
x = side of the polygonarea of the polygon = 1 / 2 × 3x × 4√3 / 3
Hence,
area of the polygon = 3 / 2 x × 4√3 / 3
area of the polygon = 6x√3 / 3 units²
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All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
Answers
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
Explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this case,
the set comprises of all figures higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This predicts that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
Thus, in set builder form, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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Provide evidence of how you manage your staff to manage complain
Answers
One way to manage your staff to manage complaints would be to establish clear procedures for handling complaints and regularly train staff on these procedures.
How to manage staff complaints ?Establishing clear procedures for handling complaints and training staff helps to ensure that all complaints are handled consistently and effectively, reducing the potential for misunderstandings or conflicts to arise.
Additionally, creating an open-door policy for staff to voice their concerns and providing regular opportunities for feedback can help to identify and address issues before they escalate into complaints. Regular communication and coaching can also help to build strong working relationships and foster a positive workplace culture, reducing the likelihood of complaints in the first place.
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HELPPPP
Mr. Hagan writes an equation on the board.
8k−14=−4k+10+12(k−2)
Which statement is true about Mr. Hagan’s equation when solving for k?
A. The equation has exactly one solution.
B. The equation has exactly two solutions.
C. The equation has infinitely many solutions.
D. The equation has zero solutions.
Answers
C - this equation is simplified to a numeric identity. the variable has infinite solutions.
8k - 14 = -4k + 10 + 12(k - 2) --> use distributive property
8k - 14 = -4k + 10 + 12k -24 --> combine like terms
8k - 14 = 8k -14 --> combine like to each side
8k - 8k = -14 + 14 --> simplify
0 = 0
note, the variable cancels out, therefore there is no identity and ANY numeroc value can be used, as ant value will cancel itself out.
this means there is an infinite numbers of solutions.
Simplify imporper fractions as mixed number 14 1/4 -10 3/7 =
Answers
The value of the expression [tex]14\frac{1}{4} -10\frac{3}{7}[/tex] is 107/28.
What is Fraction?A fraction represents a part of a whole.
The given expression is [tex]14\frac{1}{4} -10\frac{3}{7}[/tex]
A proper fraction is a fraction that has no whole number part and its numerator is smaller than its denominator.
An improper fraction is a fraction that has a larger numerator than denominator and it represents a number greater than one.
[tex]14\frac{1}{4}[/tex] to improper fraction is 57/4
[tex]10\frac{3}{7}[/tex] to improper fraction is 73/7
Now 57/4-73/7 we have to solve
LCM of 4 and 7 is 28
399-292/28
107/28
Hence, 107/28 is the value of the expression [tex]14\frac{1}{4} -10\frac{3}{7}[/tex]
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To build a new skate park, a community board must have at least 50% of the voters agree to the build. At a recent voters meeting, 125 voters were asked if they would vote for the new skate park and 72 responded yes. Should the community board go ahead and start planning the park?
No, they should not plan for the skate park because the sample had about 42.4% people vote no.
No, they should not plan for the skate park because the sample had about 57.6% people vote no.
Yes, they should plan for the skate park because the sample had about 42.4% people vote yes.
Yes, they should plan for the skate park because the sample had about 57.6% people vote yes.
Answers
The solution is Option D.
The skate park should be build as the percentage of votes was 57.6 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage of votes be represented as A
Now , the skate park will be built if the percentage of votes is greater than 50 %
Now , the total number of voters = 125 voters
The number of voters who responded to building the park = 72 voters
Substituting the values in the equation , we get
A = ( number of voters who responded to building the park / total number of voters ) x 100
On simplifying the equation , we get
A = ( 72 / 125 ) x 100
A = 0.576 x 100
A = 57.6 %
And , A > 50 %
Therefore , they should plan for the skate park because the sample had about 57.6% people vote yes
Hence , the percentage of votes is 57.6 %
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