Answers
Answer:
[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]
Rewrite the third fraction:
[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]
Apply the difference of two squares to the denominator of the third fraction:
[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]
Therefore the expression can be written as:
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).
Adjust the fractions based on the LCM:
[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]
[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]
Factor out 3 from the numerator:
[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]
Cancel the common factor (a + 6):
[tex]\implies \dfrac{3}{a-6}[/tex]
Therefore:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Related Questions
help me answer this question??
Answers
Part (i)
The square has area of 12*12 = 144 square meters. From that, we carve out four quarter-circles from each corner, as the diagram shows. Imagine that we rearranged the quarter circles so that they would then form a full circle. This circle would have radius 6 (half of the 12 meters), so the area of the circle is pi*r^2 = pi*6^2 = 36pi exactly
The four white sections combine to an exact area of 36pi, which approximates to 36*3.14 = 113.04 square meters. Use more decimal digits in pi to get a better approximation.
Exact answer: 36pi square meters
Approximate answer: 113.04 square meters (when using pi = 3.14)
=======================================================
Part (ii)
Once we know what the white sections combine to, we can subtract that area from the total overall area of 144 m^2
We end up with 144 - 36pi as the exact area of the red section
This approximates to 144 - 36*3.14 = 30.96 m^2
Exact answer: 144 - 36pi square meters
Approximate answer: 30.96 square meters (when using pi = 3.14)
If , what is the truncation error for S4?
Answers
Truncation error for S4 is 0.037.
What is Truncation Error?Truncation errors are defined as the errors formed when we use approximation instead of actual procedures.
Given is a series.
S4 means,
6/(3¹) + 6/(3²) + 6/(3³) + 6/(3⁴)
The actual sum of these values gives,
2 + 0.6666..7 + 0.2222.. + 0.074074...
= 2.962962..
≈ 2.963
Truncation error = 3 - 2.963 = 0.037
Hence the truncation error is 0.037.
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Harry wants to buy a MP3 player that costs $46.95. He has $10.25 in his piggy bank. He gets $4.25 for allowance each week. How many weeks will he have to save to have enough money for the MP3 player? I NEED THIS NOW
Answers
Answer: If Henry wants to buy the MP3 player he needs 9weeks worth of allowance.
Step-by-step explanation:
What is the factor of 3x² 12xy?
Answers
The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. Finally, we divide the y terms, y divided by y is 1. Therefore, the factor of 3x² 12xy is 3x².
The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. This means that the x part of the factor is 3x. Next, we divide the y terms, y divided by y is 1. This means that the y part of the factor is y. When we combine the two parts, 3x and y, we get the factor of 3x². Therefore, the factor of 3x² 12xy is 3x². This means that 3x² is a factor of 12xy, which can be seen by multiplying 3x² by 4y, which results in 12xy. This shows that 3x² is a factor of 12xy.
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How do the faces of
a three-dimensional figure determine che
two-dimensional shapes created by slicing
the figure?
Answers
The process of the faces of a three-dimensional figure determine two-dimensional shapes created by slicing the figure is explained below.
The term three dimensional figure is defined as solid shapes or figures that have three dimensions.
Basically these kind of shapes has length, width and height are the dimensions of 3D shapes and the common names of these shapes are cube, cuboid, cone, cylinder and sphere.
Where as the two dimensional figure is defined as horizontal and vertical axes that is x-axis and y-axis) and it is also known as 2d shapes are flat figures that have only length and width. And thus shapes do not have thickness or height.
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Exponential from Two Points (Level 1)
Write an exponential function in the form y = ab* that goes through points (0, 13)
and (2, 325).
Answers
a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25
b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points
What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variableTo learn more about Exponential function refers to:
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HELP LAST QUESTION......
c) The height of each cylinder in a set of food-storage containers is 30 cm.
The radius of the largest container is 10 cm.
The volume of the smallest container is one-third the volume of the largest
container.
The volume of the middle-sized container is two-thirds the volume of the largest
container. What is the volume of each container?
Answers
Answer:
9424.78cm^3
3141.59cm^3
6282.67 cm^3
Step-by-step explanation:
the equation for a cylinder's volume is pi(r)^2(height)
The volume of the largest cylinder is 3.14(10)^2(30) = 9424.78cm^3 (remember the units!)
The volume of t he smallest cylinder is 1/3 the largest or: 9424.78/3 = 3141.59cm^3 (remember the units!)
The volume of the medium cylinder is 2/3 the largest or 9424.78(2/3) = 6282.67 cm^3
If f(1)=1 f(2)=2 and f(n)=2f(n-1)+3f(n-2) then find the value of f(6).
Answers
Answer:
f(6) = 182
Step-by-step explanation:
f(1) = 1
f(2) = 2
f(3) = 2f(2) + 3f(1) = 2(2) + 3(1) = 4 + 3 = 7
f(4) = 2f(3) + 3f(2) = 2(7) + 3(2) = 14 + 6 = 20
f(5) = 2f(4) + 3f(3) = 2(20) + 3(7) = 40 + 21 = 61
f(6) = 2f(5) + 3f(4) = 2(61) + 3(20) = 122 + 60 = 182
Answer:
-486
Step-by-step explanation:
The radius of a circle is 4 kilometers. What is the circumference?
Answers
Answer:
25.12 kilometers
Step-by-step explanation:
[tex]c = 2\pi \: r[/tex]
C = 2 × 3.14 × 4
C = 25.12
7. The West Warriors scored 25 points. This was 12 points less than the Flinn Falcons.
Write and solve an equation to find how many points the Flinn Falcons scored.
Answers
explanation:
The Flinn Falcons only scored 13 points.
8 x 10000 + 0 x 1000 + 2 x 100 + n + 6 x 1 . what is n
Answers
Step-by-step explanation:
8 × 10000 + 0×1000 + 2× 100 + n + 6 x 1=0
80000 + 0 + 200 + n + 6 =0
80206n = 0
n = -80206
ILL BRAINLIEST YOU PLEASE HELP ME
Answers
Answer:
Step-by-step explanation:
Answer:
Your answer is D
Step-by-step explanation:
Your base is 7cm. The hypotenuse is 2x or 2(7)=14 and the height is x[tex]\sqrt{3[/tex] or 7[tex]\sqrt3[/tex]
Please help due soon pleaseeee!!!!!! Help
Answers
Answer:
see attached
Step-by-step explanation:
Given the pictorial equations, you want to know the single-digit values of each of the images.
EquationsThere are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.
Let the icons be represented by letter variables as follows:
hat = hboot = bsock = stennis shoe = tmitten = mRewriting the equations to standard form, we have ...
h +b -m -s = 0 . . . . . [eq1]
h -b +t = 0 . . . . . . . . [eq2]
b -3s = 0 . . . . . . . . . [eq3]
h -s -t +m = 0 . . . . . [eq4]
h +2s -m = 0 . . . . . . [eq5]
h +b +s -2t = 0 . . . . . [eq6]
SolutionWe can add [eq4] to [eq1] and [eq5] to eliminate the m variable.
(h +b -m -s) +(h -s -t +m) = 0 ⇒ 2h +b -2s -t = 0 . . . . [eq7]
(h +2s -m) +(h -s -t +m) = 0 ⇒ 2h +s -t = 0 . . . . . . . . . [eq8]
Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.
(h +b +s -2t) +(h -b +t) = 0 ⇒ 2h +s -t = 0 . . . . same as [eq8]; no help
(2h +b -2s -t) +(h -b +t) = 0 ⇒ 3h -2s = 0 . . . . . [eq9]
Now, we have 3 equations in 4 unknowns:
b -3s = 0 . . . . . . . [eq3]
3h -2s = 0 . . . . . . [eq9]
2h +s -t = 0 . . . . . [eq8]
The smallest positive integer values that will satisfy [eq9] are ...
h = 2, s = 3
Using these in the remaining equations gives ...
b -3·3 = 0 ⇒ b = 9
2·2 +3 -t = 0 ⇒ t = 7
And we can find m using [eq5]:
m = h +2s = 2 +2·3 = 8
Then the solution is ...
hat = 2boot = 9sock = 3tennis shoe = 7mitten = 8When rolling a fair, eight-ided number cube, determine P(number greater than 4). (A) 0. 25
(B) 0. 50
(C) 0. 66
(D) 0. 75
Answers
The correct answer is (D) 0.75. The probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%
We know that there are 8 possible outcomes when rolling the number cube (1, 2, 3, 4, 5, 6, 7, 8). Of these 8 outcomes, 5 of them are numbers greater than 4 (5, 6, 7, 8). So, the number of favorable outcomes is 5.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: P(number greater than 4) = 5/8. As a decimal, this is 0.625. However, the question asked for P(number greater than 4) which means we have to add 0.125 to 0.625, the answer is 0.75.
Therefore, the probability of rolling a number greater than 4 on a fair, eight-sided number cube is 0.75 or 75%. This means that if we roll the cube many times, we expect 75% of the rolls to be numbers greater than 4.
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What is the value of angle ABC?
Answers
Answer:
74
Step-by-step explanation:
What is Y 1 on a graph?
Answers
The graph of y is a straight line parallel to the x−axis through the point (0,1)
Now, According to the question:
Let's know:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The equation is Y = 1
A straight line in slope (m) and intercept (c) form is:
y = mx + c
y is a straight line of slope 0 and y- intercept of 1
y = 0.x + 1
y = 1
Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)
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ok pls help pls pls pls if you care for the future generation you will me to improve the future
Answers
Answer:
G.
Step-by-step explanation:
$12 is the flat fee and it costs 25 dollars per hour to rent a kayak. x is the number of hours, so 25x+12=y, the total cost for renting the kayak
which expression is equivalent to 36a-12b 4(6a-9b) 4(8a3b) 4(9a+3b) 4(9a-3b)
Answers
Answer:
d). 4(9a - 3b)
Step-by-step explanation:
a). 4(6a-9b)
= 24a - 36b
b). 4(8a-3b)
= 32a - 12b
c). 4(9a+3b)
= 36a + 12b
d). 4(9a - 3b)
= 36a - 12b
What is the Area of an equilateral triangle whose sides are 8 feet long each?
Answers
Answer:
27.71281 ft
Step-by-step explanation:
The height of males aged between 17 and 20 follows a normal distribution, with a mean of 71.1 inches and a standard deviation of 2.3 inches.
If the number of males between ages 17 and 20 is 11.0 million, how many males in this age group have heights between 69 inches and 73 inches?
A)3.6 million
B)4.1 million
C)6.8 million
D)9.7 million
Answers
Answer:
B
Step-by-step explanation:
Mark as Brainliest
Help me please this is due in 10 minutes.
Answers
Answer:
Top left quadrant (Quadrant 2)
Step-by-step explanation:
PIE CHART question, PLEASE dont guess. im USING ALL MY POINTS and brainiest
Answers
Answer
its the last one
Sally’s wallet contains:
5 quarters
3 dimes
8 nickels
4 pennies
A coin is drawn from the purse and replaced 240 times. How many times can you predict that a nickle or a penny will be drawn?
Answers
Answer:
Nickles: 96 times
Penny: 48 times
Step-by-step explanation:
5+3+8+4 = 20 coins in total
20x = 240
x=12 (chance of a coin being picked)
8 nickles(12) = 96
4 pennies(12) = 48
Question 2 of 15
Select the table that represents a linear function (Graph them if necessary)
OA
0123
1437
8 x 0
-
012
#2
203
23
24816
2
m
19
1125
Answers
x| 0 1 2 3
y| 2 0 -2 -4
Step by step
The x values are all +1 rate
The y values are all -2 rate
When the values are a consistent rate or slope, the graph will be linear. See attached graph.
The other 3 tables do not have a consistent rate or slope
Robin tosses a pair of 6-sided dice. The odds in favor of the sum of the 2 dice rolls being greater than 8 are 5:13.
What is the probability that the sum of the 2 dice rolls will not be greater than 8?
Answers
The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.
How to evaluate for the probabilityWhen the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.
the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13
then;
probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13
probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13
probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13
Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13
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What is the additive inverse of a 3 by 2 by 3?
Answers
The Additive inverse of 3/2 is -2/3.
Additive Reciprocal
An additive reciprocal is a number that is added to a given number to bring the sum to zero. For example, adding -3 to the number 3 will result in zero. So the additive reciprocal of 3 is -3. In our daily life, we come across situations where we cancel the value of a quantity by forming its additive reciprocal.
Additive Reciprocal in Fraction:
The additive reciprocal of the fraction a/b is -a/b and vice versa. This is because a/b + (-a/b) = 0. The additive reciprocal of a positive fraction is the same fraction with a negative sign, but for negative fractions the additive reciprocal is the same fraction without a negative sign.
Given, the number is 2/3
We have to find the additive inverse of the given number.
In mathematics, the additive inverse of a number ‘a’ is the number that, when added to ‘a’, yields zero.
So, 2/3 + (-2/3)= 0
Therefore, the additive inverse of 2/3 is -2/3.
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Someone help please, picture attached
Answers
Answer:
6
Step-by-step explanation:
x² + 8² = 10²
x² + 64 = 100
x² = 36
x = 6
Is 5 an algebraic term?
Answers
5 is not an algebraic expression.
Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.
It follows that 5 cannot be an algebraic expression.
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Which of the following statements correctly describes the graph? A. The graph represents a nonlinear function with a constant rate of change. B. The graph represents a nonlinear function with an increasing rate of change. C. The graph represents a linear function with a constant rate of change.
Answers
The statement that correctly describes the graph is given as follows:
C. The graph represents a linear function with a constant rate of change.
How to classify the functions as linear or non-linear?A function is classified as linear or non-linear depending on the rate of change of the function.
If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.
Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.
As the graph presented at the end of the answer shows a linear function with constant slope, it has a constant rate of change, thus it is linear and option c is correct.
Missing InformationThe graph is given by the image presented at the end of the answer.
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help lol, will mark brainlest
Answers
a=11
Hope this Helped! :T