The sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x) and the type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.
To find f(x) + g(x), we need to add the two functions together:
f(x) + g(x) = (x+2)/(x²-9) + 11/(x²+3x)
To add these fractions, we need a common denominator.
The common denominator in this case is (x² - 9)(x² + 3x), which is the product of the denominators.
Rewriting the fractions with the common denominator, we have:
f(x) + g(x) = [(x+2)(x² + 3x)]/[(x²-9)(x² + 3x)] + [11(x²-9)]/[(x²-9)(x² + 3x)]
Combining the fractions, we have:
f(x) + g(x) = [(x+2)(x² + 3x) + 11(x²-9)]/[(x²-9)(x² + 3x)]
Simplifying the numerator:
[(x+2)(x² + 3x) + 11(x²-9)] = (x³ + 5x² + 6x + 11x² - 99)
= (x³ + 16x² + 6x - 99)
Therefore, the sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x).
The excluded values for the function f(x) are x = ±3, and for the function g(x), the excluded value is x = 0.
The type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.
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Find the unknown 9,006-7,474?
A banner is made of a square and a semicircle. The square has side lengths of 22 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.
Answer:
673.97 in²
Step-by-step explanation:
Area Square: l²
22 x 22484Area Semi Circle: 1/2(πr²) using 3.14 for π
1/2(3.14*11*11)1/2(379.94)189.97Total Area:
189.97 + 484673.97-Chetan K
Answer:
673.42
Step-by-step explanation:
You have to put3;4 and divided by 22 inches
Greg has 4 shirts: a white one, a black one, a red one, and a blue one. He also has two pairs of pants, one blue and one tan. What is the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants? Show your work. (10 points)
MARKING BRINLIEST AND GIVING A LOT OF POINTS PLSSSS HELP
The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.
To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.
Total number of Outfit Combinations:
There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.
No of favourable options:
As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .
Probability = Number of favourable outcomes/Total no. of combinations
Probability = 1/8
Probability = 0.125 or 12.5%
Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.
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10 = 3/5 (x+5) simplified ??
Answer:
35/3 is your answer
Step-by-step explanation:
also if you want it in decimal form its 11.6
If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? Explain your answer. Company A: Using linear regression models from both data sets, she determines that it pays about $14 more. Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more. Company B: Using linear regression models from both data sets, she determines that it pays about $10 more. Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.
Answer:
B
Step-by-step explanation:
Answer:
Company A
Step-by-step explanation:
She should work for company A because they pay the most. Also because she would earn $308 during 22 hours. Hopes this helps! :)
Please help me to do this i really need it.
First correct Answer gets Brainliest.
Answer:
Step-by-step explanation:
-3≤ x = graph 6
-3 > x = graph 3
x≥ 3 = graph 2
x ≤ 3 = graph 4
3 > x = graph 1
x > 3 = graph 5
the closed circles means greater/less than or equal to
the open circle means greater/less than
the direction of the arrow tells you if the number is greater than x or less than x
Solve the following system of equations. 4x + 3y = -5
- 3x + 7y=13
Answer: 13
Step-by-step explanation:
4x+3y=-5 solve x :
4x = -3y + -5 | -3y
1x = -0.75y + -1.25 | : 4
-3x + 7y = 13 solve x :
-3x + 7y = 13 | -7y
-3x = -7y = 13 | : (-3)
Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333
-0, 75y - 1,25 = 2,333y - 4, 333 solve y:
-0, 75y - 1,25 = 2,333y -4, 333 | -2,333y
-3, 083y - 1,25 = -4,333 | + 1, 25
-3. 083y = -3,088 | : (-3, 083)
y = 1
Plug y = 1 into the equation 4x + 3y = -5 :
4x + 3 · 1 | Multiply 3 with 1
4x + 3 = -5 | -3
4x = -8 | : 4
x = -2
So the solution is:
y = 1, x = -2
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Find the value of n in the following
equation. Give your answer as a
decimal.
n+3.1:6.4= 96
What is the first step in graphing a line that has a linear equation in slope intercept form? Question 2 options: Plot the point on the y-intercept Find the slope Draw your line Use your table
The first step in graphing a line that has a linear equation in slope intercept form include the following: B. find the slope.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
In conclusion, you should first of all calculate the slope of a line in order to graph it in slope-intercept form.
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binary add:
(e) 10110₂ +1010₂ = (?)
Answer:
278,861,394
Step-by-step explanation:
put in the calculator e but then just square the numbers add it and there is your answer
You choose a marble from the bag. What is the probability you will NOT choose blue?1/25/72/72
Given a sample and required to get the probability of a particular outcome, we make a couple of considerations including:
- Sample Space: The universal set
- Required Outcome
We can identify these variables as:
Sample space: total number of marbles = 7
Required outcome: Not blue = 7 - 2 = 5
Probability is given as:
\(\begin{gathered} P=\text{ }\frac{\text{number of required outcome}}{Sample\text{ space}}=\frac{5}{7} \\ P=\frac{5}{7} \end{gathered}\)How many terms are in the expression when simplified
Answer:
There are four (4) different terms
Step-by-step explanation:
Given;
2x + 3xy - (x + y) + 2
The terms are simplified as follows;
=2x + 3xy - (x + y) + 2
= 2x + 3xy - x - y + 2
collect like terms;
= 2x - x - y + 3xy + 2
= x - y + 3xy + 2
Thus, there are four (4) different terms in the simplified expression.
HELP
If 10% of x is 20, what is 23% of x?
Answer:
46
Step-by-step explanation:
Answer:
46
According to question,
10% × x = 20
x = 20 ÷ 10%
x = 20 ÷ 0.1
x = 200
Now find 23% of x
23% × 200
0.23 × 200
46
h(x)=√1407.3x
Find h(2.2). Round to the nearest hundredth.
The correct answer to the given mathematical function is 82.530.
What is a mathematical function?
The network of the function, a common method of illuminating the function, is the set of all pairings (x, f (x)) that uniquely represents a function. Each such pair can be considered the Cartesian dimensions of a point inside the plane whenever the domain and also the codomain are subsets of real values.In research, engineering, and the majority of the branches of mathematics, functions are frequently utilized. Functions are allegedly "the main objects of inquiry" in the majority of mathematical disciplines.Given that,
\(h(x) = \sqrt{1407.3 x}\)
Putting x= 2.2 in given mathematical function, we will get,
\(h(2.2) = \sqrt{1407.3\ X\ 2.2}\)h(2.2)= √1407.3(2.2)
=82.530
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How to find derivative of x^5(1- (5/x+8))
Answer:
\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)
Step-by-step explanation:
\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)
Drag and drop the answers into the boxes to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A sequence of transformations that maps △DEF to △D′E′F′is a Response area followed by a Response area.
The two right triangles are on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 with an increment of 1. The vertical y-axis ranges from negative 5 to 5 with an increment of 1. A dashed triangle has vertex F prime at begin ordered pair 0 comma 1 end ordered pair, vertex D prime at begin ordered pair 1 comma 1 end ordered pair and vertex E prime at begin ordered pair 1 comma 4 end ordered pair. A solid triangle has vertex F at begin ordered pair negative 1 comma negative 1 end ordered pair, vertex D at begin ordered pair negative 2 comma negative 1 end ordered pair and vertex E at begin ordered pair negative 2 comma negative 4 end ordered pair.
A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.
Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation
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A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
What is the sequence of transformations?The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.
The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.
Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.
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2 more than n is the quotient of n and 6
Answer:
6n+2
Step-by-step explanation:
3/5 t =6
Pls help I’ll brainlest
Find the midpoint of AB if a (-1,7) and B (11,-1)
Answer:
(5, 3)Step-by-step explanation:
Given Points A(-1,7) and B (11,-1)To findMidpoint of ABSolutionUsing midpoint formula
x = (-1 + 11)/2 = 10/2 = 5y = (7 -1)/2 = 6/2 = 3Midpoint is (5, 3)
Answer:
mid point = 5, 3Step-by-step explanation:
A(-1, 7) B(11, 1)
use the midpoint formula:
mid point = (x₁ + x₂) , (y₁ + y₂)
2 2
= (-1 + 11) , (7 - 1)
2 2
mid point = 5, 3
Two ordinary fair dice are thrown. The resulting score is found as follows.
• If the two dice show different numbers, the score is the smaller of the two numbers.
• If the two dice show equal numbers, the score is 0.
(i) Draw up the probability distribution table for the score.
The probability distribution table is shown below
How to determine the probability distribution tableFrom the question, we have the following parameters that can be used in our computation:
Dice = 2
This means that
Sample size = 6 * 6
Sample size = 36
So, the number of outcomes is 36
To determine the distribution table, we need to identify that the dice are distinct.
This means that (1, 2) and (2, 1) are not the same outcomes
We can create a probability distribution table for the score by listing all possible outcomes and their probabilities, and then determining the score for each outcome based on the rules given.
So, we have
Outcomes Probability
(1, 1) 1/36
(1, 2) 1/36
(1, 3) 1/36
(1, 4) 1/36
(1, 5) 1/36
(1, 6) 1/36
........
(6, 1) 1/36
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The quotient of the difference between five and a number and and 2
Answer:
(x-5)/2
Step-by-step explanation:
Let the number be x.
The difference between 5 and a number is x - 5.
The quotient of this means to divide, so the answer is (x-5)/2.
The statements below represent some possible deposits and withdrawals from Rachel's bank account. Match each statement with the total amount that Rachel's account would change. -47.50 -22.50 22.50 She deposits $35 to her account. Then spends $12.50 from her account on lunch. She withdraws $35 from her account. Then spends $12.50 from her account on lunch. She spends $35 from her account on clothes. Then she deposits $12.50 to her account. 000 OO
merlyumanzor23, this is the solution:
A. 35 - 12.50 =
CAN SOMEONE HELP PLEASE ASAP!!! ILL MAKE YOU BRAINLIEST
Answer:
I think the answer is D but I'm not 100 percent sure. I hope this helps
Step-by-step explanation:
I think I took this test before
Please help 30 points!!
Answer:
(4,0)
x is 4.
y-intercept is 0.
AB, BC and CD are sides of a regular 12-sided polygon. CDMN is a square. Prove that points A, C and M lie on a straight line.
As we have proved that points A, C and M lie on a straight line.
To begin with, let's recall what a regular polygon is. A regular polygon is a polygon with all sides of equal length and all angles of equal measure. In this case, we are given a 12-sided regular polygon. That means all the sides of this polygon are of equal length, and all the angles are of equal measure.
Now, let's look at point A. Point A is a vertex of the 12-sided polygon, which means it is one of the points where two sides of the polygon meet. Let's call the vertex adjacent to A as vertex B. Since the polygon is regular, the line segment AB is a side of the polygon, which means it is of equal length to all other sides of the polygon.
Since A and B are vertices of the polygon and AB is a side of the polygon, the line segment AB is a straight line. Since CM is of equal length to all sides of the square CDMN, it is also a straight line.
To show that AB and CM intersect at C, we just need to show that they are not parallel. If they are not parallel, they will intersect at some point, and that point will be C.
Now, let's consider the angle that CM makes with CD. Since CD is a straight line, the angle that CM makes with CD is just the difference between the angles that CM and CD make with AB. We know that the angle between AB and CD is x, and we know that the angle between CM and AB is 90 degrees (because CM is a straight line and AB is a side of the polygon). Therefore, the angle between CM and CD is (90 - x) degrees.
Since x is an angle in a regular 12-sided polygon, we can calculate its value using the formula (12 - 2) * 180 / 12, which simplifies to 150 degrees. Therefore, the angle between CM and CD is (90 - 150) degrees, which is -60 degrees.
Now, let's consider the angle that AB makes with CD. We already know that the angle between AB and CD is x. Since AB is a side of a regular 12-sided polygon, we can also calculate its interior angle using the same formula as before. Therefore, the interior angle of the 12-sided polygon is (12 - 2) * 180 / 12 = 150 degrees, and the angle between AB and CD is 150 degrees.
Therefore, AB and CM must intersect at some point, and that point must be C. This means that A, C, and M lie on the same straight line, which is what we needed to prove.
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A nursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost
$19.60. Unfortunately, he breaks 3 more panes while repairing the damage. What is the cost of
another 3 panes of glass?
Another 3 panes of glass cost $
Answer:
$8.85
Step-by-step explanation:
Step-by-step explanation: well if you take 23.60 and divide it by 8 you would get 2.95 times that by three and you would get 8.85 and there's your answer.
Answer:
7.35
because my kid got the question wrong
Convert 4/5 into a percent
Answer:
80%
Step-by-step explanation:
Multiply 4/5 by 100 to get your percentage of 80.
Given the equation, what is the center and radius of the circle?
(x-7) ^2 + (Y-4) ^2= 64 ^2
We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;
So, consider the equation of circle ;
\({:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}\)
On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows
Centre = (7, 4)Radius = 64 unitsDetermine whether the figure has line symmetry. If so, draw the line(s) of symmetry.
Yes
No
Yes, the given figure has the horizontal symmetry.
What is a line of symmetry?Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc.
The horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.
The given figure has horizontal symmetry.
Yes, the given figure has the horizontal symmetry.
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If f(x) =3x-2,find f(8)-g(-5)
Answer:
f(3) = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
|Absolute Value| - makes any negative number positiveStep-by-step explanation:
Step 1: Define
f(x) = |5x - 17|
f(3) is x = 3
Step 2: Evaluate
Substitute in x: f(3) = |5(3) - 17|Multiply: f(3) = |15 - 17|Subtract: f(3) = |-2|Absolute value: f(3) = 2