Answers
=======================================================
Explanation:
If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first
x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator
So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]
Allowing us to say,
[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]
The solution is 5
The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) be equation (1)
On simplifying the equation , we get
Taking the common factors on numerator , we get
A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )
A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )
Taking the common factor as ( x + 2 ) , we get
A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )
So , the equation is
A = lim x tends to 3 ( x + 2 )
Substitute the value of x = 3 , in the equation , we get
A = ( 3 + 2 )
A = 5
Therefore , the value of A is 5
Hence , the equation is A = 5
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Related Questions
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Answers
Answer:
There has been no change in the classifications between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The expected values are computed using the formula:
[tex]E_{i}=p_{i}\times N[/tex]
Here, N = 300
Use Excel to compute the values.
The test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]
The test statistic value is, 1.662.
The degrees of freedom of the test is:
n - 1 = 4 - 1 = 3
The significance level is, α = 0.05.
Compute the p-value of the test as follows:
p-value = 0.6454
*Use a Chi-square table.
p-value = 0.6454 > α = 0.05.
So, the null hypothesis will not be rejected at 5% significance level.
Thus, concluding that there has been no change in the classifications between the last school year and this school year.
Milo receives a commission of 8% on all sales. If his commission on a sale was $97.84 find the cost of the item he sold
Answers
Answer:
Cost of the item sold= $1,223
Step-by-step explanation:
Let
x= cost of the item sold
$97.84=commission on the item
Percentage of the commission=8%
To find the cost of the item sold
Commission=8% of cost of the item
97.84=0.08 * x
97.84=0.08x
Divide both sides by 0.08
97.84 / 0.08 = 0.08x / 0.08
1,223=x
x=$1,223
Therefore, cost of the item sold= $1,223
Find the inverse of the function f(x)= 6x^3-8
Answers
Hello, please consider the following.
[tex](\forall x \in \mathbb{R}) \\ \\ x=(f^{-1}of)(x)\\\\=(fof^{-1})(x)\\\\=f(f^{-1}(x))\\\\=6\left( f^{-1}(x) \right) ^3-8 = x\\\\\text{We need to express }f^{-1}(x) \text{ in function of x.}\\\\\text{Let's do it!}[/tex]
[tex]6\left( f^{-1}(x) \right) ^3-8 = x\\\\\left( f^{-1}(x) \right) ^3 =\dfrac{x+8}{6}\\\\\Large \boxed{\sf \bf \ \ f^{-1}(x)=\sqrt[3]{\dfrac{x+8}{6}}\ \ }[/tex]
Thank you
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8*10^4 is how many times as large as large as 4*10^-5
Answers
Answer:
D. 2 . 10^9
Step-by-step explanation:
( 8 * 10^4 ) / ( 4* 10^-5 )
( 8*10^4 ) 10^5 / ( 4 )
2 * 10^ 9
Find the measure of ∠ 1 in O.
Answers
Answer:
10°
Step-by-step explanation:
The angle subtended at the circumference is half the angle subtended at the centre of the circle i.e. 20°÷2=10°
what is 826 x 3,569 equal to
Answers
Answer:
826×3569=2947994 ans
Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.
r=12/3--10 Cosθ
Answers
Answer:
a) 10/3
b) hyperbola
c) x = ± 6/5
Step-by-step explanation:
a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
Given the conic equation: [tex]r=\frac{12}{3-10cos\theta}[/tex]
We have to make it to be in the form [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]:
[tex]r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }[/tex]
Comparing with [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
e = 10/3 = 3.3333, p = 6/5
b) since the eccentricity = 3.33 > 1, it is a hyperbola
c) The equation of the directrix is x = ±p = ± 6/5
ASAP: “Use a number line to order the numbers from least to greatest.” 1/5, -0.5, 0, 0.4, 1 1/2, -1.
Answers
Answer:
-1, -0.5, 0, 0.4, 1/5, 11/2
Step-by-step explanation:
PLEASE HELP! A) 7 B) 5.7 C) 4.7 D) 8.2
Answers
Answer:
[tex]\Large \boxed{\mathrm{A) \ 7}}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve the problem.
tan(θ) = opp/adj
tan(35) = x/10
Multiply both sides by 10.
10 tan(35) = x
x = 7.00207538...
ANSWER. 7
consider the set of A={0,3,5,8}
Answers
Trigonometry!! NEED HELP!!
Answers
=============================================
Explanation:
If angle x is the reference angle, then the side 9 is the adjacent side (it is the closer leg to angle x). The hypotenuse is 17 as it is opposite the largest angle. The largest side is always opposite the largest angle in a triangle.
-----------------
cos(angle) = adjacent/hypotenuse
cos(x) = 9/17
x = arccos(9/17)
x = 58.034281249203
x = 58
Arccosine is the same as inverse cosine, written as [tex]\cos^{-1}[/tex]
Make sure your calculator is in degree mode.
-------------
Edit:
After finding x, we can find y
x+y = 90
58+y = 90
y = 90-58
y = 32
PLEASE HELP IM CONFUSED
If angle ACB is 1 degree 25 minutes (1°25’) what is angle ACD. Please give your answer as degrees and minutes.
Answers
Answer:
178° 35'
Step-by-step explanation:
∠ACB and ∠ACD are supplementary, so they add up to 180°.
First, convert to degrees (there are 60 minutes in a degree).
∠ACB = 1°25' = 1° + (25/60)° = 1.4167°
Now find the supplementary:
∠ACD = 180° − 1.4167°
∠ACD = 178.5833°
∠ACD = 178° 35'
Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables
Answers
Answer:
Explained below.
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The formula to compute correlation coefficient is:
[tex]r(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)\cdot V (Y)}}[/tex]
[tex]=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^{2}-(\sum X)^{2}][n\cdot\sum Y^{2}-(\sum Y)^{2}]}}[/tex]
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.
In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.
Find the ratio of the area inside the square but outside the circle to the area of the square in the picture
Answers
Answer:
0.2146
Step-by-step explanation:
From the picture:
The radius of the circle = r. This means that the area of the circle = πr²
Also For the square, the length of the square = 2r, Therefore the area of the square = Length × length = 2r × 2r = 4r²
The area inside the square but outside the circle = Area of square - Area of circle = 4r² - πr² = r²(4 - π) = 0.8584r²
The ratio of the area inside the square but outside the circle to the area of the square = r²(4 - π) / 4r² = (4 - π) / 4 = 1 - π/4 = 0.2146
The amount of paint used on new tractors averages 18.2 gallons with a standard deviation of 0.8 gallons. A new nozzle is used on 20 tractors and averaged 17.9 gallons. What is the probability that is was just random chance
Answers
Answer:
17.9/18.2 =0.984 to 3 decimal places
Step-by-step explanation:
The initial mean/average = 18.2 gallons
A standard deviation of 0.8 gallons implies a lower-upper limit of (17.4 - 19) gallons of paint used on new tractors.
New mean/average = 17.9 gallons
It is noticeable that this value 17.9 falls within the lower range of the standard deviation of the initial mean; hence the question
What is the probability that this happened by chance?
17.9 ÷ 18.2 = 0.9835
Therefore, there is a high probability that this happened by chance. 0.9 is closer to 1 than to 0.
The following is a list of 5 measurements. 16,13,5,20,14 Suppose that these 5 measurements are respectively labeled
Answers
=====================================================
Explanation:
The fancy or strange looking E symbol is the greek uppercase letter sigma, to mean sum. So they want you to add the terms in the form x^2. The x values are from the list given to us.
x = 16 leads to x^2 = 256
x = 13 leads to x^2 = 169
etc etc
After squaring all the x values, we have this new list {256, 169, 25, 400, 196}
Lastly, you add up all the squared values to get the final answer of 256+169+25+400+196 = 1046
5. Which of the following illustrates the Distributive
Property?
F. 3(2x + 4) = 5x + 4
G. 3(2x + 4) = 5x + 7
H. 3(2x + 4) = 6x + 4
I. 3(2r + 4) = 6 + 12
plz answer quickly yikess
Answers
Answer: Hi!
Option I is correct. 3(2x + 4) = 6x + 12
When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)
Hope this helps!
-38 - 7y = 2 - 7(y + 6)
Answers
Answer:
No solution
Step-by-step explanation:
[tex]-38 - 7y = 2 - 7(y + 6)\\\\\mathrm{Expand\:}2-7\left(y+6\right):\quad -7y-40\\-38-7y=-7y-40\\\\\mathrm{Add\:}38\mathrm{\:to\:both\:sides}\\-38-7y+38=-7y-40+38\\\\Simplify\\-7y=-7y-2\\\\\mathrm{Add\:}7y\mathrm{\:to\:both\:sides}\\-7y+7y=-7y-2+7y\\\\Simplify\\\\0=-2\\\mathrm{The\:sides\:are\:not\:equal}\\No\: solution[/tex]
Answer:
No solution
Step-by-step explanation:
First do distribute property
-38-7y=2-7y-42
then combine like terms the 2 and the -42
-38-7y=-40-7y add 7y from both sides
-38+y=-40 add 38 to -40 you get -2
0=-2 no solution
Can someone help ! Please !!!! I don’t understand!
Answers
Answer:
(A∩B')∪(A'∩B)(A∩B)'Step-by-step explanation:
Here, we'll use an apostrophe to signify the complement of a set.
__
(a) The shaded portion is two disjoint (non-overlapping) sections, so must be the union of something. The shaded space on the left is that part of A that is not in B, so it is A∩B'. Similarly, the shaded space on the right is that part of set B that is not in set A: A'∩B. Then the shaded area altogether is the union of these sets:
(A∩B')∪(A'∩B)
__
(b) For this one, it might be easier to identify the unshaded area. That is where the sets A and B overlap, so it is A∩B. Then the area that is not that area is the complement of this:
(A∩B)'
Stavros is 1.6m tall. His sister is 95cm tall. How many centimeters taller is Stavros than his sister?
Answers
Find the value of x.
Answers
Answer:
[tex]\sqrt{205}[/tex]
Step-by-step explanation:
Using the pythagorean theorem, [tex]x^{2} +18^{2} =23^{2} \\[/tex] so that means [tex]x^{2} = 23^{2} -18^{2} =205[/tex] so x = [tex]\sqrt{205}[/tex]
Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.To the nearest tenth of a foot how long can a side of his garden be?
Answers
Answer:
o the nearest tenth of ft
Length of one of the side= 14.6 ft
Step-by-step explanation:
Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.
His square garden is a square one, and the area of a square is the square of one of it's sides .
So if the area= 214 ft²
Length of one of the side = √(214 ft²)
Length of one of the side= 14.6287 ft
To the nearest tenth of ft
Length of one of the side= 14.6 ft
which expression is equivalent to 2(x-3) + 4
Answers
Answer:
2x - 2
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Distribute parenthesis
2x - 6 + 4
Step 2: Combine like terms
2x - 2
And we have our answer!
Answer:
[tex]2( x -3) + 4 \\ 2x - 6 + 4 \\ [/tex]
f the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime ? Type the numeric answer only in the box below
Answers
Answer:
8 inches
Step-by-step explanation:
The computation of the length, in inches of Segment line G prime A prime is shown below:-
Data provided
In two quadrilateral GAME and G'A'M'E',
ME = 35 inches
AM = GE = 56 inches
M'E' = 14 inches
Also, the perimeter of quadrilateral GAME = 167 inches
GA + AM + ME + GE = 167
Now we will put the values into the above equation
GA + 56 + 35 + 56 = 167
GA + 147 = 167
So,
GA = 20 inch
Therefore
GAME is closely related to G'A'M'E'
Now,
By the property of similar figures,
[tex]\frac{M E}{M' E'} = \frac{GA}{G'A'}[/tex]
[tex]G'A' = \frac{M'E'\times GA}{ME} \\\\ = \frac{14\times 20}{35}[/tex]
= 8 inches
Adam was curious if quadrilaterals ABCDABCDA, B, C, D and GFEHGFEHG, F, E, H were congruent, so he tried to map one figure onto the other using transformations:
Adam concluded:
"It's not possible to map ABCDABCDA, B, C, D onto GFEHGFEHG, F, E, H using a sequence of rigid transformations, so the quadrilaterals are not congruent."
What error did Adam make in his conclusion?
Answers
Answers reflection (b)
Step-by-step explanation:
it’s right on 8th grade khan ywwww
So he tried to reflect(b) map one figure onto the other using transformations.
Are quadrilaterals congruent?If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Are two quadrilaterals congruent?Both the theorems are proved now which states that quadrilaterals are congruent to one another. Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent.
Learn more about the quadrilaterals are not congruent at
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y- (-3y) combine the like terms to create an equivalent expression
Answers
Answer:
4y
Step-by-step explanation:
[tex]y- (-3y)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\\=4y[/tex]
Hello there! :D
I love showing people how to use this concept, so lets get right to it! If you have trouble with negative (-) signs and how they interact with each other, I suggest you watch some Khan academy videos, it could realy help you in the future! :)
Alright, so here's the general rule: (multiplication and division)
-,-= +
-,+ = -
+,+=+
So, with this rule, I think we can solve!
Firstly, remember PEMDAS.
Let's look at the signs first. Two negatives equal a positive. Make the 3y in the parenthesis positive. Think of the negative sign as a -1 that is being multiplied by the (-3y) and the y.
That would look like this:
(y) (-1) (-3y)
Now we have:
y*(3y)
So when multiplying a variable by a variable, it becomes squared.
So, we would have 3y^2 or [tex]3y^{2}[/tex]
If you have any questions about this problem feel free to comment on this answer.
I hope this helped you and you have a wonderful day,
Kai xx
Linear function g is shown in the graph. Write the slope-intercept form of the equation representing this function.
Answers
Answer:
y = -2x + 1
Step-by-step explanation:
First, find the slope with rise/run (y2 - y1) / (x2 - x1)
We can use the points (-1, 3) and (0, 1)
Plug in the points:
(1 - 3) / (0 + 1)
-2/1
= -2
The y-intercept is (0, 1) because that is the point where the line intercepts the y axis. So, we can plug in the slope and y-intercept into the equation:
y = mx + b
y = -2x + 1
Note: Enter your answer and show all the steps that you use to solve this problem.
*btw the note is the same thing for question 6*
1. 7x=42
6.simplify the expression 8to the 2power +9(12÷3×2)-7.
Answers
Answer:
1) x = 6
2) 129
Step-by-step explanation:
For equation 1:
[tex]7x=42\\\\\frac{7x=42}{7}\\\\ \boxed{x=6}[/tex]
Expression 2:
Apply PEMDAS Rule.
[tex]8^2+9((12/3)*2)-7\\\\8^2+9(4*2)-7\\\\8^2+9(8)-7\\\\64+9(8)-7\\\\64+72-7\\\\136-7\\\\\boxed{129}[/tex]
Hope this helps.
A fitness center is interested in the average amount of time a client exercises in the center each week. Match the vocabulary word with its corresponding example.
Answers
Answer:
Step-by-step explanation:
A. Data of the study: All 45 exercise times there were recorded from the participants in the study
B. Parameter of the study: The average amount of time that all clients exercise in one week.
C. Variable of the study: The amount of time that any given client from the fitness center exercises.
D. Population for the study: All clients at the fitness center.
E. Sample of this study: The 45 client from the fitness center who participated in the study.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
Mr. Coelho and Ms. Steiner are grading math and science tests of sixth-grade and seventh-grade students, respectively,
Mr. Coelho graded 25 science tests in 50 minutes and 30 math tests in 40 minutes. Ms. Steiner graded 20 science tests in
50 minutes and 12 math tests in 30 minutes.
Whose grading shows a proportional relationship between the number of tests graded and the time spent grading?
The answer is only ms.Steiner’s grading
Answers
Answer:
Ms. Steiner
Step-by-step explanation:
Mr. Coelho
science = 25 / 50 = 1/2
math = 30 / 40 = 3/4
not the same rate
Ms. Steiner
science = 20 / 50 = 2/5
math = 12 / 30 = 2/5
It is the same rate, so they are proportional
Mr. Coelho: Science: 50 minutes / 25 tests = 2 minutes per test
Math: 40 minutes / 30 tests = 1.33 minutes per test.
Ms. Steiner: Science: 50 minutes / 20 tests = 2.5 minutes per test.
Math: 30 minutes / 12 tests = 2.5 minutes per test.
The answer is Ms. Steiner.