Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the resulting values to the corresponding limits.
Answers
The correct solution to the limits of x in the tiles can be seen below.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex][tex]\mathbf{ = -\dfrac{1}{52} }[/tex][tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex][tex]\mathbf{=\dfrac{1}{79} }[/tex][tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]= -31 [tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex][tex]\mathbf{ =\dfrac{1}{98}}[/tex]What are the corresponding limits of x?The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.
From the given diagram, we have:
1.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex]
So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }[/tex]
Simplifying the quadratic equation, we have:
[tex]\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }[/tex]
Replacing the value of x = 9
[tex]\mathbf{ = (-\dfrac{1}{9+43}) }[/tex]
[tex]\mathbf{ = -\dfrac{1}{52} }[/tex]
2.
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex]
-x²-63x+568 is positive when x → 8⁻.Thus |-x²-63x+568| = -x²-63x+568
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }[/tex]
[tex]\mathbf{=\dfrac{1}{8+71} }[/tex]
[tex]\mathbf{=\dfrac{1}{79} }[/tex]
3.
[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]
x -7 is positive, therefore |x-7| = x - 7[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-x-24)}[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-7-24)}[/tex]
= -31
4.
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex]
x-6 is negative when x → 6⁻. Therefore, |x-6| = -x + 6[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }[/tex]
[tex]\mathbf{ =\dfrac{1}{98}}[/tex]
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Related Questions
Carlos spent a total of $40 at the grocery store. Of this amount, he spent $14 on fruit. What percentage of the total did he spend on fruit?
Answers
how to determine area of the following,in some cases leave the answer in term of x ABJH
Answers
Answer:
x²
Step-by-step explanation:
The area of rectangle ABJH is the product of its dimensions.
__
The dimensions are given as ...
AB = x
AH = x
The area of ABJH is ...
area = length × width = (x) × (x) = x²
The area of ABJH is x².
What is the algebraic equation of the sum of 28?
Answers
Answer:
There can be alot of equations for this since you didn't say anything specific. But since u didnt say anything specific, this can be one of the equations: 20 + 8, 30 - 2, 4 x 7
bivariate data is the type of data that a scatterplot is used to analyze?
True
or
False
Answers
If f(x) = 3x²+2 and g(x)=x2-9, find (f- g)(x).
Answers
Answer:
Step-by-step explanation:
Depending on whether or not the g(x) is x^2 or 2x, I have both ways.
If g(x) is x^2 - 9...
--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11
If g(x) is 2x...
--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11
Hope this helps!
1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
Answers
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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Here is an equilateral triangle. The length of each side is units. A height is drawn. In an equilateral triangle, a line drawn from one corner to the center of the opposite side represents the height. 1. Find the exact height. 2. Find the area of the equilateral triangle. 3. (Challenge) Using for the length of each side in an equilateral triangle, express its area in terms of .
Answers
1. Height of the equilateral triangle is: √3 units
2. Area of the equilateral triangle = √3 units²
3. Area = √3/4 x², when each side is x.
What is an Equilateral Triangle?A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.
1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:
h = √(2² - 1²)
h = √(4 - 1)
h = √3
2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)
Area of the equilateral triangle = √3 units²
3. If x is the side length of the equilateral triangle, we would have:
height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x
Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²
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Simplify 3y²-4x² + xy - 2x² - 9y²
Answers
Answer:
-6x²+xy-6y²
Step-by-step explanation:
3y² - 4x² + xy - 2x² - 9y²
-4x²+ xy - 2x² - 6y²
-6y² + xy - 6y²
Answer:
−6x² + xy − 6y²
Step-by-step explanation:
Simplify 3y²-4x² + xy - 2x² - 9y²
Step 1
Subtract 9y² from 3y²
−4x² +xy −2x² −6y²
Step 2
Subtract 2x² from −4x²
−6x² + xy − 6y²
Petra is making a batch of extra large donuts by stamping circles in dough using
a pastry stamp with a diameter of 5 inches. For the donut hole, she stamps out
a circle using a pastry stamp that has a diameter of 2 inches.
How many square inches of dough are left in the donut after the hole has been
removed?
Step 1 Find the radius of each circle
Step 2 - Find the area of the large circle
Step 3 - Find the area of the small circle
Step 4 - Area of large circle minus area of small circle
Area = Tr
Answers
The answer of the following questions is discussed below
What is area of circle?Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.
The radius of each circle
r1= 2.5 inches.
r2= 1 inches
Area of circle large circle,
= πr1²
=3.14*2.5*2.5
=19.625 inch²
Area of small circle,
= πr2²
= 3.14*1*1
=3.14 inch²
Area of large circle minus area of small circle,
= 16.485 inch²
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A side of the triangle below has been extended to form an exterior angle of 131°. Find the value of x. 131⁰ to 112º
Answers
Answer:
[tex]x = 49degrees[/tex]
Step-by-step explanation:
[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]
The required value of x for the given figure is 49°.
What is a straight line?A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.
The sum of the angles on a straight line is always 180°.
In the given figure the angles 131° and x° are on the same straight line.
Since, the sum of the angles on a straight line is 180°.
The following equation can be written for the given figure,
x + 131 = 180
=> x = 180 - 131
= 49
Hence, the value of x for the given figure is 49°.
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What is the probability of getting tails and then tails
Answers
What shapes can the composite figure be decomposed into? Select two options.
A hexagon.
a rectangle and a triangle
a rectangle and two triangles
a square and two triangles
two rectangles
two trapezoids
Answers
Answer:
one of them is two trapezoids
Step-by-step explanation:
why the question “How many colors are there in the United States flag?” is NOT a statistical question.
Answers
Answer:
3
Step-by-step explanation:
blue, white, and red colors
Cos W =0.53
Does anybody know this
Answers
Answer:
58°
Step-by-step explanation:
Apply trig inverse properties
W = arccos(0.53)
W = 2[tex]\pi[/tex] - arccos(0.53)
a man invested $6000 at 8% per annum simple interest for 5 years.
a).calculate the simple interest.
b).the total amount of money collected at the end of the 5 year period.
Answers
Answer:
*r = R/100 = 8%/100 = 0.08 per year, A = P(1 + rt)
a) A = 6000[1 + (0.08 × 5)] = 8400
b) A = $8,400.00
Answer:
a) $2400
b) $8400
Step-by-step explanation:
The simple interest formula can be used to find the amount of interest. The amount collected at the end of the period is the total of principal and interest.
__
a)The simple interest is given by the formula ...
I = Prt . . . . . . P is the principal amount, r is the annual rate, and t is the number of years
For this investment, the interest is ...
I = $6000·0.08·5 = $2400
The simple interest amounts to $2400.
__
b)The amount collected at the end of 5 years is the principal plus interest:
P +I = $6000 +2400 = $8400
The total collected is $8400.
HELP PLS I'LL MARK U BRAINLIST !!
Answers
Answer:
angles in a triangle add up to 180°
5:12:13 = 30
180 ÷ 30 = 6
6 × 5 = 30°
6 × 12 = 72°
6 × 13 = 78°
angles = 30°, 72°, 78°
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From experience, an airline knows that only 70% of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that fewer than 7 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.
Answers
Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
p = 0.7, n = 8.
The probability that fewer than 7 of them show up is given by:
[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]
In which:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]
[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]
Then:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]
[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]
0.7447 = 74.47% probability that fewer than 7 of them show up.
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Starting at the point (0,0) how many ways are there to get to the point (7,4) if you have to pass through the point (2,2) and each step can only be in a positive direction. (i.e. to the right or up)?
Answers
The number of ways there are to get to the point (7,4) if you have to pass through the point (2,2) is; 1266 ways
How to find the lattice Paths?The formula to get the number of ways to get to the lattice point (x, y) (supposing x, y ≥ 0) by taking steps of one unit each either in the eastward or northward direction is exactly;
(x + y)
= (x + y)!/(x!y!)
( x )
Thus, number of ways from (0, 0) to (2, 2) = (2 + 2)!/(2!2!) = 6 ways
Number of ways to get to point (7,4) from (2, 2) is;
((7 - 2) + (4 - 2))!/(2!2!) = 7!/(2!2!) = 1260
Thus, total number of ways = 1266 ways
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dependent or independent
Answers
The probability of coin landing with heads is an independent event.
The probability of winning 1st and 2nd prize is a dependent event.
What are independent and dependent events?
Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.
Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.
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Please help, this is due by 2:18pm est
Answers
71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.
71 + y = 180
y = 109
The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.
109 + 46 + x = 180
x = 25
Answer: x = 25 degrees
Hope this helps!
need help asap please!
Answers
Answer:
determinant: -15x = 3; y = 4; z = 1Step-by-step explanation:
The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.
coefficient matrix, determinantThe first attachment shows the coefficient matrix and its determinant.
__
solutionThe solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.
[tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]
This multiplication is shown in the second attachment. It tells us ...
[tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]
Expand (x^22-3x^5 + x^-2 - 7) * (5x^4).
Can someone please explain in detail how to remove the parentheses step by step?
Answers
Let's see
[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]
Use distributive law
a(b+c)=ab+ac[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]
[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]
Answer:
[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
Step-by-explanation:
Given expression:
[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]
Use the Distributive Property Law (b ± c)a = ab ± ac
to remove the parentheses:
[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]
Simplify by multiplying the coefficients of each term:
[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:
[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]
[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
help me with this question
Answers
Answer:
a) 150
b) 2650
Step-by-step explanation:
6% of 2500 is 150
150 + 2500 = 2650
3. Here is a list of questions about the students and teachers at a school. Select all the
questions that are statistical questions.
A. What is the most popular lunch choice?
B. What school do these students attend?
C. How many math teachers are in the school?
D. What is a common age for the teachers at the school?
E. About how many hours of sleep do students generally get on a school night?
F. How do students usually travel from home to school?
Answers
education Roman Catholic School one five two weeks
On last week math tests Mr.Jones class had an average of 82 points with a standard deviation of 10 points.Mrs.Potters class had an average of 79 points with a standard deviation of 3 points.Which class was more constant and how can you tell
Answers
Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.
What is a statistical dispersion?A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.
In Mathematics, there are four measures of dispersion for a data set and these include the following:
RangeInterquartile rangeVarianceStandard deviationIn this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.
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The 2 main support rods for a barbeque grill are each 7.5 cm from the centre of the
grill. the grill is 60 cm in diameter, how long is each support rod?
Answers
Answer:
58.1 cm
Step-by-step explanation:
The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.
__
Pythagorean theoremThe theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...
c² = a² +b²
applicationFor the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.
30² = 7.5 +b²
b² = 900 -56.25 = 843.75
b = √843.75 ≈ 29.0473
The length of each support rod is twice this value, so ...
rod length = 2b = 2(29.0473) = 58.0947
Each support rod is about 58.1 cm long.
The product of 7 and x is the same as the sum of nine and three and two. What is the value of x?
Answers
Answer:
Given:
The product of 7 & x is the same as the sum of 9 and 3 and 2.To Find:
The value of x ?Solution:
According to the question:
(1) The product of 7 & x
➝ 7x
(2) The sum of 9 and 3 and 2
➝ 9 + 3 + 2
➝ 14
From (1) and (2) , we get:
➝ 7x = 14
➝ x = 14 ÷ 7
➝ x = 2
Let's Check:Let's check whether our answer is correct or not:
• To check our answerer, let's putting the value of x :
♣ 7(2) = 14
♣ 14 = 14 ✅
Thus, our answer is correct....The value of x is 2.
Solve for x.
40°
x + 71
75°
Answers
Answer:
x = -6.
Step-by-step explanation:
First thing to notice is that this is the third angle in a triangle, and all 3 angles have to equal 180.
Subtract 75 and 40 from 180 to get the missing angles value.
180 - 75 - 40 = 65
So now we know the missing angle has to be 65, or can be written as:
x + 71 = 65.
To solve this, just subtract 71 from both sides.
x = -6.
Solve for the coordinates of the midpoint of (13, 27) and (-31, 53). Show your work to receive full credit.
Answers
Answer:
-9,40
Step-by-step explanation:
Midpoint Formula:
[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]
Answer:
Midpoint = (−9,40)
Step-by-step explanation:
Julia buys a spool with 12 yards of wire. The students in
her jewelry-making class use 4 yards 2 feet of the wire
for one project and 7 feet of the wire for another
project. How many feet of wire does Julia have left?
Answers
12 yrd x 3 ft = 36 ft
one jewelry project uses 4 yrd + 2 ft OR 14 ft
the second project uses 7 ft
14 ft + 7 ft = 21 ft
36 ft - 21 ft = 15 ft of wire left over