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

Answer 1

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:

[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]

[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]

[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

[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

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

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.

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.

The amount collected at the end of 5 years is the principal plus interest:

P +I = $6000 +2400 = $8400

The total collected is $8400.

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.

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 theorem

The 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

application

For 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.

bivariate data is the type of data that a scatterplot is used to analyze?
True
or
False

Answers

True because I got a 100 on the test

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.

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 deviation

In 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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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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What is the probability of getting tails and then tails

Answers

1/4 I believe this is the answer sorry if it’s not

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

35 percent :) (or 14/40)

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.

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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helpppppppppp meeeeeeeeee pllzzzzzzzzz

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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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

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 parking

How 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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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

1 yrd = 3 ft
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

help me with this question

Answers

Answer:

a) 150

b) 2650

Step-by-step explanation:

6% of 2500 is 150

150 + 2500 = 2650

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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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

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]

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!

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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need help asap please!

Answers

Answer:

determinant: -15x = 3; y = 4; z = 1

Step-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, determinant

The first attachment shows the coefficient matrix and its determinant.

solution

The 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]

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