Use the definition of continuity and the properties of limits to show that the function

Step-by-step explanation:

brackets are missing.

it should look like

lim x→2 (x² + 3x - 10)/(x² - x - 2) =

= (x - 2)(x + 5)/((x - 2)(x + 1)) = (x + 5)/(x + 1) =

= (2 + 5)/(2 + 1) = 7/3

content-wise there is nothing wrong with the argument.

left and right limits are the same.

so, the result is correct.

Answer:

Supplementary angles are angles that add up to 180 degrees, or on a straight line. If one angle is 163.6 degrees less than its supplementary, then all you have to do is subtract that number from 180. The angles are

180 - 163.6 = 16.4

180 - 16.4 = 163.6

One angle is 16.4 degrees, the other is 163.6. They both add up to make 180.

Step-by-step explanation:

a) The probability that Stephen wins can be estimated by dividing the number of times he wins by the total number of matches:

P(Stephen wins) = 11/27 = 0.407 (or 40.7%)

b) The probability that Natasha wins can be estimated by subtracting the probability of Stephen winning from 1:

P(Natasha wins) = 1 - P(Stephen wins) = 1 - 0.407 = 0.593 (or 59.3%)

Answer:

C. 5

D. 5√3*

*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.

Otherwise only choice C is the correct answer

Step-by-step explanation:

The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.

If the side opposite the 90° angle(the hypotenuse)  = a

If the side opposite the 30° angle: PQ = a

Then the side opposite the 90° angle = 2a

The side opposite the 60° angle = √3a

Since here we are given the hypotenuse = 10

Side opposite the 30° angle = 2a/2 = 10/2 = 5

Side opposite the 60° angle = √3a = √3 · 5 = 5√3

I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct

Answer:

Options C) and D) are correct

Step-by-step explanation:

Given:  The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To choose: the correct option

Solution:

ΔKBO is a right-angled triangle.

[tex]sinO=\frac{side opposite to angle}{sideadjacent to angle}[/tex]

[tex]= \frac{BK}{KO} \\= \frac{BK}{10}[/tex]

⇒ sin 60°= [tex]\frac{BK}{10}[/tex]

[tex]\frac{\sqrt{3} }{2} = \frac{BK}{10}[/tex]

BK = [tex]\frac{\sqrt{3} }{2} (10) = 5\sqrt{3}[/tex]

CosO = [tex]\frac{side adjacent to angle}{side opposite to angle}[/tex]

          [tex]= \frac{BK}{KO} \\= \frac{BO}{10}[/tex]

          ⇒ cos 60° = [tex]\frac{BO}{10}[/tex]

            [tex]\frac{1}{2}= \frac{BO}{10} \\BO = \frac{10}{2} = 5[/tex]

Answer:

After 100 days, the amount of the substance will decrease to half its original value, so Yo/2 = 5 mg. The half-life of a substance is the time it takes for half of it to decay or disappear. So, every 100 days, the amount of the substance will be halved until there is none left.

Question is not clear.

Answer:

630

Step-by-step explanation:

36x250 = 9000 ÷ 7 =630

The solution is, she got commission of 2%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission.

so, she got commission = 1200/60000 * 100

                                        =2%

Hence, The solution is, she got commission of 2%.

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Answer:

1620 lines / minute.

Step-by-step explanation:

Proportions:

1 minute = 60 seconds

Then:

108 lines ⇒ 4 seconds

A lines ⇒ 60 seconds

A = 108 lines * 60 seconds / 4 seconds

A = 1620 Lines

Answer:

Student most likely forgot to form 2nd equation.

Step-by-step explanation:

The answers appear to be cut off, but I can clearly see that the other solution isn't considered. When solving an absolute value equation, you form two equations. In this case, we have x-3=4 and x-3=-4 as our equations because |-4|=|4|=4 so this is accounted for. Hence, the two solutions should be x=7 AND x=-1.

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Let's call the number of words Trei spelled correctly "x". Then, the number of words she spelled incorrectly is 100 - 60 = 40 words.

Therefore, the ratio of correctly spelled words to incorrectly spelled words is x to 40.

To find the number of words she spelled correctly for each word she spelled wrong, we can simplify the ratio by dividing both values by the greatest common factor:

x / 40 = x / (2 * 20) = x / 2 * 20 / 2 = x / 20.

So for every word Trei spelled incorrectly, she spelled 20 / 1 = 20 words correctly.

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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Answer:

The rate of interest required to make Rs. 2500 amount to Rs. 3200 in 7 years is 8.5%. This can be determined by using the information from pa01000192.schoolwires.net, which states that the formula for finding the rate of interest is: Rate of Interest = (Future Value - Present Value) / (Present Value * Time). Applying this formula to the given values gives a rate of interest of 8.5%.

Step-by-step explanation:

Situations with constant rates are represented using linear equations.

The parameters that have been provided are:1 third of an ounce of milkshake every second, 20 ounces at first.

A linear equation is denoted by the following:

Where:

The rate is shown by m.

The starting value is represented by b.

The equation that summarizes Lin's circumstance is as follows:

The graph is shown in the attachment.

Since the other equation is missing, the solution cannot be found.

Situations with constant rates are represented using linear equations.

The parameters that have been provided are:

1 third of an ounce of milkshake every second

20 ounces at first.

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Answer:

5/18

Step-by-step explanation:

We assume they share equally.

5/6 ÷ 3 = 5/6 × 1/3 = 5/18

Answer:

5.08

Step-by-step explanation:

2.17+2.91 = 5.08

Answer:

D all of the above is the answer

Answer:

D) All of the above

Runoff can end up in ponds, streams, and rivers.

Step-by-step explanation:

Hope it helps! =D

The equation is $230,000 x 0.97^5.

The worth of the house in five years is  $197,508.83.

Depreciation is the decline in the carrying value of an asset. Depreciation occurs as a result of wear and tear.

The equation that would be used to determine the worth of the house in 5 years is

Worth of the house = cost of the house x (1 - depreciation/100)^number of years

= $230,000 x (1 - 3/100)^5

$230,000 x (1 - 0.03)^5

$230,000 x 0.97^5  = $197,508.83

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The length of the line segment QM which is half the diagonal MP is equal to 21 in the parallelogram LMNP.

A parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.

For the parallelogram LMNP; the lines MP and LN are its diagonals, and the both bisect each other, that is they cut each other to form two equal parts.

So QM and PQ are equal halves of the line MP

Therefore, since PQ = 21 then QM = 21 because they form a diagonal of the parallelogram LMNP bisected by the diagonal LN.

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Answer: 0.5km per hour

Step-by-step explanation:

1: Unique solution: the solution: (0, 3)

2: The system have no solution.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two system of equations,

1.  x + y = 3

   x - y = -3

Adding both the equations,

2x = 0,

x = 0

And y = 3.

The solution: (0, 3)

And 2. 5x + y = 7

   10x + 2y = 16

The system have no solution.

Because lines are parallel.

Therefore, all the required solutions are given above.

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Answer:

the answer is 8 just divide

Answer:

8 is the answer just divide

The number of artists that are interns is solved to get 77

From the problem, showing circle graph, it can be deduced that the interns occupy 5 percent of the total number

The total number is 1540

5% of 1540 is solved by

= 5/100 * 1540

= 0.05 * 1540

= 77

The number of interns is 77

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The equivalent expression is t - 9

From the question, we have the following parameters that can be used in our computation:

− 3 +t-6

Collect the like terms

So, we have the following representation

t - 3 - 6

Evaluate the like terms

This gives

t - 9

Hence, the expression is t - 9

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Answer:

4,080,000,000,000

Step-by-step explanation:

1,200 * 3.4*10⁹

=4080*10⁹

=4,080,000,000,000

The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

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Six times the difference of a number and two us forty - two less than the number is 6.

What are the arithmetic calculations?

Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer. These operations can be performed using mental arithmetic, pencil, and paper, or with the help of a calculator.

Let the number be x. We can write the given expression as:

6(x - 2) = x - 42

Expanding the left side:

6x - 12 = x - 42

Solving for x:

5x = 30

x = 6

Therefore, the number is 6.

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The given function is continuous at  x = 3,  RHL = LHL = F(2)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  (x²-9)/(x² - x -6)(x² + 6x +9)

To check whether it is continuous at x = 2

First taking LHL,

[tex]\lim_{h \to \ 0}[/tex]  ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)

⇒  -5/(-4x25)

⇒   1/20

Now, taking RHL

[tex]\lim_{h \to \ 0}[/tex]  ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)

⇒  -5/(-4x25)

⇒   1/20

The value at x = 3

F(3)  =   ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)

       =  -5/(-4x25)

       =   1/20

Hence Proved,   RHL = LHL = F(2)

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The number of subsets for R { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 } is given by the equation A = 255 subsets

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the relation set be represented as R

Now , the set R = { x|||xis an odd, negative integer and x>−16 }

The number of elements in the set R is given by

R = { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }

So , the number of elements n = 8 elements

The number of subsets of any arbitrary set  is equal to 2ⁿ

This means that the number of proper subsets (which is the number of subset minus the set itself, for finite subsets) is equal to 2ⁿ-1

So , the number of subsets for R = 2⁸ - 1 = 255 subsets

Hence , the solution set is  { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }

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The correct form of the expression is x² -9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y = (x − 3)(x + 3) =

This can be done by opening the brackets

x²+3x-3x-9

⇒x²-9

Therefore, the correct form of the equation is x²-9

The x-intercept  = 1 and the y intercept is -9

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