for the following excercises, determine the point(s), if any, at which each function is discontinuous. classify any discontinuity, jump, removable, infinite, or other.

Answer:

c = √52

Step-by-step explanation:

→ Write Pythagoras' theorem

a² + b² = c²

→ Substitute in the numbers

4² + 6² = c²

→ Simplify

52 = c²

→ Square root both sides

√52 = c

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer:

Proof below

Step-by-step explanation:

A number, p, is divisible by another number, d, if and only if there is some non-negative integer, n, such that n*d=p.

To prove that, 300 is divisible by 10 because, 30 is a non-negative integer, and 10*30=300.

Strategies for Divisibility by a composite number

Note that in the previous example, 10 is a composite number.  This means that both one 2 and one 5 (the full list of 10s factors) had to be factored out of the 300.

In the given problem, we are to prove that the number is divisible by 14.  Observe 14 is composite with factors of 2 and 7.

Since the expression is given with exponents, it will be helpful to recall a few exponent properties to algebraically manipulate the expression.

Recall the following property of exponents:

Original expression...

\(8^{10}-2^{27}\)

Recognizing 8 as a power of 2...

\((2^3)^{10}-2^{27}\)

Simplifying and rewriting so that both terms are powers of 2...

\(2^{30}-2^{27}\)

Observing that both terms have 27 twos as factors...

\(2^{27}*2^{3}-2^{27}\)

Factoring out 27 twos...

\(2^{27}*(2^{3}-1)\)

Simplifying the expression in the parenthesis:

\(2^{27}*(8-1)\)

\(2^{27}*(7)\)

Knowing that we also need a factor of 2, use properties of exponents, and associative property of multiplication...

\((2^{26}*2^1)*7\)

\(2^{26}*(2^1*7)\)

\(2^{26}*(2*7)\)

\(2^{26}*14\)

Since 2^26 is a non-negative integer, the original expression is divisible by 14.

Answer:

C. 12x

Each box has 12 envelopes.

The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x

There are over 6 quadrillion ways to make starting hands for Derek, Margaret, and Lenny!

We can start by finding the number of ways to choose 7 cards out of the 52 for Derek, then the number of ways to choose 7 cards out of the remaining 45 for Margaret, and then the remaining cards (which will form Lenny's hand).

The number of ways to choose 7 cards out of 52 is:

C(52,7) = 133,784,560

Once Derek has his 7 cards, there are 45 cards remaining, so the number of ways to choose 7 cards for Margaret is:

C(45,7) = 45,379,620

Finally, Lenny gets the remaining cards, so there is only one way to choose his hand.

Therefore, the total number of ways to make starting hands for all three players is:

133,784,560 x 45,379,620 x 1 = 6,081,679,822,404,800

So there are over 6 quadrillion ways to make starting hands for Derek, Margaret, and Lenny!

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Answer:

\(y=-\frac{63}{1} x+1500\)

Step-by-step explanation:

Create a table:

1500 - 63(0) = 1500

1500 - 63(1) = 1437

1500 - 63(2) = 1374

1500 - 63(3) = 1311

Turn them into ordered pair:

(0, 1500)

(1, 1437)

(2, 1374)

(3, 1311)

Answer:

4.93

Step-by-step explanation:

Use calculator

Mark me as brainliest

Answer:

\(4\sqrt3-2\)

Step-by-step explanation:

\((\sqrt3+5)(\sqrt3-1)\\\\3+5\sqrt3-\sqrt3-5\\\\4\sqrt3-2\)

Hope this helps, please award brainliest! Have a nice night.

Step-by-step explanation:

Answer is 3 because it is alternate with 3 also it is interior too.

Answer:

The percentage of decrease from 63.2 to 35 is 44.5%.

Step-by-step explanation:

To calculate the percent of decrease from 63.2 to 35, we can use the following formula:

percent of decrease = (original value - new value) / original value * 100%

Plugging in the values given in the question, we get:

percent of decrease = (63.2 - 35) / 63.2 * 100%

Solving for the percent of decrease, we get:

percent of decrease = 44.5%

Therefore, the percentage of decrease from 63.2 to 35 is 44.5%.

Answer:

44.6202532 % decrease

Step-by-step explanation:

To find the percent decrease, take the original amount, subtract the new amount and then divide by the original amount

(63.2 - 35) /63.2

28.2/63.2

.446202532

Change to percent form

44.6202532 %

Answer:

Option A.

Step-by-step explanation:

The general transformation works as follows:

T<a,b>(x, y) = (x + a, y + b)

Then for our transformation, we will have:

T<0,7>(x, y) = (x, y + 7)

So now that we know how the transformation works, we need to apply it to the vertices.

Looking at the graph we can see that the vertices are:

X = (-4, -5)

W = (-3, -3)

L = (-5, -2)

Then the new points will be:

X' = (-4, - 5 + 7) = (-4, 2)

W' = (-3, -3 + 7) = (-3, 4)

L' = (-5, -2 + 7) = (-5, 5)

Then the correct option is A.

The factored form of the equation is g(x) = -(x + 2)(x − 4)..

A quadratic expression that is written as the product of a constant times two linear factors is said to be in factored form.

Given:

As, the equation of the function in factored form,

g(x) = a(x − \(r_1\))(x − \(r_2\)),

The function has x-intercepts of -2 and 4.

So (x + 2 )and (x − 4) are factors of the equation.

Now, the value of y changes for 1 unit to the right of the vertex.

The y-value goes down 1 unit for a point 1 unit to the right of the vertex, so a = -1.

So, the equation of this quadratic function is

g(x) = -(x + 2)(x − 4).

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To construct a nonzero 2x2 matrix A such that the solution set of the equation is the line passing through (0,1) and the origin, we can choose A = [0, 1; 0, 0].

To find a vector b such that the solution set of Ax = b is not a line parallel to the solution set of Ax = 0, we can choose b = [1, 1].
This does not contradict the theorem that states if the equation Ax = b is consistent for some given b and p is a solution, then the solution set of Ax = b is the set of all vectors of the form p + v, where v is any solution of the homogeneous equation Ax = 0.
In this case, the solution set of Ax = b is the line passing through (0,1) and the origin, while the solution set of Ax = 0 is just the origin. Thus, the set of all vectors of the form p + v will not form a line parallel to the line passing through (0,1) and the origin, since it will include additional vectors from the solution set of Ax = 0.

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The correct answer is (B) 50%. To find the experimental probability of the coin coming up heads, we need to count the number of times heads appear in the random number table and divide it by the total number of tosses.

Since even digits represent heads, we look for even digits in the table.

Counting the number of even digits in the table, we find that there are 45 even digits out of a total of 90 digits.

To find the experimental probability, we divide the number of even digits (45) by the total number of digits (90) and multiply by 100 to convert it to a percentage.

(45/90) * 100 = 50%

Therefore, the experimental probability, to the nearest percent, of the coin coming up heads is 50%.

The correct answer is (B) 50%.

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Answer:

46$ in total

y=2r+20

If Isabella goes on 13 rides, she would have to pay a total of $46. If she rides 'r' times, the total cost would be expressed by the mathematical equation 20 + 2r.

This question relates to a linear relationship involving a fixed cost and a variable cost. In Isabella's case, the fixed cost is the admission fee, which is $20. The variable cost is the rides, where each ride costs $2.

So, if she goes on 13 rides, she will have to pay: $20 (for admission) + ($2 * 13 (rides)) = $20 + $26 = $46.

For r rides, the total cost would be: $20 (for admission) + ($2 * r (rides)). So the total cost for r rides can be expressed in a mathematical equation as: 20 + 2r.

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Batting common is the the wide variety of runs scored via way of means of the batsman withinside the wide variety of fits performed via way of means of him in that supply weeks Walk to strike out is the wide variety of wickets taken via way of means of the sports activities character withinside the wide variety of fits performed via way of means of him in that week Home runs are the house run hit via way of means of that participant in that 5 weeks throughout which the sports activities creator cited these types of happenings

The number of hits A got is 186 hits.

​A player's batting average is calculated by dividing the number of hits by the number of at-bats.

Player A batting average =  0.312

Number of at-bats A did =  596

We have to find the number of hits A got.

0.312 = Number of hits / 596

Number of hits = 0.312 x 596

                        = 185.952 hits.

Rounding to a whole number we get,

= 186 hits

Thus, the number of hits A got is 186 hits.

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A unit for each quantity in the worksheet for the mat width are 5.357 inches.

The size of a rectangle. A = l × b. Once the length and width are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.

Add the height and the width together to get the area of a rectangle. Given that each side of a square is the same length, all you need to do to determine its area is multiply the length of one of its sides by itself.

Length = 7 inches  

Width = 6 inches

Area of photograph = length  width = 7  6 = 42

Total area of photograph and frame = 84

frame length ( 7 + 2x)

frame width ( 6 + 2x)

Total area = Total area of photograph and frame

( 7 + 2x)  ( 6 + 2x) = 84

2 + 13x - 21 = 0

x = 5. 357

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If two pairs of corresponding angles in two triangles are of equal measure, then the third set of angles must also be equal.

Let's consider two triangles, ∆ABC and ∆DEF. If two pairs of corresponding angles are of equal measure, then we can say that:

∠A = ∠D, and

∠B = ∠E

Now, we need to prove that ∠C = ∠F.

We know that the sum of angles in a triangle is 180°. Therefore:

∠A + ∠B + ∠C = 180° (for triangle ∆ABC)

∠D + ∠E + ∠F = 180° (for triangle ∆DEF)

From the above equations, we can write:

∠C = 180° - ∠A - ∠B

∠F = 180° - ∠D - ∠E

As ∠A = ∠D and ∠B = ∠E, we can substitute the values in the above equations:

∠C = 180° - ∠A - ∠B = 180° - ∠D - ∠E = ∠F

Therefore, we have proved that if two pairs of corresponding angles in two triangles are of equal measure, then the third set of angles must also be equal.

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6y² - 13y + 6 is the product of 2y -3 and 3y - 2.

Given the following linear expression

(2y-3)(3y-2)

We need to expand the expression to get a quadratic function as shown below:

(2y-3)(3y-2) = 2y(3y) - 2(2y) - 3(3y) -3(-2)

(2y-3)(3y-2) = 6y² - 4y - 9y + 6

(2y-3)(3y-2) = 6y² - 13y + 6

Hence the product of 2y - 3 and 3y - 2 is equivalent to 6y² - 13y + 6

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a) \(x=2\)

b) see below

a) Since the first three terms are \(\sqrt{x}-1}\), 1 and \(\sqrt{x}+1}\), the middle term, 1, must be the geometric mean of the other two. Hence

\(1^2=(\sqrt{x} -1)(\sqrt{x} +1)\implies\)

\(1=x-1\implies x=2\)

b)

The common ratio is then \(\sqrt{2}+1\), and the first term is \(\sqrt{2} -1\).

Thus, the fifth term is

\((\sqrt{2} -1)\times(\sqrt{2} +1)^4=(\sqrt{2} +1)^3\)

    \(=(\sqrt{2} )3+3(\sqrt{2} )2+3(\sqrt{2} )+1\)

    \(=2\sqrt{2} +6+3\sqrt{2} +1\)

    \(=7+5\sqrt{2}\)

Answer:

Step-by-step explanation:

The importance of sampling, from a managerial perspective, is to obtain information to draw a valid inference about a population.

Sampling allows managers to collect data from a subset of the population in a cost-effective and efficient manner. By studying the sample, managers can gather insights and make informed decisions about the larger population. This enables them to understand the characteristics, preferences, behaviors, and needs of the population they are interested in.

Sampling helps managers to estimate population parameters accurately. By collecting data from a representative sample and applying statistical techniques, they can make reliable estimates of population parameters such as means, proportions, or correlations. This information is crucial for making informed decisions, developing strategies, and allocating resources effectively.

Testing the correlation between the values of the population is one specific application of sampling, but it is not the sole purpose. Sampling serves a broader purpose of providing information for decision-making, understanding populations, and drawing valid inferences.

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Answer:

The correct answer would be 8 root symbol 3

Step-by-step explanation:

because i chose it and got it right

The length of the line segment YX is \(8\sqrt{3}\) if the line XW is of 24 units.

It is a ratio of sides of a right angled triangle.

It can be seen that the diagonal is making a right angle triangle XWV so

we will use the trigonometric function to determine the value of WV which will then be equal to XY because it is a rectangle.

tan(30)=VW/XW

1/\(\sqrt{3}\)=VW/24

VW=24/\(\sqrt{3}\)

VW=8\(\sqrt{3}\) UNITS by multiplying and divide by root 3.

Hence the length of the side XY =8 root 3 units.

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The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

1. x= -1 & x= -13

2. x= -3 & x= -4

3. x= -3 & x= -5

4. x= -6 & x= -2

5. x= -5 & x= -2

8. x= -7 & x= -3

9. x= -8 & x= -2

10. x= -3 & x= -3

11. x= -5 & x= -4

12. x= -2 & x= -2

13. x= -6 & x= -7

14. x= -6 & x= -3

15. x= -10 & x= -7

Answer:

x = - 24

Step-by-step explanation:

- \(\frac{2}{3}\) (\(\frac{3}{8}\) x + 9) = \(\frac{3}{5}\) (\(\frac{5}{12}\) x + 10) ← distribute parenthesis on both sides

- \(\frac{1}{4}\) x - 6 = \(\frac{1}{4}\) x + 6 ( multiply through by 4 to clear the fractions )

- x - 24 = x + 24 ( subtract x from both sides )

- 2x - 24 = 24 ( add 24 to both sides )

- 2x = 48 ( divide both sides by - 2 )

x = - 24

\( \sf - \frac{2}{3} ( \frac{3}{8} x + 9) = \frac{3}{5} ( \frac{5}{12} x + 10)\)

\( \sf \: - 10( \frac{3}{8} x + 9) = 9( \frac{5}{12} x + 10)\)

\( \sf \: - \frac{15}{4} x - 90 = 9( \frac{5}{12} x + 10)\)

\( \sf \: - \frac{15}{4} x - 90 = \frac{15}{4} x + 90\)

\( \sf \: - 15x - 360 = 15x + 360\)

\( \sf \: - 15x - 360 - 15x = 360\)

\( \sf \: - 15x - 15x = 360 + 360\)

\( \sf \: - 30x = 720\)

\( \boxed{ \tt \: x = - 24}\)

Five pairs of shoes = 5(4x² - 9) = 20x² - 45.

Four bags = 4(2x² - 3x + 5) = 8x² - 12x + 20

-> Total cost = 20x² - 45 + 8x² - 12x + 20 = 28x² - 12x - 25.

The mass of 6.56 pints of blood is 3.92 grams.

Given

The density of blood = 1.060 g/mL and mass of 6.56 pints

We have 1L = 2.113 pints

The density of a substance can be defined as the ratio of the mass of the substance to the volume of the substance. In chemistry, density is used to measure the concentration of the substance in the solution.

The expression for density = mass/volume

ρ = m/V

m = ρV

Mass = 1.060(1000ml/1L) × 6.56(1L/ 2.113)

= 3290.8 /1000

= 3.29g

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Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

Answer:

y=-x+5

Step-by-step explanation:

Since the slope you mentioned is -1, it is usually the same thing as -x.  Add 2 from 3 to get 5 as your y-intercept in which your slope should be y = -x + 5 as your result.

Answer:

4xy

Step-by-step explanation:

(x+y) (x+y) - (x-y) (x-y)​

(x² + xy + xy + y²) - (x² - xy - xy + y²)

(x² + 2xy + y²) - (x² - 2xy + y²)

x² + 2xy + y² - x² + 2xy - y²

x² - x² + 2xy + 2xy + y² - y²

4xy

Answer:

that could literally be anything, as long as the first sum is greater then the second.

example;

(2+4) (3+5) - (6+1) (5+2)

(or, 6+8 = 14, 7+7 = 14, 14 - 14 = 0)

hope this helped :)