Solve for x. Round to the nearest tenth, if necessary.
X=???

The removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).

Holes in the graph of function, where its undefined, or non-continuous, is called discontinuity.

The points in the domain of the function over which its not continuous, is called point of discontinuity for that function.

A discontinuity is removable if the limit of the function at the point of discontinuity exists but this limiting value is not the value of the function at that point.

We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.

The given function is:

[tex]f(x) = \dfrac{(x+5)}{(x^2 +3x-10)}[/tex]

Factoring the denominator, we get:

[tex]x^2 + 3x -10 = x^2 + 5x - 2x - 10 =x(x+5) - 2(x+5) = (x+5)(x-2)[/tex]

Therefore, we get:

[tex]f(x) = \dfrac{(x+5)}{(x+5)(x-2)}[/tex]

The function is not defined if x = -5, or x = 2 since at those places, the denominator would become 0. (we cannot cancel out (x+5) from numerator and denominator for all x, as it isn't defined for x = -5

Also, we have:

[tex]\lim_{x\rightarrow 2}f(x)= \infty\\\lim_{x\rightarrow -5}f(x) = \lim_{x\rightarrow -5}\dfrac{(x+5)}{(x+5)(x-2)} = \lim_{x\rightarrow -5}\dfrac{1}{(x-2)} = -\dfrac{1}{7}[/tex]

We cancelled out (x+5) from numerator and denominator because x is limiting to -5 but isn't equal to -5.

For discontinuity of x = -5, the limit of f(x) exist (left and right limit both will come as 1/3). But f(-5) is not defined. So we can remove this discontinuity by defining f(-5) = 1/3 and for rest of the values of x, it is same as before.

Thus, the removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).

Learn more about discontinuities here:

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Answer: Option A  -5

Step-by-step explanation: Just took the test

Answer:

D

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

y = k*x                    This is the formula for a direct variation.

20 = 4 * k                        Divide by 4

20/4 = 4k/4

k = 5

Answer: the constant of variation is 5

Answer:

your answer to this question is option c

please consider as brainlest if i helped you

we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill[/tex]

Answer:

60

Step-by-step explanation:

After 1.5 hour the train travel 60 mille (1.5 × 40) and the car travel 45 (1.5 × 30) which make the train travel 15 more than the car at the same amount of time.

Given the proportional relationship representing the speed, Paul ran faster. The equation for Paul is, y = 7x (Option D).

Proportional relationship between two variables that has a constant rate or unit rate of m, is given as y = mx.

In a graph, the steeper the slope, the larger the constant rate or unit rate.

The graph for Paul is steeper than that of Melinda. Since Melinda's constant speed is 5, therefore, Paul's constant speed cannot be less than 5. It should be more than 5, i.e. 7.

This means that Paul ran at a faster constant speed than Melinda did.

Paul's equation for distance covered over time can be expressed as, y = 7x. (Option D).

Learn more about proprotional relationship on:

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Answer: The measure of the missing angle is 115∘.

Step-by-step explanation: To find missing interior angles, you have to add the two angles that are known and see how much they add up.  The work is done below:

40∘ + 75∘ = 115∘.

In order to find out the missing interior angle, we have to subtract 115∘ from 180∘ to find that angle:

180∘ - 115∘ = 65∘, which is the missing angle that is inside the triangle.

Now, you're probably wondering how any of this has to do with finding the angle that has a ? on it.  Well, us finding the missing interior angle inside of the triangle is what's going to help us find that angle with a ? on it.  To find that angle, you need to subtract 65∘ from 180∘ to find the angle that you need:

180∘ - 65∘ = 115∘.

Therefore, 115∘ is your answer.

Let me know if this is right! :)

Answer:

2 terms

Explanation:

[tex]\dashrightarrow \ \ \sf 5(6 + 4x)[/tex]

[tex]\dashrightarrow \ \ \sf 5(6) + 5(4x)[/tex]

[tex]\dashrightarrow \ \ \sf 30 + 20x[/tex]

→ There are total two terms in this factor.

Answer:

2 Terms

Step-by-step explanation:

There will be two terms ..

=> 5(6 + 4x)

=> 30 + 20x

Answer:

To increase a price, add the percentage you wish to increase it by to 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.

To decrease a price, subtract the percentage you wish to decrease it by from 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.

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100% represents the original price.

Therefore, 100% = $599.99

A 20% discount means that the price is now 80% of the original price,
as 100% - 20% = 80%

To find 80% of the original price, convert 80% to a decimal and multiply it by the original price:

80% = 80/100 = 0.8

Therefore, 80% of $599.99 = 0.8 x $599.99

                                              = $479.992

Finally, we need to apply a sales tax of 6%.  We can do this in 2 ways:

Way 1

Work out 6% of the discounted price, then add this to the discounted price to find the final price:

Sales tax = 6% of $479.992

               = 0.06 x $479.992

               = $28.79952

Final price = discounted price + sales tax

                  = $479.992 + $28.79952

                  = $508.79 (nearest cent)

Way 2

We need to increase the discounted price of $479.992 by 6%.  Therefore, the final price will be 106% of the discounted price as
100% + 6% = 106%

Final price = 106% of discounted price

                  = 1.06 x $479.992

                  = $508.79 (nearest cent)

Answer:

Step-by-step explanation:

The 3 angles add up to 180 degrees

2y + 2y + 5y = 180

9y = 180

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

As we know, Sum of all three Angles of Triangle is equal to 180° [ by Angle sum property of triangle ]

So, the required expression is :

[tex]\qquad \tt \dashrightarrow \:5y + 2y + 2y = 180[/tex]

or

[tex]\qquad \tt \dashrightarrow \:9y = 180[/tex]

if you solve for y, you will get y = 20°

And the angles as 100°, 40° and 40°

Answer:

Step-by-step explanation:

Exponential equation:

           [tex]\boxed{y=a*b^{x}}[/tex]

Choose the point whose x-coordiante is 0, so that we can find the value of a.  (0,2)

[tex]2 = a*b^0\\\\2 = a*1 \ [\text{\bf any \ variable raised to 0 is 1}][/tex]

[tex]\sf \boxed{a = 2}[/tex]

Now, choose (1 , 1) and find the value of b

[tex]1 = 2*b^{1}\\\\1 = 2*b\\\\\dfrac{1}{2}=b[/tex]

Exponential equation:

            [tex]\bf \boxed{y =2* \left(\dfrac{1}{2}\right)^{x}}[/tex]

Answer:

D

Step-by-step explanation:

By subtracting the second part of the equation, you are doing the same as adding a negative.

Answer:

Step-by-step explanation:

In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...

  A = 1/2bh

where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.

You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.

__

For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).

In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.

__

The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...

__

By way of example, we can "show work" for problem 1:

1. S = Ph +2B

  S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2

Answer:

120%

Step-by-step explanation:

1998/1665 = 1.2

1.2x100 = 120%

Answer:

3. 40 4. 132

Step-by-step explanation:

you multiply the length and the width

Answer:

3. 40. 4. 132

Step-by-step explanation:

You find the area by doing base x height so 10 x 4 is 40 and 12 x 11 is 132.

Answer: 27

Step-by-step explanation:

8 cups of water is 64 Ounce. If she had 37, She needs 64 - 37 To balance up

Answer:

C- 1:3

Step-by-step explanation:

You have to simply 4 and 12, which becomes 1 and 3 (by dividing both numbers by 4). Then I guess you just keep a colon symbol in between 1 and 3.

Answer

12 feet high

Step-by-step explanation:

Answer:

Recycling etc.

Step-by-step explanation:

Eliminate Waste from Lunches.

Stop Littering.

Reduce Paper Consumption.

Save Electricity.

Save Water.

Swap Regular School Supplies.

Bring Reusable Bags to the Grocery Store.

Walk to School or Take a Bike, Avoid Taking Cars or Carpool When Possible.

Answer:

C = 2πr = 2·π·20 ≈ 40π ft (125.6)

The number line is shown below. The numbers 0.2, 0.4, √0.2, and √0.4 are in ascending order.

A number line is a line on which numbers are plotted in a particular interval.

The numbers are given below.

[tex]\sqrt{0.2}, \sqrt{0.4}, 0.2, 0.4[/tex]

Arrange in ascending order, then we have

[tex]0.2, 0.4, \sqrt{0.2}, \sqrt{0.4}[/tex]

Then mark these numbers on the number line.

The number line is shown below.

More about the number line link is given below.

https://brainly.com/question/13189025

Answer:

√0.2   ✔3

√0.4   ✔4

0.2   ✔1

0.4   ✔2

Step-by-step explanation:

My image shows that I got it correct on edge! Hope this helps:D

Answer:

Its a graph. Each of those black dots represent a person answering the survey. For example: 2 people only chose 3 letters, 1 person only chose 4 letters, 2 people chose 5 letters, and so on. So the answer is 10. Hope this helps!

Step-by-step explanation:

Answer:

$11390.30

Step-by-step explanation:

Discount

12916 x 0.15 = 1937.4

Discounted price

12916 - 1937.4 = 10978.6

Tax of 3 and 3/4 percent which I think is 0.0375

10978.6 x 0.0375 = 411.6975

Total

10978.6 + 411.6975 = $11390.2975

Answer:

B'(-3, 2)

Step-by-step explanation:

The rule for a reflection over the y-axis is (x, y) → (-x, y)

This means that the x-values change while the y-values stay the same.

B(x, y) → (-x, y)

B(3, 2) → (-3, 2)

B'(-3, 2)

Hope this helps!

Answer:

55 ≤ 3.5x + 15

Step-by-step explanation:

Missing Inequality.

Given that:

Josh has a reward card for movie theater.

He receives 15 points for becoming a rewards card holder.

He earns 3.5 points for each visit to the movie theater.

He needs at least 55 points to earn a free movie ticket.

To Find:

Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?

Solution:

From the given we know that:

Points Josh received for becoming a member = 15

Points Josh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

Note that:

< = Less than

> = Greater than

≤ = Less than or equal to

≥ = Greater than or equal to

Thus, We know that Josh need to get less than or equal to 55.

Therefore, we use this sign ≤

Since we know that we need to get less than or equal to 55 then

we get

55 ≤ 3.5x + 15.

Hence, the inequality that Josh can use to determine x, the minimum number of visits he needs to earn his first free movie tickets is:

55 ≤ 3.5x + 15

Kavinsky

Answer: 5 feet

Step-by-step explanation:

Answer: 5 feet

Step-by-step explanation: