20 points for this question ​

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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The cost of the two plans is same after 6 GB of data use.

Both the plan cost the same for 6 GB of data use. So, you can use any one of the two data plans.

Plan B is cheaper in the long run.

A) Carrier A

For \(3\) GB, cost \(=\) $\(35\)

For \(4\) GB, cost \(=\) $\(35+\)$\(8=\)$\(43\)

For \(5\) GB, cost \(=\) $\(43+\)$\(8=\)$\(51\)

For \(6\) GB, cost \(=\) $\(51+\)$\(8=\)$\(59\)

For \(7\) GB, cost \(=\) $\(59+\)$\(8=\)$\(67\)

For \(8\) GB, cost \(=\) $\(67+\)$\(8=\)$\(75\)

Carrier B

For \(5\) GB, cost \(=\) $\(55\)

For \(6\) GB, cost \(=\) $\(55+\)$\(4=\)$\(59\)

For \(7\) GB, cost \(=\) $\(59+\)$\(4=\)$\(63\)

For \(8\) GB, cost \(=\) $\(63+\)$\(4=\)$\(67\)

So, the cost of the two plans is same after \(6\) GB of data use.

B) Here, both the plan cost the same for 6 GB of data use. So, you can use any one of the two data plans.

C) Clearly plan B is cheaper in the long run.

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Answer:

V= 6/w

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

the question says that he has 5 to 2 and if you put it in a fraction you cant reduce it so therefore the answer has to be 5:2

Answer:

D. 5:2

Step-by-step explanation:

He has 5 games so 5: for every 2 school apps so 5:2

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Answer:

y = 4x + 17

Step-by-step explanation:

y = 1 - 1/4x = - 1/4 x + 1 .... slope -1/4

perpendicular line slope = - (1 / (-1/4) = 4

pass (-3,5): (y-5) / (x - -3) = 4

y-5 = 4x + 12

y = 4x + 17

1,4,9,16,25,36,49,........

7th pattern =49.....

Answer:

1, 4, 9, 16, 25, 36, 49…................the 7 the pattern is 49

Answer:

Their average speed is 18 miles per hour

Step-by-step explanation:

First off find out how long 2hrs and 30mins is in minutes:

60 mins per hour x 2 hours = 120 minutes

120 minutes + 30 minutes = 150 minutes total

He traveled 45 miles in 150 minutes.

Next divide 150 minutes by 60

150 minutes / 60 minutes = 2.5 rate

This means you have to now divide 45 miles by 2.5 as that's the rate

45 miles / 2.5 = 18 miles per 1 hour (60 minutes)

(a) We have ⌊x⌋ = 5 if 5 ≤ x < 6, and similarly ⌊x/3⌋ = 5 if

5 ≤ x/3 < 6   ==>   15 ≤ x < 18

(b) ⌊x⌋ = -2 if -2 ≤ x < -1, so ⌊x/3⌋ = -2 if

-2 ≤ x/3 < -1   ==>   -6 ≤ x < -3

In general, ⌊x⌋ = n if n ≤ x < n + 1, where n is any integer.

I do not understand what is being asked in (c) and (d), so you'll have to clarify...

The saving $100 at the end of each quarter for 15 years in an ordinary annuity that earns 5.4% interest, compounded quarterly, the Smith family would have $29,161.66 to travel the world.

An ordinary annuity is a stream of regular payments that are paid at the end of each period, such as quarterly, annually, or monthly. The Smith family intends to invest in an ordinary annuity to save money for a trip around the world.To compute the future value of a regular annuity,

the following formula is used:FV= PMT [ (1+r/n)^n*t - 1 ] / (r/n)where FV = future value, PMT = payment amount, r = interest rate per compounding period, n = number of compounding periods per year, and t = number of years of the investment.The Smith family's ordinary annuity has a 5.4% interest rate, compounded quarterly. As a result, the quarterly interest rate is: 5.4% / 4 = 1.35%.

The interest rate per compounding period is then converted to decimal form: 1.35% / 100 = 0.0135.The number of compounding periods per year is calculated by dividing the annual interest rate by the quarterly interest rate: 5.4% / 1.35% = 4.The number of payments the Smith family would make over a period of 15 years is: 15 years * 4 payments/year = 60 payments.

Finally, the future value of the annuity is calculated using the formula:FV= PMT [ (1+r/n)^n*t - 1 ] / (r/n) = PMT [(1+0.0135)^60 - 1]/ (0.0135)If the Smith family wants to save $100 at the end of each quarter, the calculation is as follows:FV = $100 [ (1+0.0135)^60 - 1 ] / (0.0135) = $29,161.66

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Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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Answer:

it is the first one because you times the 9 because it says twice and divide it by 3 because you donate to 3 parks

Step-by-step explanation:

The calculated measure of t from the given equation is 15 degrees

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

10

to

25°

When expressed properly, we have

10° + t° = 25°

Evaluate the like terms

So, we have

t° = 15°

Hence, the value of t° is 25°

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Answer:

Step-by-step explanation:

To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.

The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:

x-coordinate of C' = 1111 * 8 = 8888

y-coordinate of C' = 1111 * 8 = 8888

Therefore, the coordinates of point C' are (8888, 8888).

I cannot really graph it but I will try my best to explain.

When you have a coordinate plane draw from right to left, up to down.

Now starting from righthand top corner, draw a smooth curve just like how you will draw a quadratic equation, through the x axis then curve back making the graph touch the axis at 2 points. That's the 2 real roots

Now make another curve down but this time not touching the x axis and then curving back up to the top left corner, this meant the 2 complex roots.

This is not the only way to do it, as long as one complete curve is not touching the x axis and another complete curve, weather as a whole or combined is touching the x axis at 2 points, it has 2 real and complex roots.

Answer: true

Step-by-step explanation:

Answer:

yes, obtuse angles have only one obtuse angle.

hence, it's true.

Step-by-step explanation:

A triangle can't have more than one obtuse angle , because if there are more than one obtuse angle the sum of measures of all interior angles will exceed 180°, which isn't possible.

Answer:

256 feet

Step-by-step explanation:

To find the maximum height, we have to find the vertex of the parabola, which is formed by the situation.

First, find the axis of symmetry using -(b/2a). This will give us the x value of the vertex.

Plug in b into the equation:

-(b/2a)

-(96 / 2(-16))

-(96 / -32)

-(-3)

= 3

Now, plug in 3 as x into the given equation, to find the maximum height that the rock will reach:

H(t) = -16t² + 96t + 112

H(3) = -16(3²) + 96(3) + 112

H(3) = 256

So, the maximum height that the rock will reach is 256 feet

Maximum height achieved by the rock on the parabolic path will be 256 ft.

    Expression modeling the height of the rock is given by,

Since, this equation is a quadratic equation, path followed by the rock will be a parabolic path and the highest point attained by the rock will be the vertex of the parabola.

And the vertex will be → \([-\frac{b}{2a},H(-\frac{b}{2a})]\)

Compare the given equation with standard form of the quadratic equation.

\(y=ax^{2}+bx+c\)

By comparing the equations → a = -16, b = 96 and c = 112

Therefore, x-coordinate → \(-\frac{b}{2a}=-\frac{96}{(-2\times 16)}\)

                                                   \(=3\)

And y-coordinate → \(H(-\frac{b}{2a})=H(3)\)

                                              \(=-16(3)^2+96(3)+112\)

                                              \(=-144+288+112\)

                                              \(=256\)

Therefore, vertex of the parabola will be → (3, 256)

Here, x-coordinate represents the period or time taken by the rock to reach the highest point and y-coordinate represents the height achieved.

   Therefore, maximum height the rock will reach will be 256 feet.

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Answer:

hacunamatata

Step-by-step explanation:

it means no worrys

The area of the region shown in the coordinate plane is 2.7823 units square.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

The graph of a function:

y = sinx

And a line segment passed through:

(0, 0) and (7π/6, -1/2)

First, find the equation of the line:

y = (-1/2)/(7π/6)[x]

y = (-3/7π)x

The area by definite integration:

\(\rm Area = \int\limits^{7\pi/6}_0 {[sinx - (-3/7\pi)x]} \, dx\)

\(\rm Area = \int\limits^{7\pi/6}_0 {[sinx +3x/7\pi ]} \, dx\)

After solving the above definite integral:

Area = 2.7823 units square

Thus, the area of the region shown in the coordinate plane is 2.7823 units square.

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Answer: A line that is parallel to another line has the same slope. The slope of the line x-2y=6 can be found by rearranging it into slope-intercept form, y = mx + b, where m is the slope:

x - 2y = 6

Add 2y to both sides:

x = 2y + 6

Divide both sides by 2:

y = (1/2)x + 3

So the slope of the line x - 2y = 6 is m = 1/2.

Since the line through the point (−6,−8) must have the same slope as the line x-2y=6, its slope is also 1/2. To find the equation of this line, we can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope. Substituting the values m = 1/2, x1 = -6, and y1 = -8 into the point-slope form gives:

y - (-8) = (1/2)(x - (-6))

Expanding the right side:

y + 8 = (1/2)x + (1/2)(-6)

y + 8 = (1/2)x - 3

Multiplying both sides by 2:

2y + 16 = x - 6

Adding 6 to both sides:

2y + 22 = x

So the equation of the line that passes through the point (−6,−8) and is parallel to the line x - 2y = 6 is:

2y + 22 = x

Step-by-step explanation:

Answer:

  41,850

Step-by-step explanation:

The 4th digit from the left is in the 10s place, so you need to round to that place. This requires rounding up, since the 1s digit is more than 4.

  41,850 . . . . to 4 significant figures

Step-by-step explanation:

only smile for youuuuuuuu

Answer:

I only smile for the money, lol

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

this question is horribly phrased.

as far as I can tell after reading this multiple times, this is again looking for the GCF : the greatest common factor.

so, again, prime factor analysis :

168 :

168 ÷ 2 = 84

84 ÷ 2 = 42

42 ÷ 2 = 21

21 ÷ 2 no

21 ÷ 3 = 7

7 ÷ 3 no

7 ÷ 5 no

7 ÷ 7 = 1 finished

168 = 2³×3×7

120 :

120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 2 no

15 ÷ 3 = 5

5 ÷ 3 no

5 ÷ 5 = 1 finished

120 = 2³×3×5

the GCF is the part of the prime factors both numbers share :

2³×3 = 8×3 = 24

so, they can make 24 fruit cups with identical content and using all the fruits.

these pieces of information were missing in the text.

based on the text without the answer options I was already going for the maximum that each fruit cup has one piece of fruit, and that gives us 168 + 120 = 288 fruit cups max.

The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5

The series is given as:

0.5+ (-1) +2+...

The above series is a geometric series, with the following parameters:

The sum of the first 14 terms is calculated using:

\(S_n= a *(1 - r^n) \div (1 - r)\)

So, we have:

\(S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)\)

Evaluate

\(S_{14}= -2730.5\)

Hence, the sum of the series is -2730.5

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Answer:

11. 6/10

12.60 percent

5. the size of the photograph would decrease

6) the size of the photograph would increase

7) h

3)46

Step-by-step explanation:

Answer:

it is 5 inches squared

Step-by-step explanation:

1 inches. sjwjqkqkwjhed

Given the expression:

first we solve what is inside the parenthesis:

Notice how we have the same number but with different exponents. We can use the following rule to simplify the expression:

therefore, the simplifed expression is 6^5 = 7776

Answer:

1/2x+7

Step-by-step explanation:

seven more than half of a number is  (x/2) + 7.

The correct option is (C).

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.

We have to find an algebraic expression which represents the phrase "seven more than half of a number".

Consider a number x,

half of x = (x/2)

seven more than half = (x/2) + 7

Hence, seven more than half of a number is  (x/2) + 7.

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Answer: Yes, it is a function

Step-by-step explanation: