Find the quotient and remainder using synthetic division.


x^4
-
3
x^3
+
9
x
+
6/
x
+
1


The quotient is

The remainder is

1. f(x) =  (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞

2. g(x)  = (2x²  +  4x  + 4)/x² = ∞; as lim x→∞, and lim x→-∞]

3.  h(x)  = (2x²  +  4x  + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.

To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.

For  f(x)  = (2x²  +  4x  + 4)/x³;

lim x→∞ (2x² + 4x + 4) / x³ = 0

lim x→-∞ (2x² + 4x + 4) / x³ = 0

f(x) approaches zero as x approaches positive or negative infinity.

For  g(x)  = (2x²  +  4x  + 4)/x²;

lim x→∞ (2x² + 4x + 4) / x² = ∞

lim x→-∞ (2x² + 4x + 4) / x² = ∞

g(x) approaches infinity as x approaches positive or negative infinity.

For  h(x)  = (2x²  +  4x  + 4)/x

lim x→∞ (2x² + 4x + 4) / x = ∞

lim x→-∞ (2x² + 4x + 4) / x = -∞

h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.

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The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle

The given equation is

4x² + 9xy + 4y² - 36y - 125 =0

The above equation is an illustration of a circle equation

The standard form of a circle equation is

(x - a)² + (y - b)² = r²

Where

(a, b) is the center

r is the radius

While the general form of the equation is

ax² + fx + by² + gy + c =0

Where c is a constant

Recall that, we have

4x² + 9x + 4y² - 36y - 125 =0

This is the general form

We can convert to the standard form as follows

Divide through by 4

x² + 2.25x + y² - 9y - 31.25 =0

Next, we complete the square of the x-terms and the y-terms

For the x-terms, we have

x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²

x² + 2.25x = (x + 2.25/2)² - (2.25/2)²

For the y-terms, we have

y² - 9y = y² - 9y + (9/2)² - (9/2)²

y² - 9y = (y - 9/2)² - (9/2)²

Substitute the new x and y terms

So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes

(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0

Evaluate the sum of like terms

(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0

So, we have

(x + 9/8)² + (y - 9/2)² = 3377/64

Using the above as a guide, we can conclude that the conic section of the equation is a circle

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The salary $50,780 per year is lower than the yearly median.

The yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

a. As, the median weekly earnings for males with a bachelor's degree are $1,384.

To convert this to yearly earnings, we can multiply by the number of weeks in a year (52):

= $1,384 x 52

= $71,968

So, the salary $50,780 per year is lower than the yearly median earnings for a male with a bachelor's degree.

b. Now, The yearly median earnings for a male with a high school diploma (no college) are $607 per week. Converting this to yearly earnings:

Yearly median earnings for a male with a high school diploma

= $607 x 52 = $31,564

The difference between the yearly median earnings for a male with a bachelor's degree and a male with a high school diploma is:

= $71,968 - $31,564 = $40,404

So, the yearly median earnings for a male with a bachelor's degree are $40,404 higher than those for a male with a high school diploma.

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Answer:

I'd like to explain more but I have limited comment

chat me up

A

The set of capacity measures related to cubic meter are ordered from the greatest to the least:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

In this problem we need to order a group of capacity measures in cubic meters and its related units from the greateast to the least. To make this we need to understand the following relations:

Now we proceed to order the following set of information:

First, write the set of measures:

5 dam³, 530 m³, 5.480 m³, 5.5 dam³, 5 dam³, 61 m³

Second, convert all measures in cubic decameters into cubic meters:

5.000 m³, 530 m³, 5.480 m³, 5.500 m³, 5.000 m³, 61 m³

Third, order all the set from the greatest to the least:

5.500 m³, 5.480 m³, 5.000 m³, 5.000 m³, 530 m³, 61 m³

Fourth, rewrite the set of measures in its original units:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

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The diameter of the second pile of phosphate is found to be approximately 62.6 feet.

The volume of a right circular cone is given by the formula,

V = (1/3)πr²h where volume is V, radius of the base is r, height is h, and π is approximately 3.14159. For the first pile of phosphate,

h = 15.3 feet

d = 48.6 feet

r = d/2 = 24.3 feet

Using the formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)π(24.3)²(15.3)

V = 24,249.8 cubic feet

For the second pile of phosphate,

h = 15.3 - 3.6 = 11.7 feet

r = ? (to be determined)

Using the same formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)πr²(11.7)

Since the volume of both piles is the same, we can set the two volume formulas equal to each other,

(1/3)π(24.3)²(15.3) = (1/3)πr²(11.7)

Simplifying,

(24.3)²(15.3) = r²(11.7)

r² = (24.3)²(15.3)/11.7

r = 31.3 feet (rounded to the nearest tenth)

Therefore, the diameter of the second pile of phosphate is d = 2r = 62.6 feet (rounded to the nearest tenth).

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Complete question - As phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone, as shown.

Height of the cone is 15.3 feet

Diameter of the base of cone is 48.6 feet

A shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same. To the nearest tenth of a foot, what is the diameter of the second pile of phosphate?

Answer:

[tex]C = 25.1 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

[tex]C = \pi d[/tex]

Note: This formula can also be written as [tex]C = 2\pi r[/tex] because [tex]2r = d[/tex].

↓ plugging in the given radius

[tex]C = 8\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 25.1 \text{ cm}}[/tex]

Answer:True

Lower interest rates reuslt in saving more money.

The interquartile range for the average of 15 cities is 1.8.

a) X ~ N(9.6, 1.3)

b) X bar ~ N(9.6, 0.13)

c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.

d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.

e) The assumption that the distribution is normal is indeed necessary for part d.

f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.

Therefore, the interquartile range for the average of 15 cities is 1.8.

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The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.

Since the population doubles every 4 years, we can use the formula:

P = P0 x [tex]2^{t/4}[/tex]

where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.

In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:

P = 28,100  2^(12/4)

  = 28,100 x 2³

  = 28,100 * 8 = 224,800

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.

We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.

Total luggage  that she has to pack;

Mass of empty suitcase + mass of her clothes + mass of 4 gifts

Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg

This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

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Answer:

98 mm²

Step-by-step explanation:

This parallelogram has a base of 7 and height of 14 mm.

The height is the vertical distance between the two bases

The area = b x h = 7 x 14 = 98 mm²

[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{➳Aɳʂɯҽɾ}}}[/tex]

Refer the attachment for clarity:-

[tex] \colorbox{yellow}{\red{Formula\: Base\: x \:Height= Area}}[/tex]

[tex]\sf{\leadsto 7×14}[/tex]

[tex]{ \red{ \sf 98m {m}^{2} }}[/tex]

______________________________

[tex]\bold{Thank ~you~:)}[/tex]

The solution of the equation, | x + 10 / 2x + 1 | = 20 is x = 10 / 39 or x = -30 / 41.

The absolute equation can be solved as follows:

| x + 10 / 2x + 1 | = 20

Therefore,

x + 10 / 2x + 1 = 20  or  x + 10 / 2x + 1 = - 20

cross multiply

x + 10 / 2x + 1 = 20

x + 10 = 20(2x + 1)

x + 10 = 40x + 20

x - 40x  = 20 - 10

-39x = -10

x = 10 / 39

x + 10 / 2x + 1 = - 20

cross multiply

x + 10 = -20(2x + 1)

x + 10 = -40x - 20

x + 40x = -20 - 10

41x = -30

divide both sides of the equation by 41

x = - 30 / 41

Therefore, x = 10 / 39 or x = -30 / 41

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Step-by-step explanation:

5 P 5 = 120 ways = 5!

Answer:

28 in²

Step-by-step explanation:

Area of parallelogram = base X vertical height

= 7 X 4

= 28 in²

The area of the figure is 183.5 ft².

We have,

The figure has two types of shapes.

Two rectangles and one triangle.

Now,

Area of rectangle = Length x Width

Area of triangle = 1/2 x base x height

Now,

Rectangle 1:

Area = 7 x 5 = 35 ft²

Rectangle 2:

Area = 4 x (4 + 5) = 4 x 9 = 36 ft²

Triangle:

Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²

Now,

The area of the figure.
= 35 + 36 + 112.5

= 183.5 ft²

Thus,

The area of the figure is 183.5 ft².

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Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

The total surface area of the given pyramid is: 95 ft²

To get the surface area of the given pyramid, we will find the individual areas of all surfaces and add up to get the total surface area.

Formula for area of a triangle is:

A = ¹/₂bh

where:

b is base

h is height

Formula for area of a rectangle is:

A = Length * Width

Thus:

Total surface area of pyramid = 4(¹/₂ * 5 * 7) + (5 * 5)

Total surface area of pyramid = 70 + 25

Total surface area of pyramid = 95 ft²

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The measure of angle QRS in triangle QRS is 56.8 degrees.

To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

We know that:

- The measure of angle RSQ is 48.2 degrees

- The measure of angle SQR is 75 degrees

Let x be the measure of angle QRS. Then, we can write:

RSQ + SQR + QRS = 180

Substituting the known values, we get:

48.2 + 75 + x = 180

Simplifying and solving for x, we get:

x = 180 - 48.2 - 75x = 56.8

Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.

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The two triangles are similar because angle C = C' and angle A = A'. The scale factor is 4/3

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent.

Also, the ratio of corresponding sides of similar triangles are equal.

Therefore to show that that the two triangles are equal;

Tan A = 4/3

Tan A = 1.333

A = 53.1°

Tan A' = 5.3/4

Tan A' = 1.33

A' = 53.1°

Therefore the two triangles are similar.

The scale factor = 4/3

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The reason that Rachel could give for her proof is given as follows:

<1 ≅ <5 by the Corresponding Angle Theorem.

When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal.

Corresponding angles are always congruent, which means that they have the same measure.

A pair of corresponding angles in this problem is given as follows:

<1 and <5.

Hence they are congruent. <8 is opposite by the same vertex with <5, hence they are also congruent, and by the transitive property of congruence, we have that:

<8 ≅ <1, as <8 ≅ <5 and <5 ≅ <1.

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Answer:

⟶ We can express the sum 1^2 + 2^2 + 3^2 + ... + 750^2 using summation notation as:

∑i^2, where i goes from 1 to 750.

⟶ Here, the symbol ∑ represents the summation, and i is the index variable, which takes on the values 1, 2, 3, ..., 750. The expression i^2 is the term being summed.

⟶ So the sum can be written as:

∑i^2 = 1^2 + 2^2 + 3^2 + ... + 750^2

⟶ Note that the upper limit of the index variable is 750, which corresponds to the last term in the sum.

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Answer:

[tex]\sum \limits^{750}_{n=1} {n^2}[/tex]

Step-by-step explanation:

General explanation of summation notation

Any sum of terms whose format is the same can be represented more concisely using a Summation symbol.

The Summation symbol is a capital greek letter Sigma:  [tex]\sum[/tex]

The summation will take a general format of each term, and increase a "dummy variable" by 1, summing together terms until the summation is complete.  To write the summation expression, find the common format of each term, and write it using a "dummy variable" to represent the number that is changing.

If the change of the number within each term increases by 1 each time, that makes the transition easier because the dummy variable increases by 1.  If the change of the number within each term does not change by 1 each time, using summation notation can be more challenging, as one needs to develop a formula to represent the amount that it is changing each time.

The common format of each term & the changing number

In our case, each term is some number squared, and the number that is squared changes from 1, to 2, to 3, ... and so on .. up to 750 (changing by 1 each time).  Since the number that is square changes by 1 each time, that will be our "dummy variable".

Using "n" for the "dummy variable", our terms look like [tex]n^2[/tex]

The start and end of the list

Lastly, to specify where the list starts and ends, we write where the list starts (lowest number) at the bottom with the "dummy variable", and where the list ends (largest number) at the top.

So, in the end, the summation would look like this:  [tex]\sum \limits^{750}_{n=1} {n^2}[/tex]

This represents adding a bunch of terms that look like [tex]n^2[/tex], starting at n=1, each time, increasing the value of n by 1, and stopping with the last term when n=750.

Extension of knowledge (NOT about THIS problem)

For a similar example where the changing number doesn't increase by 1 each time, look at a similar sequence of, where it's just the odd numbers squared up to 99:

1^2 + 3^2 + 5^2 + … + 99^2

While the terms do have the format of a number squared, since the number that is squared isn't just increasing by 1 each time, there would need to be a formula to describe how they are increasing.  One way to represent that would be:

[tex]\sum \limits^{50}_{n=1} {(2n-1)^2}[/tex]

Note that this does cause the final endpoint of the dummy variable to not necessarily be intuitive, but the "99 squared" is the 50th term (observe 2*50-1 is 99).

Answer:

Hi!, if you need help right away, chat with a tutor!

Step-by-step explanation:

A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

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your wrong you divide by 4 60/4=15 there