Consider the line y = -2x + 6. Find the equation of the line that is parallel to this line and passes through the point (7,-4). Find the equation of the line that is perpendicular to this line and passes through the point (7,-4). Note that the ALEKS graphing calculator may be helpful in checking your answer.​

1) The first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:

32, -80y, and [tex]80y^2[/tex]

2)The [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.

As the power increases, the expansion gets more difficult to compute. The Binomial Theorem can be used to easily calculate a binomial statement that has been raised to very big power.

(i) Using the binomial theorem, we can expand [tex](2 - y)^{5}[/tex] as follows:

[tex](2 - y)^{5}[/tex] = [tex]2^{5} - 5(24)y^{1} + 10(23)y^{2} + 10(23)y^{3} + 5(2)y^{4} - y^{5}[/tex]

By combining the powers of two and simplifying, we get:

[tex]32 - 80y + 80y^{2} - 40y^3 + 10y^4 - y^5[/tex]

As a result, the first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:

32, -80y, and [tex]80y^2[/tex]

(ii) Using the result of section (i), we can expand [tex](2 - (2x - x^{2} ))^{5}[/tex] by substituting y with 2x - x2:

[tex](2 - (2x - x^2))^5 = 2^5 - 5(2^4)(2x - x^2) + 10(2^3)(2x - x^2)^2 - 10(2^2)(2x - x^2)^3 + 5(2)(2x - x^2)^4 - (2x - x^2)^5[/tex]

By combining the powers of two and simplifying, we get:

[tex]32 - 80x + 80x^2 - 40x^3 + 10x^4 - x^5[/tex]

As a result, the [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.

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a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

[tex]PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }[/tex]

putting the given values,

⇒ [tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }[/tex]

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

[tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }[/tex]

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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The slant height of the cone is about 11 cm. Using the Pythagorean theorem, the height is approximately 41.4 cm to the nearest tenth.

Use the formula for the lateral area of a cone: L = πrs, where L is the lateral area, r is the radius of the base, and s is the slant height.

Plug in the given values: L = 473π cm² and r = 43 cm. Then solve for s

L = πrs

473π = π(43)s

s = 473/43 ≈ 11

So the slant height of the cone is approximately 11 cm.

Use the Pythagorean theorem to find the height of the cone. Let h be the height of the cone. Then the Pythagorean theorem gives

h² + s² = r²

Substituting in the values for s and r, we get

h² + 11² = 43²

Simplifying this equation, we get

h² = 43² - 11²

Evaluating the right-hand side, we get

h² = 1764

Taking the square root of both sides, we get

h ≈ 41.4

So the height of the cone is approximately 41.4 cm to the nearest tenth.

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Answer:

240

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(x-3)(x-3)=27

x^2-3x-3x+9=27

x^2-6x+9=27

          -27.   -27

x^2-6x-18=0

Answer:

(x-3)²=27

Step-by-step explanation:

x²+6x-18=0

add 18 to both sides of the equation

To complete the square add 3² to both sides and factor what is on the left side. You will be getting

(x-3)² = 27 is the answer to this problem

Answer:

C

Step-by-step explanation:

(x-3)(x-3)=27

x^2-3x-3x+9=27

x^2-6x+9=27

          -27.   -27

x^2-6x-18=0

Answer:

(x-3)²=27

Step-by-step explanation:

x²+6x-18=0

add 18 to both sides of the equation

To complete the square add 3² to both sides and factor what is on the left side. You will be getting

(x-3)² = 27 is the answer to this problem

The friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book is given by the order Nancy > Barbara > Judy

Given data ,

The total number of pages in each friend's book as follows:

Barbara's book: 320 pages

Judy's book: 260 pages

Nancy's book: 480 pages

Now, we can calculate their reading rates as pages read per day:

Barbara's reading rate: 100 pages / 4 days = 25 pages/day

Judy's reading rate: 54 pages / 3 days = 18 pages/day

Nancy's reading rate: 160 pages / 5 days = 32 pages/day

Hence , the descending order is Nancy > Barbara > Judy

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Step-by-step explanation:

We can use the proportion of males in the sample to estimate the proportion of males in the population, and then use that proportion to find the expected number of male workers.

The proportion of males in the sample is:

p = 28/50 = 0.56

We can use this proportion to estimate the proportion of males in the population:

p' = 0.56

The expected number of male workers is then:

E(X) = n * p'

where n is the total number of workers in the population:

E(X) = 1300 * 0.56

E(X) = 728

Therefore, we would expect there to be approximately 728 male workers in the company.

Answer:

44 feet in 10 seconds = 44 x 6 (since there are 60 seconds in a minute) = 264 feet per minute

264 feet per minute x 60 minutes (since there are 60 minutes in one hour) = 15,840 feet per hour

15,840 feet per hour / 5,280 feet (since there are 5,280 feet in 1 mile) = 3 miles per hour

Answer:   [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Males who got a C = 4

Total amount of people who got a C = 20

[tex]\frac{4}{20}[/tex]

[tex]\frac{4}{20}[/tex]  simplifies to  [tex]\frac{1}{5}[/tex]

well, let's first find out how much is 30% of 30000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 30000}}{\left( \cfrac{30}{100} \right)30000}\implies 9000[/tex]

ok, that means if we split that down the middle, each will get 4500.

so the remaining is 21000, and that's split on a 3:4 ratio, assuming from A to B, so let's simply divide the total 21000 by (3 + 4) and distribute accordingly.

[tex]\stackrel{A}{3}~~ : ~~\stackrel{B}{4} ~~ \implies ~~ \stackrel{A}{3\cdot \frac{21000}{3+4}}~~ : ~~\stackrel{B}{4\cdot \frac{21000}{3+4}}\implies \stackrel{A}{3\cdot 3000}~~ : ~~\stackrel{B}{4\cdot 3000} \\\\\\ \stackrel{A}{9000}~~ : ~~\stackrel{B}{12000}\hspace{9em}\underset{ \textit{share for A} }{\stackrel{ 4500~~ + ~~9000 }{\text{\LARGE 13500}}}[/tex]

The most descriptive name for the illustration below is C. rhombus.

Because it has four sides, a rhombus is a geometric shape that is a quadrilateral. Because its opposite sides are parallel and their angles are equal, it is a unique kind of parallelogram.

The most descriptive name for the illustration above is C. rhombus.

A rhombus is a type of quadrilateral with four sides of equal length and opposite angles that are equal to each other. It can also be defined as a parallelogram with equal diagonals. The illustration appears to have all sides of equal length and opposite angles that are equal, thus making it a rhombus.

While the other options, such as quadrilateral, polygon, and trapezoid, also apply to the illustration, they are less specific than the term rhombus.

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Answer:

(a) 4.356% (b) 1.089%

Step-by-step explanation:

The rolling of a single die is an example of a discrete uniform distribution, where each of the six possible outcomes has an equal probability of 1/6.

(a) After 1010 rolls of the die, observing a "one" 44 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 44 / 1010

= 0.04356

Therefore, approximately 4.356% of the rolls resulted in a "one".

(b) After 2020 rolls of the die, observing a "one" 22 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 22 / 2020

= 0.01089

Therefore, approximately 1.089% of the rolls resulted in a "one".

Answer:

A) 40%

B) 10%

Step-by-step explanation:

A) p = 4/10 = 40%

B) p = 2/20 = 10%

7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

Time is a measurable and non-spatial quantity used to describe or quantify the sequence, duration, or occurrence of events. It is a concept used to understand the order in which events occur and to measure the duration of those events.

10:44 - Yes, the statement is true. The time is 44 minutes after 10:00.

9:47 - No, the statement is false. The time is 13 minutes before 10:00.

12:13 - Yes, the statement is true. The time is 13 minutes after 12:00.

11:00 - Yes, the statement is true. The time is exactly 11:00.

7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

1:05 - Yes, the statement is true. The time is 5 minutes after 1:00.

5:02 - No information is provided about this time on the clock.

2:00 - Yes, the statement is true. The time is exactly 2:00.

4:00 - Yes, the statement is true. The time is exactly 4:00.

3:00 - Yes, the statement is true. The time is exactly 3:00.

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Answer:

log b.c^z

Step-by-step explanation:

from the theorem a log b=log b^a

z log c= log c^z

from the theorem log a + log b= log ab

log b+ log c^z= logb. c^z will be the final answer

The length of side b is given as follows:

b = 2.86 m.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is obtained as follows:

B + 30 + 80 = 180

B = 70º.

Then the relation, by the law of sines, is given as follows:

sin(70º)/b = sin(80º)/3

Meaning that the length of side b is given as follows:

b = 3 x sine of 70 degrees/sine of 80 degrees

b = 2.86 m.

The triangle is given by the image presented at the end of the answer.

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Answer:2nd one

Step-by-step explanation:

The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

The height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.

Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.

Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:

h_A = radius + center's height

h_A = 85 + 100

h_A = 185 feet

So, the height of point A off the ground is 185 feet.

To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:

h_A = radius * sin(0)

h_A = 85 * 0

h_A = 0

So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

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Answer:

C. d = 163t

Step-by-step explanation:

This equation represents a direct proportionality between the number of dollars earned (d) and the amount of time worked (t), with a constant of proportionality of 163 dollars per hour.

Hope this helps!

The first shape does NOT have a Hamilton circuit

The second shape has a Hamilton circuit

The third shape does NOT have a Hamilton circuit

In mathematical graph theory, a Hamiltonian circuit- named after its originator William Rowan Hamilton, an acclaimed Irish mathematician of the 19th century– is a path within a graph that covers every vertex only once and begins and ends at the same vertex.

To put it differently, it's an enclosed movement that goes through each point in the graph exactly once. When the graph consists of a Hamiltonian circuit, this indicates to be a Hamiltonian graph. One can see many practical uses of Hamiltonian circuits such as computer science where they play a crucial role in algorithm analysis and design.

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first you need to find the gradient of the line and to do that you divide the height of a part of the line by its length. so to find the height we do -3-0=-3 and to find the length we do 2-1=1. then divide -3 by 1 and the gradient is -3. so now we know the equation is y=-3x+b. to find b we replace y with the y coordinate of one of the 2 points. lets take the first point. so it will be 0=-3+b. Now we can easily find b by doing 0-(-3) which is 3. so the equation of the line is y=-3x+3. Also please mark this as brainliest answer if you found it helpful thanks.

Answer:

y = - 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ )  = (1, 0 ) and (x₂, y₂ ) = (2, - 3 )

m = [tex]\frac{-3-0}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 3 )

- 3 = - 3(2) + c = - 6 + c ( add 6 to both sides )

3 = c

y = - 3x + 3 ← equation of line

Answer:

28 mph

Step-by-step explanation:

let x= rate of cyclist

3/11(x)=6

x=66/3=22 mph

22mph+ 6mph=28 mph

they move towards each other with a relative speed of 28 mph

Okay, here are the steps to solve this problem:

* There are 15 sections of English 102 to choose from

* There are 9 sections of Spanish 102 to choose from

* There are 12 sections of History 102 to choose from

* There are 13 sections of College Algebra to choose from

So for English 102 Felicia has 15 options, for Spanish 102 she has 9 options, for History 102 she has 12 options, and for College Algebra she has 13 options.

By the Fundamental Principle of Counting, the total number of possible schedules is:

15 * 9 * 12 * 13 = 16,920

Therefore, the total number of possible schedules for Felicia is 16,920

Answer:

The common ratio of this sequence is 120/150 = 4/5, so we have:

[tex] \frac{150}{1 - \frac{4}{5} } = \frac{150}{ \frac{1}{5} } = 150 \times 5 = 750[/tex]

So the sum of all the terms in this sequence is 750.

The interval of times that represents the middle 99.7% of Caroline's finishing times is (63.5, 72.5) seconds

In this case, we are looking for the interval of times that represents the middle 99.7% of Caroline's finishing times.

The middle 99.7% of the data corresponds to three standard deviations from the mean in both directions

Three standard deviations from the mean is 3 x 1.5 = 4.5 seconds.

Therefore, the interval of times that represents the middle 99.7% of Caroline's finishing times is (68 - 4.5, 68 + 4.5) = (63.5, 72.5) seconds

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The base angles a and b have their measures to be 45 degrees each

If the diagonal of a square produces an isosceles right triangle, then the two legs of the right triangle are congruent, meaning the two base angles are congruent as well.

Since the triangle is a right triangle, one of the base angles must be 45 degrees (which is half of the right angle).

Therefore, both base angles are 45 degrees.

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