Construct parametric equations describing the graph of the line passing through the following points.(20, -14) and (12, -12)If y = 1-5, find the parametric equation for x,

Answer

The equation for the amount of drug received on the 7th day in terms of u and d is

a₇ = u + 6d

Explanation

The description of the amount of drug administered on the first day and how the amount increases each day by d shows that this is an arithmetic progression question.

For an arithmetic progression with first term, u, and common difference, d, the nth term is given as

aₙ = u + (n - 1) d

a) So, for the 7th day

a₇ = u + (7 - 1) d

a₇ = u + 6d

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Answer:

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Polynomials are used in engineering, computer and math based jobs, in management, business and even in farming. In all careers requiring knowledge of polynomials, variables and constants are used to create expressions defining quantities which are known and unknown.

Step-by-step explanation:

hope this helps you

Answer:

The value of 5/7 recurring numbers is 714285

Explanation:

The given fraction 5/7 is the equivalent of

0.7142857142857142857142857142857142857142857142857142857142857142...

Notice that the recurring numbers are:

714285

After the 6 months of work he has $1000 on the account, and with that, he can spend $200 each month for 5 months.

We know that Nick initially had $100 on his savings account.

Then each month (for 6 months) he earns $400 and spends $250 and puts the rest in the savings account, the rest will be:

$400 - $250 = $150

If he saves this for 6 months, then he adds:

6*$150 = $900

And he already had $100 on the account, so now he has a total of:

$900 + $100 = $1000

For how many months can he take $200 of the account?

To see that, we need to take the quotient between the total amount and what he takes each month:

$100/$200 = 5

5 months.

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There will be 3 water stations along the fun run using the mathematical operation of division.

A mathematical operation uses addition, subtraction, division, or multiplication to reach a result after combining variables, numbers, and mathematical operands.

In this situation, we only use division to get the quotient, which is the number of water stations along the fun run.

The total distance for a fun run = 3/5 miles (0.75 miles)

The spread of the water station along a mile = every 1/4 mile (0.25 miles)

The number of water stations along the run = 3 (0.75/0.25)

Thus, Hana needs to station 3 water stations along the run by dividing the total distance by the expected spread.

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Given the equations of the lines:

the given equations written in standard form, we will rewrite in in the slope-intercept form

So,

So, the slopes of the lines are { -1/2, -1/3 }

The acute angle between the lines of slopes m1 and m2 is given by the formula:

Substitute with slopes of the lines

So,

so, the angle will be:

So, the answer will be the acute angle = 8.13°

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The probability that the 2 students chosen are not varsity athletes is 38/87

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

Number of students = 30

Number of varsity athletes = 10

Number of non-varsity athletes = 20

Number of students chosen at random = 2

The probability that the 2 students chosen are not varsity athletes:

= [tex]\frac{^{20}C_2}{^{30}C_2}[/tex]

= 10 x 19 / 15 x 29

= 2 x 19 / 3 x 29

= 38 / 87

Thus,

The probability that the 2 students chosen are not varsity athletes is 38/87

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1) To determine a reflection across the x-axis, the rule to be followed is

Pre-Image Image

(x,y) --------------------> (x, -y)

A reflection across the y-axis follows this one:

Pre-Image Image

(x,y) --------------------> (-x, y)

2) Let's pick one point from the pre-image and the image on the graph

Since A (-2,0) and F (1,-3) then we cannot state that there was a reflection across the x-axis or y-axis.

3) The answer is neither

The probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.

As per the question statement, in the country of United States, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.8 inches and standard deviation of 9.4 inches. We are supposed to find the probability that a randomly chosen child has a height of less than 33.3 inches.

z = (X - μ) / σ, where X is the data data, μ = mean, σ = standard deviation

z = (66.09 - 56.8) / 9.4

z = 0.988 or 98%

So, the probability that a randomly chosen child has a height of less than 33.3 inches when mean height is 56.8 inches and standard deviation is 9.4 inches will be 98%.

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The true statement about the triangle is the value of c must be greater than 3.

The figure that completes the question is added as an attachment

From the figure, we have the following parameters

The length of segment of BC is represented by the variable c

By the triangle inequality theorem, we have:

The sum of any two sides length is greater than the third length

This means that

12 + 15 > c

c < 27

Also, we have

15 + c > 12

c >-3

Lastly, we have

12 + c > 15

c >3

Using the list of options as a guide, we have x > 3 to be true

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After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.

So, the amount Irene spends on gas:

Then, the amount of 6.5 gallons of gas:

Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.

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Given data:

The given function of amount of mmoney after m months is f(m)=1500(1.003)^m.

Substitute 30 for m in the given expression.

f(30)=1500(1.003)^(30)

=1500(1.094)

=1641

Thus, the total amount of money after 30 monnths is 1641.

Answer:

$1297

Explanation:

First, let's add all the costs that Wesley has each month, so

$294 + $199 + $110 = $603

Because the health insurance cost $294, the electric bill is $199 and the phone/internet/cable cost $110.

Then, To find the amount of money that he will have after paying these bills, we need to subtract $603 from his salary, so

$1900 - $603 = $1297

Therefore, the answer is $1297

12 fittings can a sheet metal worker make in 8 hours.

What is ratio calculator?

Ratio Calculator is a formula used to solve ratio problems to express two or three numbers ratio to its simplest form.

2/3 hours taken to  fabricate = 1 sheet

8 hours taken to fabricate = 8/2/3

= 4(3)

= 12

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Answer:

4/5 to 1

Step-by-step explanation:

you just put the numbers next to each other

Answer:

4 : 5 are 8 : 10 and 12 : 15

Step-by-step explanation:

Therefore, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15. Note: In this question we can't apply division method to get the answer in integer form because the G.C.F. of 4 and 5 is 1. That means, 4 and 5 cannot be divisible by any other number except 1.

If you use the values of the table for each of the equations, you can find the answers

ANSWER

5/7

EXPLANATION

The word ALFALFA has 7 letters, of which there are:

• 3 A

• 2 L

• 2 F

If we choose a single letter, the probability of choosing an F is,

And the probability of choosing an A is,

Since we are choosing a single letter, there is no event where we can choose both an F and an A at the same time, so the probability of choosing an F or an A is,

Hence, the probability of choosing an F or an A is 5/7.

Answer:

Step-by-step explanation:

We are required to find the distance Nathan will travel.

Total distance travelled of Nathan is 2 miles

speed = Total distance travelled ÷ Total time take

total distance travelled = Speed × Total time taken.

Speed = 5 miles per hour

Time = 24 minutes

Convert minutes to hour

60 minutes = 1 hour

24 minutes = 0.4 hour

total distance travelled = Speed × Total time taken

= 5 miles per hour × 0.4 hour

= 2 miles

Therefore, total distance travelled of Nathan is 2 miles

Answer:

Choice A: x = -3, x = -7

Explanation:

To solve the equation for x, we use the quadratic formula which says that if you have an equation

In 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.

It is defined as the systematic way of representing of loan payments according to the time in which the principal amount and interest are mentioned in a list manner

It is given that:

P = 63,000

i = 5.3%

t = 30 years

[tex]\rm Total \ amount = P\times\dfrac{(\dfrac{r}{n})(1 + r/n)^{tn}}{(1 + r/n)^{tn}-1}[/tex]

After putting the values in the formula we get:

Total amount = $1,259,430.95

Thus, in 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.

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Answer:

A

Step-by-step explanation:

Corresponding sides of similar figures are in proportion.

The solution of the system of equations 2xy = z, 4x + z = 4y, y = x + 1 are:

x = 1, y = 2, z = 4 and;

x = - 2, y = - 1, z = 4.

Consider the system of equations,

2xy = z                                                                                              ------------(1)

4x + z = 4y                                                                                       ------------(2)

y = x + 1                                                                                            -------------(3)

Substituting equation (3) in equation (2),

4x + z = 4y

4x + z = 4( x + 1)

4x + z = 4x + 4

z = 4

Substituting equation (3) in equation (1),

2xy = z

2x( x + 1 ) = z

2x² + 2x = 4

x² + x = 2

Hence, x = 1, - 2

Therefore,

When x = 1,

y = x + 1 = 2

When x = - 2, y = x + 1 = - 1

So, the solution for the system of the equations are x = 1, y = 2, x = 4 and x = - 2, y = - 1, z = 4.

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The function given is,

We need to find the degree and leading coefficient of the function.

The degree is the highest power of the polynomial.

We can see that it is a cubic polynomial, or, a third degree function.

The leading coefficient is the coefficient of the highest degree term.

In our case, -2 is the leading coefficient because it is the coefficient of x^3.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Let's graph the function:

From the graph, we can see,

• As x approaches infinity, the function approaches negative infinity

• As x approaches negative infinity, the function approaches positive infinity

This describes the end behavior of the function.

From our function graphed above, we see that "D", from the answer choices, represents the correct graph of this function.

The degree of the polynomial is 3 and the leading coefficient is - 2.

The curve opens down to the right because the leading coefficient is negative. Because the polynomial is cubic, the graph has end behaviors in the opposite direction, so the other end opens up to the left.

D

The relationship between p, the number of pages she reads, and m, the number of minutes she spends reading is 8p = 3m.

It is given in the question that Hannah reads at a constant rate of 3 pages every 8 minutes.

We have to write an equation that represents the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading.

If she reads 3 pages every 8 minutes, then

She reads 1 page every 8/3 minutes.

If she reads p pages , she will take 8p/3 minutes

If m represents the number of minutes she she spends reading p pages.

Then, we can write,

8p/3 = m

8p = 3m

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Absolute value means take the non-negative number of what is between the bars

|97|

Since 97 is already positive, the absolute value of 97 is 97

Yes, they are similar triangles.

The answer is SSS

Answer:

Domain: [1, 7], Range: [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.