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,
Answers
ANSWER :
x = -4t - 16
EXPLANATION :
From the problem, we have the points :
[tex](20,-14)\quad and\quad(12,-12)[/tex]Solve for the equation of the line using two-point formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]That will be :
[tex]\begin{gathered} y-(-14)=\frac{-12-(-14)}{12-20}(x-20) \\ y+14=\frac{2}{-8}(x-20) \\ y+14=-\frac{1}{4}(x-20) \\ y+14=-\frac{1}{4}x+5 \\ y=-\frac{1}{4}x+5-14 \\ y=-\frac{1}{4}x-9 \end{gathered}[/tex]Next is to substitute the given paremetric equation for y :
[tex]y=t-5[/tex]That will be :
[tex]\begin{gathered} y=-\frac{1}{4}x-9 \\ y=t-5 \\ t-5=-\frac{1}{4}x-9 \\ t-5+9=-\frac{1}{4}x \\ t+4=-\frac{1}{4}x \\ 4t+16=-x \\ x=-4t-16 \end{gathered}[/tex]Related Questions
help me decide wheter this is SSS, SAS, or AA problemsI choose SAS, am I right?
Answers
Yes, they are similar triangles.
The answer is SSS
Nick had $100 in his savings account.over the next 6 months, he worked at a seasonal store, where each month he earned $400 and spent $250.He put the remaining amount in his savings account each month.Now that the job is over, he plans to spend $200 per month. For how many months can he
Make withdrawals from his savings account until his balance is $0
Answers
After the 6 months of work he has $1000 on the account, and with that, he can spend $200 each month for 5 months.
For how many months can he make withdrawls?
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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Hannah reads at a constant rate of
3pages every 8minutes.
Write an equation that shows the relationship between
p, the number of pages she reads, and
m
mm, the number of minutes she spends reading.
Answers
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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Use the equation of the polynomial function f(x)=−2x3−x to complete the following.(a) State the degree and the leading coefficient.(b) Describe the end behavior of the graph of the function.(c) Support your answer by graphing the function.
Answers
The function given is,
[tex]f(x)=-2x^3-x[/tex](a)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.
(b)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.
(c)From our function graphed above, we see that "D", from the answer choices, represents the correct graph of this function.
Answer(s)(a)The degree of the polynomial is 3 and the leading coefficient is - 2.
(b)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.
(c)D
How do i write 4/5inch per hour as a ratio
Answers
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.
find the acute angle between the lines 2y+x=1 and x+3y=6
Answers
Given the equations of the lines:
[tex]\begin{gathered} 2y+x=1 \\ x+3y=6 \end{gathered}[/tex]the given equations written in standard form, we will rewrite in in the slope-intercept form
So,
[tex]\begin{gathered} y=-\frac{1}{2}x+\frac{1}{2} \\ y=-\frac{1}{3}x+\frac{6}{3} \end{gathered}[/tex]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:
[tex]\text{tan}\theta=|\frac{m_{1_{}}-m_2}{1+m_1m_2}|[/tex]Substitute with slopes of the lines
So,
[tex]\tan \theta=|\frac{-\frac{1}{2}-(-\frac{1}{3})}{1+(-\frac{1}{2})(-\frac{1}{3})}|=|\frac{-\frac{1}{6}}{1+\frac{1}{6}}|=\frac{1}{7}[/tex]so, the angle will be:
[tex]\theta=\tan ^{-1}(\frac{1}{7})=8.13\degree[/tex]So, the answer will be the acute angle = 8.13°
On her first day in a hospital, Kiri receives u, milligrams (mg) of a therapeutic drug. The amountof the drug Kiri receives increases by the same amount, d, each day. On the seventh day,she receives 21 mg of the drug, and on the eleventh day she receives 29 mg.(a)Write down an equation, in terms of u, and d, for the amount of the drug that she receives(0)on the seventh day;
Answers
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
Hope this Helps!!!
30 year term calculation
Answers
In 30 years, the total amount would be $1,259,430.95 if the principal value is $63,000.
What is a loan amortization schedule?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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find the absolute value |97| =
Answers
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
Match the function to the table of values 2. 7. yurt 3 8. y=r-7 9. y=x+2 I 10. = 3+1
Answers
If you use the values of the table for each of the equations, you can find the answers
single letter from the word ALFALFA is chosen. What is the probability of choosing an For an A? Express your answer as a fraction in owest terms or a decimal rounded to the nearest millionth
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,
[tex]P(F)=\frac{2}{7}[/tex]And the probability of choosing an A is,
[tex]P(A)=\frac{3}{7}[/tex]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,
[tex]P(F\text{ }or\text{ }A)=P(F)+P(A)=\frac{2}{7}+\frac{3}{7}=\frac{5}{7}[/tex]Hence, the probability of choosing an F or an A is 5/7.
Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither.O neitherO X-axisy-axis
Answers
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
Hey does anyone mind helping me and explaining? I would Appreciate it!
Photo is attached
Answers
Answer:
A
Step-by-step explanation:
Corresponding sides of similar figures are in proportion.
The function shown can be used to determine the amount of money, indollars, in a savings account after m months. If no money is added orwithdrawn, which of the following is closest to the amount of money inthe account after 30 months?f(m) = 1500(1.003)^m
Answers
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.
Wesley has just been hired for a new job and wants to work out his budget for each month. The healthinsurance plan he selected has an average monthly premium of $294. The average monthly cost of hiselectric bill is $199 and the phone/internet/cable package he wants costs an average of $110 eachmonth. If his monthly salary is $1900, estimate the amount of money he will have after paying thesebills each month.
Answers
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
4. Sampling students A statistics class with 30 students has 10 varsity athletes and 20 who are not. Choose 2 of th students in the class at random. Find the probability that both are not varsity athletes. a. Draw a tree diagram to model this chance process.
Answers
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
What is a combination?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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help me please
thank you
Answers
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.
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene’s car had 6.5 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cos $3.70 per gallon.
How much did Irene spend on gas?
Answers
After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
What are mathematical operations?An operation is a mathematical function that converts zero or more input values into an output value with a known value.The number of operands affects how complex the operation is.The order of operations refers to the rules that define the sequence in which multiple operations should be performed to solve an expression.PEMDAS is an abbreviation for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the amount Irene spends on gas:
The gas in the tank is 6.5 gallons.The gas amount per gallon is $3.70.Then, the amount of 6.5 gallons of gas:
6.5 × 3.70 = $24.05Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.
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solve the system of equations for each variable x, y, and z. please show your work 2xy=z 4x+z=4y y=x+1
Answers
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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In the country of United States of Heightlandia, 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.
Answers
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%.
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about probability, click on the link given below:
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Given a 10 sided figure how many diagonals can you draw from one vertex?
Answers
Try Again3Graph the line with slopepassing through the point (-4,5)
Answers
Help pleasee i want it today
Answers
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
Nathan is planning to ride his bike for 24 minutes. Write an equation that Nathan can use to find d, the distance he will travel in 24 minutes, if his rate in miles per hours is represented by r
Answers
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
state the value of as a 5/7 recurring decimal
Answers
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
It takes a sheet metal worker 2/3 of an hour to fabricate a fitting, How many fittings can a sheet metal worker
make in an 8 hour day?
Answers
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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The value of c must be greater than 0 1 3 7
Answers
The true statement about the triangle is the value of c must be greater than 3.
How to complete the statementThe figure that completes the question is added as an attachment
From the figure, we have the following parameters
The length of segment AB is 12 units.The length of segment AC is 15 units.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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Hana is organizing a 3/4 mile fun run. There will be a water station every 1/4 of a mile after the start. How many water station will there be?
Answers
There will be 3 water stations along the fun run using the mathematical operation of division.
What is a mathematical operation?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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y = 2x + 1y = -x - 2Solve the following system by graphing. What isthe solution?1. (-1, -3)2. (-1, 3)3. (-1, -1)4. (3, -1)
Answers
Find the solution(s) for x in the equation below. 12 + 10.1 + 21 = 0 O A. I = -3; I = -7 OB. I = -3; 1 -3; r = 7 O c. 3; 1 = -7 3; D = 7 OD..I
Answers
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
