Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)
Answer:
thx for free 50
lol
Step-by-step explanation:
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)
Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
A=1 ≥ 2x
B=6x ≥ 3 + 8x – 4
and on a graph
.5 shaded to the left
- .5 shaded to the right
.5 shaded to the right
checking all that apply the correct answers would be A B and C
The correct answers are:
A) 1 ≥ 2x ; B) 6x ≥ 3 + 8x – 4 ; and .5 shaded to the left
Explanation:
Our inequality given is 6x ≥ 3 + 4(2x - 1). First we use the distributive property:
6x ≥ 3 + 4(2x) + 4(-1)
6x ≥ 3 + 8x - 4
This means A is correct.
Next we can subtract 8x from each side:
6x-8x ≥ 3+8x-4-8x
-2x ≥ 3-4
-2x ≥ -1
Divide both sides by -1 (remember to flip the inequality symbol):
-2x/-1 ≥ -1/-1
2x ≤ 1
This can also be written as 1 ≥ 2x, so B is correct.
To finish solving this, divide both sides by 2:
2x/2 ≤ 1/2
x ≤ 0.5
To graph this, we circle 0.5 and fill it in (since it is less than or equal to), and shade to the left (since it is less than).
Which of the following approaches can be used to construct a parallelogram? Select one: a. Measure equal segments on parallel lines, then join the endpoints of these segments. b. Construct two congruent angles, then bisect them. c. Construct the perpendicular bisector of a segment, then bisect two of the right angles. d. Construct two perpendiculars to a parallel line.
Final answer:
The correct approach to constructing a parallelogram is to measure equal segments on parallel lines and then join the endpoints of these segments, which ensures opposite sides are equal and parallel.
Explanation:
The student has asked which of the following approaches can be used to construct a parallelogram. The correct approach is Measure equal segments on parallel lines, then join the endpoints of these segments, which corresponds to option a. This method utilizes the properties of parallelograms, where opposite sides are equal in length and parallel to each other. The Euclidean Geometry postulates that relate to this method include E1 Two points determine a line, E2 Line segments can be extended, and the Parallel postulate: Given a line and a point not on the line, no more than one line can be drawn through the point and parallel to the given line.
To construct a parallelogram, you can follow these simplified steps:
Select any two parallel lines.
Measure and mark equal length segments on each of the lines.
Join the corresponding endpoints of these segments to form the parallelogram.
Which decimal is equal to 4/20
A carnival ride has a sign at the beginning of the line that says "Must be at least 48 inches tall to ride." Which of the following inequalities best represents the allowable height of riders?
h > 48
h < 48
h ≥ 48
h ≤ 48
Answer: h ≥ 48
Step-by-step explanation: h ≥ 48
I just took test got it right
A dance competition on television had five elimination rounds. After each elimination, only one-fourth of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 512 128 32 8 2 Compute the average rate of change of f(x) from x = 2 to x = 4 and describe what it represents.
−60 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−120 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−60 contestants per round, and it represents the number of contestants who will reach the final round
−120 contestants per round, and it represents the number of contestants who will reach the final round
Answer:
A
Step-by-step explanation:
A high school student volunteers to present a report to the administration about the types of lunches students prefer. He surveys members of his class and records their choices. What type of sampling did the student use? systematic random sampling
Answer:
the answer is convenience sampling
Step-by-step explanation:
A triangle can have sides whose lengths are 9cm, 16cm, and
Ravi and Tikiera are making Halloween Pencil Toppers to raise money for the Math Club. Ravi can make one pencil topper in 10 minutes and Tikiera can make one pencil topper in 9 minutes. If they work together, how quickly can they make one pencil topper? Round your answer to the nearest tenth of a minute.
what number is greater than 535 but rounded to the nearest 100 is 500?
which one?
523 535 545 550
write and expression with an exponent that has a value between 0 and 1
Numbers that are divisible by 2,4,6,8,10 have to be.
Dorothy types 120 words per minute .How many words does Dorothy type in 1.75 minutes ?
A construction company was contracted to build a cylindrical storage tank with a diameter of 48 feet and height of 25 feet. Just before construction was to begin, it was learned that a new law allows tanks to be a maximum of 9 feet in height. If the tank is redesigned to meet the law, but has the same volume, what is its new diameter?
A plant is already 11.50 meters tall, and it will grow 9 centimeters every month. The plant's height, H (in meters), after x months is given by the following function.
H (x) = 0.09x + 11.50
What is the plant's height after 15 months?
The plants height after 15 months is:
What are linear equations?"A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution."
Given the function is
[tex]H(x)= 0.09x + 11.50[/tex]
Also given,
Number of months are 15
[tex]\(H(x)= 0.09*15 + 11.50 \\H(x)= 1.35 + 11.50 = 12.85[/tex]
Hence, the plant's height after 15 months is 12.85 meters.
To know more about linear equation here,
https://brainly.com/question/11897796
#SPJ2
solve the inequality 2(p – 7) > 8
The solution to the given inequality 2(p – 7) > 8 is p > 11.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question following as:
2(p – 7) > 8
We have to determine the solution to the given inequality.
As per the question, we have
2(p – 7) > 8
Open the parentheses and apply the distributive property of multiplication,
2p - 14 > 8
Add 14 both sides of the above in inequality,
2p - 14 + 14 > 8 + 14
2p > 22
Divided by 2 into both sides of the above in inequality,
p > 11
Therefore, the solution to the given inequality is p > 11.
Learn more about inequalities here:
brainly.com/question/20383699
#SPJ2
Every day, the number of network blackouts has a distribution (probability mass function)
x | 0 | 1 | 2
P(x)| 0.7| 0.2| 0.1
A small internet trading company estimates that each network blackout results in a $500
loss. Compute expectation and variance of this company’s daily loss due to blackouts.
I computed this E(x)= .4 , varX= .44, but I don't know how i can find the answer?
The answer is
E(Y ) = 200 dollars,
Var(Y ) = 110, 000 squared dollars.
The expected daily loss of the company due to blackouts, E(Y), can be calculated by multiplying each possible loss (which is the number of blackouts times 500) by the probability of that loss occurring, and summing these products. The variance, Var(Y), is found by first finding the expected value of the square of the loss, E(Y^2), which is done in a similar way to finding E(Y), but by squaring each loss before multiplying by its probability. The variance is then given by E(Y^2) - [E(Y)]^2, resulting in a variance of $110,000.
Explanation:The expectation (or mean) of a random variable Y can be computed by multiplying each outcome by its probability and summing all these products. The random variable Y here is the daily loss corresponding to x blackouts, which is given by 500*x, where x is the number of blackouts. Hence to find the expected daily loss, E(Y), you need to calculate:
E(Y) = 0*0.7 + 1*500*0.2 + 2*500*0.1 = $200
The variance of a random variable is found by taking the expected value of the squared variation of that variable from its mean. In this case, you'll calculate:
Var(Y) = E(Y^2) - [E(Y)]^2.
To find E(Y^2), you'll calculate:
E(Y^2) = 0*0.7 + (1*500)^2*0.2 + (2*500)^2*0.1
Substitute E(Y) and E(Y^2) into the variance formulas to get Var(Y) = 110,000.
So, the expectation and variance of the company's daily loss due to blackouts are $200 and $110,000 respectively.
Learn more about Expectation and Variance here:https://brainly.com/question/38785531
#SPJ12
During one day on the stock market, an investor lost $2500 on one stock, but gained $1700 on another. At the end of trading that day, the investor's holdings were worth $52500. What were they worth when the market closed that day?
How do you convert from a radical expression to a rational exponent?
Im just a little confused so if someone could explain this to me, thatd be great!
To convert a radical expression to a rational exponent, identify the root index of the radical as this will be the denominator of the rational exponent. The base remains unchanged. The rational exponent is 1 over the root index.
Explanation:To convert a radical expression to a rational exponent, you need to understand the connection between them. In mathematics, the 'nth root of a' can be written as a radical expression or as a to the power of 1/n, which is the rational exponent form.
For example, if we have √a (square root of a), which is a radical expression, it can be written as a^(1/2) in rational exponent form. Similarly, the cube root of a (3√a) translates to a^(1/3).
Here are the steps for conversion:
Learn more about Radical to Rational Exponent Conversion here:
https://brainly.com/question/10921616
#SPJ3
Identify each expression as a monomial, binomial, trinomial, or none of the above.
1) 24x²y
2) 9q + 4q/5p - 3p²
how do you slove this problem
Connor is asked to find the probability of rolling a prime number on a die. He states that this is a simple event. True or false? A. True B. False
I WILL GIVE BRAINLIEST
Julian compared numbers with similar digits. Using mathematical language, explain how each set of numbers is different
SET A: 13.542 and 35.42
SET B: 781 and 78.1
SET C: 1.2 and 01.20
Consecutive terms are __________________. A. even B. terms that are next to each other C. terms added together D. the Fibonacci sequence
A building contractor has a piece of crown molding that is 48 1/2 inches long he cuts off one piece measuring 10 1/4 inches and another piece 2 feet 1/8 inch how much does he have left
A soccer team played 160 games and won 65 percent of them. How many games did it win ? Please show work
The number of games won is 104.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of games = 160
Percentage of games won = 65%
Now,
The number of games won.
= 65% of 160
= 65/100 x 160
= 104
Thus,
The number of games won is 104.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ2
A boy moves 4 miles south. Then he turns 90 degrees to the left. He moves forward 6 miles. H turns 90 degrees to the left. He moves forward 4 miles. How far is he now than from his starting point?
Find the sum. And simplify 1 4/9 + 3 1/3
Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He has 72 pencils and 24 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
Answer:
3 pencils
Step-by-step explanation:
We are given Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.
Number of pencils=72
Number of calculators=24
If Zayed creates the greatest number of identical packages
Then , we find GCF of 72 and 24
[tex]72=2\times 2\times 2\times 3\times 3[/tex]
[tex]24=2\times 2\times 2\times 3[/tex]
GCF=[tex]2\times 2\times 2\times 3[/tex]
Hence, Zayed creates 24 packages.
Number of pencils in each package=[tex]\frac{72}{24}=3[/tex]
Hence, 3 pencils and one calculator will be in each package .
Answer:
3 pencils
Step-by-step explanation: