The distance function for Aubrey and Charlie's trip is d(t) = 20 + 50t, accounting for an initial 20 miles already traveled. The reasonable domain for time t in this situation is from 0 to 2 hours since they are traveling at 50 miles per hour and have 100 miles remaining.
Aubrey and Charlie have already traveled 20 miles and are continuing to travel towards a city that is 120 miles away from their start at a constant rate of 50 miles per hour. To complete the function that models the distance they drive as a function of time, we use the formula distance traveled is velocity imes time. With a start of 20 miles, the function can be written as:
d(t) = 20 + 50t
Where d(t) represents the distance traveled at time t in hours. For the domain, since they have already traveled 20 miles, the remaining distance is 100 miles. At a rate of 50 miles/hour, the maximum time needed to cover the remaining distance is 2 hours. Hence, the reasonable domain for time t is 0 ≤ t ≤ 2.
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which is the equation in standard form of the line that contains points C and D
30. The perimeter of a rectangle is 292 feet. The length of the rectangle is 4 feet less than 5 times the width. What is the length and width of the rectangle?
a. length = 121, width = 25b. length = 114.3, width = 23.7
c. length = 25, width = 121d. length = 121.7, width = 24.3
Final answer:
To find the dimensions of the rectangle, the problem was solved by setting up and solving equations based on the given perimeter and the relationship between the length and the width. It was found that the width is 25 feet and the length is 121 feet.
Explanation:
To solve the problem, we first need to set up equations based on the information given. We are told the perimeter of a rectangle is 292 feet and that the length (L) is 4 feet less than 5 times the width (W). The formulas for the perimeter (P) of a rectangle is P = 2L + 2W. The relationship between the length and the width can be expressed as L = 5W - 4.
Substituting the second equation into the first, we get: 292 = 2(5W - 4) + 2W.
Simplifying, we find that 292 = 10W - 8 + 2W, leading to 300 = 12W. Therefore, W = 25 feet. Substituting back to find L, we find that L = 5(25) - 4 = 121 feet.
Thus, the width of the rectangle is 25 feet, and the length is 121 feet, which corresponds to option C).
There is an average of 3.5×10−2 kilograms of dissolved salt in each liter of seawater.
The Indian Ocean contains approximately 2.64×1020 liters of seawater.
About how many kilograms of dissolved salt are in the Indian Ocean?
Enter your answer, in scientific notation, in the boxes.
math question down below
Two students are playing a math game. The object of the game is to make the least possible number by arranging the given digits inside absolute value bars on a card. In the first round, each player will use the digits 3, 5, and 7 to fill in the card. What is the least possible number the card can show?
in order to have the smallest possible number the numbers need to be arranged from smallest to largest
using 3, 5 & 7 the smallest number would be 357
Abel makes the following statement:
"I have a 30% chance of being selected as the captain of the baseball team and a 20% chance of being elected student body president."
What is the probability that Abel will be selected as the captain of the baseball team and will be elected student body president?
Answers:
6%
10%
20%
50%
A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface too fast, he may suffer from a physical condition called “the bends.” Suppose the diver started at 82 feet below the surface and rose in five steps of 15 feet each. Use an integer to describe his new position in relation to the water surface. is it positive or negative?
The deep-sea diver started at 82 feet below the surface and rose in five steps of 15 feet each, which resulted in a new position of -7 feet. This indicates that the diver is still 7 feet underwater, so the integer representing his position is negative.
The diver starts at 82 feet below the surface and rises in five steps of 15 feet each. To find the new position, we start with the initial position and subtract the distance risen in each step:
Initial position: -82 feet (below water is considered negative)
Total rise: 5 steps × 15 feet/step = 75 feet
New position: -82 feet + 75 feet = -7 feet
Therefore, the diver's new position is -7 feet relative to the surface, indicating he is still 7 feet underwater, thus the integer is negative.
what is 5y-4=-3x in standard form
The required standard form is 5y + 3x = 4 of the given linear equation.
What is the standard form of a linear equation?A linear equation in one variable indicates an equation with just one variable. This indicates that there is just one solution to this linear equation. The standard or generic form of linear equations in one variable is expressed as follows:
Ax + B = 0
In this equation, A and B are integers, and x is a variable.
Ax + By = C is the standard form for a line equation. In this situation, using the equation 5y-4=-3x B=5 and A=-3 and C=-4, we may add both -4 and -3x to both sides to get Ax and By on the same side, and we get 5y+3x=4.
Thus, the required standard form is 5y + 3x = 4 of the given linear equation.
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Consider the following statement: If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's. Write the Given statement:
I just saw that my answer to this was removed because brainly is removing some content to make room for more learning.
Since my answer seemed to help a lot of people, i'm reposting it!
Here's my answer: Paul is the oldest, then bill, and Fred is the youngest.
Choose a non-integer between 0 and 1
at 5:00 pm in atlanta, georgia, ethan noticed the temperature outside was 72°F . The temperature decreases at a steady rate of 2°F per hour. At what time was the temperature less than 64°F .
The length of the ears on the shadow puppet is 3 inches. The length of the ears on the shadow is 4 inches. What is the scale factor?
In linear equation, 4/3 is the scale factor.
What are instances of linear equations?Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.given,
The length of the ears on the shadow puppet = 3 inches
The length of the ears on the shadow = 4 inches.
so according to question we apply the formula of scale factor ,
scale factor = length of ears on the shadow/length of ears on the shadow
scale factor = 4/3
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Markers are sold in boxes, packs, or as single markers. Each box has 10 packs. Each pack has 10 markers. Draw pictures to show two ways to buy 276 markers.
the porportion of red marbles to blue marbles jar is 2 to 5. If there are 35 blue the jar, how many red mables are there?
give a counterexample to disprove the statement "all squares are congruent"
using what you know about percents,explain why a commercial that says"80% of dentists use this toothpaste"might be misleading?
The lizards in the show eat 250 crickets per week.About how any crickets do the lizards eat each day?Explain.
Each day the lizards eat about 36 crickets when we round to the nearest whole number
To calculate how many crickets the lizards eat each day, we need to divide the weekly intake by the number of days in a week. The lizards eat 250 crickets per week. There are 7 days in a week.
So, we divide 250 by 7 which equals approximately 35.71 crickets per day.
Therefore, each day the lizards eat about 36 crickets when we round to the nearest whole number, since you can't have a fraction of a cricket.
Find the product. (3p 4)3 · (p 2)7
The product of the expressions (3p⁴)³ * (p²)⁷ is 27p²⁶
How to evaluate the product of the expressions
From the question, we have the following parameters that can be used in our computation:
(3p⁴)³ * (p²)⁷
Expanding the brackets, we have
(27p¹²) * (p¹⁴)
Remove the brackets
So, we have
27p¹² * p¹⁴
Evaluate using the law of indices
27p²⁶
Hence, the product of the expressions is 27p²⁶
Question
Find the product
(3p⁴)³ * (p²)⁷
Which type of weathering is caused by plants?
A.mechanical weathering
B. ice wedging
C. both mechanical and chemical weathering
D. chemical weathering
Please help
10 points!!
Use conversion factors to convert. Write the factor you used.
5 quarts to cups __________
600 centimeters to meters ________
The cooking time for a piece of meat is proportional to the weight of the meat. What is the value of the constant for this relationship
The constant for relationship is 20.
What is ratio and proportions?When comparing two quantities of the same kind, ratio is utilized. For two numbers, a and b, the ratio formula is written as a: b or a/b. Two or more ratios are said to be in proportion if they are all equal. Fractions are the foundation of the concepts of ratio and proportion. The fundamental building blocks of numerous other mathematical notions are ratio and proportion.
Given The cooking time for a piece of meat is proportional to the weight of the meat.
given Weight (lb) 1.5 2.5 3.5
time (min) 30 50 70
Acc. to question time/weight = constant
= 30/1.5 = 50/2.5 = 70/3.5 = 20
Hence the constant is 20.
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The complete question is
The cooking time for a piece of meat is proportional to the weight of the meat.
Weight (lb) 1.5 2.5 3.5
time (min) 30 50 70
What is the value of the constant for this relationship.
last week Chen bought 8 1/2 gallons of gas at 2.30 per gallon. This week he bought 4 3/10 gallons of gas at 2.70 per gallon
What is his total cost
30 points !!!!!!!!Solve the following problem. Show ALL steps to receive full credit.
5x + x + x – 6 – 2 = 8 + 2x + x a.
Simplify by combining like terms. State your equation
Malik borrowed $105 from his brother and plans to repay $12 per week. He creates a table to help him determine the number of weeks it will take to repay his brother. How many weeks will it take Malik to repay his brother? 8 9 10 11
How can we best show or describe the change in a position of a figure?
A holiday display is made up of several strands of lights. There are 2970 lights in the display. Each light strand has 135 lights. How many strands of lights are in the display?
A pattern maker uses 526 yards of muslin cloth each month. The cloth comes on bolts, or rolls, that hold 15 yards each. How many bolts of muslin cloth does the pattern maker use each month?
A) 35
B) 35 1/15
C) 35 1/5
D) 35 1/3
Your grade point average is 3.48. How can you write your grade point average as a fraction?
If the train that Megan is riding covers 120 miles in 4 hours, how fast is the train traveling?