The velocity of the car is represented by the equation y = 4x + 39, where 'x' is time and 'y' is the velocity. You can graph this for the first six hours by substituting x=6 to find: y=63 km/h. Thus, the car's velocity after six hours would be 63 km/h.
Explanation:In order to solve this problem, we first find the equation representing the change in the car's velocity. The point (3, 51) represents the condition that after three hours, the car is moving at 51 km/h. Similarly, the point (5, 59) stands for the velocity being 59 km/h after five hours. We derive the slope of the line connecting these two points by subtracting the y-coordinates and dividing by the difference of the x-coordinates, (59-51)/(5-3) = 4.
This slope represents an increase of 4 km/h for every hour that passes. Our equation then becomes y - 51 = 4(x - 3) which simplifies to y = 4x + 39. In this equation, 'x' represents time in hours and 'y' is the car's velocity at any given time 'x'.
For Part B, we graph the equation over the first six hours by inputting x=6 into the equation, giving us y = 4*6 + 39 = 63 km/h. Therefore, after six hours, the car would be moving at a velocity of 63 km/h.
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What is the measure of an exterior angle in a regular dodecagon?
how many outliers are there in this data set 1, 4, 6, 9, 12, 13, 13, 17, 19
A. 2
B. 3
C. None
D. 1
need help with this geometry question, solving for x and please explain the formula for this
FOR 30 POINTS WILL MARK BRAINLIEST you have 500 sheets of notebook paper after one week you have 72% of the sheets left. you use the same number of sheets each week write an equation that represents the number y of pages remaining after 8 weeks
Solve for x: |2x + 12| = 18
Deon is saving money to buy a game. so far he has saved $20 , which is four-fifths of the total cost of the game. how much does the game cost?
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
24.8 units
27.8 units
28.5 units
30.9 units
Answer:
The answer would be 27.8
The value of 110 coins, consisting of dimes and quarters, is $20.30. how many of each kind of coin are there?
6.
The sum of two consecutive odd integers is 236. What is the smaller integer? (4 points)
a) 115
b) 117
c) 119
d) 113
Your survey indicates the following favorite beverage choices: 20 milk, 13 water, 22 soda, 32 coffee. What percentage of customers can you satisfy if you just serve milk or water?
Carla bought a shirt for $14 and a jacket for $69. She gave the cashier $100.
How much change should Carla get back?
Jana is on a two-day hike. The function graphed shows the total distance she hiked, in miles, after x hours on the second day.
Select from the drop-down menus to correctly identify the information about Jana's hike provided by the graph.
Answer:
The slope is 2.
Step-by-step explanation:
The function graphed shows the total distance she hiked, in miles, after x hours on the second day.
Seeing at the graph, we have the following points.
(2,8) , (3,10) , (4,12)
For slope we will do the following.
[tex]\frac{10-8}{3-2} =\frac{2}{1}[/tex] = 2
[tex]\frac{12-10}{4-3} =\frac{2}{1}[/tex] = 2
So, the slope is 2.
The slope represents that 2 miles is hiked in each hour.
what is the vertex of the graph of the function below y=x^2-10x+21
which equation best represents the line graphed above
a x=4
b x= _ 4
y= x -4
y= - 4
The correct answer is option B. The equation best represents the line graphed is x = -4.
What is an equation of a line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Since x = -4 is a vertical line(perpendicular to horizontal), there is no y-intercept and the slope is undefined.
A vertical line has an undefined slope because all points on the line have the same x-coordinate.
So, the slope is undefined and we also don't have the y-intercept.
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Points d, e, and f are plotted on a number line. the coordinate of point f is 5. points d and e are the same distance from point f. what could be the coordinates of d and e?
a. d = –7, e = –1
b. d = –2, e = 12
c. d = 0, e = 5
d. d = 8, e = 11
The coordinates of d and e b. d = –2, e = 12.
To find the coordinates of points D and E, we need to remember that they are the same distance from point F, which has a coordinate of 5. This means D and E are equidistant from F on the number line. Let's check each option to see which one satisfies this condition:
Option a: d = -7, e = -1
The distance from -7 to 5 is 12.
The distance from -1 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Option b: d = -2, e = 12
The distance from -2 to 5 is 7.
The distance from 12 to 5 is also 7.
Since the distances are equal, this option is correct.
Option c: d = 0, e = 5
The distance from 0 to 5 is 5.
The distance from 5 to 5 is 0.
Since the distances are not equal, this option is incorrect.
Option d: d = 8, e = 11
The distance from 8 to 5 is 3.
The distance from 11 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Therefore, the correct answer is option b: d = -2, e = 12.
The solution to the equation 4(x – 7) = 64 is shown. Which step is a result of combining like terms?
A) Step 2
B) Step 3
C) Step 4
D) Step 5
A cheetah can run 103 feet per second. A zebra can run x feet per second. Use the Distributive Property to write and simplify an expression for how much farther the cheetah can run in 10 seconds
We are given that the rate of cheetah Rc is:
Rc = 103 ft / sec
And the rate of zebra Rz is:
Rz = x ft / sec
We are to find the distance between the two after 10 seconds, that is:
distance = (103 – x) 10
distance = 1030 – 10 x
The expression for how much farther a cheetah can run than a zebra in 10 seconds, given that the zebra's speed is x feet/second, is 1030 - 10x feet.
Explanation:To find out how much farther the cheetah can run in 10 seconds, we need to determine the difference between the cheetah's speed and the zebra's speed, and then multiply by time.
Firstly, the cheetah's speed is 103 feet per second. Let x denote the zebra's speed. The difference in speed is expressed as (103 - x) feet per second.
To find out how much farther the cheetah runs in a given time, we multiply the difference in speed by time. Therefore, the expression for how much farther the cheetah can run in 10 seconds is 10 * (103 - x), which simplifies to 1030 - 10x feet.
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what is the constant rate of change of y=7-13x
The constant rate of change in the linear equation y=7-13x is -13, representing the slope of the line which remains constant for any value of x. This is different from nonlinear functions, where the rate can vary with x.
Explanation:The constant rate of change in the equation y=7-13x refers to the slope of the line represented by this linear equation. In this case, the constant rate of change, or the slope, is -13. This means for every one unit increase in x, y decreases by 13 units. Since the equation is linear, this rate does not change regardless of the value of x, unlike in nonlinear functions where the rate of change can vary with x.
To elaborate, if we have a nonlinear function, the rate of change depends on the interval of x we are looking at. For a linear function like this one, the slope is the same over any interval, so there's no need to compute it over smaller ranges of x to understand the rate of change.
Moreover, in calculus, the derivative represents the rate of change, and for a linear function, the derivative is simply the coefficient of x. Hence, the derivative of y with respect to x is -13. The derivative is zero for any constant term in a function, such as the 7 in the given equation.
Evaluate the determination for the following matrix [144] [522] [155]
-10x-2(5x+4)-[-2(3x-4)-2x]=0
Which ordered pair (a,b) is a solution to the given system of linear equations.
Answer:
A. (-13,-3)
Step-by-step explanation:
Solve the system of two equations:
[tex]\left\{\begin{array}{l}-2a+3b=14\\a-4b=3\end{array}\right.[/tex]
From the second equation:
[tex]a=3+4b[/tex]
Substitute it into the first equation:
[tex]-2(3+4b)+3b=14\\ \\-6-8b+3b=14\\ \\-8b+3b=14+6\\ \\-5b=20\\ \\5b=-20\\ \\b=-4[/tex]
So,
[tex]a=3+4b=3+4\cdot (-4)=3-16=-13[/tex]
The solution is (-13,-4)
Answer:
A
Step-by-step explanation:
The sum of 2 numbers is 44 the smaller number is 16 less than the larger number what are the numbers
Mrs. Noyes fills up a 5 gallon can of gas from the McIntosh’s local convenience store. They are selling gas at $2.099 a gallon. How much is she going to pay at the pump
Children younger than ______ years of age must be restrained in an approved child passenger safety seats unless they are at least 4 ft, 9 inches in height.
Two trains leave a station at 11:00am. one train travels north at a rate of 75 mph and another travels east at a rate of 60 mph. assuming the trains do not stop, about how many minutes will it take for the trains to be 150 miles apart
What is an equation of the line that passes through the points (1 3) and (8 5)? y+1+2/7(x+3), y-5=2/7(x-8), y-1=2/7(x+3), y+5=2/7(x-8)?
Calculate the loss on selling 50 shares of stock originally bought at 13 and 3/4 and sold at 12
Kevin's bucket contains 2 1/2 gal of water. If he gives his horse 2/3 of the water, how much water does the horse get?
Answer:
2.5
Step-by-step explanation:
Marc earned $1,650 per month as an assistant technician at a recording studio. His new job pays $9.80 per hour with time and a half for all hours over 36 hours per week. How many hours of overtime per week will he need to work to earn the same amount per week as his current job?
Marc will need to work just over 4 hours of overtime each week at his new job, which pays $9.80 per hour and $14.70 per hour for overtime, to earn the equivalent of his previous monthly income of $1,650.
To determine the number of overtime hours Marc needs to work at his new job to earn the same monthly income he did at his previous job, we'll first calculate his weekly income at his old job, then use the overtime pay rates at the new job to find the equivalent number of hours needed.
Marc previously earned $1,650 per month. Assuming a standard 4-week month, his weekly income was:
$1,650 per month / 4 weeks per month = $412.50 per week.
At his new job, Marc earns $9.80 per hour with time and a half for all hours over 36 hours a week. This means his overtime pay is 1.5 times his hourly rate, which is:
$9.80 per hour x 1.5 = $14.70 per hour for overtime.
Marc's income for the first 36 hours at his new job would be:
36 hours x $9.80 per hour = $352.80
To earn the equivalent of his old weekly salary, we must make up the difference with overtime pay:
$412.50 (old weekly income) - $352.80 (new regular pay) = $59.70 needed from overtime.
To determine the overtime hours needed to make $59.70: $59.70 / $14.70 per hour = approximately 4.06 hours.
Therefore, Marc will need to work just over 4 hours of overtime each week to earn the same amount he did at his previous job.
2. Pat is six years older than twice his Cousin Zach’s age. The sum of their ages is less than 36.
What is the greatest age that Zach could be?