Primo car rental agency charges $21 per day plus $0.25 per mile. Ultimo car rental agency charges $17 per day plus $0.75 per mile. Find the daily mileage for which the Ultimo charge is twice the Primo charge.
Let's say the daily mileage is x miles.
Primo's charge would be $21 + $0.25x.
Ultimo's charge would be $17 + $0.75x.
We want to find the value of x for which Ultimo's charge is twice Primo's charge:
$17 + $0.75x = 2($21 + $0.25x)
Simplifying, we get:
$17 + $0.75x = $42 + $0.5x
Subtracting $17 and $0.5x from both sides:
$0.25x = $25
Dividing by 0.25:
x = 100
Therefore, the daily mileage for which Ultimo's charge is twice Primo's charge is 100 miles.
Lindsey drew was the top score in a women’s professional basketball league for the 2006 regular season with a total of 820 points the number of two point field goals that Lindsey made with 60 less than double the number of three-point field goals she made the number of free throws each worth one point she may was 17 less than the number of two point field goals. She may find how many free throws to point field goal and three point field goal Lindsey drew made during the 2006 regular season.
Let's say the number of three-point field goals Lindsey made is x.
Then, the number of two-point field goals she made is 2x - 60 (since it's 60 less than double the number of three-point field goals).
And the number of free throws she made is 2x - 60 - 17 = 2x - 77 (since it's 17 less than the number of two-point field goals).
We know that the total number of points Lindsey made is 820, and we can use this information to set up an equation:
3x + 2(2x - 60) + (2x - 77) = 820
Simplifying, we get:
7x = 1037
Dividing by 7:
x = 148
So Lindsey made 148 three-point field goals.
Using this, we can find the number of two-point field goals and free throws she made:
Number of two-point field goals = 2x - 60 = 2(148) - 60 = 236
Number of free throws = 2x - 77 = 2(148) - 77 = 219
Therefore, Lindsey made 148 three-point field goals, 236 two-point field goals, and 219 free throws during the 2006 regular season.
Lindsey drew what’s the top score in a women’s professional basketball league in 2006 regular season with a total of 820 points the number of two-point field goals that Lindsey made was 60 less than double the number of three-point field goals she made the number of free throws each worth one point she may was 17 less than the number of two point field goals she made find how many free throws two point field goals and three point field goals Lindsey Drew, made during the 2006 regular season
Discuss whether a vertical line ever has a Y intercept
A vertical line is a line that runs straight up and down, parallel to the y-axis, and it can be represented by the equation x = a, where "a" is a constant that gives the x-coordinate of all points on the line.
Since a vertical line is parallel to the y-axis, it does not intersect the y-axis at any point, except at infinity. Therefore, a vertical line does not have a y-intercept in the traditional sense.
By definition, the y-intercept of a line is the y-coordinate of the point where the line intersects the y-axis. However, since a vertical line never intersects the y-axis, it does not have a y-intercept.
In conclusion, it can be said that a vertical line never has a y-intercept.
Determine whether the pair of lines is parallel, perpendicular, or neither line one goes through parentheses (0,5) and (15, 0) line to go through (0, -15) and (5,0)
To determine whether the pair of lines is parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
Line one goes through (0, 5) and (15, 0), so we can find the slope using the slope formula:
slope = (change in y) / (change in x) = (0 - 5) / (15 - 0) = -5/15 = -1/3
Line two goes through (0, -15) and (5, 0), so we can find the slope using the slope formula:
slope = (change in y) / (change in x) = (0 - (-15)) / (5 - 0) = 15/5 = 3
Since the slopes have opposite signs and are reciprocals of each other (i.e., (-1/3) and 3 are reciprocals), we can conclude that the pair of lines is perpendicular.
One of the top 10 occupations in terms of job growth is the next few years is expected to be physician assistance the number of people, why, and thousands employed at physicians assistance in a country can be estimated by the linear equation 35x-2y=-144 where x is the number of years after 2008
a. Find the slope and the y-intercept of the linear equation
b. What does the slope mean in the next context?
c. What does the y-intercept mean in this context?
a. To find the slope and y-intercept of the linear equation 35x - 2y = -144, we need to rearrange it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:
35x - 2y = -144
-2y = -35x - 144
y = (35/2)x + 72
So the slope is 35/2 and the y-intercept is 72.
b. The slope of the linear equation 35x - 2y = -144 is 35/2, which means that for every one year after 2008 (one unit increase in x), the number of physician assistants employed in thousands (y) is expected to increase by an average of 35/2 thousand or 17.5 thousand per year.
c. The y-intercept of the linear equation 35x - 2y = -144 is 72, which means that in the year 2008 (when x = 0), the estimated number of physician assistants employed in thousands was 72 thousand. Therefore, the y-intercept is an estimate of the initial number of physician assistants employed in the country at the beginning of the time period being analyzed (in this case, the beginning of the years after 2008).
Right and equation of the line through (-4, -7) and parallel to 5x+ 4y=9 write the equation in the form, x=a, y=b or y=mx+b
What is the equation of the line?
Write an equation of the line through (-4, -7) and parallel to 5x+ 4y=9. Write the equation in the form, x=a, y=b
The equation of the line is
To find the equation of the line through (-4, -7) and parallel to 5x + 4y = 9, we need to start by finding the slope of the line 5x + 4y = 9.
We can rewrite this equation in slope-intercept form y = mx + b by solving for y:
5x + 4y = 9
4y = -5x + 9
y = (-5/4)x + 9/4
The slope of this line is -5/4, since it's the coefficient of x.
Since the line we want to find is parallel to this line, it must also have a slope of -5/4.
Now we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Plugging in the point (-4, -7) and the slope -5/4, we get:
y - (-7) = (-5/4)(x - (-4))
Simplifying:
y + 7 = (-5/4)(x + 4)
Multiplying both sides by 4 to eliminate the fraction:
4y + 28 = -5(x + 4)
Distributing the -5:
4y + 28 = -5x - 20
Moving the terms with y to one side:
4y = -5x - 48
Dividing both sides by 4:
y = (-5/4)x - 12
Therefore, the equation of the line through (-4, -7) and parallel to 5x + 4y = 9 is y = (-5/4)x - 12, written in the form y = mx + b.
Find an equation of the line passing through (8,2) and parallel to 9x-y=9. Write the equation in standard form
To find an equation of the line passing through (8, 2) and parallel to 9x - y = 9, we need to start by finding the slope of the line 9x - y = 9.
We can rewrite this equation in slope-intercept form y = mx + b by solving for y:
9x - y = 9
-y = -9x + 9
y = 9x - 9
The slope of this line is 9, since it's the coefficient of x.
Since the line we want to find is parallel to this line, it must also have a slope of 9.
Now we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Plugging in the point (8, 2) and the slope 9, we get:
y - 2 = 9(x - 8)
Simplifying:
y - 2 = 9x - 72
Moving the terms with y to one side:
9x - y = 70
Therefore, the equation of the line passing through (8, 2) and parallel to 9x - y = 9 is 9x - y = 70, written in standard form.
The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $2, sales will reach 7000 Fun Noodles per day during the summer. Raising the $3 will cause the sales to fall 6000 Fun Noodles per day.
To analyze the relationship between price and quantity of the Fun Noodle sold, we can use the concept of price elasticity of demand, which measures the responsiveness of the quantity demanded to a change in price.
The price elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price:
Price elasticity = (% change in quantity demanded) / (% change in price)
Using the information given in the problem, we can first calculate the percentage change in quantity demanded when the price changes from $2 to $3:
% change in quantity demanded = (new quantity demanded - original quantity demanded) / original quantity demanded x 100%
% change in quantity demanded = (7000 - 6000) / 7000 x 100%
% change in quantity demanded = 1000 / 7000 x 100%
% change in quantity demanded = 14.3%
Next, we can calculate the percentage change in price from $2 to $3:
% change in price = (new price - original price) / original price x 100%
% change in price = (3 - 2) / 2 x 100%
% change in price = 50%
Now, we can plug in these values into the formula for price elasticity:
Price elasticity = (% change in quantity demanded) / (% change in price)
Price elasticity = 14.3% / 50%
Price elasticity = 0.286
Since the price elasticity is less than 1, we can conclude that the demand for Fun Noodles is inelastic in this price range. That is, a 50% increase in price leads to only a 14.3% decrease in quantity demanded, indicating that consumers are not very responsive to price changes.
Based on this analysis, the Pool Fun Company can adjust its pricing strategy to maximize its revenue. For example, it may consider increasing the price of Fun Noodles slightly higher than $2, since the demand is relatively inelastic, which can result in higher revenues without causing a significant decrease in sales.
The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $2, sales will reach 7000 Fun Noodles per day during the summer. Raising the $3 will cause the sales to fall 6000 Fun Noodles per day.
a. Assume that the relationship between sales price, x and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold).
The equation is ( Type your answer in slope-intercept form.)
b. Predict the daily sales of Fun Noodles if the price is $2.50
a. We can determine the equation in slope-intercept form by using the two ordered pairs given: (2, 7000) and (3, 1000). The slope, m, can be calculated as the change in y divided by the change in x:
m = (y2 - y1) / (x2 - x1) = (1000 - 7000) / (3 - 2) = -6000
Using the point-slope form of the equation, y - y1 = m(x - x1), with the point (2, 7000):
y - 7000 = -6000(x - 2)
y - 7000 = -6000x + 12000
y = -6000x + 19000
Therefore, the equation in slope-intercept form describing the relationship between sales price and number sold is y = -6000x + 19000.
b. To predict the daily sales of Fun Noodles if the price is $2.50, we can plug in x = 2.5 into the equation and solve for y:
y = -6000(2.5) + 19000
y = -15000 + 19000
y = 4000
Therefore, the predicted daily sales of Fun Noodles if the price is $2.50 is 4000.
If f(x) =-2x-4, g(x)= -5x^2-2x+5, and h(x) =6x^2+6, find g(0)
To find g(0), we need to substitute x=0 into the function g(x):
g(0) = -5(0)^2 - 2(0) + 5
g(0) = 0 - 0 + 5
g(0) = 5
Therefore, g(0) = 5.
The dosage in milligrams D of a medicine, a heart worm preventive, for a dog who weighs X pounds is given by D(x) =136/25x. Find the proper dosage for a dog that weighs 25 pounds
To find the proper dosage for a dog that weighs 25 pounds, we need to substitute x=25 into the function D(x):
D(25) = (136/25)(25)
D(25) = 136
Therefore, the proper dosage for a dog that weighs 25 pounds is 136 milligrams.
The dosage in milligrams D of a medicine, a heart worm preventive, for a dog who weighs X pounds is given by D(x) =(136/25)x. Find the proper dosage for a dog that weighs 25 pounds
To find the proper dosage for a dog that weighs 25
An airplane takes 4 hours to travel a distance of 2200 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane on still air and the speed of the wind.
An airplane takes 4 hours to travel a distance of 2200 miles with the wind. The return trip takes 5 hours against the wind. What is the speed of the plane on still air and the speed of the wind.
The problem is asking us to find the number of made free throws, two-point field goals, and three-point field goals that Lindsey Drew made during the 2006 regular season.
Let's use the following variables to represent the number of field goals made:
- x represents the number of made three-point field goals
- 2x - 60 represents the number of made two-point field goals (60 less than double the number of made three-point field goals since each two-point field goal is worth twice as much as a three-point field goal)
- (2x - 60) - 17 represents the number of made free throws (17 less than the number of made two-point field goals since Lindsey Drew made each free throw worth one point)
The problem also tells us that Lindsey Drew made a total of 820 points, so we can set up an equation:
3x + 2(2x - 60) + ((2x - 60) - 17) = 820
Simplifying, we get:
7x - 55 = 820
Adding 55 to both sides:
7x = 875
Dividing by 7:
x = 125
So, Lindsey Drew made 125 three-point field goals.
To find the number of made two-point field goals, we can substitute x = 125 into 2x - 60:
2x - 60 = 2(125) - 60 = 190
So, Lindsey Drew made 190 made two-point field goals.
To find the number of made free throws, we can substitute x = 125 into (2x - 60) - 17:
(2x - 60) - 17 = 2(125) - 60 - 17 = 243
So, Lindsey Drew made 243 made free throws.
Therefore, Lindsey Drew made 125 made three-point field goals, 190 made two-point field goals, and 243 made free throws during the 2006 regular season.