Bard

🔍

question:he toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ?

answer:To find the toll for the 18-wheel truck, we first need to determine the number of axles the truck has. Since the truck has 2 wheels on its front axle and 2 wheels on each of its other axles, we can divide the total number of wheels by 2 to find the number of axles. The truck has 18 wheels, so: Number of axles (x) = Total number of wheels / Number of wheels per axle x = 18 / 2 x = 9 Now that we know the truck has 9 axles, we can use the given formula to calculate the toll: t = 1.50 + 0.50(x − 2) Substitute x with 9: t = 1.50 + 0.50(9 − 2) t = 1.50 + 0.50(7) t = 1.50 + 3.50 t = 5.00 The toll for the 18-wheel truck with 9 axles is boxed{5.00} .

question:Given that the line ax+y2=0 intersects with the circle centered at C, (x1)^2+(ya)^2=4 at points A and B, and triangle ABC is an equilateral triangle, then the real number a= boxed{______}.

answer:Solution: The center of the circle C is at (1, a), and the radius r=2, Since triangle ABC is an equilateral triangle, Therefore, the distance d from the center C to the line AB is sqrt{2^2-1} = sqrt{3}, That is, d= frac{|a+a-2|}{sqrt{a^2+1}}= frac{|2a-2|}{sqrt{a^2+1}}= sqrt{3}, Squaring both sides, we get a^2-8a+1=0, Solving this, we find a=4pm sqrt{15}, Thus, the answer is: boxed{4pm sqrt{15}} By using the standard equation of a circle, we can find the center and radius of the circle. The conclusion can be reached by applying the formula for the distance from a point to a line. This problem mainly examines the application of the formula for the distance from a point to a line. Using the given conditions to find the center and radius of the circle, and combining it with the distance formula is key to solving this problem.

question:costs 5 cents to copy a page. How many pages can you copy with 50 but not exceed 45?

answer:First, convert fifty dollars to cents, which is 50 times 100 = 5000 cents. Each page costs 5 cents. To find the number of pages without exceeding 45, convert forty-five dollars to cents: 45 times 100 = 4500 cents. Now, calculate the maximum pages that can be copied with 4500 cents at 5 cents per page: text{Max Pages} = frac{4500 text{ cents}}{5 text{ cents per page}} = 900 text{ pages}. Thus, you can copy boxed{900} pages for 45, while staying under the 50 budget.

question:A swim team has 5 times as many girls as boys. There are 80 girls on the team. How many people are there in total on the swim team?

answer:If there are 80 girls on the swim team and the team has 5 times as many girls as boys, we can find the number of boys by dividing the number of girls by 5. Number of boys = Number of girls / 5 Number of boys = 80 / 5 Number of boys = 16 Now that we know there are 16 boys on the team, we can find the total number of people on the swim team by adding the number of girls and boys together. Total number of people = Number of girls + Number of boys Total number of people = 80 + 16 Total number of people = 96 So, there are boxed{96} people in total on the swim team.