idyllic

the perimeter of the countertop would be 

1.5 + (7-3) + 7 + 4 + 3 + (4 - 1.5) = 1.5 + 4 + 7 + 4 + 3 + 2.5 = 22.

for the area, we can divide the shape into two rectangles.

the area of the smaller rectangle would be 1.5 * (7 - 3) = 1.5 * 4 = 6.

the area of the larger rectangle would be 3 * 4 = 12.

so, the area of the countertop is simply 12 + 6 = 18.

hope this helped! sorry if my explanations weren't too clear. i hope you can follow what i did above. feel free to ask any questions! :)

if Raj paid 35.00 for 4 meters of fabric, that means he paid 35/4 = 8.75 dollars for each meter of fabric.

so, for 6.5 meters of fabric, Raj would pay 8.75 * 6.5 = ~56.88 dollars.

hope this helped! please let me know if you have any questions. 

we can use Pythagoren theorem for this one. 

20^2 - 16^2 = h^2 (h is the height of the screen).

400 - 256 = h^2

144 = h^2

h = 12

hope this helped! please let me know if you are confused about anything i did :)

a) 24 meters is equal to 2400 centimeters.

so the average speed for the fastest pole clime is \(\frac{2400}{10.75}\) = ~ 223.3 centimeters per second.

b) the average speed would be \(\frac{888}{4.88} \) = ~182 centimeters per second.

so the average speed for question a is greater.

hope this helped! please let me know if you are confused about anything i did :)

angle a and angle b are on the same line, so they must add up to 180 degrees.

since we already know the value of angle a, all we have to do to solve for angle b is 

180 - 109 = 71.

so angle b is 71 degrees, which is the second option. 

hope this helped! please let me know if you are confused about anything i did 

let's start by defining two variables: A and B, for trains A and B, respectively.

we can now create a system of equations:

A + B = 368 ("...weigh a total of 368 tons.")

A - B = 340 ("The difference of their weights is 340 tons.")

now, let's add up these two equations.

A + B + A - B = 368 + 340 

2A = 708

A = 354

to solve for B, we just plug in our value of A into one of our initial equations.

354 + B = 368

B = 368 - 354

B = 14

hope this helped! please let me know if you have any questions :)

angles 5 and 1 are vertical angles. i'm not exactly sure how to explain this.

here is a site that may explain the relationships between angles with a transversal better:

https://tutors.com/math-tutors/geometry-help/types-of-angle-relationships#:~:text=When%20two%20parallel%20lines%20are%20intersected%20by%20a,all%20the%20types%20of%20angle%20relationships.%20Congruent%20Angles

hope this helped! i strongly recommend that you check out the site i linked above. if you have any other questions about this, feel free to ask ! 

we know that angles ABC and DBE are equal (vertical angles, i believe).

if x is 6, angle ABC would be:

17(6) + 18 = 102 + 18 = 120

now, we'll have this equation:

14y - 20 = 120

14y = 140

y = 10

hope this helped! please let me know if you are still confused :)

sure... but next time you should just post a separate question, i'll see it there too.

we know that angle 1 plus angle 2 must equal 90, because they are on the same line as the other right angle.

if angle 2 is 40, that means angle 1 must be 90 - 40 = 50, the second option.

hope this helped! please let me know if you are confused about anything i did 

the area of this figure is simply the area of the trapezoid plus the area of the triangle.

to find the area of the trapezoid, we do \(\frac{10+16}{2} \cdot 9\) = \(\frac{26}2 \cdot 9\) = \(\frac{234}2 \) = \(117\).

now, to find the area of the triangle, we do \(\frac{6 \cdot 8}{2} = \frac{48}{2} = 24\).

117 + 24 = 141, so i believe your answer is 141. 

hope this helped! sorry if any of my explanations weren't too clear. if you have any questions about anything i did, feel free to ask! :)