Answer:
£59.25
Step-by-step explanation:
Hello!
To solve this problem, we must:
- Solve for the length of the fence (aka height)
- Find the area of the lawn (trapezoid)
- Find the number of cans needed
- Find the price of all the cans
Area of a trapezoid, and why the formula works:
A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.
To find the area of a trapezoid, we use the formula:

This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.
Solve for height:
The height is unknown but can be found using the Pythagorean Theorem.
The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.
Difference = 20 - 12 = 8
Hypotenuse = 17
- 8² + fence² = 17²
- 64 + fence² = 289
- 225 = fence²
- fence = 15
The height is 15
Solve for area:
Now we can solve for the area.
The area is 240
Cans:
The area of the lawn is 240 square meters. Each can cover 100 square meters.
Since we can't use part of a can, we round up to three whole cans.
The price of 3 cans :
£59.25
The Pythagorean Theorem:
The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.
The formula is : 
- a is a leg
- b is a leg
- c is the hypotenuse
Images attached for your reference
Answer:
-2(2x-1)
Step-by-step explanation:
x+4-5x-2
1) collect like like terms
-4x+2
2) factor out the -2
-2(2x-1)
3) that gives you the final answer of
-2(2x-1)
Answer:
j² - 5j²k - 2
Step-by-step explanation:
3j² - j²k - 6 - 4j²k - 2j² + 4
To simplify this polynomial, we can collect like terms. A term is number(s) or variable(s) that are grouped together by multiplication. <u>Like terms have the same variable and exponent</u>.
We have three groups of like terms:
The j-squares (j²), the j-squared k (j²k) and the constants (no variable).
Remember to include the negatives!
The j-squares are: 3j² ; -2j²
The j-squares k are: - j²k ; - 4j²k
The constants are: - 6 ; 4
Simplify:
3j² - j²k - 6 - 4j²k - 2j² + 4
Rearrange the polynomial by like terms
= (- j²k - 4j²k) + (3j² - 2j²) + (- 6 + 4)
Add or subtract the like terms
= (-5j²k) + (j²) + (-2)
Remove brackets and rearrange so the negative is not first
= j² + - 5j²k + - 2
Simplify where two signs are together. Adding a negative is subtraction.
= j² - 5j²k - 2 Simplified
Answer:

Step-by-step explanation:
Given,
Art electives = 3,
History electives = 4,
Computer electives = 5,
Total number of electives = 3 + 4 + 5 = 12,
Since, if a student chooses an art elective and a history elective,
So, the total combination of choosing an art elective and a history elective = 
Also, the total combination of choosing any 2 subjects out of 12 subjects = 
Hence, the probability that a student chooses an art elective and a history elective = 

Which is the required expression.
1)X=3
2)X=3
3)X=2
4)P=2
5)Y=12
6)M=3