Just need 5 and 6 done due in 20 minutes plz help

Step-by-step explanation:

5. Let the equation of the line be y = mx + c

m = (6-15)/(2-(-1)) = -3

sub (2, 6) and m = -3:

6 = -3(2) + c

c = 12

Equation of the line: y = -3x + 12

6. Let the equation of the line be y = mx + c

y-intercept of 7 means c = 7

y = mx + 7

x-intercept: value of x when y = 0

therefore, sub (4, 0):

0 = m(4) + 7

m = -7/4

Equation of the line: y = -7/4x + 7

this is a topic on coordinate geometry. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I'll be posting the notes for this topic soon and will also be posting other topics' notes and some tips :)

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

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