Answer:
(a) 
(b) 
(c) 
Step-by-step explanation:
The formula for calculating the equation of line in point - slope form is given as :
where m is the slope
Given from the question :
m = - 4
= 2
= 6
Substituting into the formula , we have :
Therefore :
(a) the equation of the line in point - slope form is
(b) to write it in slope - intercept form , we will make y the subject of the formula , which will give :
(c) the equation of line in standard form is ;
Answer:7/8!!!
Step-by-step explanation:
Not 2 I think it’s a carrot
Answer: The area of the rectangle is: " 77 m² " .
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Note: The formula for the area, "A" of a rectangle:
→ A = L * w ;
in which:
A = "area (of rectangle)" ; [in units of "m² " ; that is: "square meters" ] ;
L = length = "(4 + w)" {in units of "meters (m)" } ;
w = width {in units of "meters (m)" } ;
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So; " A = L * w " ;
Substitute the known expression for the "length, L" ; & rewrite the formula for the given area of OUR area for the rectangle in OUR GIVEN PROBLEM:
→ A = (4 + w) * w '' ;
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Note the formula for the perimeter, "P" ;
→ P = 2L + 2w ;
↔ 2L + 2w = P
→ 2L + 2w = 36 m ;
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We want to find the "area" , "A" :
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Using the formula for the "perimeter, "P" (of the rectangle) ; & given that the perimeter is: "36" (meters) ;
→ 2L + 2w = 36 ;
→ Let us plug in the values for "Length (L)" & "width (w)" ;
→ 2(w + 4) + 2w = 36 ;
So; (2*w) + (2*4) + 2w = 36 ; Solve for "w" ;
→ 2w + 8 + 2w = 36 ;
→ Combine the "like terms" :
+ 2w + 2w = 4w ;
→ And rewrite:
4w + 8 = 36 ;
Now, subtract "8" from EACH SIDE of the equation:
4w + 8 − 8 = 36 <span>− 8 ;
</span>
to get:
4w = 28 ;
Now, divide EACH SIDE of the equation by "4" ;
to isolate "w" on EACH SIDE of the equation ; & to solve for "w" ;
4w / 4 = 28 / 4 ;
→ w = 7 ; → The "width" of the rectangle is: " 7 m " .
Now, we can find the "length" of the rectangle:
The length, "L" , of the rectangle = 4 + w = 4 + 7 = 11 .
→ L = 11 . → The "length" of the rectangle is: " 11 m " .
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Now, we can find the area, "A", of the rectangle.
A = L * w = 11 m * 7 m = " 77 m² " .
→ The area of the rectangle is: " 77 m² <span>" .
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To check our answer:
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→ " P = 2L + 2w " ;
Given that "P = 36 m" ;
Plug in "36 m" (for "P") ; into the equation ;
and plug in our calculated values for
"length, L" (which is "11 m") ; & "width, w" (which is "7 m") ;
to see if the equation holds true ; that is, to see if both sides of the equation are equal ;
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→ 36 m = ? 2L + 2w ?? ;
→ 36 m = ? 2(11 m) + 2(7 m) ?? ;
→ 36 m = ? 22 m + 14 m ?? ;
→ 36 m = ? 36 m ? Yes!
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Let's start by the first column. The symbol ~ means negation. ~s will be the opposite of s.
Since s from top to bottom is T F T F, ~s will be F T F T(from top to bottom).
The second symbol that appears is ∧. This symbols means that p∧q is only true when both p and q are true. It needs to satisfy both of them.
From top to bottom, in the first line for ~s∧r we have ~s false and r is true, since ~s is false the combination is also false. For the second line, we have ~s true and r is true, since both are true the combination is also true. and in the last 2 elements, we have a false r which indicates both of them are also false.
This means, the second column will be F T F F(from top to bottom).
