Answer:
Let L be the length of the rectangle and w be the width of the rectangle.
"The lenght of a rectangle is one less than twice the width" means L=2W-1
Using perimeter formula of a rectangle which is P=2(L+W) you have:
P=2(L+W)
130=2(2W-1+W)
Solve equation above to find W
130=2(3W-1)
130=6W-2
130+2=6W
132=6W
W=22
From here you find L=2W-1=2x22-1=43
Only thing left is to find area A=LxW
To find the GCF of the two terms, continuous division must be done.
What can be used to divide both terms such that there is not a remainder?
Start small, let's take 2. It could be a GCF.
Move up higher, say 3. Yes, it can be a GCF.
To see if there might be a greater common factor, divide the constants by 3.
48/3 = 16
81/3 = 27
Upon inspection and contemplation, there is no more common factor between 16 and 27. So, 3 is the GCF.
Moving on, when it comes to variables. The variable with the least exponents is easily the GCF. For the variable m, the GCF is m2 and for n, the GCF is n.
Combining the three, we have the overall GCF = 3m2n
Answer:
(1, 8.5 ) and ( - 17, 80.5 )
Step-by-step explanation:
Given the 2 equations
y = 
x² + 4x + 4 → (1)
y = - 4x + 12 → (2)
Substitute (1) into (2), that is
x² + 4x + 4 = - 4x + 12 ( multiply through by 2 to clear the fractions )
x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )
x² + 16x + 8 = 25 ( subtract 25 from both sides )
x² + 16x - 17 = 0 ← in standard form
(x + 17)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 17 = 0 ⇒ x = - 17
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 equations and evaluate for y
Substituting into (2 )
x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )
x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )
Answer:
m = 4.5
Step-by-step explanation:
2 = 2m - 7
add 7 to both sides
9 = 2m
divide by 2 on each side
4.5 = m
CHECK:
2 = 2(4.5) -7 (TRUE)
2 · 4.5 = 9
9 - 7 = 2
I hope this helps!
