Assume that the length of the rectangle is "l" and that the width is "w".
We are given that:
(1) The length is one more than twice the base. This means that:
l = 2w + 1 .......> equation I
(2) The perimeter is 92 cm. This means that:
92 = 2(l+w) ...........> equation II
Substitute with equation I in equation II to get the width as follows:
92 = 2(l+w)
92 = 2(2w+1+w)
92/2 = 3w + 1
46 = 3w + 1
3w = 46-1 = 45
w = 45/3
w = 15
Substitute with w in equation I to get the length as follows:
l = 2w + 1
l = 2(15) + 1
l = 30 + 1 = 31
Based on the above calculations:
length of base = 31 cm
width of base = 15 cm
Answer:
5 hours
Step-by-step explanation:
Step one:'
given data
Angelo charges a one time fee of $50 plus $15 per hour
let the total charge be y
and the number of hours be x
y= 50+15x----------------1
Deborah charges a one time fee of $25 plus $20 per hour
y= 25+20x----------------2
equate 1 and 2 to find x
50+15x=25+20x
collect like terms
50-25= 20x-15x
25= 5x
divide both sides by 5
x= 25/5
x= 5 hours
Answer:
x = 1, y = 2, z = -1
Step-by-step explanation:
2x + 4y = 10
2x = -4y + 10
x = -2y + 5
now sub -2y + 5 in for x, back into the other 2 equations
2x + 2y + 3z = 3 -3x + y + 2z = -3
2(-2y + 5) + 2y + 3z = 3 -3(-2y + 5) + y + 2z = -3
-4y + 10 + 2y + 3z = 3 6y - 15 + y + 2z = -3
-2y + 3z = 3 - 10 7y + 2z = - 3 + 15
-2y + 3z = - 7 7y + 2z = 12
-2y + 3z = -7....multiply by 2
7y + 2z = 12...multiply by -3
--------------------------
-4y + 6z = -14 (result of multiplying by 2)
-21y - 6z = -36 (result of multiplying by -3)
---------------------------add
-25y = - 50
y = -50/-25
y = 2 <===
2x + 4y = 10 2x + 2y + 3z = 3
2x + 4(2) = 10 2(1) + 2(2) + 3z = 3
2x + 8 = 10 2 + 4 + 3z = 3
2x = 10 - 8 6 + 3z = 3
2x = 2 3z = 3 - 6
x = 2/2 3z = -3
x = 1 <== z = -3/3
z = -1 <===
ANSWER
P'(6,-1)
EXPLANATION
The mapping for a reflection in the line y=x is
The line y=x is the mirror line for a function and it's inverse.
The x and y coordinates swap position.
The reflection of point P(−1, 6) across the line y = x is
P'(6,-1)
2b - 15 > 21
add 15 to both sides:
2b-15+15 > 21 + 15
2b > 36
Divide both sides by 2 :
2b/2 > 36/2
2b = 36
b = 36 / 2
b > 18
hope this helps!
