EOC algebra. 1.The floor of a rectangular cage has a length 4 feet greater than its width, w. James will increase both dimensions of the floor by 2 feet.
Which equation represents the new area, N, of the floor of the cage?
A N = w2 + 4w
B N = w2 + 6w
C N = w2 + 6w + 8
D N = w2 + 8w + 12
2. Two boys, Shawn and Curtis, went for a walk.
Shawn began walking 20 secondsearlier than Curtis.
• Shawn walked at a speed of 5 feet per second.
• Curtis walked at a speed of 6 feet per second.
For how many seconds had Shawn been walking at the moment when the two boys had walked exactly the same distance?
Answers
1) The equation that represents the new area, N, of the floor of the cage is D) N = w² + 8w + 12.
2) Shawn had been walking for 120 seconds.
What is algebraic Expression?
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
The original area of the rectangular cage is:
A = lw, where l is the length and w is the width.
We are given that the length of the floor is 4 feet greater than its width, so we can write l = w + 4.
The new dimensions of the floor are w + 2 and (w + 4) + 2 = w + 6. Therefore, the new area of the floor is:
N = (w + 2)(w + 6) = w² + 6w + 2w + 12 = w² + 8w + 12
Let t be the time in seconds that Curtis has been walking. Then Shawn has been walking for t + 20 seconds.
The distance that Curtis has walked is d = 6t, and the distance that Shawn has walked is d = 5(t + 20), since Shawn started 20 seconds earlier and walks at a slower pace.
We want to find the time when they have walked the same distance, so we set the two expressions for d equal to each other:
6t = 5(t + 20)
Simplifying and solving for t, we get:
6t = 5t + 100
t = 100
Therefore, Curtis had been walking for 100 seconds when the two boys had walked exactly the same distance. At that time, Shawn had been walking for t + 20 = 120 seconds.
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N=w2+4w which would be a
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What is 1 48/100 written as a money amount
Answers
Area of full circle = πr^2
= 3.14 * 12^2
=3.14 * 144
=452.16 cm^2
Area of rectangle = l x w
= 10 * 3
= 30 cm^2
Area of shaded region:
452.16 - 30 = 422.16 cm^2
Answers
Answers
$24.60 - $18 = $6.60
24.60x = $6.60
x = 6.60/24.60
x = 0.2683
So the percent increase is 26.83%
Answer:
26.83%
Step-by-step explanation:
All rectangles are squares.
All squares are parallelograms.
No trapezoids are parallelograms.
All rectangles are quadrilaterals.
Answers
Answers
For 1 and 2, you plot both lines, and wherever they intersect is the solution to the system. Given the equation of a line, I think the easiest way to plot it is to find two points on the line, then draw a line through them. For example, if , then when
, you get
; when
, you get
. So plot the points (0, -1) and (1, 4), then strike a line through.
1. Notice that dividing both sides of by 2 returns
, same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of
or
, you can always find a corresponding value for the other variable.)
2. See attached image. is given by the purple line.
For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.
3. Like with (1), notice that dividing both sides of the first equation by 2 gives , so there will be an infinite number of solutions.
4. (by substitution) Since , we can replace
in the second equation:
but this is false, so there are no solutions to this system.
5. (by substitution) Since , in the first equation we have
Then back in the second equation we find
So (-4, -3) is the only solution here.
6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.