Algebra 1 neeed help ASAP?

Question

1. Find a number which is 150 greater than its opposite.



2. Find 3 consecutive numbers whose sum is 60.



3. The perimeter of a rectangle is 420 inches. The width is 4 inches less than the length.what is the length?

Answer 1

these are so easy its WHACK

1.75
2.19,20,21
3.107

Answer 2

1). did not answer
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Find 3 consecutive numbers whose sum is 60

x + x + 1 + x + 2 = 60

3x + 3 = 60

Collecting Like terms

3x + 3 = 60
- 3 -3

Subtract 3 from both sides

3x = 57

3x/3 = 57/3

Dividing 3 from both sides

x = 19

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insert 19 into the equation

x + x + 1 + x + 2 = 60

19 + 19 + 1 + 19 + 2 = 60

19 + 20 + 21 = 60

60 = 60


The answer: the three consecutive numbers are 19, 20 and 21

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Perimeter Equation

P = 2L + 2W

w = L - 4

P = 420

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420 = 2l + 2(L - 4)

420 = 2L + 2L - 8

420 = 4L - 8
+8 +8

Add 8 to both sides

428 = 4L

428/4 = 4L/4

Divide 4 from both sides

107 = L

Since the Width is 4 inches less than the Length, the answer is 103 inches

The solution set is { 103}

Answer 3

1. I'm assuming that the opposite number of 150 is -150...so if that's true...150 greater than -150 would be zero.

2. the three numbers would be x, x+1, x+2....so the sum of 3 consecutive numbers whose sum is 60 would be:

x + x+1 + x +2 = 60

giving you:

3x +3 = 60

subtracting 3 from both sides gives u:

3x = 57

dividing by 3 on both sides gives you:

x = 19

so plugging in 19 for x for each of the three numbers... you get:

x = 19, x+1 = 20, x+2 =21.....19,20,21


3. the perimeter of a retangle is the 4 sides of the retangle added together.

so if the width is 4 inches less than the length...make x the length of the retangle and the width x-4 (helps if you draw this out)

since there are 2 lengths and 2 widths....adding all of the sides together gives you:

x + x + x -4 + x -4 = 420

simplifying you get:

4x - 8 = 420

add 8 to both sides and you get:

4x = 428

divide 4 from both sides and you have:

x = 107....this is your length...and your width is 4 less than that..so it's 103.

Answer 4

1. Let the number be X. The number is 150 greater than its opposite. So, X=150-X
2X=150
Therefore X = 75

2. Let the first number be X. Second number is X+1, third number X+2. Sum of all three numbers is 60, so
X+(X+1)+(X+2)=60
3X+3=60
3X=57
X=19
The three consecutive numbers are 19,20 and 21

3. Let the length be X inches. Width is therefore (X-4) inches.
Perimeter: X + X + (X-4) + (X-4) = 420
4X - 8 = 420
4X = 428
X = 107 inches
Length is 107 inches

Answer 5

answer 1 is 75.Because 75 is 150 greater than its opposite -75.

answer 2 is 19+20+21=60

answer 3 is length=71.333 width=67.333
alot of people put 107 for that answer but I dont think they were doing perimeter math.Perimeter of rectangles is 2(L) + 2(W).If 107 was the answer then that would mean the width was 4 inches shorter so it would be 103. Wrong, 107 times 2 + 103 times 2 =634 not 420. My answer is correct. It comes to 419.99 which rounds to 420.You wont get closer than that believe me I tried.

Answer 6

1>first question cant have any defenite solution based on the data given by you.

2>let first number be x. so, second number is {x+1} and third number is{ x+2}. now x+x+1+X+2=60
=> 3x + 3 =60
=> 3x = 57
=> x = 19.
so numbers are 19,20,21. answer.

3>perimeter of a rectangle = 2 (l+b) , where l=length, b= breadth/width.
now----The width is 4 inches less than the length.
so b= (L-4)
by the problem, 420= 2{l +l-4}
solving we get lenght = 107inches. ans
now i wanna know are they alzebra or child's play????

Answer 7

1) the opposite of a number x is 1/x for instance the opposite of -1 is -1 since 1/-1 = -1.
x - 1/x = 150 <=> x^2 -1 -150x = 0 <=>
x= 1/2*(150 + sqrt(150^2 - 4)) or x= 1/2*(150 - sqrt(150^2 - 4))

2) x-1 + x + x +1 = 60
3x = 60, x = 20.
numbers are thus 19,20,21

3) 420 = 2W + 2L and W + 4 = L
420 = 2L-8 + 2L
420 = 4L - 8
L = (420-8)/4 = 107, W = 103

Answer 8

1. 75
2. 19, 20, 21
3. 107, 103

Explanation:
1. x = answer
x - opposite = 150
opposite = "-x"
x - (-x) = 150
x + x = 150
2x = 150
x=75

2.
60/3 = 20
take two numbers on either side of 20 (that is 19 and 21), add them up and voila! they equal 60. It's like magic!

3.
x = width of rectangle
y = length
First equation: 2x + 2y = perimeter = 420
Second equation: x = y - 4
Two equations...two variables...easy answer
2(y - 4) + 2y = 420
2[(y - 4) + y] = 420 (distributive law)
2[y -4 + y]/2 = 420/2
[y -4 + y] = 210
2y - 4 = 210
(2y - 4) + 4 = 210 + 4
2y = 214
y = 107
x = 103 (remember width "x" is 4 less than the length "y")

Hope this helps

Answer 9

19+20+21=60

Answer 10

#2 is 19 20 21

Answer 11

okay:

1. 10x+y+150= 10y+x
9x+150=9y
so solve from there...


2. x+x+1+x+2=60
3x+3=60
3x=57
x=19
so, 19, 20, and 21


3. 2L+2(L-4)=420
2L+2L-8=420
4L=428
L=107
107 inches