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Murljashka [212]
3 years ago
12

A rectangle has a perimeter of 18 inches. a new rectangle is formed by doubling the with W in tripling the length L as shown the

new rectangle has a perimeter P of 46 inches a)write and solve a system of linear equation to find the length and width of the original rectangle
b)find the length and width of the new rectangle
Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0

a) The dimensions of original rectangle are length= 5 and width= 4.

b) The dimensions of new rectangle are length= 15 and width=8.

<u>Step-by-step explanation</u>:

  • length of a rectangle = l
  • width of a rectangle = w
  • Perimeter of a rectangle = 2(l+w)

<u>Original rectangle</u> :

18 = 2(l+w)

18 = 2l + 2w ---------(1)

<u>New rectangle</u> :

46 = 2(3l+2w)

46 = 6l + 4w ---------(2)

<u>Solving the equations</u> :

Multiply (1) by 2 and subtract (2) from (1)

 4l + 4w = 36

-(<u>6l + 4w = 46</u>)

 <u>-2l        = -10</u>

l = 10/2

length = 5 inches.

Substitute l=5 in (1)

18 = 2(5)+2w

18 = 10+2w

2w = 8

w = 8/2

width = 4 inches.

length of new rectangle = 3(l) = 3\times5 = 15 inches.

width of new rectangle = 2(w) = 2\times4 = 8 inches.

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Pavlova-9 [17]

Answer:

230 * (30/100) = 23 * 3 = 69

Step-by-step explanation:

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4 years ago
Read 2 more answers
Given the function f(x) = | -2x + 4 |. Complete the table.
Finger [1]

Answer:

See below.

Step-by-step explanation:

To complete the table, start by copying the given function.

f(x) = |-2x + 4|

Now let's start with the first line of the table: x = 6.

You are finding the value of function f when x = 6.

Replace x with 6 and evaluate the expression.

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

Second line of table:

x = -1

f(x) = |-2x + 4|

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = 6

For the third and fourth lines, you are given a y value, or the value of function f, and you are looking for x. Now you use the given value to set the function equal to, and you solve for x.

Line 3: f(x) = 4

f(x) = |-2x + 4|

|-2x + 4| = 4

-2x + 4 = 4   or   -2x + 4 = -4

-2x = 0   or   -2x = -8

x = 0    or   x = 4

Line 4: f(x) = 14

f(x) = |-2x + 4|

|-2x + 4| = 14

-2x + 4 = 14   or   -2x + 4 = -14

-2x = 10   or   -2x = -18

x = -5    or   x = 9

The table looks like this:

x          f(x)

6         8

-1         6

0,4      4

-5, 9     14

\end{center}

6 0
3 years ago
I need answers for all! thank you will mark brainlist!! please help me i’m begging you &lt;3
Darina [25.2K]

Step-by-step explanation:

y = 2/5 x - 9/5

when x = -1,

the value of y = 2/5(-1) - 9/5

= -2/5 - 9/5 = -11/5

when x = 0

=> y = 2/5(0) -9/5

= 0-9/5 = -9/5

when x=1

=> y = 2/5(1) - 9/5

= 2/5 - 9/5 = 7/5

6 0
3 years ago
Solving each system by eliminating <br> x-y+z= -1<br> x+y+3z= -3<br> 2x-y+2z= 0
Pie

There's only one system of equations here.

Let's eliminate x first,

x - y + z = -1

x = -1 + y - z

Substituting into  x + y + 3z = -3 gives

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2y + 2z = -2

y + z = -1

Substituting for x into 2x-y+2z = 0 gives

2(-1 + y - z) - y + 2z = 0

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y = 2

Got lucky on that one.  

z = -1 - y = -1 - 2 = -3

x = -1 + y - z = -1 + 2  - -3 = 4

Answer: x=4, y=2, z= -3

Check:

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x+y+3x = 4+2+3(-3) =  -3, good

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4 years ago
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