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svlad2 [7]
3 years ago
7

The perimeter of a rectangle is 40cm. If the length were doubled and the width halved, the perimeter would be increased by 16cm.

Find the dimensions of the original rectangle.
Create a linear system to model the situation.
Determine, by substitution, the dimensions of the original rectangle (sketch and label rectangles to help) PLS SHOW ALL WORK NEED ASAP
Mathematics
1 answer:
alexgriva [62]3 years ago
5 0

Answer:

The dimensions of the original rectangle are Length =12cm, Width=8cm

Step-by-step explanation:

Let the length of the rectangle be x

Let the width of the rectangle be y

The perimeter of a rectangle is 40cm.

2(x+y)=40

Divide both sides by 2

x+y=20

If the length were doubled(2x) and the width halved(y/2), the perimeter would be increased by 16cm,i.e.(40+16)cm

Therefore:

2(2x+\dfrac{y}{2})=56

Divide both sides by 2

2x+\dfrac{y}{2}=28

From the first equation, x=20-y.

Substitute x=20-y into 2x+\dfrac{y}{2}=28

2x+\dfrac{y}{2}=28

2(20-y)+\dfrac{y}{2}=28\\\dfrac{4(20-y)+y}{2}=28\\80-4y+y=56\\-3y=-24\\$Divide both sides by -3\\y=8cm\\Recall:x=20-y\\x=20-8=12cm\\The dimensions of the original rectangle are Length =12cm, Width=8cm

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Pls help these are test corrections
GREYUIT [131]

Answer:

See explanation

Step-by-step explanation:

Given triangle has its vertices at points A(-4,-2), B(1,3) and C(3,-2).

Find all sides lengths:

AC=\sqrt{(-4-3)^2+(-2-(-2))^2}=\sqrt{(-7)^2+(0)^2}=\sqrt{49+0}=\sqrt{49}=7\ units\\ \\AB=\sqrt{(-4-1)^2+(-2-3)^2}=\sqrt{(-5)^2+(-5)^2}=\sqrt{25+25}=5\sqrt{2}\ units\\ \\BC=\sqrt{(1-3)^2+(3-(-2))^2}=\sqrt{(-2)^2+(5)^2}=\sqrt{4+25}=\sqrt{29}\ units

The longest side is AB.

By the Pythagorean theorem,

AB^2=AC^2+BC^2\\ \\(5\sqrt{2})^2=7^2+\sqrt{29}^2\\ \\50=49+29\\ \\50=78

This is false statemnt, so this triangle is not right triangle.

6 0
3 years ago
Greg has 60 building blocks. His sister gives him 17 more blocks. He uses 38 blocks to make a tower. How many blacks are not use
kykrilka [37]

Answer:

Greg has 39 remaining blocks that are not used in the tower.

Step-by-step explanation:

According to the question, Greg started with 60 building blocks.  However, his sister gives him 17 more blocks.  The key word 'more' means we need to add these blocks to the original 60:  60 + 17 = 77.  Greg then decides to use 38 blocks to make a tower.  Since he is using these blocks from his total of 77, we need to subtract this number to see how many he has left:  77 - 38 = 39.  This means that Greg has 39 blocks left that were not used to build his tower.  

8 0
3 years ago
What is the value of x?
Marat540 [252]
X = 2. I am pretty sure!


Hope i get brainiest!
3 0
4 years ago
Can some one help please!!!!!!!
trapecia [35]

Answer:

yes it's easy

Step-by-step explanation:

y=-2x

it may help you to understand.

8 0
3 years ago
Forth time I had to ask this!!
lubasha [3.4K]
A.) Yes you can, the expression would be (2.95 x Y) + 4 = X
B.) (2.95 x 24) + 4 = $74.80
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so basically they can buy 57 books without going over $175
7 0
3 years ago
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