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3 years ago

The pair of figures are simular.find the value of each variable

Mathematics

1 answer:

kkurt [141]3 years ago

5 0

Y=12 because the triangles have proportional side lengths

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The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions

Art [367]

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
$x(2x - 6) = 2 {x}^{2} - 6x$

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

$2 {x}^{2} - 6x = 108$
Subtract 108

$2 {x}^{2} - 6x - 108 = 0$
Divide by 2.

${x}^{2} - 3x - 54$
$(x - 9)(x + 6) = 0$
Rule AB = 0, gives A is 0 or B is 0.

$x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6$

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
$x = 9$
Width
$2x - 6 = 2 \times 9- 6 = 18 - 6 = 12$

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

6 0

3 years ago

A display of cans in a grocery store consists of 15 rows. There are 45 cans on the bottom , 42 cans on the next row, and so on,

Alchen [17]

Answer:

n = 9

Step-by-step explanation:

20 + 18 + ... + 6 + 4

---------------------------

a = 20 ; d = -2 ; n = ?

--------

4 = 20 + (n-1)(-2)

-16 = (n-1)(-2)

---------

n-1 = 8

n = 9

-------

S(9) = (9/2)(20+4)

S(9) = 4.5*24

S(9) = 108

8 0

4 years ago

The price of a pair of shoes is $52. This price is 15% lower than last week. What was the price of the shoes last week? Round yo

drek231 [11]

Answer:

$61.18

Step-by-step explanation:

The price last week was an unknown. We will call it x. x is an entire amount, so it is 100% of x.

This week, the price is 15% lower. Since 100% - 15% = 85%, the price this week is 85% of what it was last week. Last week it was x, so this week, the price is 85% of x.

85% of x = $52

0.85x = $52

Divide both sides by 0.85:

0.85x/0.85 = $52/0.85

x = $61.1764...

Answer: $61.18

7 0

3 years ago

Please help me on all 7 if you can only solve some don't hesitate & say those

Lana71 [14]

1) let say a + b = -16
than 3times larger equal smaller can be represent by 3a = b.
now sub 3a into the b of the equation and simplify you will get 4a = -16 where a = -4 and a is the larger nymber since b will =-12 which is smaller than a

4 0

3 years ago

Marcus delivers papers at a rate of 9 papers in 18 minutes. How much longer would it take him to deliver 100 papers than 72 pape

Strike441 [17]

It would take him 66 minutes longer to deliver 100 papers than 72 papers

5 0

3 years ago