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3 years ago

13

What is the measure of angle LKJ?

1 answer:

Dmitry_Shevchenko [17]3 years ago

8 0

Where is the angle? How can I solve this without the problem?

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In the figure to the right, AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Find the perimeter of the figu

nasty-shy [4]

Answer:

<em>P= 5.5 cm</em>

Step-by-step explanation:

<u>The Perimeter of Plane Shapes</u>

If we are given a plane shape, the perimeter is the measurement of the boundary of it. In case the shape is made of lines, the perimeter is the sum of the lengths of all of them.

We are given an irregular shape, we only need to add all the sides. But we don't have all the individual sides. Let's write the expression for the perimeter.

P=AE+ED+DC+CB+BA

We have: AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Note we don't have AE or DC, but we have their sum, so

P=AE+DC+ED+CB+BA

Recall that AB=BA, the order of the letters is not important. The perimeter is

$\displaystyle P=1\frac{1}{5}+1\frac{1}{4}+1\frac{3}{10}+1\frac{3}{4}$

We add the integer parts separate from the fractions

$\displaystyle P=4+\frac{1}{5}+\frac{1}{4}+\frac{3}{10}+\frac{3}{4}$

Now we use the common denominator (Least Common Multiple or LCM ) which is 20:

$\displaystyle P=4+\frac{4+5+6+15}{20}$

Operating

$\displaystyle P=4+\frac{30}{20}$

Simplifying

$\displaystyle P=4+\frac{3}{2}$

$\displaystyle P=\frac{11}{2}=5.5\ cm$

5 0

3 years ago

Which of the following is the graph of f(x) = -0.5|x + 31 -2?

slega [8]

Answer:

It is the third answer

Step-by-step explanation:

3 0

3 years ago

What is x given circle Z? please help !!

mojhsa [17]

Answer:

x=6

Step-by-step explanation:

because of vertical angles, 9x-4=12x-22

3x=18

x=6

plz give thx and brainliest!

6 0

3 years ago

Read 2 more answers

HELP! Number 13 please! Any other help would be amazing too.

juin [17]

The answer is probably d

7 0

3 years ago

Read 2 more answers

The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = len

FinnZ [79.3K]

Answer:

$PQ = x + 13$

The dimension of the garden is 52.5ft by 43.5ft

Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

$W = x$

$L = x + 9$

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

$PQ = L + 4$

Substitute $x + 9$ for $L$

$PQ = x + 9 + 4$

$PQ = x + 13$

Also;

$QR = W + 4$

Substitute $x$ for $W$

$QR = x + 4$

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

$Area_1 = L * W$

Recall that $W = x$ and $L = x + 9$

So;

$Area_1 = x * (x + 9)$

For the bigger rectangle

$Area_2 = PQ * QR$

Recall that $PQ = x + 13$ and $QR = x + 4$

So;

$Area_2 = (x + 13)(x + 4)$

Given that the Area of the walkway is $400ft^2$

This implies that

$Area_2 = Area_1 + 400$

Substitute $Area_1 = x * (x + 9)$ and $Area_2 = (x + 13)(x + 4)$

$(x + 13)(x + 4) = x * (x + 9) + 400$

Open All Brackets

$x^2 + 13x + 4x + 52 = x^2 + 9x + 400$

$x^2 + 17x + 52 = x^2 + 9x + 400$

Collect Like Terms

$x^2 - x^2 + 17x - 9x = 400- 52$

$8x = 348$

Divide both sides by 8

$\frac{8x}{8} = \frac{348}{8}$

$x = \frac{348}{8}$

$x =43.5$

Since the dimensions of the garden is $W = x$ and $L = x + 9$

<em>Substitute 43.5 for x in both cases</em>

$L = 43.5 + 9 = 52.5$

$W = 43.5$

<em>Hence, the dimension of the garden is 52.5ft by 43.5ft</em>

5 0

3 years ago