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2 years ago

Rhombus JKLM is shown below. Find m∠KLM.

Mathematics

1 answer:

lianna [129]2 years ago

7 0

Answer:

Option D

Step-by-step explanation:

Properties of a rhombus,

1). Diagonals of a rhombus bisect the opposite angles.

2). Sum of adjacent two angles of a rhombus is 180°.

By property (1),

Diagonal JL will bisect the angles ∠MJK and ∠KLM.

Therefore, m∠KLM = 2(5x + 3)°

Similarly, diagonal KM will bisect the angles ∠JKL and JML.

Therefore, m∠JKL = 2(9x - 11)°

By property (2),

2(9x - 11)° + 2(5x + 3)° = 180°

9x - 11 + 5x + 3 = 90

14x - 8 = 90

14x = 98

x = 7

Since, m∠KLM = 2(5x + 3)°

= 2(5×7 + 3)°

= 76°

Therefore, Option D will be the answer.

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In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some poin

Mademuasel [1]

Answer: $7\frac{5}{7}$ unit and 18 unit

Step-by-step explanation:

Let ABCD is a trapezoid where AB and CD are the bases. ( In which AB is greatest base which shown in below figure)

AD and BC are the legs of the trapezoid ABCD.

Now, we have ( According to the question ),

AB = 18 unit, BC = 7 unit, AD = 3 unit and DC = 11 unit.

Here the leg AD extends from point D.

Similarly leg BC extends from point C.

Let they meet at point P ( shown in below diagram)

Since In triangles PAB and PDC,

∠PDC ≅ ∠PAB ( because DC ║ AB )

And, ∠ PAB ≅ ∠ PBA

∠DPC ≅ ∠ APB ( reflexive)

Therefore, By AAA similarity postulate,

$\triangle PDC \sim \triangle PAB$

Thus, By the definition of similarity,

$\frac{PD}{PA} = \frac{DC}{AB}$

$\frac{PD}{PD+3} = \frac{11}{18}$ ( because PA = PD+DA)

⇒ 18 PD = 11 PD +33

⇒7PD = 33

⇒ PD = 33/7

Again by the definition of similarity,

$\frac{PC}{PB} = \frac{DC}{AB}$

$\frac{PC}{PC+7} = \frac{11}{18}$ ( because PB = PC + CB)

⇒ 18 PC = 11 PD +77

⇒7PC = 77

⇒ PC = 11

Thus, PA = PD+DA = 33/7 + 3 = $7\frac{5}{7}$

And, PB = PC + CB = 11 + 7 = 18

8 0

2 years ago

Graph the inequality.<br> -6 ≤y + 2x < 15

omeli [17]

Inequalities help us to compare two unequal expressions. The correct option is B.

<h3>What are inequalities?</h3>

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality -6 ≤y + 2x < 15 can be broken into two small inequality, as shown below.

-6 ≤y + 2x
y + 2x < 15

Now, if we plot the inequality as shown below, then the area in which both the shaded region overlap is the area of the this inequality.

Hence, the correct option is B.

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6 0

1 year ago

Find the solutions of the system y = –2x – 1 and y = 3–x–1.

sweet [91]

There are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two equations:

y = –2x – 1 and

$\rm y = 3^{-x-1}$

From the graph, we can see:

There are two intersection points:

(-1, 1) and (-2, 3)

The x coordinates are -1 and -2

x = -1, y = 1

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Thus, there are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

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1 year ago

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sveta [45]

Answer:

I think A

Step-by-step explanation:

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2 years ago

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max2010maxim [7]

The correct answer is water

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