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3 years ago

Examine parallelogram ABCD below.

Mathematics

1 answer:

gtnhenbr [62]3 years ago

6 0

Given that,

∠C = (6x-21)° and ∠A = (4x+11)°

To find,

Choose the correct option.

Solution,

For a parallelogram, the opposite angles are equal. ATQ,

(6x-21)° = (4x+11)°

Taking like terms together,

6x-4x = 21 + 11

2x = 32

x = 16

∠C = (6x-21)° = 6(16) -21 = 75°

So, ∠A = 75°

So, ∠A = ∠C = 75°. Hence, the correct option is (B).

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klemol [59]

Answer:

$x^2-10x+18=0$

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Step-by-step explanation:

Let w represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

$20=2(x + w)$

Let's put w in terms of x. Divide both sides by two:

$10=x+w$

And solve for w:

$w=10-x$

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According to the Pythagorean Theorem:

$a^2+b^2=c^2$

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$x^2+w^2=8^2$

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$x^2+(10-x)^2=64$

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$x^2+(100-20x+x^2)=64$

Isolate the equation. So:

$2x^2-20x+36=0$

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$x^2-10x+18=0$

Therefore, a = -10 and b = 18.

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2 years ago

Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?

lara [203]

Answer:

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Step-by-step explanation:

x=smaller

y=larger

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2(x+1)=3x-9

2x+2=3x-9

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11+1=y

12=y

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