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3 years ago

Please find the unknown with all steps

Mathematics

1 answer:

kirill [66]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

Since AC = BC then ΔABC is isosceles with base angles

∠BAC =∠ABC, thus

3x + x = 70

4x = 70 ( divide both sides by 4 )

x = 17.5

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

∠ADC is an external angle of ΔABD and the external angle is equal to the 2 opposite interior angles, hence

y = 70 + x = 70 + 17.5 = 87.5

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Determine if triangle ABC with coordinates A (0, 2), B (2, 5), and C (−1, 7) is an isosceles triangle. Use evidence to support y

kirill115 [55]

Answer:

The triangle ABC is an isosceles right triangle

Step-by-step explanation:

we have

The coordinates of triangle ABC are

A (0, 2), B (2, 5), and C (−1, 7)

we know that

An isosceles triangle has two equal sides and two equal internal angles

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance AB

substitute in the formula

$d=\sqrt{(5-2)^{2}+(2-0)^{2}}$

$d=\sqrt{(3)^{2}+(2)^{2}}$

$dAB=\sqrt{13}\ units$

step 2

Find the distance BC

substitute in the formula

$d=\sqrt{(7-5)^{2}+(-1-2)^{2}}$

$d=\sqrt{(2)^{2}+(-3)^{2}}$

$dBC=\sqrt{13}\ units$

step 3

Find the distance AC

substitute in the formula

$d=\sqrt{(7-2)^{2}+(-1-0)^{2}}$

$d=\sqrt{(5)^{2}+(-1)^{2}}$

$dAC=\sqrt{26}\ units$

step 4

Compare the length sides

$dAB=\sqrt{13}\ units$

$dBC=\sqrt{13}\ units$

$dAC=\sqrt{26}\ units$

$dAB=dBC$

therefore

Is an isosceles triangle

Applying the Pythagoras Theorem

$(AC)^{2} =(AB)^{2}+(BC)^{2}$

substitute

$(\sqrt{26})^{2} =(\sqrt{13})^{2}+(\sqrt{13})^{2}$

$26=13+13$

$26=26$ -----> is true

therefore

Is an isosceles right triangle

8 0

3 years ago

Joseph has 48 comic books. He sold one-fourth of his collection to his friend. He brought twice the number of comic books as he

Tresset [83]

Answer:

108

Step-by-step explanation:

Given that Joseph has 48 comic books.

As he sold 1/4 of his collection to his friend, so

The number of books, Josef sold = 1/4 x 48 = 12.

The number of remaining books, Josef has = 48 - 12 = 36.

As he brought twice the number of comic books as he has now, so,

the number of comic books, Josef brought = 2 x 36 = 72.

Now, total number of comic books, Josef has = 36 + 72 = 108.

6 0

3 years ago

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Mekhanik [1.2K]

Answer:

0.012

Step-by-step explanation:

3 0

2 years ago

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Please find the unknown with all steps ​

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