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masya89 [10]
3 years ago
11

In the problem we’re supposed to find the value of x that makes ABC ~ RST I can’t figure it out can someone please help

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0

Answer:

Step-by-step explanation:

if the triangles are similar then their sides are in proportion ( or you can think that they make equivalent fractions like 2/3 = 4/6 )

44/ (x+2) = 20/7 = 3x+1 /5 ( all of those are equivalent  fractions)

use that  \frac{a}{b} =\frac{c}{d}  is the same as a*d = b*c

\frac{44}{x+2} =\frac{20}{7}  is the same as 20(x+2) = 7*44

20x +40 = 308; subtract 40 from both sides

20x = 268; divide by 20 both sides

x= 13.4

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Triangle ABC has a right angle at C. Select all measurements which would mean it has a hypotenuse with a length of 10 units. a.
Delvig [45]

Option d: Angle A is 30 degrees, BC is 5 units

Option e: AC is 8 units, BC is 6 units

Explanation:

The triangle ABC has a right angle at C.

The length of the hypotenuse is 10 units.

The image of the triangle with this measurement is attached below:

Option a: Angle A is 20 degrees, BC is 2 units

\begin{aligned}\sin 20 &=\frac{2}{h y p} \\h y p &=\frac{2}{\sin 20} \\&=5.8476\end{aligned}

Since, hypotenuse is 10 units, Option a is not correct answer.

Option b: AC is 7 units, BC is 3 units

\begin{aligned}A B &=\sqrt{7^{2}+3^{2}} \\&=\sqrt{49+9} \\&=\sqrt{58}\end{aligned}

Since, hypotenuse is 10 units, Option b is not correct answer.

Option c: Angle B is 50 degrees, BC is 4 units

\begin{aligned}\cos 50 &=\frac{4}{h y p} \\h y p &=\frac{4}{\cos 50} \\&=6.222\end{aligned}

Since, hypotenuse is 10 units, Option c is not correct answer.

Option d: Angle A is 30 degrees, BC is 5 units

\begin{aligned}\sin 30 &=\frac{5}{h y p} \\h y p &=\frac{5}{\sin 30} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option d is the correct answer.

Option e: AC is 8 units, BC is 6 units

\begin{aligned}A B &=\sqrt{8^{2}+6^{2}} \\&=\sqrt{64+36} \\&=\sqrt{100} \\&=10\end{aligned}

Since, hypotenuse is 10 units, Option e is the correct answer.

Thus, Option d and e are the correct answers.

3 0
3 years ago
Number 14 Help Please
omeli [17]

Answer:

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Step-by-step explanation:

there is no right answer i dont know why

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Solve the following quadratic by<br> completing the square.<br> y = x2 + 4x - 2
iogann1982 [59]

Answer:

x = √6 - 2 , -√6-2

Step-by-step explanation:

We have ,

=> y = x² + 4x - 2

  • Let y = 0

=> x² + 4x - 2 = 0

=> x² + 2(2)(x) - 2 = 0

=> x² + 2(2)(x) +2² - 2² -2 = 0

=> x² + 2(2)(x) + 2² -4-2 = 0

=> ( x + 2 )² -6 = 0

=> ( x +2)² = 6

=> ( x + 2) = √6

=> x + 2 = ±√6

=> x = √6 - 2 , -√6-2

4 0
3 years ago
Read 2 more answers
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