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3 years ago

Triangle ABC has a perimeter of 22cm.

2 answers:

4 0

First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
22cm - 13cm = 9cm

The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.

Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.
If a² + b² do equal c², then the triangle is a right triangle.

8² + 5² = 9²
64 + 25 = 81
89 > 81

The triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.

e-lub [12.9K]3 years ago

3 0

Answer:

No, ABC is not a right Angled triangle.

Step-by-step explanation:

Given AB = 8, BC = 5

Then AC = 22 - (8 + 5) = 22 - 13 = 9 cm

Using the converse of Pythagoras' identity

If the square of the longest side equals the sum of the squares of the other 2 sides then triangle is right.

AC² = 9² = 81

AB² + BC² = 8² + 5² = 64 + 25 = 89

81 ≠ 89, hence ΔABC is not right- angled

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Please help me out............................

Alina [70]

Answer:

Step-by-step explanation:

If Pq = RQ then ΔPQR is the isosceles triangle. The angles QPR and PRQ have the same measures.

We know: The sum of the measures of the angeles in the triangle is equal 180°. Therefore we have the equation:

m∠QPR + m∠PRQ + m∠RQP = 180°

We have

m∠QPR = m∠PRQ and m∠RQP = 60°

Therefore

2(m∠QPR) + 60° = 180° <em>subtract 60° from both sides</em>

2(m∠QPR) = 120° <em>divide both sides by 2</em>

m∠QPR = 60° and m∠PRQ = 60°

Therefore ΔPRQ is equaliteral.

ΔPSR is isosceles. Therefore ∠SPR and ∠PRS are congruent. Therefore

m∠SPR = m∠PRS

In ΔAPS we have:

m∠SPR + m∠PRS + m∠RSP = 180°

2(m∠SPR) + 90° = 180° <em>subtract 90° from both sides</em>

2(m∠SPR) = 90° <em>divide both sides by 2</em>

m∠SPR = 45° and m∠PRS = 45°

m∠PRQ = m∠PRS + b

Susbtitute:

60° = 45° + b <em>subtract 45° from both sides</em>

15° = b

3 0

3 years ago

Which statement is true?

love history [14]

<h2>Hello!</h2>

The answer is:

The second option,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Discarding each given option in order to find the correct one, we have:

<h2>First option,</h2>

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}$

<h2>Second option,</h2>

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

The statement is true, we can prove it by using the following properties of exponents:

$(a^{b})^{c}=a^{bc}$

$\sqrt[n]{x^{m} }=x^{\frac{m}{n} }$

We are given the expression:

$(\sqrt[m]{x^{a} } )^{b}$

So, applying the properties, we have:

$(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }$

Hence,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

<h2>Third option,</h2>

$a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}$

<h2>Fourth option,</h2>

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }$

Hence, the answer is, the statement that is true is the second statement:

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Have a nice day!

6 0

2 years ago

At school 161 students play at least one sport.This is 70% of the number of the student at the school. How many suenos are at th

kondor19780726 [428]

X=number total of student at the school.
70% of x=161
can suggest this equation:
(70/100)x=161
0.7x=161
x=161/0.7=230

Answer: the school has 230 students

7 0

3 years ago

Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like

Vilka [71]

Answer:

a) 9% , not unusual

b) 42.4%

c) 48.4%

d) 11.1% , 44.4% , 44.4%

Step-by-step explanation:

We have the following information from the statement:

n = 12

r = 4

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 3/11

P = 0.09 = 9%

The probability is not unusual, unusual is considered less than 0.05 or 5%

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 7/11

P = 0.424 = 42.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/11) + (8/12 * 4/11)

P = 0.484 = 48.4%

P (likebothofthem) = P (likefirstsong) * P (likesecondsong)

P = 4/12 * 4/12

P = 0.111 = 11.1%

The probability is not unusual, unusual is considered less than 0.05 or 5%

P (likeneither) = P (notlikefirstsong) * P (notlikesecondsong)

P = 8/12 * 8/12

P = 0.444 = 44.4%

c) P (likeexactlyoneofthem) = P (firstsongliked) * P (secondsongnotliked) + P (firstsongnotliked) * P (secondsongliked)

P = (4/12 * 8/12) + (8/12 * 4/12)

P = 0.444 = 44.4%

8 0

3 years ago

What is the equation of the line that has a slope of 3 and passes through the point (1, -2)

Gnesinka [82]

Answer:

. JUST LOAD

Step-by-step explanation:

3 0

2 years ago