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4 years ago

Based only on the information given in the diagram, it is guaranteed that ABC XYZ

Mathematics

2 answers:

serious [3.7K]4 years ago

5 0

This statement is true

Scilla [17]4 years ago

3 0

Answer:

Statement is true.

Step-by-step explanation:

The given triangles ΔABC and ΔXYZ will be similar if the two angles of these triangles are equal Or all sides of both the triangles are equal Or two corresponding sides and the angle between these lines are same.

Here in ΔABC

∠ACB = 52°

∠ABC = 90°

Then we can find the third angle ∠CAB = 180°-(∠ACB+∠ABC)

= 180 - (52+90)

= 180 - 142

= 38°

Similarly in ΔXYZ, ∠YXZ = 38°, ∠XYZ = 90°

Then ∠YZX = 180-(∠YXZ+∠XYZ)

= 180-(90+38) = 180-128 = 52°

Now we can say that in two triangles

∠ACB = ∠YZX =52°

∠CAB = ∠YXZ = 38°

Therefore These triangle are similar and the statement is true.

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What is 3 multiplied by 4 1/3 as a mixed number or fraction

viva [34]

Answer:

Step-by-step explanation:

First, change 4 1/3 into an improper fraction. 4 1/3= 13/3

Next, you multiply the numerators by the numerators and the denominators by the denominators. 13*3=39 (numerators) 3*1=3 (denominators)

39/3 = 13/1 = 13

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4 years ago

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If f(x)=x+7 and g(x)=1/x-13, what is the domain of (f o g)(x)

astra-53 [7]

(f o g)(x) = 1/(x - 13) +7
domain of the function is all real x except x = 13

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3 years ago

Suppose the radius of a circle is 4. What is its area?

kati45 [8]

Area= r*r*π (π ≈ 3.14)
⇒ Area= 4*4* π= 50.265

The area of the circle is 50.265~

5 0

3 years ago

The sum of the series {1(2/3)}²+{2(1)3)}²+3²+{3(2/3)}²+....to 10 term is

ryzh [129]

Step-by-step explanation:

<h3><u>Given Question </u></h3>

The sum of the series is

$\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms}$

$\green{\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n}1 = n \: }}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n}k = \frac{n(n + 1)}{2} \: }}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n} {k}^{2} = \frac{n(n + 1)(2n + 1)}{6} \: }}$

$\large\underline{\sf{Solution-}}$

Given series is

$\rm :\longmapsto\: {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - - 10 \: terms$

can be rewritten as

$\rm \: = \: {\bigg[\dfrac{5}{3} \bigg]}^{2} + {\bigg[\dfrac{7}{3} \bigg]}^{2} + {\bigg[\dfrac{9}{3} \bigg]}^{2} + {\bigg[\dfrac{11}{3} \bigg]}^{2} + - - - 10 \: terms$

$\rm \: = \: \dfrac{1}{9}[ {5}^{2} + {7}^{2} + {9}^{2} + - - - 10 \: terms \: ]$

Now, here, 5, 7, 9 forms an AP series with first term 5 and common difference 2.

So, its general term is given by 5 + ( n - 1 )2 = 5 + 2n - 2 = 2n + 3

So, above series can be represented as

$\rm \: = \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}(2n + 3) ^{2}$

$\rm \: = \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}\bigg[ {4n}^{2} + 9 + 12n\bigg]$

$\rm \: = \: \dfrac{1}{9}\bigg[\displaystyle\sum_{n=1}^{10} {4n}^{2} + \displaystyle\sum_{n=1}^{10}9 + 12\displaystyle\sum_{n=1}^{10}n\bigg]$

$\rm \: = \: \dfrac{1}{9}\bigg[4\displaystyle\sum_{n=1}^{10} {n}^{2} +9 \displaystyle\sum_{n=1}^{10}1 + 12\displaystyle\sum_{n=1}^{10}n\bigg]$

$\rm \: = \: \dfrac{4}{9}\bigg[\dfrac{10(10 + 1)(20 + 1)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(10 + 1)}{2} \bigg]$

$\rm \: = \: \dfrac{4}{9}\bigg[\dfrac{10(11)(21)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(11)}{2} \bigg]$

$\rm \: = \: \dfrac{1540}{9} + 10 + \dfrac{220}{3}$

$\rm \: = \: \dfrac{1540 + 90 + 660}{9}$

$\rm \: = \: \dfrac{2290}{9}$

Hence,

$\boxed{\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms = \frac{2290}{9}}}$

6 0

3 years ago

05.02 find the measure of the angle x in the figure below

lilavasa [31]

Answer:

Step-by-step explanation:

52+59=111 180-111=69 69+63=132 180-132=48

7 0

4 years ago