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3 years ago

Find the length of CD

Mathematics

2 answers:

astraxan [27]3 years ago

8 0

Step-by-step explanation:

$\underline{ \underline{ \text{Given \: points}}} :$

C ( 3 , -2 ) & D ( 7 , -8 )

Let the point C ( 3 , -2 ) be ( x₁ , y₁ ) & the point D ( 7 , -8 ) be ( x₂ , y₂ ) .

$\underline{ \underline{ \text{To \: find}}} :$

Length of CD

$\underline{ \underline{ \text{Solution}}} :$

$\boxed{ \sf{Distance = \sqrt{(x_{2} -x_{1} )^{2} + (y_{2} - y_{1})^{2} } }}$

⇢ $\tt{CD = \sqrt{ {(7 - 3)}^{2} + {( - 8 - ( - 2))}^{2} } }$

⇢ $\tt{CD = \sqrt{ {(4)}^{2} + {( - 8 + 2)}^{2} } }$

⇢ $\tt{CD = \sqrt{16 + {( - 6)}^{2} } }$

⇢ $\tt{CD = \sqrt{16 + 36}}$

⇢ $\tt{CD = \sqrt{52}}$

⇢ $\tt{CD = 7.2 \: units}$

$\pink{ \boxed{\underline{ \underline{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{7.2 \: \text{units}}}}}}}}}$

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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KiRa [710]3 years ago

5 0

Answer: (B)

Explain:

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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

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A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$