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dsp73
3 years ago
8

Find the missing lengths. If needed, round the answers to the nearest tenth.

Mathematics
1 answer:
dmitriy555 [2]3 years ago
6 0

Answer:

The value of y is <u>64</u>.

The value of z is <u>225</u>.

Step-by-step explanation:

Given,

AB = 136

BC = 255

∠B = 90°

We have to find the value of 'y' and 'z'.

Solution,

Let assume D is a point on AC.

Then BD = 120

And also given ∠D = 90°

Now in ΔABD

AB = 136    and     BD = 120

∠D = 90°

So according to Pythagoras theorem;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides".

AB^2=BD^2+AD^2

On substituting the values, we get;

136^2=120^2+y^2\\\\18496=14400+y^2\\\\y^2=18496-14400\\\\y^2=4096

Now taking square root on both side, we get;

\sqrt{y^2} =\sqrt{4096} \\\\y=64

Hence the value of y is 64.

Again, in ΔBDC

BC = 255    and     BD = 120

∠D = 90°

So according to Pythagoras theorem;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides".

BC^2=BD^2+DC^2

On substituting the values, we get;

255^2=120^2+z^2\\\\65025=14400+z^2\\\\z^2=65025-14400\\\\z^2=50625

Now taking square root on both side, we get;

\sqrt{z^2}=\sqrt{50625}\\\\z=225

Hence the value of z is 225.

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DENIUS [597]

All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.

<h3>What is congruence transformation?</h3>

A congruence transformation is defined as a movement of shape such that it can produce a shape that is congruent to the original.

There are three types of congruence transformation;

1. Translation

2. Reflection

3. Rotation

Given;

Shape B is made by applying a single transformation to shape A.

Hence, All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.

Learn more about transformations ;

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5 0
1 year ago
Please help me!!!!!!!!
zavuch27 [327]
Are you kidding are you sure you want this
3 0
3 years ago
PLZ help me fast 2 mins left
jek_recluse [69]

Answer:

\sqrt{-5}=i\sqrt{5}

\sqrt{-25}=5i

Step-by-step explanation:

i is an imaginary unit, this means

i^2=-1

Rewrite -5 as 5\cdot (-1)=5\cdot i^2,

then

\sqrt{-5}=\sqrt{5i^2}=\sqrt{5}\cdot \sqrt{i^2}=\sqrt{5}\cdot i=i\sqrt{5}

Rewrite -25 as -25=25\cdot (-1)=25\cdot i^2,

then

\sqrt{-25}=\sqrt{25\cdot i^2}=\sqrt{25}\cdot \sqrt{i^2}=5\cdot i=5i

6 0
2 years ago
On a coordinate plane, 2 polygons are shown. Polygon A B C D has points (1, negative 6), (5, negative 6), (6, negative 2), and (
irga5000 [103]

Answer:

The correct option is;

Use a scale factor of 2

Step-by-step explanation:

The parameters given are;

A = (1, -6)

B = (5, -6)

C = (6, -2)

D = (0, -2)

A'' = (1.5, 4)

B'' = (3.5, 4)

C'' = (4, 2)

D'' = ( 1, 2)

We note that the length of side AB in polygon ABCD = √((5 -1)² + (-6 - (-6))²) = 4

The length of side A''B'' in polygon A''B''C''D'' = √((3.5 -1.5)² + (4 - 4)²) = 2

Which gives;

AB/A''B'' = 4/2 = 2

Similarly;

The length of side BC in polygon ABCD = √((6 -5)² + (-2 - (-6))²) = √17

The length of side B''C'' in polygon A''B''C''D'' = √((4 -3.5)² + (2 - 4)²) = (√17)/2

Also we have;

The length of side CD in polygon ABCD = √((6 -0)² + (-2 - (-2))²) = 6

The length of side C''D'' in polygon A''B''C''D'' = √((4 -1)² + (2 - 2)²) = 3

For the side DA  and D''A'', we have;

The length of side DA in polygon ABCD = √((1 -0)² + (-6 - (-2))²) = √17

The length of side D''A'' in polygon A''B''C''D'' = √((1.5 -1)² + (4 - 2)²) = (√17)/2

Therefore the Polygon A B C D can be obtained from polygon A''B''C''D'' by multiplying each side of polygon A''B''C''D'' by 2

The correct option is therefore;

Use a scale factor of 2.

3 0
3 years ago
Read 2 more answers
What is the experamental probability that the coin lands on heads?
sammy [17]

Answer:

The experamental probability that the coin lands on head is 50 %

Step-by-step explanation:

Given:

Experiment:

A coin is Toss

Let the Sample Space be 'S' that is total number of outcomes for a coin has been tossed = { Head, Tail }

∴ n ( S ) =  2

Let A be the event of getting a Head on tossing a coin i.e  { Head }

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Now,

\textrm{Probability} =\frac{\textrm{outcomes for the experiment}}{\textrm{total number of outcomes}}

Substituting the values we get

P(A) = \frac{n(A)}{n(S)} \\\\P(A) = \frac{1}{2} \\\\P(A) = 0.5\\\\P(A) = 50\%

The experamental probability that the coin lands on head is 50 %

5 0
3 years ago
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