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alex41 [277]
2 years ago
9

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

Mathematics
1 answer:
skelet666 [1.2K]2 years ago
4 0

Angles formed by the segment \overline{XZ} in the triangles ΔWXZ, and ΔXYZ, are equal and the given corresponding sides are proportional.

  • The option that best completes the proof showing that ΔWXZ ~ ΔXYZ is; <u>16 over 12 equals 12 over 9</u>

Reasons:

The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;

Segment \overline{XZ} is perpendicular to segment \overline{WY}

∠WZX and ∠XZY are right angles by definition of \overline{XZ}  perpendicular to \overline{WY}

∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)

\displaystyle \frac{WZ}{XZ} = \frac{16}{12} = \mathbf{ \frac{4}{3}}

\displaystyle \mathbf{ \frac{XZ}{ZY}}  = \frac{12}{9}  = \frac{4}{3}

Therefore;

  • \displaystyle \frac{16}{12} = \frac{12}{9}, which gives, \displaystyle \mathbf{\frac{WZ}{XZ} }= \frac{XZ}{ZY}

Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and

that the included angles between the two sides, ∠WZX and ∠XZY are

congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-

Side, SAS, similarity postulate.

The option that best completes the proof is therefore;

  • \displaystyle \frac{16}{12} = \frac{12}{9} which is; <u>16 over 12 equals 12 over 9</u>

Learn more about the SAS similarity postulate here:

brainly.com/question/11923416

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vlabodo [156]

Answer:

A, C, D and K

Step-by-step explanation:

First, plot the solution set to the system of two inequalities.

The inequality y\le -2x+10 determines solid line and bottom shaded region under this line.

The inequality y>\dfrac{1}{2}x-2 determines dotted line and top shaded region under this line.

The intersection of these two regions is the solution set to the system of two inequalities.

Points A, C, D and K belong to this region.

4 0
3 years ago
(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =
frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0
3 years ago
An artificial lake is in the shape of a rectangle and has an area of 9/20 square mile. The width of the lake is 1/5 the length o
Zina [86]
X=width of the lake
y=length of the lake.
we set out this system of equiations
x*y=9/20
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we solve by sustitution method
(y/5)*y=9/20
y²/5=9/20
y²=(5*9)/ 20
y²=2.25
y=√2.25=1.5

x=y/5
x=1.5/5=0.3

Solution:
width of the lake=0.3 miles
lenght of the lake=1.5 miles
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Answer:

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2nd way.  $48,000 x .044.  =  $2,112 .044 is 4.4% in decimal form. So you found the increase here.  Add the increase to the original price.  $48,000 + $2,112 to get the new price of $50,112.

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