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3 years ago

Instructions: Find the missing length indicated.

Mathematics

1 answer:

nata0808 [166]3 years ago

8 0

Answer:

x = 12

Step-by-step explanation:

By applying geometric root theorem in the given triangle,

$\frac{BD}{DC}= \frac{AD}{BD}$

$BD^2=AD\times DC$

$x^{2} =16\times 9$

$x=\sqrt{144}$

$x=12$

Therefore, x = 12 will be the answer.

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3 years ago

A rabbit population doubles every 4 weeks.There are currently five rabbits in a restricted area. If t represents the time in wee

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4 years ago

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4 years ago

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

skelet666 [1.2K]

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

4 0

3 years ago

A container has 360 gallons ; daniel took 1/3 of water to give to the animals in the ranch; how many gallons of water are left?

Mrrafil [7]

Answer: 240 gallons

Step-by-step explanation:

From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:

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= 120 gallons

Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:

= 360 - 120

= 240 gallons

8 0

3 years ago