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zepelin [54]
3 years ago
6

( 1/2 )2 · ( 1/3 )2=?

Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

Answer:

2/3

Step-by-step explanation:

1/2 x 2/1 = 1/1

1/3 x 2/1= 2/3

2/3 x 1/1 = 2/3

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Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest
galben [10]

First we dra a triangle:

To prove that the triangles are similar we have to do the following:

Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:

\Delta ABC\approx\Delta ACD

Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:

\Delta ABC\approx\Delta BCD

With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:

\Delta ACD\approx BCD

Now that we know that both triangles are similar we can use the following proportion:

\frac{h}{x}=\frac{y}{h}

this comes from the fact that the ratios should be the same in similar triangles.

From this equation we can find h:

\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}

Plugging the values we have for x and y we have that h (that is the segment CD) has length:

\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}

Therefore, the length of segment CD is:

CD=2\sqrt[]{10}

6 0
2 years ago
PLEASE HELP ME!!!!!!!!! (100 points)
velikii [3]

Answer:

Domain [2,5)

Range (-6,18]

Step-by-step explanation:

Domain is shifted 2 units to the right because of the horizontal shift so it is [2,5)

Range is multiplied by 3 because of the vertical stretch so it is (-6,18]

6 0
3 years ago
Read 2 more answers
The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm. Approximately how much
Zanzabum
The space between the two spheres will be the volume of the larger sphere minus the volume of the smaller sphere.  Given that the volume of any sphere is:

V=(4πr^3)/3  The space between to sphere of different radius and positioned about the same center is:

S=(4πR^3)/3-(4πr^3)/3  I used S=volume of space, R=larger radius and r=smaller radius...

S=(4π/3)(R^3-r^3), we are told that R=5 and r=4 so

S=(4π/3)(5^3-4^3)

S=(4π/3)(125-64)

S=(4π/3)(61)

S=244π/61

S=4π cm^3

S≈12.57 cm^3  (to nearest hundredth of a ml)
5 0
4 years ago
In a school with only sixth and seventh-grade students, 2/5 of the 200 students are seventh graders
san4es73 [151]
To find how many sixth graders there are we need to find out how many students there are in 1/5 in the school. Divide 200 by 2 to find 1/5 of the school.
Since 3/5 of the school is 6th graders we multiply 100 by 3 to find that there are 300 students in the 6th grade.
7 0
3 years ago
Read 2 more answers
The ratio of the number of boys to the number of girls in orchestra is 3 to 2. There are 40 girls in the orchestra, how many boy
postnew [5]

Answer:

there are 30 boys in the orchestra

7 0
3 years ago
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