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Triss [41]
2 years ago
15

n="absmiddle" class="latex-formula"> and $\overline{CZ}$ are angle bisectors of triangle ABC that meet at I as shown below, with CY = 4, AY = 6, and AB = 8. Find BZ.

Mathematics
1 answer:
erica [24]2 years ago
6 0

Answer:

  BZ = 64/23 = 2 18/23

Step-by-step explanation:

The angle bisectors divide the triangle into proportional parts, so we have ...

  CB/CY = AB/AY

  CB = CY(AB/AY) = 4(8/6) = 16/3 . . . . multiply by CY and evaluate

and ...

  BZ/CB = AZ/AC

  BZ = AZ(CB/AC) . . . . multiply by CB

But we have ...

  AZ = 8 -BZ, so this becomes ...

  BZ = (8 -BZ)(16/3)/(10)

  BZ(1 +8/15) = 64/15 . . . . add the BZ term on the right to both sides

  BZ = (64/15)(15/23) = 64/23 . . . . divide by the coefficient of BZ

BZ = 64/23 = 2 18/23

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Step-by-step explanation: first you have to take the 3x and split it up so it can make 3(x-3y) then you have to rewrite it to -9 as 3x3 and then factor out common term 3 which would be your final answer 3(x-3y)

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Write a recursive rule for the sequence. Assume it starts with the 1st term. 10, 14, 18, 21...
Papessa [141]

Option D is correct. The correct option for the recursive formula is f(0) =6;f(n)=f(n - 1)+4

Given the sequence 10, 14, 18...

The first term is 10, hence

a1 = 10

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From the sequence, we can see that <em>4 is being added to the previous term to get the next term</em>. Hence the nth term will be expressed as:

a_n = a_{n-1} + 4

Get the term before the first term a_0

If n = 1

a_1 = a_{1-1} + 4\\a_1 = a_{0} + 4\\a_0=a_1-4\\a_0=10-4\\a_0=6

Hence the correct option for the recursive formula is f(0) =6;f(n)=f(n - 1)+4

Learn more here: brainly.com/question/18233843

3 0
2 years ago
n a study of the accuracy of fast food​ drive-through orders, Restaurant A had 314 accurate orders and 61 that were not accurate
Varvara68 [4.7K]

Answer:

a. 0.1576<p<0.2310

b. The two restaurants likely have similar order rates which are inaccurate.

Step-by-step explanation:

a. We first calculate the proportion, \hat p:

\hat p=\frac{61}{314}\\\\=0.1943

-We use the z-value alongside the proportion to calculate the margin of error:

MOE=z\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=1.645\times \sqrt{\frac{0.1943(1-0.1943)}{314}}\\\\=0.0367

The confidence interval at 90% is then calculated as:

CI=\hat p\pm MOE\\\\=0.1943\pm 0.0367\\\\=[0.1576,0.2310]

Hence, the confidence interval at 90% is [0.1576,0.2310]

b. From a above, the calculated confidence interval is 0.1576<p<0.2310

-We compare the calculated CI to the stated CI of 0.147<p<0.206

-The two confidence intervals overlap each other and have the same value for 0.1576<p<0.206

-Hence, we conclude that the two restaurants likely have similar order rates which are inaccurate.

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Answer:

32.5

Step-by-step explanation:

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