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3 years ago

The lengths of the legs of a right triangle are 6 cm and 3 cm.

Mathematics

1 answer:

Alenkinab [10]3 years ago

5 0

We will calculate the length of the hypotenuse using the Pythagorean theorem. Suppose that the hypotenuse = c, then:

c^2 = 6^2 + 3^2

c^2 = 36 + 9

c^2 = 45

c = square root of 45

c = square root of 9 * square root of 5

c = 3 * square root of 5 ; <em>square root of 5 = approximately 2,24</em>

c = 3 * 2,24 = 6,72 = 6,7

The correct answer is 6,7.

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Find the indicated sum for each sequence. S9 of –9, 36, –144, 576, ... A –585 B –471,861 C 1,887,435 D –471,852

Varvara68 [4.7K]

<h3>Answer: Choice B) -471,861</h3>

=====================================================

Explanation:

This is a geometric sequence because each new term is found by multiplying the last term by -4.

The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.

Use the geometric nth partial sum formula below to plug in the terms mentioned

$S_n = \frac{a*(1-r^n)}{1-r}\\\\S_9 = \frac{-9*(1-(-4)^9)}{1-(-4)}\\\\S_9 = \frac{-9*(1-(-262144))}{1+4}\\\\S_9 = \frac{-9*(1+262144)}{1+4}\\\\S_9 = \frac{-9*(262145)}{5}\\\\S_9 = \frac{-2359305}{5}\\\\S_9 = -471,861\\\\$

3 0

3 years ago

Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

Ronch [10]

Answer:

$4^x-5=6$ gives the solution $x=\frac{\log(11)}{\log(4)}$ .

$4^{x-5}=6$ gives the solution $x=\frac{\log(6)}{\log(4)}+5$ .

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is $4^{x}-5=6$ , then the following is the process:

$4^x-5=6$

Add 5 on both sides:

$4^x=6+5$

Simplify:

$4^x=11$

Now write an equivalent logarithm form:

$\log_4(11)=x$

$x=\log_4(11)$

Now using the change of base:

$x=\frac{\log(11)}{\log(4)}$ .

If we assume the equation is $4^{x-5}=6$ , then we use the following process:

$4^{x-5}=6$

Write an equivalent logarithm form:

$\log_4(6)=x-5$

$x-5=\log_4(6)$

Add 5 on both sides:

$x=\log_4(6)+5$

Use change of base formula:

$x=\frac{\log(6)}{\log(4)}+5$

6 0

3 years ago

Helppppppppppppppppp pleaseeeeeeeeeeee

alexandr1967 [171]

Greater than 6 it’s labeled as 1 through 6 a fair dice has a probability of 16

4 0

2 years ago

What is 0.3 divided by 0.06

slamgirl [31]

The answer to your question is 5

5 0

3 years ago

Read 2 more answers

A random sample of 11 fields of rye has a mean yield of 20.1 bushels per acre and standard deviation of 7.66 bushels per acre. D

Lady bird [3.3K]

Answer:

17.1≤x≤23.1

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as;

CI = x ± z*s/√n

x is the mean yield = 20.1

z is the 80% z-score = 1.282

s is the standard deviation = 7.66

n is the sample size = 11

Substitute

CI = 20.1 ± 1.282*7.66/√11

CI = 20.1 ± 1.282*7.66/3.3166

CI = 20.1 ± 1.282*2.3095

CI = 20.1 ±2.9609

CI = (20.1-2.9609, 20.1+2.9609)

CI = (17.139, 23.0609)

hence the required confidence interval to 1dp is 17.1≤x≤23.1

8 0

3 years ago