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3 years ago

How do I prove that (1+sinx)/cosx=cos(-x)/(1+sine(-x))

Mathematics

1 answer:

stira [4]3 years ago

5 0

$\dfrac{1+\sin x}{\cos x}=\dfrac{\cos (-x)}{1+\sin(-x)}\\
\dfrac{1+\sin x}{\cos x}=\dfrac{\cos x}{1-\sin x}\\
\cos^2 x=(1+\sin x)(1-\sin x)\\
\cos^2 x=1-\sin^2 x\\
\sin^2 x+\cos^2 x=1
$

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Answer:

First blank - SSS congruent condition

Second blank - Congruent 

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2 years ago

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What is the value of -16 divided by 2.5

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Hey the answer to your question is -6.4

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2 years ago

14/2 three equivalent ratios

Anna71 [15]

Answer:

Three equivalent ratios of $\frac{14}{2}$ are $\frac{7}{1}$ , $\frac{21}{3}$ and $\frac{28}{8}$ .

Step-by-step explanation:

We are given a fraction $\frac{14}{2}$ .

We need to find the three equivalent ratios/fractions of $\frac{14}{2}$ .

The common factor of 14 and 2 is 2.

So, dividing top and bottom by 2, we get

14÷2 = 7 and 2÷2 that is $\frac{7}{1}$ .

Multiplying $\frac{7}{1}$ fraction by a common number 3 in top and bottom, we get

7 × 3 = 21

1 × 3 = 6

So, we get another equivalent fraction $\frac{21}{6}$ .

Multiplying $\frac{7}{1}$ fraction by a common number 3 in top and bottom, we get

7 × 4 = 28

1 × 4 = 4

So, we get another equivalent fraction $\frac{28}{4}$ .

Therefore, three equivalent ratios of $\frac{14}{2}$ are $\frac{7}{1}$ , $\frac{21}{3}$ and $\frac{28}{4}$ .

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3 years ago

Solve the following x/5=10

sergey [27]

Answer:

x = 50

Step-by-step explanation:

x/5 = 10

Multiply both sides of the equation by 5.

5(x/5) = 5(10)

x = 5(10)

x = 50

The value of x is 50.

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3 years ago

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A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sa

Semenov [28]

Answer:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

(–2975, 175)

Do not reject H₀

Step-by-step explanation:

Hello!

The objective of this experiment is to test if the salaries of elementary school teachers are equal in two districts. You can test this trough the population means of the salaries of the teachers if they are either equal or different or directly test if the difference between the salaries of the two districts is cero or not, symbolically: μ₁ - μ₂ = 0

Remember, in the null hypothesis is usually stated the known information, is the "no change" premise and always carries the = symbol.

The hypothesis is:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

You have two normally distributed variables and you are studying the difference of the means. You can use a pooled Z to make the interval, the formula is:

X[bar]₁-X[bar]₂ ± $Z_{1-\alpha /2}$ *(√(σ₁²/n₁+σ₂²/n₂)

Since the test is two-tailed and at a signification level of 5% I've made the interval at the complementary confidence level of 95% so that I can use it to decide over the hypothesis.

X[bar]₁-X[bar]₂ ± $Z_{1-\alpha /2}$ *(√(σ₁²/n₁+σ₂²/n₂)

$Z_{1-\alpha /2}$ = $Z_{0,975}$ = 1,96

[28900-30300 ± 1.96*(√((2300)²/15+(2100)²/15)]

[-1400 ± 1576,15]

[-2976.15;176,15]

Since I've approximated to two decimal units in the intermediate calculations, the values differ slightly, but the interval is:

(–2975, 175)Now, since the 0 is contained in the Confidence interval, the decision is to not reject the null hypothesis. In other words, the difference in average salaries between the two districts is cero.

I hope it helps!

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3 years ago