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3 years ago

What are the solutions of x2 = 8 - 5x?

Mathematics

1 answer:

jonny [76]3 years ago

5 0

Answer:

That can be re-written:

x^2 + 5x -8 = 0

We use the Quadratic Formula

a=1

b = 5

c = -8

x = [-b +- sq root (b^2 - 4ac) ] / 2a

x = [-5 +- sq root (25 - - 32)] / 2

x1 = [-5 + sq root (57)] / 2

x1 = 1.27491722

x2 = [-5 - sq root (57)] / 2

x2 = -6.2749172176

Step-by-step explanation:

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Pls remember to give your answer in metres

spin [16.1K]

Answer: 500m

Explanation:
If the scale of the drawing is 1:500 then the real playground should be 500:1 which is 500m

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3 years ago

Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 5% of all

Gnom [1K]

Answer:

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

Step-by-step explanation:

For each visitor of the website, there are only two possible outcomes. Either they are looking for the website, or they are not. The probability of a customer being looking for the website is independent of other customers. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of all visitors to the website are looking for other websites.

So 100 - 5 = 95% are looking for the website, which means that $p = 0.95$

Find the probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

This is P(X = 2) when n = 4. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = x) = C_{4,2}.(0.95)^{2}.(0.05)^{2} = 0.0135$

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

5 0

2 years ago

(cotx+cscx)/(sinx+tanx)

Butoxors [25]

Answer: $\bold{\dfrac{cot(x)}{sin(x)}}$

<u>Step-by-step explanation:</u>

Convert everything to "sin" and "cos" and then cancel out the common factors.

$\dfrac{cot(x)+csc(x)}{sin(x)+tan(x)}\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)}{1}+\dfrac{sin(x)}{cos(x)}\bigg)\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg[\dfrac{sin(x)}{1}\bigg(\dfrac{cos(x)}{cos(x)}\bigg)+\dfrac{sin(x)}{cos(x)}\bigg]\\\\\\\bigg(\dfrac{cos(x)}{sin(x)}+\dfrac{1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)}{cos(x)}+\dfrac{sin(x)}{cos(x)}\bigg)$

$\text{Simplify:}\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\div\bigg(\dfrac{sin(x)cos(x)+sin(x)}{cos(x)}\bigg)\\\\\\\text{Multiply by the reciprocal (fraction rules)}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)cos(x)+sin(x)}\bigg)\\\\\\\text{Factor out the common term on the right side denominator}:\\\\\bigg(\dfrac{cos(x)+1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)(cos(x)+1)}\bigg)$

$\text{Cross out the common factor of (cos(x) + 1) from the top and bottom}:\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times\bigg(\dfrac{cos(x)}{sin(x)}\bigg)\\\\\\\bigg(\dfrac{1}{sin(x)}\bigg)\times cot(x)}\qquad \rightarrow \qquad \dfrac{cot(x)}{sin(x)}$

6 0

3 years ago

Porter is visiting India and would like to purchase some local spices. He finds some spices that cost 401.39 rupees. If the curr

Murljashka [212]

The cost of spices in US dollars is $5.45

The cost of spices in Indian rupees = 401.39 rupees

The exchange rate is

1 dollar:73.6500 rupees

So we have to exchange the Indian rupees to the US dollars

The cost of spices in Indian rupees = 401.39 rupees

The cost of spices in US dollars = The cost of spices in Indian rupees / 73.6500

Substitute the values in the equation and fins the cost of spices in US dollars

The cost of spices in US dollars = 401.39 / 73.6500

Divide the numbers

= $5.45

Hence, the cost of spices in US dollars is $5.45

Learn more about exchange rate here

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1 year ago

13 and 5/8 plus 7/8 please answer quickly

Salsk061 [2.6K]

13 5/8 + 7/8 = 14 1/2

5/8 + 7/8 = 1 4/8 = 1 1/2

1 1/2 + 13 = 14 1/2

8 0

3 years ago