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2 years ago

Factorise the following

Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

7 0

Answer:

Below.

Step-by-step explanation:

a) 5x-x² = x(5 - x).

b) x²-6x-27 = (x - 9)(x + 3).

c) x²+x-56 = (x - 7)(x + 8).

d) x³+8 = (x + 2)(x^2 - 2x + 4)

e) 3x⁴-54t = 3(x^4 - 18t)

f) x²+3x-10 = (x - 2)(x + 5)

g) 2(x⁴+x³-12x²) = 2x^2(x + 4)(x - 3)

h) 20(x³-1) = 20(x - 1)(x^2 + x + 1)

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F(x) = 3x + 2

Vinvika [58]

Answer:

g(f(x)) = 9x² + 12x + 5

Step-by-step explanation:

g(f(x))

= g(3x + 2) ← substitute x = 3x + 2 into g(x)

= (3x + 2)² + 1

to expand (3x + 2)² = (3x + 2)(3x + 2)

each term in the second factor is multiplied by each term in the first factor

3x(3x + 2) + 2(3x + 2) ← distribute both parenthesis

= 9x² + 6x + 6x + 4 ← collect like terms

= 9x² + 12x + 4

then

g(f(x)) = (3x + 2)² + 1 = 9x² + 12x + 4 + 1 = 9x² + 12x + 5

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2 years ago

On a test with 25 problems, Grace got 88% correct. How Manny problems did Grace get correct?

Sloan [31]

She got 22 problems correct

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3 years ago

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For dinner, Abelita chooses the Italian salad that costs $3.99 before tax, and Franco chooses the fettuccini alfredo that costs

ivolga24 [154]

Answer

Find out the total cost for their dinner.

To prove

As given

For dinner, Abelita chooses the Italian salad that costs $3.99 before tax.

Franco chooses the fettuccini alfredo that costs $7.17 before tax.

Total cost of the dinner before tax = $ 3.99 + $7.17

= $ 11.16

As given

If the sales tax is 5 percent .

5 % is written in the decimal form.

$= \frac{5}{100}$

= 0.05

5% tax on the dinner cost = 0.05 × 11.16

= $0.558

Total cost of the dinner = Total cost of the dinner before tax + tax cost

= $11.16 + $0.558

= $ 11.718

= $11.72 (approx)

Therefore the total cost for their dinner is $ 11.72 (approx)

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3 years ago

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Which table represents the same proportional relationship as the graph? On a coordinate plane, a line goes through points (0, 0)

saveliy_v [14]

Answer:

the answer is C !!!!!!

Step-by-step explanation:

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3 years ago

A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

AveGali [126]

Answer:

a) 68% probability that the sample mean will be within ±5 of the population mean.

b) 95% probability that the sample mean will be within ±10 of the population mean.

Step-by-step explanation:

To solve this problem, we have to understand the Empirical Rule and the Central Limit Theorem

Empirical Rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s= \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

Mean: $\mu = 200$

Standard deviation of the population: $\sigma = 50$

Size of the sample: $n = 100$

Standard deviation for the sample mean: $s = \frac{50}{\sqrt{100}} = 5$

a.What is the probability that the sample mean will be within ±5 of the population mean?

5 is one standard deviation from the mean.

By the Empirical Rule, 68% probability that the sample mean will be within ±5 of the population mean.

b.What is the probability that the sample mean will be within ±10 of the population mean?

10 is two standard deviations from the mean

By the Empirical Rule, 95% probability that the sample mean will be within ±10 of the population mean.

4 0

3 years ago