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2 years ago

When factorising a quadratic trinomial of the form ax^2 + bx + c, we need to find two numbers which ???? (see image for options)

Mathematics

1 answer:

kupik [55]2 years ago

3 0

Answer: Choice E

multiply to give a*c and add to get b

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This is known as the AC factoring method based on how you multiply the first and last coefficients (a and c) and use that product to figure out which factors add to the middle coefficient.

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An example:

6x^2 + 35x + 50

We have a = 6, b = 35, c = 50

Multiply a and c and we get: a*c = 6*50 = 300

We need to find factors of 300 that pair up and add to 35

Through trial and error you should find,

15 * 20 = 300

15 + 20 = 35

The two numbers are therefore 15 and 20.

So we break 35x into 15x+20x and use the factor by grouping method

6x^2 + 35x + 50

6x^2 + 15x + 20x + 50

(6x^2 + 15x) + (20x + 50)

3x(2x + 5) + 10(2x + 5)

(3x + 10)(2x + 5)

We see that 6x^2 + 35x + 50 factors to (3x + 10)(2x + 5)

Use the FOIL method or the box method or distribution to help see that (3x + 10)(2x + 5) expands back to 6x^2 + 35x + 50.

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Urgent!!!!

LekaFEV [45]

Answer:

One pair of socks is $370.

Step-by-step explanation:

Sean bought three pairs of the same socks and a shoe polish for $1450. If the

polish cost $340, how much is the cost of one pair of socks.

6x - 340 = 1450

6x = 1450 -340

6x = 1110

2x = 1110 / 3

2x = 370

8 0

2 years ago

Read 2 more answers

for a class gardening project 1/3 of mrs gordon's students planted marigolds and 1/2 planted tulips what fraction of the class p

vladimir2022 [97]

Get them to have a common denominator so you can add them
(1/3)×2= 2/6 and (1/2)×3= 3/6
Add them together
(2/6)+ (3/6)= 5/6
So 5/6 of the class planted either marigolds or tulips and 1/6 of the class planted neither

5 0

2 years ago

Help me plz ???????????????

Aleksandr-060686 [28]

Its a we know its this cause its rational and if its a rational number it is also an integer and a whole number

8 0

3 years ago

Solve the quadratic equation below for the exact values of x: 4x^2-5=75

grandymaker [24]

Step-by-step explanation:

$4 {x}^{2} - 5 = 75 \\ 4 {x}^{2} = 75 + 5 \\ 4 {x}^{2} = 80 \\ {x}^{2} = \frac{80}{4} \\ {x}^{2} = 20 \\ x = \pm \sqrt{20} \\ x = \pm 2 \sqrt{5}$

6 0

2 years ago

Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa

Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 8.7% and standard deviation 20.2%.

This means that $\mu = 8.7, \sigma = 20.2$

40 years:

This means that $n = 40, s = \frac{20.2}{\sqrt{40}}$

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$