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irakobra [83]
3 years ago
7

Factorise the following:

"{3x}^{2} + 5x - 12" alt="{3x}^{2} + 5x - 12" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Fed [463]3 years ago
6 0

Answer:

(x + 3)(3x - 4)

Step-by-step explanation:

Given

3x² + 5x - 12

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 12 = - 36 and sum = + 5

The factors are + 9 and - 4

Use these factors to split the x- term

3x² + 9x - 4x - 12 ( factor first/second and third/fourth terms )

= 3x(x + 3) - 4(x + 3) ← factor out (x + 3) from each term

= (x + 3)(3x - 4)

Thus

3x² + 5x - 12 = (x + 3)(3x - 4) ← in factored form

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A 4 cm x 6 cm rectangle sits inside a circle with radius with 11 cm. What is the area of the shaded region?
Novosadov [1.4K]

Answer:

The area of the shaded region is (121\pi -24)\ cm^{2}

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of the rectangle

so

A=\pi r^{2} -bh

we have

r=11\ cm

b=4\ cm

h=6\ cm

substitute the values

A=\pi (11^{2}) -(4)(6)

A=(121\pi -24)\ cm^{2} ----> exact value of the shaded area

4 0
3 years ago
One of the relatively uncommon instances in which researchers know the population standard deviation is in the case of the Intel
Phoenix [80]

Answer:

90% confidence interval for the mean IQ score in this community is [106.58 , 109.42].

Step-by-step explanation:

We are given that in general, the average IQ score in large, diverse populations is 100 and the standard deviation is 15.

Suppose that your sample of 300 members of your community gives you a mean IQ score of 108.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

                        P.Q. = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean IQ score = 108

            \sigma = population standard deviation = 15

            n = sample of members = 300

            \mu = population mean IQ score

<em>Here for constructing 90% confidence interval we have used One-sample z test statistics because we know about population standard deviation.</em>

<em />

So, 90% confidence interval for the population mean, \mu is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                of significance are -1.645 & 1.645}  

P(-1.645 < \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } < 1.645) = 0.90

P( -1.645 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X -\mu} < 1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

P( \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

<u>90% confidence interval for</u> \mu = [ \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ]

                                      = [ 108-1.645 \times {\frac{15}{\sqrt{300} } } , 108+1.645 \times {\frac{15}{\sqrt{300} } } ]

                                      = [106.58 , 109.42]

Therefore, we can be 90% confident that the mean IQ score in this community lies between 106.58 and 109.42.

8 0
3 years ago
A family of 5 drove to a concert. They paid $4 one time for parking and all of their tickets were the same price. They paid $99
ludmilkaskok [199]

Answer:

5 + (18,8 × 5) = 99

Explaination

one ticket costs: (99$ - 5$) ÷ 5 = $18,8

7 0
3 years ago
Please help me!! math
Alisiya [41]

Answer:

that looks pretty tough i dont know what it is sorry

Step-by-step explanation:

8 0
2 years ago
Choose the correct symbol to fill in the blank: 55.56 ___ 55.65 *<br> is it <br> &gt;<br> &lt;<br> =
eduard

Answer: 55.56 < 55.65

Step-by-step explanation:

The tenth place is bigger than the other number, and since the whole number is the same, then it would be the less than sign

4 0
2 years ago
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