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3 years ago

Identify the factors of x2 − 4x − 12. (1 point)

Mathematics

2 answers:

GalinKa [24]3 years ago

7 0

X² - 4x - 12 =
x² + 2x - 6x - 12 =
x(x + 2) - 6(x + 2) =
(x + 2)(x - 6)

Jet001 [13]3 years ago

7 0

Answer:

D. $(x-6)(x+2)$

Step-by-step explanation:

We have been given a polynomial $x^2-4x-12$ . We are asked to find the factors of our given polynomial.

We will use splitting the middle term format of factoring quadratic polynomial.

We need two numbers, whose product is $-12$ and whose sum is $-4$ . Such two numbers are $-6\text{ and }2$ .

$x^2-6x+2x-12$

$(x^2-6x)+(2x-12)$

Factor out GCF of each group:

$x(x-6)+2(x-6)$

$(x-6)(x+2)$

Therefore, factors of our given expression are $(x-6)(x+2)$ and option D is the correct choice.

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−3,−8,12,−15,9 find the mean

Jobisdone [24]

Answer:

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2 years ago

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The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the q

Makovka662 [10]

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

$\frac{\sum f}{4}=\frac{100}{4}=25$

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

$Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h$

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF) $_{p}$ = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

$Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h$

$=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75$

The value of first quartile is 34.75.

Q₃ is at the position:

$\frac{3\sum f}{4}=\frac{3\times100}{4}=75$

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

$Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h$

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF) $_{p}$ = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

$Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h$

$=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83$

The value of third quartile is 44.83.

Then the inter-quartile range is:

$IQR = Q_{3}-Q_{1}$

$=44.83-34.75\\=10.08$

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

$P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}$

$=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89$

Thus, the probability that a student scored at most 50 on the examination is 0.89.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Kendra earns $70 per week mowing lawns. She saves 60% of the money she earns each week. How many weeks will it take Kendra to sa

katrin [286]

Answer:

5 weeks

Step-by-step explanation:

Let's find how much money she saves a week by multiplying the decimal form of 60% and $70.

To get the decimal form of a percent you have to move the decimal to the left twice, like this: 60 ---> .60

Now that we have the decimal form of the percent we can multiply it by the 70 to find how much she saves a week:

(70)(.6) = 42

Therefore, Kendra saves $42 each week.

To find how many weeks it will take Kendra to buy the game system you divide $210 by the $42. Like this:

(210)/(42) = 5

All in all, it will take Kendra 5 weeks to save enough money to buy a game system that costs $210.

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2 years ago

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Solve for w, x, and y. Show your work.

sveta [45]

First of all, the left triangle is an equilateral triangle. Which means that all the interior angles are 60 degrees.

4w=60

w=15

Then all 3 sides are equal thus we can set up equation 3x-y=4y then simplify,

3x=5y

Going to the triangle on the right its isosceles we can set up equation 2x+50=180

2x=130

x=75

Substitute this back into equation above 3x=5y

5y=3*75

y=45

Therefore

x=75

y=45

w=15

Done!

5 0

2 years ago