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4 years ago

Solve the quadratic equation: 3x2 − 2x − 8 = 0

2 answers:

8 0

Solutions

Factor 3x²−2x−8

1. Multiply 3 by -8, which is -24.

2. Ask: Which two numbers add up to -2 and multiply to -24?

3. Answer: 4 and -6

4. Rewrite −2x as the sum of 4x and −6x:

$3x^2+4x-6x-8=0$ 

Factor out common terms in the first two terms, then in the last two terms

$x(3x+4)-2(3x+4)=0

 
$

Factor out the common term 3x+4

 $(3x+4)(x-2)=0$

Solve for x

1. Ask: When will (3x+4)(x−2) equal zero?

2. Answer: When 3x+4=0 or x−2=0.

3. Solve each of the 2 equations above:

x = −4 / 3,2

Liula [17]4 years ago

7 0

$3x^2-2x-8=0\\
3x^2-6x+4x-8=0\\
3x(x2)+4(x-2)=0\\
(3x+4)(x-2)=0\\
x=-\dfrac{4}{3} \vee x=2$

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The difference between a number divided by 3 and 4 is 20

Rzqust [24]

Set the number to x.

$\frac{x}{3}-\frac{x}{4}=20$
$\frac{4x}{12}-\frac{3x}{12}=20$
$\frac{x}{12}=20$
$x=240$

Thus, the number is 240.

8 0

3 years ago

PLEASE HELP I WILL MARK YOU AS BRAINLEST

denpristay [2]

Answer:

(i) Five number summary: Minimum value = 1, $Q_1=18$ , $Median=18.5$ , $Q_3=20.5$ , Maximum value = 26.

(ii) IQR = 2.5, upper fence = 24.25 and lower fence = 14.25.

(iii) 26 is an outlier of the data.

Step-by-step explanation:

The given data set is

19, 18, 23, 18, 18, 26, 19, 16, 20, 18, 17, 21

Arrange the data set in ascending order.

16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 23, 26

Divide the data set in 4 equal parts.

(16, 17, 18), (18, 18, 18), (19, 19, 20), (21, 23, 26)

Minimum value = 16

$Q_1=\frac{18+18}{2}=18$

$Median=Q_2=\frac{18+19}{2}=18.5$

$Q_3=\frac{20+21}{2}=20.5$

Maximum value = 26

The inter quartile range (IQR) of the data is

$IQR=Q_3-Q_1=20.5-18=2.5$

Upper fence :

$Q_3+1.5(IQR)=20.5+1.5(2.5)=24.25$

Lower fence :

$Q_1-1.5(IQR)=18-1.5(2.5)=14.25$

If the any element of the data set lies out side the upper fence and lower fence, then it is called an outlier.

26 ∉ [14.25, 24.25]

Therefore, 26 is an outlier of the data.

4 0

3 years ago

Read 2 more answers

From a pack of 9 cards numbered 1-9, three cards are drawn at random and laid on a table from left to right.

Andreas93 [3]

Answer: 1/6
Explanation: Since we need to draw three cards from a pack of 9 and the digits require an order, then our sample space becomes: 9P3.
Now, we don't care about picking an order when picking three cards to analyse, as there is only 1 way in arranging the three cards in descending order.

Thus, we get:

$\frac{^{9}C_3}{^{9}P_3} = \frac{1}{6}$