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3 years ago

What two numbers can be multiplied to get negative 14 but also add to get positive 5

1 answer:

4 0

The numbers: x, y
x·y=-14
x+y=5 ⇒ y=5-x
Substitute y in the first equation by y from second one
x·(5-x)=-14
5x-x²=-14
-x²+5x+14=0
-x²-2x+7x+14=0
-x(x+2)+7(x+2)=0
(x+2)(-x+7)=0
Product is 0 if one of factors is 0
x+2=0    or    -x+7=0
x=-2   or -x=-7
x=-2 or x=7
Now back to the equation y=5-x
y=5-(-2) or   y=5-7
y=7 or y=-2

The numbers are -2 and 7

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A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probab

ahrayia [7]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that $0 \le x \le 8 \:and\: $0 \le y \le 4$.$

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: $x + y \le 4$ ) are:

$(0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)$

n(A)=15

Therefore:

$P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}$

5 0

3 years ago

Write 0.216 as a rational number in lowest terms

lozanna [386]

Answer:

$=\frac{27}{125}$

Step-by-step explanation:

$0.216$

$\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}$

$\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000$

$=\frac{0.216\cdot \:1000}{1000}$

$=\frac{216}{1000}$

$216,\:1000$

$\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}$

$2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3$

$2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5$

$\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}$

$=2\cdot \:2\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8$

$=8$

$=\frac{8\cdot \:27}{8\cdot \:125}$

$\mathrm{Cancel\:the\:common\:factor:}\:8$

$=\frac{27}{125}$

Hence, the correct answer is $=\frac{27}{125}$

6 0

2 years ago

What could explain what happened when the time was equal to 120 minutes

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

Alright, lets get started.

Lets split the given graph in three parts.

First part: 0 to 30 minutes

We can see between this period, 0 to 30 minutes, the distance from home keeps increasing. It means from 0 to 30 minutes, Eli is moving towards the library.

Second part: 30 to 120 minutes

between 30 to 120 minutes,the distance from home does not changes. It means during this period, Eli is at the library.

Third part : 120 minutes to 135 minutes

Between 120 to 135 minutes, the distance from home is decreasing.

It means Eli is returning home in that period.

It means, at 120minute, Eli started her bicycle , home from the library. Hence option (b) : Answer

Hope it will help :)

5 0

3 years ago

Jamal has $15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some sour straws for $1.50

frosja888 [35]

15-7.50=7.50
7.50/1.50=?

5 0

3 years ago

Write an algebraic expression that models the situation “the piggy bank contained $25, and $1.50 is added each day.” Use d to re

Kryger [21]

the answer is b because the piggy bank originally contained $25 and the person adds $1.50 per day.. so: 25+1.5d

3 0

3 years ago