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ddd [48]
3 years ago
10

Examine the system of equations.

Mathematics
1 answer:
MrMuchimi3 years ago
7 0

answer:

x =  - 2 \\ y = 2 \\  \\ ( - 2, \: 2)

explanation:

y =  -  \frac{1}{2} x + 1 \\ y = 2x + 6 \\ first \: equation \: add \:  \frac{1}{2} from \: both  \\  sides \\   \\ second \: equation \: subtract \: 2x \: from  \\  both \: sides \\  \\ y +  \frac{1}{2} x = 1 \\ y - 2x = 6 \\ solve \: the \: first \: equation \\  \\ y +  \frac{1}{2} x = 1 \\ subtract \:  \frac{x}{2} from \: both \: sides \\  \\ y =  -  \frac{1}{2} x + 1 \\ substitute \:  -  \frac{x}{2}  + 1 \: for \: y \: in \: the  \\ other \: equation \\  \\  -  \frac{1}{2} x + 1 - 2x = 6 \\ add \:   \frac{1}{2} x \: to \: 2x \\  \\  -  \frac{5}{2} x + 1 = 6 \\ subtract \: 1 \: from \: both \: sides \\  \\  -  \frac{5}{2} x = 5 \\ divide \: both \: sides \: by \:  -  \frac{5}{2}  \\  \\ x =  - 2 \\ substitute \: the \: value \: of \: x \: into \\ an \: equation \\  \\ y =  -  \frac{1}{2} ( - 2) + 1 \\ distribute \\  \\ y = 1 + 1 \\ add  \\  \\ y = 2 \\  \\ ( - 2, \: 2)

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Analyze the table below and answer the question that follows.
lora16 [44]

Answer:

C. Events E and A are independent

Step-by-step explanation:

we will verify each options

(a)

We can use independent events formula

P(B∩C)=P(B)*P(C)

we are given

P(B)=0.4

P(C)=0.25

P(B∩C)=0.05

now, we can plug these values into formula

and we get

0.05=0.4*0.25

0.05=0.1

we can see that left side is not equal to right side

so, this is FALSE

(b)

We can use independent events formula

P(D∩A)=P(D)*P(A)

we are given

P(D)=0.25

P(A)=0.6

P(D∩A)=0.1

now, we can plug these values into formula

and we get

0.1=0.25*0.6

0.1=0.15

we can see that left side is not equal to right side

so, this is FALSE

(c)

We can use independent events formula

P(E∩A)=P(E)*P(A)

we are given

P(E)=0.5

P(A)=0.6

P(E∩A)=0.3

now, we can plug these values into formula

and we get

0.3=0.5*0.6

0.3=0.3

we can see that both sides are equal

so, this is TRUE

(d)

We can use independent events formula

P(D∩B)=P(D)*P(B)

we are given

P(D)=0.25

P(B)=0.4

P(D∩A)=0.15

now, we can plug these values into formula

and we get

0.15=0.25*0.4

0.15=0.1

we can see that left side is not equal to right side

so, this is FALSE


8 0
3 years ago
Julie goes to the sports store and spends $40.50 before tax. She buys a pair of shorts for $21.75 and 3 pairs of socks that each
horsena [70]

Answer:

$6.25

Step-by-step explanation:

1. Variables

Let's the variable for socks will be s

2. Set up an equation

21.75 + 3s = 40.50

3. Subtract 21.75 from both sides

3s = 18.75

4. Divide 3 from both sides

s = $6.25

7 0
3 years ago
What is the sum of the of the infinite geometric series 0.7+0.07+0.007+...?
andrew11 [14]

Answer:

a

Step-by-step explanation:

hope it works out for you

please mark brainiest

7 0
3 years ago
3(x+4)=16 solve for x
MAXImum [283]
Hope you get it
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6 0
3 years ago
Read 2 more answers
1) Write an equation that includes a variable to show how much money matt started with
12345 [234]
1) m-13=7

2)m-13=7
m-13+13=7+13
m=20
so he had $20 he spent $13 so $7 was left!


BRAINLIEST???
7 0
3 years ago
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