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3 years ago

13

How many solutions? 2x + 6 = 3(x + 2) - x

1 answer:

Serjik [45]3 years ago

6 0

Answer:

2x = 2x

Step-by-step explanation:

2x + 6 = 3x + 6 - x

2x = 3x - x(cancel equal terms)

2x=2x

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Opposite angles of a parallelogram are congruent. <br> a. True <br> b. False

AlexFokin [52]

Correct answer is true

4 0

3 years ago

Find the length of EF

Lisa [10]

Answer:

9

Step-by-step explanation:

1. First, we need to set up an equation to find the value of x and then the length of EF.

2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of: $3x - 28 + 3x - 30 + x = 33$

3. (Solving for x)

Step 1: Simplify both sides of the equation.

$3x - 28 + 3x - 30 + x = 33$
$(3x+3x+x) + (-28-30)=33$
$7x - 58 = 33$

Step 2: Add 58 to both sides.

$7x - 58 + 58 = 33 + 58$
$7x = 91$

Step 3: Divide both sides by 7.

$\frac{7x}{7} = \frac{91}{7}$
$x = 13$

4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.

$3(13)-30$
$39 - 30$
$9$

Therefore, the length of EF is 9.

7 0

3 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

3 years ago

The united states government produced about 10.25 billion pennies one year.

Elenna [48]

1) 10.25 x 10^9 in scientific notation is 1.025 x 10^10

2) Now you have to subtract 10.25x10^9 - 3.0x10^7

To make that you have to put both numbers with the same power of ten.

1025x10^7 - 3.0x10^7 = 1022x10^7 more pennies than half-dollars.

7 0

3 years ago

Somebody plz help me with this

Leviafan [203]

Answer M=-2
Because when it’s negative it’s going from left to right and when it is to that means 2 up 1 to the right

6 0

3 years ago