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3 years ago

Solve the equation -3x-11=2(4x-8)-6

Mathematics

2 answers:

quester [9]3 years ago

7 0

Answer:

Step-by-step explanation:

PEMDAS

-3x-11=2(4x-8)-6

-3x-11=8x-16-6

-3x-11=8x-22

-11x-11=-22

-11x= -11

x=1

PSYCHO15rus [73]3 years ago

5 0

Answer:

x = 1

Step-by-step explanation:

- 3x - 11 = 2(4x - 8) - 6 ← distribute and simplify left side

- 3x - 11 = 8x - 16 - 6

- 3x - 11 = 8x - 22 ( subtract 8x from both sides )

- 11x - 11 = - 22 ( add 11 to both sides )

- 11x = - 11 ( divide both sides by - 11 )

x = 1

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3 years ago

What is the probability of drawing a black ace followed by a heart out

Verdich [7]

Correct option C) 0.98%

<u>Step-by-step explanation:</u>

We know that , there are 2 black ace cards out of 52 cards in a deck & 13 hearts out of 52 cards . Here we have to tell What is the probability of drawing a black ace followed by a heart out of a deck when the cards aren't replaced . Let's find out:

Firstly , a black ace is drawn , so probability :

⇒ $P(Black) = \frac{2}{52}$

Now , A heart is drawn out of 51 cards ( as one black ace is already drawn !):

⇒ $P(Heart) = \frac{13}{51}$

So , Probability of occurring both events is :

⇒ $P(Black)(P(Heart))$

⇒ $\frac{2}{52} (\frac{13}{51} )$

⇒ $0.0098$

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Therefore , Correct option C) 0.98%

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3 years ago

A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can s

ella [17]

The demand equation illustrates the price of an item and how it relates to the demand of the item.

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

From the question, we have:

$Plates = 300$

$Price = 20$

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

$\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}$

The slope (m) is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{25-20}{290-300}$

$m = \frac{5}{-10}$

$m = -\frac{1}{2}$

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

$R(x) = (300 - 10x) \times (20 + 5x)$

Open the brackets to calculate the maximum revenue

$R(x) =6000 + 1500x - 200x - 50x^2$

$R(x) =6000 + 1300x - 50x^2$

Equate to 0

$6000 + 1300x - 50x^2 =0$

Differentiate with respect to x

$1300 - 100x =0$

Collect like terms

$100x =1300$

Divide by 100

$x =13$

So, the price at maximum revenue is:

$Price= 20 + 5x$

$Price= 20 + 5 * 13$

$Price= 85$

In conclusion:

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85