How many solutions does the system of equations have?

Solve the system of equation with substitution. y=4x+8 y=2x-9

Firlakuza [10]

I actually just learned this. I think this is the right answer.

8 0

2 years ago

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a seco

kari74 [83]

Answer:

C. $\frac{1}{18}$

Step-by-step explanation:

Given: Six cards numbered from $1$ to $6$ are placed in an empty bowl. First one card is drawn and then put back into the bowl then a second card is drawn.

To Find: If the cards are drawn at random and if the sum of the numbers on the cards is $8$ , what is the probability that one of the two cards drawn is numbered $5$ .

Solution:

Sample space for sum of cards when two cards are drawn at random is $\{(1,1),(1,2),(1,3)......(6,6)\}$

total number of possible cases $=36$

Sample space when sum of cards is $8$ is $\{(3,5),(5,3),(6,2),(2,6),(4,4)\}$

Total number of possible cases $=5$

Sample space when one of the cards is $5$ is $\{(5,3),(3,5)\}$

Total number of possible cases $=2$

Let A be the event that sum of cards is $8$

$p(\text{A})$ $=\frac{\text{total cases when sum of cards is 8}}{\text{all possible cases}}$

$p(\text{A})=\frac{5}{36}$

Let B be the event when one of the two cards is $5$

probability than one of two cards is $5$ when sum of cards is $8$

$p(\frac{\text{B}}{\text{A}})=\frac{\text{total case when one of the number is 5}}{\text{total case when sum is 8}}$

$p(\frac{\text{B}}{\text{A}})=\frac{2}{5}$

Now,

probability that sum of cards $8$ is and one of cards is $5$

$p(\text{A and B}=p(\text{A})\times p(\frac{\text{B}}{\text{A}})$

$p(\text{A and B})=\frac{5}{36}\times\frac{2}{5}$

$p(\text{A and B})=\frac{1}{18}$

if sum of cards is $8$ then probability that one of the cards is $8$ is $\frac{1}{18}$ , option C is correct.

3 0

2 years ago

Choose the correct simplification of 8x2(5x 2x2 − 3). 16x4 − 40x3 24x2 16x4 40x3 − 24x2 40x4 16x3 − 5x2 40x4 − 10x3 5x2

yKpoI14uk [10]

The correct simplification of 8x2(5x 2x2 − 3) is $16x^{4} +40x^{3} -24x^{2}$

<h3>What do you mean by simplification?</h3>

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.
Making anything simpler is the act or process of simplification. Everyone is in favor of streamlining court procedures.
Certain "solving" issues are connected to "simplification" issues. Parentheses and even nested grouping symbols can be found in some equations, just like in some expressions. Whether we're working with equations (so we're also solving) or expressions (and only simplifying), the simplification procedure is the same in both cases.

The correct simplification of 8x2(5x 2x2 − 3).

$8x^{2} (5x+2x^{2+1} -3)=8*2x^{2+2} -8*3x^{2}$