Solve each system of equations.

6x + 5y = 10
7x - 3y = 24

Answers

Answer 1

Answer: $\begin{cases} 6x + 5y = 10 \n 7x - 3y = 24 \end{cases}\n\begin{cases} 5y = -6x+10\ \ / :5 \n 7x - 3y = 24 \end{cases}\n\begin{cases} y =-(6)/(5)x+2 \n 7x - 3y = 24 \end{cases}\n\nsubstition \n$

$7x - 3y = 24 \n 7x - 3 \cdot (-(6)/(5)x+2) = 24\n7x+(18)/(5)x-6=24\n (35)/(5)x+(18)/(5)x =24 +6\n(53)/(5)x =30 \ \ / \cdot (5)/(53)\n\nx=(150)/(53)$

$y= -(6)/(5)x+2 \ny= -(6)/(5) \cdot (150)/(53) +2\ny=-(6\cdot 30)/(53)+2\ny=-(180)/(53)+ (106)/(53)\n \n y= -(74)/(53)\n\n Answer : x=(150)/(53) \ \ and \ \y= -(74)/(53)$

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The quadratic equation (3k-2)x^2 +12x+3(k+1) =0 has equal roots. Find the two possible values of k.

Answers

$x_1=x_2 \Rightarrow \Delta=0\n\Delta=12^2-4\cdot(3k-2)\cdot3(k+1)\n\Delta=144-(36k-24)(k+1)\n\Delta=144-36k^2-36k+24k+24\n\Delta=-36k^2-12k+168\n-36k^2-12k+168=0\n-3k^2-k+14=0\n-3k^2+6k-7k+14=0\n-3k(k-2)-7(k-2)=0\n-(3k+7)(k-2)=0\nk=-(7)/(3) \vee k=2$

Express X^2-8x+5 in the for (x-a)^2-b where a and b are integers

Answers

Answer:

$x {}^(2) - 8x + 5 \n = x {}^(2) - 8 x+ 5 + 11 - 11 \n = x {}^(2) - 8x +16 - 11 \n = (x - 4) {}^(2) - 11 \n$

A is 4 and b is 11

Use elimination method to solve
5x+y=-10
7x-3y=-36

Answers

$5x+y=-10\n \n 7x-3y=-36$

Let's multiply the first equation by 3. (As you can see y's coefficient in the first one is 1 and in the second one is -3 , we will multiply the first equation by 3 so when we add the equations their sum will be 0)

$3\cdot (5x+y)=3\cdot -10\n \n 15x+3y=-30$

Now let's add this new equation and our second equation.

$7x-3y=-36\n \n 15x+3y=-30\n \n (15x+3y)+(7x-3y)=(-30)+(-36)\n \n 15x+7x+3y-3y=-30-36\n \n 22x=-66\n \n x=\frac { -66 }{ 22 } \n \n x=-3$

We found x=-3

Now let's plug x's value in one of the equations to find y's value.

$x=-3\n \n 5x+y=-10\n \n 5\cdot -3+y=-10\n \n -15+y=-10\n \n y=-10+15\n \n y=5$

So we found y=5

Solution ;

(-3, 5)

Find the zeros of x3 +2X^2-23x-60

Answers

Hello,

P(x)=x^3+2x²-23x-60
P(-4)=(-4)^3+2*(-4)²-23*(-4)-60=0
P(-3)=(-3)^4+2*(-3)²-23*(-3)-60=0
P(5)=5^3+2*5²-23*5-60=0
Zeros are -4,-3,5

Leanna guesses on four multiple choice test questions in a row. If each question has 3 possible answers, what is the probability that Leanna will guess the answer to the 4th question correctly? A. 1/81 B. 1/12 C. 1/3

Answers

the previous question don't change the probability of the next questions, so the information that it is the 4th question is not relevant.

It's only relevant that there are 3 possible answers, so the probability of getting the right one is 1/3 (C.).

Answer:

1\3

Step-by-step explanation:

1\3 is the answer....

A taxi cost $4.00 plus .50 cents per mile. Traveling from the airport there is an additional charge of $6.00. How far can you travel from the airport by taxi for $31.50

Answers

Answer: You can travel 43 miles

Step-by-step explanation:

To determine how far you can travel from the airport by taxi for $31.50, we can subtract the fixed charges from the total cost and then divide the remaining amount by the cost per mile.

Let's calculate:

$31.50 - $4.00 (base fare) - $6.00 (airport charge) = $21.50

Now, we can divide the remaining amount by the cost per mile:

$21.50 / $0.50 per mile = 43 miles

So, you can travel approximately 43 miles from the airport by taxi for $31.50.

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