Solve the equation.. I dont understand how to do it

Question 24 Multiple Choice Worth 1 points)

hammer [34]

Given:

The system of equations is:

Line A: $y=x-4$

Line B: $y=3x+4$

To find:

The solution of given system of equations.

Solution:

We have,

$y=x-4$ ...(i)

$y=3x+4$ ...(ii)

Equating (i) and (ii), we get

$x-4=3x+4$

$-4-4=3x-x$

$-8=2x$

Divide both sides by 2.

$-4=x$

Substituting $x=-4$ in (i), we get

$y=-4-4$

$y=-8$

The solution of system of equations is (-4,-8).

Now verify the solution by substituting $x=-4, y=-8$ in the given equations.

$-8=-4-4$

$-8=-8$

This statement is true.

Similarly,

$-8=3(-4)+4$

$-8=-12+4$

$-8=-8$

This statement is also true.

Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.

8 0

3 years ago

Does the function model exponential growth or decay? f(t)=1/4⋅4^t

yarga [219]

Answer:

This is an exponential decay

Because the base of the exponent is 1/4.4 which is less than 1

Step-by-step explanation:

What is exponential growth?

when the base of our exponential is bigger than 1, which means those numbers get bigger.

What is exponential decay?

when the base of our exponential is in between 1 and 0 and those numbers get smaller.

6 0

3 years ago

While grading her students' most recent quiz on equation solving, Mrs. Jones calculated that approximately forty percent of her

EastWind [94]

The given equation is,

$3(-n+4)+5n=2n$

Part 1:

Solve the above equation for n.

Using distributive property of multiplication,

$\begin{gathered} -3n+3\times4+5n=2n \\ -3n+12+5n=2n \end{gathered}$

Now, group the like terms.

$-3n+5n-2n+12=0$

Now, add the like terms.

$\begin{gathered} -5n+5n+12=0 \\ 0=-12 \end{gathered}$

0=-12 is a false statement.

Since we obtained a false statement, the given equation has no solution.

So, option b is correct.

Part 2:

The option (a) is n=3.

If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.

The option (b) is "no solution".

While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.

The option (c) is "infinitely many solutions".

While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.

8 0

1 year ago

I need help please! will mark brainliest

Dovator [93]

Answer:

g= - 3x/x-2

Step-by-step explanation:

8 0

3 years ago

QUESTION

Lorico [155]

1. For this item we just refer to the prompt to know the conjectures of Ernest and Denise. According to Ernest, they should swim 1 kilometer on the first week then add 0.25km every week while Denise believes that they should swim 1 kilometer on the first week then add 0.5km every week.

2. Yes, these distances make an arithmetic sequence. It's because an arithmetic sequence is defined as a group of increasing or decreasing numbers where the difference between any two consecutive numbers is constant. This just means that every number has the same interval. In the case of their schedule, this is true.

3. For this item we just follow the descriptions of Ernest's and Denise's schedule in item number 1. For Ernest, we just keep adding 0.25 from 1 kilometer until we added it thrice. For Denise, we also keep adding a number thrice but this time it's 0.5 instead of 0.25.

Ernest's Schedule: 1, 1.25, 1.5, 1.75
Denise's Schedule: 1, 1.5, 2, 2.5

4. Here we are asked to determine a formula that will describe the schedules of Ernest and Denise. In the given formula $a_{n}= a_{n-1}+d$ , $a_{n}$ refers to the next term in the sequence, $a_{n-1}$ refers to the previous term, while $d$ refers to the common difference. In the recursive formula all we need is to insert the value of d to the equations.

Ernest: $a_{n}= a_{n-1}+0.25$
Denise: $a_{n}= a_{n-1}+0.5$

5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form $a_{n}= a_{1}+(n-1)d$ where $a_{n}$ is still the nth term of the sequence, $a_{1}$ is the very first time, $n$ is the number of terms, and $d$ is the common difference.

Ernest: $a_{n}= 1.0+0.25(n-1)$
Denise: $a_{n}= 1.0+0.5(n-1)$

6. In this item we will just basically substitute numbers to one of the equations that we've set up in item #5. For this we need Ernest's explicit formula first. To know how far they will be swimming on week 10, the number of elements (n) must be 10.

$a_{10}= 1.0+0.25(10-1)$
$a_{10}= 1.0+0.25(9)$
$a_{10}= 1.0+2.25$
$a_{10}= 3.25$

7. Here, we just do the same thing as item #6 but this time we will consider Denise's explicit formula. Since we are also asked how far the students will be swimming on week 10, the number of elements would also be 10 and this would also be our value for n.

$a_{10}= 1.0+0.5(10-1)$
$a_{10}= 1.0+0.5(9)$
$a_{10}= 1.0+4.5$
$a_{10}= 5.5$

8. The answer for this question is obvious. You would just need to look at the 10th element in Ernest's and Denise's sequences and tell whose schedule had more than or equal to 5 as an answer. Following Ernest's schedule, you will just get 3.5 kilometers on the 10th week so it's definitely a no. Denise's schedule, on the other hand, would get you to 5.5 kilometers on week 10 so her training schedule should be followed.

7 0

3 years ago