All categories

2 years ago

How many solutions does the system have?

Mathematics

1 answer:

bearhunter [10]2 years ago

6 0

Answer:

A. Exactly one solution

Step-by-step explanation:

Solve the system of equations.

y = x + 1

y = 2x - 5

Substitute one equation into the other.

y = 2x - 5

x + 1 = 2x - 5

Subtract 2x from both sides.

-x + 1 = -5

Subtract 1 from both sides.

-x = -6

Multiply both sides by -1.

x = 6

Put it back into the other equation.

y = x + 1

y = 6 + 1

Add.

y = 7

The solution is (6, 7). Since the equations aren't equal, there are not infinitely many solutions, but since there is a solution found, we can determine that there is exactly one solution.

You might be interested in

Factorize: x^2 + (a^2+1)/a x+1

In-s [12.5K]

This is what I get not sure if the problem on numerator is together if it is then . X^2+(a^2+1) x^2+a^2+1. -----------------= ----------------- AX+1. Ax+1 Answer: a^2+x^2+1 ---------------- AX+1 If I wrote the actual problem wrong let me know. This is what I understood.

5 0

3 years ago

Test III: Translate the following equations into verbal phrase.

puteri [66]

Answer:

waiting for the bus

Step-by-step explanation:

I'm going back home wait for my answer

7 0

2 years ago

A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event

Leviafan [203]

Answer:

P(B) = 8/12

P(R | B) = 4/11

P(B ∩ R) = 8/33

The probability that the first ball chosen is black and the second ball chosen is red is about 24 percent.

Step-by-step explanation:

I just got it right on edge 2020. Good luck with school!!

6 0

3 years ago

Read 2 more answers

The Walt Whitman bridge is 2000 feet long. This is 600 feet longer than two fifths of the length of George Washington bridge. Wr

Minchanka [31]

Answer:

2000= 600+2/5x

Step-by-step explanation:

length = X Ft

(2/5)x+600=2000

multiple both sides by 5/2:

x + 1500= 5000

x= 3500 ft

3 0

3 years ago

The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?

Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

   1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3    Items = 2, Sum = 4
1, 3, 5, 7    Items = 4, Sum = 16
1, 3, 5, 7, 9, 11    Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing ! The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.

I slogged through it on my calculator, and it's true.

I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).

3 0

3 years ago