1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
storchak [24]
3 years ago
12

BRAINLIEST!!!!!!!!!!!!!!!!!!!!!

Mathematics
2 answers:
salantis [7]3 years ago
8 0
Hello there!

A. We have two lines: y = 2-x and y = 4x+3
Given two simultaneous equations that are both required to be true.. the solution is the points where the lines cross... Which is where the two equations are equal.. Thus the solution that works for both equations is when
2-x = 4x+3
because where that is true is where the two lines will cross and that is the common point that satisfies both equations.

B. 2-x = 4x+3

x 2-x 4x+3

-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15

The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3

To find the solution we need to rearrange the equation to the form x=n
2-x = 4x+3
2 -x + x = 4x + x +3
2 = 5x + 3
2-3 = 5x +3-3
5x = -1
x = -1/5

The only point that satisfies both equations is where x = -1/5
Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5
Verify we get the same in the other equation
y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5

Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)


C. To solve graphically 2-x=4x+3
we would graph both lines... y = 2-x and y = 4x+3
The point on the graph where the lines cross is the solution to the system of equations ...
[It should be, as shown above, the point (-1/5, 11/5)]

To graph y = 2-x make a table....
We have already done this in part B

x 2-x x 4x+3
_ __
-1 3 -1 -1
0 2 0 3
1 1 1 7

Just graph the points on a Cartesian coordinate system and draw the two lines. The solution is, as stated, the point where the two lines cross on the graph.


I hope I helped! 

I will still trying to see if I can solve them another way that might be clearer.



Mumz [18]3 years ago
3 0
A) Take the equation 2^x = 4^x - 2.

Write the equation in exponential form.

2^x = (2²)^x - 2

Using (a^m)^n = (a^n)^m, rewrite the equation.

2^x = (2^x)² - 2

Basically this equation states that 2 to the x = 2 to the x squared minus 2. You can use substitution.

Rewrite the equation saying that x = x² - 2.

Solve for x by using the quadratic formula.

Move x to the other side.

0 = x² - x - 2.

After a series of long steps, you would get :

x = 2 and x = -1.

Knowing this information, substitute the numbers into the previous formula : x = 2^x

2 = 2^x and -1 = 2^x

Solve for x.

1) 2^x = 2

2^x = 2¹

Since the bases are the same, the exponents are equal.

x = 1

2) -1 = 2^x

The bases are different signs so there is no solution.

Ultimately, x = 1.

If you look at the graph above, this answer is supported because the graphs intersect at where x = 1.

The point of intersection between the two graphs is (1,2).

B) If you having graphing calculator, you can input the equations 2^x and 4^x - 2 and go to check the tables for each function.

C) Use a graphing calculator to graph both functions individually and see where both functions intersect. The point on intersection is where 2^x = 4^x - 2.

You might be interested in
What logarithmic equation is equivalent to the exponential equation e^a=28.37
Tju [1.3M]

Answer:

a=ln(28.37)

Step-by-step explanation:

e^a=28.37

Take ln both sides

ln(e^a)=ln(28.37)

a=ln(28.37)

8 0
3 years ago
The lines below are parallel. If the slope of the green line is -3, what is the
julia-pushkina [17]

Answer:-3

Step-by-step explanation:

The expression is already in decimal form.

−3 slope

8 0
3 years ago
The area of a circle is 201cm² . what is the diameter ?
lisabon 2012 [21]

The answer is 16 cm approx.

Diameter= 2\sqrt{a/pi}

=>2\sqrt{201 / 22/7}

=>2\sqrt{201*7/22}

=>15.997.......

=> 16 approx

Hope this helps you!!

8 0
3 years ago
Read 2 more answers
Kyle crawled 49.8 feet in 6 minutes, how far did he crawl every minute…
Blizzard [7]

Answer:

assuming that kyle crawled at the same pace for six minute then it would be 8.3 feet each minute

Step-by-step explanation:

8 0
3 years ago
Which statement is true for the equation 3x − 3x − 2 = −2?
Mariana [72]
Has infinitely many solutions. 
3 0
3 years ago
Read 2 more answers
Other questions:
  • Which statement is true? A.27/19<11/30 B.17/31>19/14 C.16/26>30/31 D.35/30<22/12
    12·1 answer
  • Is the expression 6x+8/2<br> equivalent to 3x + 4?
    13·1 answer
  • Jim and sue both take a driving test. the probability that Jim will pass the driving test is 0.7. The probability that Sue will
    6·1 answer
  • What were some of the challenges pilgrims faced on their journey
    8·1 answer
  • Will give BRAINLIEST - Can somebody help me with this math question?
    14·1 answer
  • Find the average of the following numbers: 26, 32, 47, 55.
    9·2 answers
  • Please help me...For the third one...just say true or false.
    12·2 answers
  • The new number, 200, is 400 less then the original number. What us the approximate percent change?
    11·2 answers
  • Find the difference (-6d+2)-(7+2d)
    14·2 answers
  • HELP ASAP PLZ im in a exam rn
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!