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
Trava [24]
3 years ago
13

Bethany needs to solve the equation -x^2 + 4x = x - 4.

Mathematics
1 answer:
notsponge [240]3 years ago
5 0

Answer:

The system of equations she could write is:

   y = -x² + 4x

   y = x - 4

The solutions are (-1 , -5) and (4 , 0)

Step-by-step explanation:

-x² + 4x = x - 4

That means two equations one quadratic which is in the left hand side and the other is linear which is in the right hand side.

They represented graphically by a parabola and a line, the solution of it will be the points of intersection of the two graphs

To find the system of equations take each side and equate it by y

∵ y = -x² + 4x

∵ y = x - 4

∴ The system of equations is:

   y = -x² + 4x

   y = x - 4

Let us solve this system using -x² + 4x = x - 4

∵ -x² + 4x = x - 4

- Subtract x from both sides

∴ -x² + 3x = -4

- Add 4 to both sides

∴ -x² + 3x + 4 = 0

- Multiply both sides by -1

∴ x² - 3x - 4 = 0

Let us use the factorization to solve it

∵ x² = (x)(x)

∵ -4 = (1)(-4)

∵ (x)(1) = x

∵ (x)(-4) = -4x

∵ x + -4x = - 3x ⇒ middle term

∴ The factors of x² - 3x - 4 are (x + 1)(x - 4)

- Substitute x² - 3x - 4 by its factors

∴ (x + 1)(x - 4) = 0

Equate each factor by 0 to find the values of x

∵ x + 1 = 0

- Subtract 1 from both sides

∴ x = -1

∵ x - 4 = 0

- Add 4 to both sides

∴ x = 4

Substitute the values of x in the equation y = x - 4 to find y

∵ y = -1 - 4

∴ y = -5

∵ y = 4 - 4

∴ y = 0

The solutions are (-1 , -5) and (4 , 0)

You might be interested in
Find the Circumference and area of the circle with the center C=(-1,2) and a point on the circle A(4,-1). Round to the nearest t
Anuta_ua [19.1K]

Answer:

idk the answer but i do know this

Step-by-step explanation:

the formula for the area of a circle is pi times the radius squared

4 0
3 years ago
In rectangle ABCD, AC = -x + 21, BP = -9x + 19, and DP = -y + 5. Find the value of y.
creativ13 [48]

Answer:

y=-5

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are equal and bisect each other

so

BP=\frac{1}{2}AC

DP=BP

step 1

Find the value of x

BP=\frac{1}{2}AC

substitute the given values

(-9x+19)=\frac{1}{2} (-x+21)

solve for x

Multiply by 2 both sides

-18x+38=-x+21

18x-x=38-21\\17x=17\\x=1

step 2

Find the value of y

DP=BP

we have

BP=-9x+19

DP=-y+5

substitute

-y+5=-9x+19

substitute the value of x

-y+5=-9(1)+19\\-y+5=10\\y=5-10\\y=-5

5 0
3 years ago
Can you help show me where they belong ? pls help asap
kozerog [31]

y=3x, y=(2/7)x,-0.5=y are all on direct the other ones are on the other side i just did the question they correct. :)

5 0
3 years ago
Add 8x+6yz-3zx, 4yz+6zx-8y, -3xz+6x-4xy<br><br> pls find answer...
Butoxors [25]
Na bro i dont even know what’s that tbh
3 0
2 years ago
A box contains eight cards labeled P, Q, R, S, T, U, V, and W. One card will be randomly chosen.
Varvara68 [4.7K]

Answer:

7/8

Step-by-step explanation:

Probability= (Cards having letter Q to W)/(All cards) = 7/8

6 0
3 years ago
Other questions:
  • PLS HELP WILL MARK BRAINLEIST​
    6·2 answers
  • If 3r=18, what is the value of 6r+18 ?
    8·1 answer
  • Men's socks. Cost $8.00 for a package of three. How much would two dozen socks cost ?
    13·1 answer
  • Question 1- explain how Sheldon immediately knew howard was incorrect?
    14·1 answer
  • Tomas collects miniature cars. He bought a display case at a cost of $5.95. He also bought 3 miniature cars. If his total cost w
    15·2 answers
  • Is this a function?......​
    6·2 answers
  • What is the largest number of three consecutive integers whose sum is 42? O A. 13 B. 17 O C. 15 D. 12​
    10·1 answer
  • Please help me answer this :) <br> Explain your answer <br><br> Will give brainiest
    15·1 answer
  • ms.watson earns more than $24 per hour. The inequalit x&gt;24 represent the situation.which statement best represent the solutio
    6·1 answer
  • Write cos 71 degrees in terms of the sine. Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!