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
Llana [10]
3 years ago
11

Solve the following system. y = (1/2)x^2 + 2x - 1 and 3x - y = 1 The solutions are (____)and (______ ) (remember to include the

commas)
Mathematics
2 answers:
lubasha [3.4K]3 years ago
7 0

Answer:

x=0, 2. y=-1, 5.

Step-by-step explanation:

y=(1/2)x^2+2x-1

3x-y=1

---------------------

3x-y=1

y=3x-1

-----------

(1/2)x^2+2x-1=3x-1

(1/2)x^2+2x-3x-1-(-1)=0

(1/2)x^2-x-1+1=0

(1/2)x^2-x=0

factor out the x

x[(1/2)x-1]=0

zero property,

x=0, (1/2)x-1=0

-------------------

(1/2)x-1=0

1/2x=0+1

1/2x=1

x=1/(1/2)=(1/1)(2/1)=2/1=2

-----------------------------------

x=0, x=2

-------------

y=(1/2)(0)^2+2(0)-1=0+0-1=-1

-------------

y=3(0)-1=0-1=-1

-----------------------

y=(1/2)(2)^2+2(2)-1=(1/2)(4)+4-1=4/2+4-1=2+4-1=6-1=5

----------------------

y=3(2)-1=6-1=5

ASHA 777 [7]3 years ago
7 0

Answer:

The solutions are (0, -1) and (2, 5)

Step-by-step explanation:

y = (1/2)x^2 + 2x - 1 ------ eqn(I)

3x - y = 1

y = 3x - 1 ------------- eqn(II)

Equate eqn(I) & (II)

(1/2)x^2 + 2x - 1 = 3x - 1

Multiply each term by 2

x^2 + 4x - 2 = 6x - 2

x^2 + 4x - 6x = -2 + 2

x^2 - 2x = 0

x(x - 2) = 0

x = 0, 2

Substitute the values of x in eqn(II)

y = 3x - 1

When x = 0

y = 3(0) - 1 = 0 - 1 = -1

y = 3x - 1

When x = 2

y = 3(2) - 1 = 6 - 1 = 5

The solutions are (0, -1) and (2, 5)

You might be interested in
Practice calculating the mean of a data set.
horrorfan [7]

Total money = 150 + 95 + 210 + 45 + 55 + 165 = $720

Total months is 6

Mean = 720 / 6 = $120

5 0
3 years ago
Read 2 more answers
Hannah's monthly housing budget is $1,750. Her monthly costs are $230 for insurance, $98 for utilities, and $250 for taxes. Whic
Olegator [25]
She can afford t he $98
7 0
3 years ago
Read 2 more answers
Write a polynomial that is a trinomial, has the coefficients 3 and 4, the variable x,
vladimir1956 [14]

Answer:

3x+4x+7

Step-by-step explanation:

First, a Trinomial consists of three terms.

so we have <u>blank</u>+<u>blank</u>+<u>blank</u>

Next we need to add the coefficients.

<u>3</u>+<u>4</u>+<u>blank</u>

Add the variables.

3x+4x+<u>blank</u>

And lastly, add the constant.

3x+4x+7

Good luck!

8 0
3 years ago
An employee was randomly chosen from a company.If the expected value of the age of the employee is ____ years old, the mean age
zheka24 [161]
What is the age fo the first employee?
4 0
3 years ago
Helppppppp mmeeeeee plllzzzzz
nikdorinn [45]

Answer: the answer is 6

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Two similar bottles are shown. the smaller bottle can hold 500ml. how much can the larger bottle hold.
    13·1 answer
  • $53,000 is placed in an investment account that grows at a fixed rate of 2% (compound growth) per year. how much is in the accou
    8·1 answer
  • Factor p 2 + 18p + 32.<br> (p+ 4)(p + 8)<br> (P + 2)p+ 16)<br> (P + 16)2
    8·1 answer
  • I need help with this​
    6·1 answer
  • Sssssssssssssssssssssssss
    8·1 answer
  • What is the value of lo9279?
    14·1 answer
  • Derive the positive square root of 982081
    11·1 answer
  • Statistical models predict that the price (in dollars) of a 500 GB hard drive will change according to the function p(t) = 600 −
    8·2 answers
  • Solve the equation. x^2=1/49
    10·1 answer
  • Let f(x) = <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B11x%20-%203%20%5C%3A%7D%20determine%20%5C%3A%20%20%7Bf%7D%5
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!