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
A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to
Nastasia [14]

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

y =\frac{1}{10} x +60

This is the equation of the line

using a graph tool

see the attached figure

<u>Statements</u>

<u>case a)</u> The slope of the function is $1.00

The statement is False

The slope of the function is equal to \frac{1}{10} \frac{\$}{tokens}

<u>case b)</u> The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

so

for x=0

y =\frac{1}{10}*0 +60

y =\$60

<u>case c)</u> The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to y =\frac{1}{10} x +60

<u>case d)</u> The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

<u>case e)</u> The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure

8 0
3 years ago
Read 2 more answers
For the function y=-3+ cos (x + 4)], what is the minimum value?
Mrac [35]

Answer:

-4 is the mimumum of y=-3+cos(x+4)

Step-by-step explanation:

The minimum value of y=cos(x) is -1.

The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos(x+4) is -3-1 which is -4.  This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.

5 0
3 years ago
Clarence works at least 5 hours but not more than 7 hours. he earns $11.60 per hour. the function f(t)=11.6t represents the amou
Anarel [89]
Thank you for posting you question here at brainly. I hope the answer will help you. The <span> practical domain and the practical range for this situation is below:

</span>D: [5, 7]
<span>R: [58, 81.2]
</span>
Feel free to ask more questions here at brainly. I'd be happy to answer. 
3 0
3 years ago
Five times the sum of 173 and 32
Sladkaya [172]
173+32=205 , so 205 times 5 would equal 1,025 . so the answer would be 1,025 .
4 0
3 years ago
Read 2 more answers
Direct and Indirect Proportions
ivanzaharov [21]

Answer:

?

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Find the altitude of the triangle
    13·1 answer
  • The angle of a triangle have a sum of how many degrees
    15·2 answers
  • #4: Which property could be used to solve the equation below? *<br>15 = x + 13<br>​
    14·1 answer
  • {(-7, 4), (-5, 2), (0, -8), (1, -10)}, identify the domain.
    5·1 answer
  • What should be done to solve the following equation?
    9·2 answers
  • Evaluate the variable expression when -= 6, b= 5, and c= -3
    15·1 answer
  • The Earth has a mass of about 6 x 1024 kg. Neptune has a mass of
    9·1 answer
  • The length of a jogging trail is 3528 m. A jogger wants to complete the trail within 30 min. How many meters must the jogger tra
    10·1 answer
  • What is the surface area of the triangular prism?​
    13·1 answer
  • Image Which of the following statements is true for ∠a and ∠b in the diagram?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!