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
marissa [1.9K]
3 years ago
11

In attempting to solve the system of equations y 3x 2 and 6x 2y 4, John graphed the two equations on his calculator. Because he

saw only one line, John wrote that the answer to the system is the empty set. Is he correct? Explain your answer.
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0
No, he is not correct. The lines are the same, so there are an infinite number of solutions.

When two lines are parallel, then the solution is empty set.
You might be interested in
Use a graphing calculator to solve the equation -3 cost= 1 in the interval from . Round to the nearest hundredth.
RSB [31]
In place of t, or theta, I'm going to utilize x instead. So the equation is -3*cos(x) = 1. Get everything to one side and we have -3*cos(x)-1 = 0

Let f(x) = -3*cos(x)-1. The goal is to find the root of f(x) in the interval [0, 2pi]

I'm using the program GeoGebra to get the task done of finding the roots. In this case, there are 2 roots and they are marked by the points A and B in the attachment shown

A = (1.91, 0)
B = (4.37, 0)

So the two solutions for theta are
theta = 1.91 radians
theta = 4.37 radians

8 0
3 years ago
Which of the following requires a proof?
marshall27 [118]
A theorem requires a proof.
3 0
3 years ago
Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi
miss Akunina [59]

Answer:

\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.

Step-by-step explanation:

1st boat:

Parabola equation:

y=ax^2 +bx+c

The x-coordinate of the vertex:

x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a

Equation:

y=ax^2 -2ax+c

The y-coordinate of the vertex:

y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10

Parabola passes through the point (-8,1), so

1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1

Solve:

c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}

Parabola equation:

y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}

2nd boat:

Parabola equation:

y=ax^2 +bx+c

The x-coordinate of the vertex:

x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0

Equation:

y=ax^2+c

The y-coordinate of the vertex:

y_v=a\cdot 0^2+c\Rightarrow c=-7

Parabola passes through the point (-8,1), so

1=a\cdot (-8)^2-7\\ \\64a-7=1

Solve:

a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7

Parabola equation:

y=\dfrac{1}{8}x^2 -7

System of two equations:

\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.

7 0
4 years ago
Read 2 more answers
Do you know what 2/9 x 3 is?
ohaa [14]

Answer:

answer =  \frac{2}{3}

\frac{2}{9}  \times  \frac{3}{1}  \\   =  \frac{6}{9}  =  \frac{2}{3}

7 0
3 years ago
Read 2 more answers
The sum of two numbers is -9. The difference of the two numbers is -41. What are the two numbers?
Nataly [62]

Answer:

the two numbers are 16 and -25

Step-by-step explanation:

Let the two numbers be x and y

x+y=-9

x-y=-41

By substitution

y=-9-x

x-(-9-x)=-41

x+9+x=-41

2x=-41-9

2x=-50

x=-25

y=-9-(-25)

y=16

6 0
3 years ago
Other questions:
  • Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales. If Jamie makes $475 in one week, wh
    10·1 answer
  • Write the expression in the form a+bi<br>(3-5i)(2+2i)
    12·1 answer
  • County
    15·1 answer
  • Can anyone help me in this pls
    14·2 answers
  • A 1 : 6<br> B 1 : 3<br> C 2:1<br> D 3:1
    15·1 answer
  • Find the value of x and y.
    15·2 answers
  • Explain whether the graph represents a function.
    12·1 answer
  • Omggg thank you so much for helping meeee ily
    10·1 answer
  • No links, will give brainliest
    5·1 answer
  • PLS help i've been trying this for an hour i still don't get it
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!