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
jekas [21]
3 years ago
9

How many solutions does the system have?

Mathematics
1 answer:
umka21 [38]3 years ago
3 0

One solution

<h2>Explanation:</h2>

For a system of linear equations in two variables, we could have three possible cases:

<h3>Case 1. No solution.</h3>

This happens when the lines are parallel and have different y-intercepts.

<h3>Case 2. One solution.</h3>

This happens when the lines intersect at a single point.

<h3>Case 1. Infinitely many solutions</h3>

This happens when the lines are basically the same having the same slope and y-intercept.

So, let's rewrite our lines in Slope-intercept form y=mx+b:

Line \ 1: \\ \\  4x-2y = 8 \\ \\ 2y=4x-8 \\ \\ y=\frac{4}{2}x-\frac{8}{2} \\ \\ y=2x-4 \\ \\ \\ Line \ 2: \\ \\ 2x + y = 2 \\ \\ y=-2x+2

As you can see, they have different slopes and y-intercepts. So they will intersect at a single point which is the solution of the system. By using graphing tool we get that this point is (1.5, -1) as indicated in the figure below.

<h2>Learn more:</h2>

Parametric equations: brainly.com/question/10022596

#LearnWithBrainly

You might be interested in
Write y=1/6x+7 in standard form using integers
Law Incorporation [45]

The standard form using integers of the equation is 6y - x = 42

<h3>How to determine the standard form</h3>

Note that solving in standard form means writing it as a simple equation

Given y = 1/6x + 7

Find the LCM of the right side, we have

y = \frac{x + 42}{6}

Cross multiply

6 × y = x + 42

6y = x + 42

Make the variables move to the left side

6y - x = 42

Thus, the standard form using integers of the equation is 6y - x = 42

Learn more about algebraic expressions here:

brainly.com/question/723406

#SPJ1

8 0
2 years ago
1. Ellie has at most $25 to spend on miscellaneous items each week. She has already spent
gregori [183]

Answer:

y= $25-$10.50

Step-by-step explanation:

5 0
3 years ago
HELP PLSS
atroni [7]

The balloon reaches a height of 7 feet at 0.1 seconds and 2.13 seconds

<h3>How to determine the time the balloon is at the height?</h3>

The equation of the function is given as

h(t)= -16t^2 + 35t + 5

The above equation is a quadratic equation

When the balloon is at a height of 7 feet, we have

h(t) = 7

So, we have the following equations

h(t)= -16t^2 + 35t + 5

h(t) = 7

Next, we plot the equations on a graph (see attachment)

The equations intersect at

t = 0.059 and t = 2.129

Approximate

t = 0.1 and 2.13

Hence, the times are 0.1 seconds and 2.13 seconds

Read more about quadratic equation at

brainly.com/question/15709421

#SPJ1

8 0
1 year ago
A l-meter steel rod is bent into a rectangle so that its length exceeds quadruple its width
Dmitry_Shevchenko [17]

Answer:

The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

Step-by-step explanation:

Given,

A 1 meter steel rod is bent into a rectangle.

That means the perimeter of the rectangle is 1 meter.

So, Perimeter = 1\ m=100\ cm

Let the width of the rectangle be 'x'.

Now According to question, length exceeds quadruple its width by 5 cm.

Hence framing the above sentence in equation form, we get;

Length=4x+5

Now we use the formula of  perimeter of rectangle,

Perimeter=2(Length+width)

On substituting the values, we get;

2(4x+5+x)=100\\\\(5x+5)=\frac{100}{2}\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=\frac{45}{5}=9

Now, we substitute the value of x to get the value of length;

Length=4x+5=4\times9+5=36+5=41\ cm

Thus, Width=9 cm    Length=41 cm

Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

6 0
3 years ago
A cube has volume 216cm find total surface area of cube​
Katena32 [7]

Answer:

Answer: 216 cm2 (square centimetres cm^{2}, in your question you had to put cm3, cubic centimetres, it's IMPORTANT )

Step-by-step explanation:

A perfect cube by definition has 3 equal dimensions, as an immediate rule: volume and total surface are equal, only the unit of measure changes (cubic for the volume, square for surface).

But let's calculate it anyway:

Volume  = Edge * Edge * Edge = length * width * depth = Edge^{3}  (remember: all edges are equal in this case)

so Edge = \sqrt[3]{Volume}

in your example Edge = \sqrt[3]{216} = 6cm

So the surface of one side is 6*6 = 36cm^{2}

There are 6 sides in total, so the total surface is 6*36 = 216 cm^{2}

Note: I call them "edges" but in case of a cube most say just "length"

3 0
3 years ago
Other questions:
  • Probability:
    9·1 answer
  • A salesman make both a base salary and also a commission which is a percentage of what he sells . Each month if his sales total
    11·1 answer
  • What is the slope of the line y= 7x + 19 (5)
    8·2 answers
  • Is my answer actually incorrect and if so how?
    13·1 answer
  • The manager of a restaurant found that the cost to produce 300 cups of coffee is ​$30.43​, while the cost to produce 500 cups is
    12·1 answer
  • If the principle is $12,000 and the rate of interest is 6% (simple interest), what
    14·1 answer
  • chris and Michelle are professional divers. During one of their dives, Chris goes 40 meters below the surface of the water, and
    9·1 answer
  • HELPPPPPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
    9·2 answers
  • If you complete it and it's correct I give you (brainlist)​help
    8·1 answer
  • IN Date OUT IN OUT Employee Time Card: 7:30 10/1 11:30 4:15 12:00 John Apple 10/2 8:15 11:00 5:15 11:45 10/3 11:15 3:55 7:00 12:
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!