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
k0ka [10]
2 years ago
15

What are the solutions for the following system of equations?

Mathematics
1 answer:
Alenkasestr [34]2 years ago
6 0

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(0,7),(-13,-97)

Equation Form:

x=0,y=7\\x=-13,y=-97

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(8*x+7)=0

Equation of a Straight Line

Solve   y-8x-7  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'

n this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-8x-7  = 0 and calculate its properties

Graph of a Straight Line :

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000

 y-intercept = 7/1  =  7.00000

Calculate the X-Intercept :

When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500

 x-intercept = 7/-8  = -0.87500

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = 16.000/2.000 =  8.000

Geometric figure: Straight Line

 Slope = 16.000/2.000 = 8.000

 x-intercept = 7/-8 = -0.87500

 y-intercept = 7/1 = 7.00000

Pull out like factors :

  -x2 - 5x - 7  =   -1 • (x2 + 5x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  x2 + 5x + 7

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   5 .

     -7    +    -1    =    -8

     -1    +    -7    =    -8

     1    +    7    =    8

     7    +    1    =    8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Find the Vertex of   y = -x2-5x-7

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens down and accordingly has a highest point (AKA absolute maximum) .    We know this even before plotting  "y"  because the coefficient of the first term, -1 , is negative (smaller than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -2.5000  

Plugging into the parabola formula  -2.5000  for  x  we can calculate the  y -coordinate :

 y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0

or   y = -0.750

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -x2-5x-7

Axis of Symmetry (dashed)  {x}={-2.50}

Vertex at  {x,y} = {-2.50,-0.75}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   -x2-5x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

x2+5x+7 = 0  Subtract  7  from both side of the equation :

  x2+5x = -7

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  -7  +  25/4    or,  (-7/1)+(25/4)

 The common denominator of the two fractions is  4   Adding  (-28/4)+(25/4)  gives  -3/4

 So adding to both sides we finally get :

  x2+5x+(25/4) = -3/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2+5x+(25/4)  =

  (x+(5/2)) • (x+(5/2))  =

 (x+(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2+5x+(25/4) = -3/4 and

  x2+5x+(25/4) = (x+(5/2))2

then, according to the law of transitivity,

  (x+(5/2))2 = -3/4

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(5/2))2   is

  (x+(5/2))2/2 =

 (x+(5/2))1 =

  x+(5/2)

You might be interested in
Solving fp<br> Algebra 2<br> I do not understand how to solve this, could someone please explain?
Olenka [21]

f(x) =  \sqrt{x + 2}
What's The Fixed Point? Well, Let's Assume X=0, this is our point.

f(0) =  \sqrt{0 + 2}  \\ f(0) =  \sqrt{2}  \\ this \: is \: our \: fixed \: point \:  \\ (0, \sqrt{2} )
OR

f(p) =  \sqrt{p + 2}  \\  \\  or \:  \sqrt{x + 2}  = 0 \\ ( \sqrt{x + 2} ) ^{2}  =  {0}^{2}  \\ x + 2 = 0 \\ x  =  - 2
I'm unaware of the nature of the question, so here are some different ways a fixed point is found based on the merits of the question.
4 0
3 years ago
Alex made an eyeglass case and sold it for $12.00. He spent $1.29 on felt and $2.75 on a needle and thread. What was his profit?
madreJ [45]
D because 1.29 plus 2.75 is 4.04(the money that he used to make the case) and subtract that with $12 and you get $7.96 as the profit.
5 0
3 years ago
Read 2 more answers
Fill in the missing factor to show that 2/3 equivalent to 8/12.
Studentka2010 [4]

Answer:

4/4

Step-by-step explanation:

2/3 * what = 8/12

Multiply the top and bottom by 4/4

2/3 *4/4 = 8/12

3 0
2 years ago
X2+y2=r2 Solve for y
Kaylis [27]

Answer: y=\sqrt{r^{2} -x^{2} }

Step-by-step explanation:

x^2+y^2=r^2 --> subtract x^2 to other side

y^2=r^2-x^2 --> square root both sides

y=sqrt(r^2-x^2)

3 0
2 years ago
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Nimfa-mama [501]

Answer:

d is the answer

Step-by-step explanation:

just read the statements properly

6 0
2 years ago
Read 2 more answers
Other questions:
  • 1/2s=4s-21 I don't understand
    7·1 answer
  • If the cylinder has a diameter of 8 cm and a volume of approximately 502.65 cm3, what is the approximate area of the cross-secti
    9·2 answers
  • PLEASE HELP FOR MATH. I NEED HELP WITH THIS. 15 POINTS
    14·1 answer
  • Im thinking of a number 1-10. first one to get it right gets brainliest!
    8·1 answer
  • Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 14 small cakes per hour. The kitchen i
    11·1 answer
  • Please someone help I really need it and please answer if you can give me the answer I will give brainleast just please help me
    6·1 answer
  • Find the value of x.
    12·2 answers
  • GIVING BRAINLY
    10·1 answer
  • Cora works as a plumber and earns $50 per house call, plus $18 for every hour of work. She billed a customer $104, but forgot ho
    14·1 answer
  • Given that sinθ=-3/4 in quadrant 4 find cosθ
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!