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polet [3.4K]
3 years ago
15

Solve the equation by completing the square

Mathematics
1 answer:
Ilya [14]3 years ago
4 0

Answer:

We got the quadratic equation:

x^2+8x-3=0

Solving by completing the square:

x^2+8x-3=0\\x^2+8x+16-16-3=0\\(x+4)^2-16-3=0\\(x+4)^2-19=0\\(x+4)^2=19\\x+4=\pm \sqrt{19} \\x=-4\pm \sqrt{19} \\\\x_{1} =-4+\sqrt{19} \\x_{2} =-4-\sqrt{19}

Therefore, the answer is letter C

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Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15
Digiron [165]

\huge \boxed{\mathfrak{Question} \downarrow}

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\left. \begin{array}  { l  }  { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.

  • To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

2x-5y=-13, \: 3x+4y=15

  • Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

2x-5y=-13

  • Add 5y to both sides of the equation.

2x=5y-13

  • Divide both sides by 2.

x=\frac{1}{2}\left(5y-13\right)  \\

  • Multiply \frac{1}{2}\\ times 5y - 13.

x=\frac{5}{2}y-\frac{13}{2}  \\

  • Substitute \frac{5y-13}{2}\\ for x in the other equation, 3x + 4y = 15.

3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15  \\

  • Multiply 3 times \frac{5y-13}{2}\\.

\frac{15}{2}y-\frac{39}{2}+4y=15  \\

  • Add \frac{15y}{2} \\ to 4y.

\frac{23}{2}y-\frac{39}{2}=15  \\

  • Add \frac{39}{2}\\ to both sides of the equation.

\frac{23}{2}y=\frac{69}{2}  \\

  • Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

\large \underline{ \underline{ \sf \: y=3 }}

  • Substitute 3 for y in x=\frac{5}{2}y-\frac{13}{2}\\. Because the resulting equation contains only one variable, you can solve for x directly.

x=\frac{5}{2}\times 3-\frac{13}{2}  \\

  • Multiply 5/2 times 3.

x=\frac{15-13}{2}  \\

  • Add -\frac{13}{2}\\ to \frac{15}{2}\\ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

\large\underline{ \underline{ \sf \: x=1 }}

  • The system is now solved. The value of x & y will be 1 & 3 respectively.

\huge\boxed{  \boxed{\bf \: x=1, \: y=3 }}

8 0
2 years ago
for the following questions, determine how many solutions each equation has. if one solution, state the value of x. x+6+8=2x-x+1
vichka [17]

Answer:

infinite solutions

Step-by-step explanation:

x+6+8=2x-x+14

x+6+8=x+14

x+14=x+14

14=14

or

x=x

plug in any number

2+6+8=2(2)-2+14

16=16

another example

8+6+8=2(8)-8=14

22=22

5 0
3 years ago
Which of the following best describes the relationship between the variables on the scatter plot below?
CaHeK987 [17]

Answer:

A. negative correlation

Step-by-step explanation:

Let two variables x and y, the correlation coefficient r measure to what degree the variables x and y are related.

--- If this coefficient is positive then the relationship will be positive. This means that even an increase in the variable x will produce an increase in the variable y. In the dispersion diagram the points will be grouped, simulating a line of positive slope.

--- If this coefficient is negative then the relation will be negative. This means that even an increase in the variable x will produce a decrease in the variable y. In the dispersion diagram the points will be grouped, simulating a negative slope line.

In the diagram shown it can be noted that as the variable x increases the variable y decreases.

Therefore it can be concluded that the correlation between x and y is negative. The correct option is option A

4 0
3 years ago
HELP‼️‼️‼️‼️‼️‼️<br><br> 1. If 8x + 4y = 44, what is the value of 6x + 3y?
Gnom [1K]

Answer:

33.

Step-by-step explanation:

8x + 4y = 44

4(2x + y) = 44

2x + y =  44/4 = 11.

6x + 3y

= 3(2x + y)

= 3 * 11

= 33.

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2 years ago
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
sveticcg [70]

Answer:

Oh lordy I hope this is correct

Step-by-step explanation:

Type: Irrational Numbers. Example: 1.17513698...

Type: Natural Numbers. Example: 56

Type: Rational Numbers: Example: 1/3

Type: Integers. Example: -5

Type: Whole Numbers. Example: 0

6 0
3 years ago
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