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aleksklad [387]
3 years ago
7

What are the roots of x^2 - 4x - 7 = 0

Mathematics
1 answer:
lyudmila [28]3 years ago
8 0

For the given equation, the solutions are x=2 \pm\sqrt{11} .

Step-by-step explanation:

Step 1:

For an equation of the form ax^{2} +bx+c=0 the solution is x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}.

Here a is the coefficient of x^{2}, b is the coefficient of x and c is the constant term.

Comparing x^{2} -4x-7=0 with ax^{2} +bx+c=0, we get that a is 1, b is -4 and c is -7.

To get the solution, we substitute the values of a, b, and c in x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}.

Step 2:

Substituting the values, we get

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{-(-4) \pm \sqrt{(-4)^{2}-4(1)(-7)}}{2(1)}.

\frac{-(-4) \pm \sqrt{(-4)^{2}-4(1)(-7)}}{2(1)}= \frac{4 \pm \sqrt{16+28}}{2}.

\frac{4 \pm \sqrt{16+28}}{2} = \frac{4 \pm \sqrt{44}}{2}.

\frac{4 \pm \sqrt{44}}{2} =  \frac{4 \pm 2\sqrt{11}}{2} = 2 \pm\sqrt{11} .

So x=2 \pm\sqrt{11} .

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zubka84 [21]
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6 0
2 years ago
Rectangle STUV has square PQRS removed, leaving an area of 92 m^2. Side PT is 4 m in length and side RV is 8m in length
Andrei [34K]

Answer:

117 m^{2}

Step-by-step explanation:

First think of the square that was removed.  All 4 sides are equal but you don't know the length so lets gives them the variable X.

So to find the area of the rectangle, insert those variables into the area equation for a rectangle.

(RV + (X) ) (PT +(X)) = rectangle area

Now you are given what the area is if you remove the square.  So subtract the the square's area from the equation above and set it equal to the size they told you.

(RV + (X)) (PT + (X))  - [(X)(X)] = 92m^{2}

      rectangle          -  square  =  remaining area

Now plug in the numbers you know and solve for X.

(8 + X) (4 + X) - ((X)(X)) = 92    

Use FOIL to multiply the first part of the equation (first, outer, inner, last)

32 + 8x + 4x + x^{2} -  x^{2}  =  92

32 + 12x = 92

12x = 60

x = 5

So now you know the size of the square.  Each side is 5m.  So add 5m onto the top of the rectangle and onto the side.  The top is 13m and the side is 9m.  The area of the rectangle is the length times the height to 13 x 9 which is 117 m^{2}

6 0
2 years ago
Whats a linear function
slega [8]

Answer:

A Linear Function is any function that graphs to any straight line. It can be consist of one or 2 or more variables but the degree or the exponent value of the variable shouldn't be greater than 1. it can be 0 but not greater than one .

Step-by-step explanation:

f(x)= y= a +bx , is the example of linear fucntion where the variable x has the exponent value of 1 ,

but the function f(x)= y= a+bx^2 is not a linear function because the exponent value of variable x is 2 .

Also if the Value of Exponent of the variable  is in negative, that will be also a non linear function  .

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2 years ago
coal mines have shafts that can be as much as 7 feet deep. About how many feet deep into earth's crust are these shafts?
NikAS [45]

Answer:

i have no clue

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The balance of an investment account is $308.32
Nady [450]

The balance was $4400.25 before 4 years.

<h3>What is an Equation?</h3>

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, and quadratic equations.

The balance of an investment account is $308.32

Let the balance 4 years ago was $x

Then the balance today is represented by x + 308.32

The current balance is $4708.57

The expressions can be equated to get the value of the balance 4 years ago.

x + 308.32 = 4708.57

x = 4708.57 - 308.32

x = $4400.25

The balance 4 years ago was $4400.25

To know more about Equation

brainly.com/question/10413253

#SPJ1

4 0
2 years ago
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