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leonid [27]
3 years ago
15

Find the roots of the parabola given by the following equation. 2x2+ 5x - 9 = 2x

Mathematics
1 answer:
dem82 [27]3 years ago
5 0

Answer:

x=-3 or x=3/2

Step-by-step explanation:

We are given the following equation:

2x^2+5x-9=2x

We are asked to find the roots.  That means just solve it for x.

2x^2+5x-9=2x

Subtract 2x on both sides:

2x^2+3x-9=0

Let's see if we can put this in factored form.

Compare

2x^2+3x-9=0

and

ax^2+bx+c=0.

a=2, b=3 , c=-9

We have to find two numbers that multiply to be ac and add up to be b.

ac=-18

b=3

What are two numbers that multiply to be -18 and add to be 3?

Say -3 and 6.

So we are going to factor 2x^2-3x+6x-9=0

The first two terms have a common factor of x.

The last two terms have a common factor of 3.

2x^2-3x+6x-9=0

x(2x-3)+3(2x-3)=0

Now we can factor the (x-3) out of those 2 terms there since they share that common factor:

(x+3)(2x-3)=0

(x+3)(2x-3)=0 implies x+3=0  or 2x-3=0.

So we must solve x+3=0   and 2x-3=0

x+3=0

Subtract 3 on both sides:

x=-3

2x-3=0

Add 3 on both sides:

2x=3

Divide both sides by 2:

x=3/2

The solutions are x=3 or x=-3/2

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Let u,v,wu,v,w be three linearly independent vectors in R7R7. Determine a value of kk, k=k= , so that the set S={u−3v,v−2w,w−ku}
11Alexandr11 [23.1K]

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

6 0
3 years ago
2. Reece is playing a carnival game in which he
Maslowich
25% or 2/4 and to win one game 50% or 1/2
6 0
3 years ago
What is the quotient ? a-3/7 divided by 3-a/21
LUCKY_DIMON [66]
Final result :  -3



Step by step solution :Step  1  :            3 - a Simplify   —————             21  Equation at the end of step  1  :  (a - 3)   (3 - a)  ——————— ÷ ———————     7        21   Step  2  :            a - 3 Simplify   —————              7  Equation at the end of step  2  :  (a - 3)   (3 - a)  ——————— ÷ ———————     7        21   Step  3  :         a-3      3-a Divide  ———  by  ———          7       21 
 3.1    Dividing fractions 
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
a - 3     3 - a       a - 3        21  —————  ÷  —————   =   —————  •  ———————  7        21           7       (3 - a)
 3.2    Rewrite   (3-a)    as  (-1) •  (a-3) Canceling Out : 3.3    Cancel out  (a-3)  which now appears on both sides of the fraction line.
Final result :  -3
4 0
3 years ago
Read 2 more answers
• 6x – 15y = 15<br> y=2 x - 1<br> 5
yuradex [85]

Answer:

Slope=  

2.000

0.800

​  

=0.400

x−intercept=  

2 /5

​  

=2.50000

y−intercept=  

−5 /5

​  

=  

−1

1

​  

=−1.00000

Step-by-step explanation:

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  6x - 15y - 15  =   3 • (2x - 5y - 5)  

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   2x-5y-5  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"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.

In 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  2x-5y-5  = 0 and calculate its properties

8 0
3 years ago
The measure of angle 1 is 130°.
eimsori [14]

Answer:

The angle opposite angle 1

Step-by-step explanation:

Opposite angles have the same degree when two lines intersect because they are vertical angles.

4 0
3 years ago
Read 2 more answers
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