Compute the value of the discriminant and give the number of real solutions of the Quadratic equation 3x^2+5x-2=0

If we know the quadratic formula, the quadratic formula is

x = [-b ± √(b²- 4ac)] / 2a

Gosh! So overwhelming! But let's look at the composition of a quadratic equation:

ax² + bx + c = 0

And we have 6x² - 3x = 1. So, what do we do? We need to put this quadratic equation into an easy form to find the value of a, b, and c to plug in to the equation.

We can just minus one on both sides to get this:

6x² - 3x - 1 = 0

Is it in the form of ax² + bx + c? Yes! a = 6, b = -3, and c = -1. Now, all we have to do is plug it into the quadratic formula.

x = [-b ± √(b²- 4ac)] / 2a

x = [-(-3) ± √((-3)²- 4(6)(-1))] / 2(6)

     [3 ± √(9- 4(6)(-1))] / 12

     [3 ± √(9 + 24)] / 12

     [3 ± √(33)] / 12

At this point, we should just use a calculator, and recognize we have two answers because of the plus-or-minus sign! (or this sign: ±)

[3 ± √(33)] / 12

1) [3 + √(33)] / 12 = 0.73 approximately

2) [3 - √(33)] / 12 = -0.23 approximately

So, x=0.73 and x= -0.23.

Answer:

Distributive

Step-by-step explanation:

Answer:

This should be distributive

Answer:

Yes

Step-by-step explanation:

Yes. It could be a square if all sides are also the same measure.

A parallelogram will be a square when all four sides are of equal in length and all four angles are same.

Learn more:

https://brainly.com/question/16702162

Answer:

-1/3x + 5

Step-by-step explanation:

The slope-intercept is y = mx + b

The m is the slope and b is the y-intercept.

The equation is:

y = -1/3x + 5

Answer:

4

Step-by-step explanation:

the area of a square = length²

16 = length²

find the square root of both sides of the equation

length = 4

Answer:

364.42 ft.

Step-by-step explanation:

For step 1 we should multiply pi by r and 2.

π x r x 2

For step 2 we should multiply pi by 58 and 2.

π x 58 x 2

In result, we should end up with 364.424748 ft. or for short 364.42 ft.

I hope I helped you... Have a great and nice day! :D

Answer:

B. 10, 2, -6, -14, ...

Step-by-step explanation:

substitute each sequence from the options into the function f(n) = -8n + 18

Answer:

B.

Step-by-step explanation:

find the first, second, and third term using the equation and check them with the options

f(1) = -8(1) + 18 = -8 + 18 = 10

f(2) = -8(2) + 18 = -16 + 18 = 2

f(3) = -8(3) + 18 = -24 + 18 = -6

which sequence has 10, 2, -6, ...? B.

7). 1/(√7-√11)

= 1×(√7+√11)/(√7-√11)(√7+√11)

= √7+√11 / (√7)² - (√11)²

= √7 + √11 / 7 - 11

= √7 + √11 / (-4)

EXPLAINATION:

to rationalize the denominator we multiply the numerator and the denominator by the denominator, but with the opposite sign.

For example - in the first question we multiplied 1 and √7 - √11 by √7 + √11 .

Step-by-step explanation:

√256

it's a 16in x16in patio

all four sides are 16

Answer:

1/4

Step-by-step explanation:

Answer:

7/32

(btw thats the simplified version....look at the bottom for non-simplified if you didnt need it simplified)

Step-by-step explanation:

first count how many squares there are in total

its 8 by 8 so in total there are 64!

now there is the green triangle.....

count all the whole squares in it = 10

now count all the half squares (little triangles in it)= 8

Now if you put those little triangles together it would make one small unit square so it is 4 of all

10 + 4 = 14

So there is a Total of 14 unit squares in the green triangle

Fraction Time......

now lets take 14/64 and simplify it

that would be 7/32

We cant make it any more simplified now if you werent looking for the simplified version the your answser would be 14/64

Answer:

The angle between the two vectors is 84.813°.

Step-by-step explanation:

Statement is incomplete. Complete form is presented below:

Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors.

Let [tex]\vec u = \langle 6, -3, 1 \rangle[/tex] and [tex]\vec v = \langle 8,9,-11 \rangle[/tex], the angle between the two vectors is determined from definition of dot product:

[tex]\theta = \cos^{-1} \left(\frac{\vec u \,\bullet \,\vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex] (1)

Where:

[tex]\vec u[/tex], [tex]\vec v[/tex] - Vectors.

[tex]\|\vec u\|[/tex], [tex]\|\vec v\|[/tex] - Norms of each vector.

Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.

If we know that [tex]\vec u = \langle 6,-3,1 \rangle[/tex] and [tex]\vec v = \langle 8, 9,-11 \rangle[/tex], then the angle between the two vectors is:

[tex]\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right][/tex]

[tex]\theta \approx 84.813^{\circ}[/tex]

The angle between the two vectors is 84.813°.

Answer:

2/17

Step-by-step explanation:

6+6+3+2=17

There are two purple marbles

Answer:

I'd have to say, C: 13

Step-by-step explanation:

Answer:

C. 13 meters

Step-by-step explanation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex]c^{2} = 12^{2} + 5^{2}[/tex]

12 x 12 = 144

5 x 5 = 25

[tex]c^{2} = 144 + 25[/tex]

[tex]c^{2} = 169[/tex]

[tex]\sqrt{c^{2} } = \sqrt{169}[/tex]

c = [tex]\sqrt{169}[/tex]

169 ÷ 13 = 13

1 [tex]\sqrt{13 m}[/tex]

Please let me know if this helps!

Answer:

Volume of the shaded space = 4480.0 yd³

Step-by-step explanation:

Volume of the shaded space = Volume of cuboid - Volume of Pyramid placed inside

Volume of cuboid = Length × Width × Height

                              = 28 × 12 × 20

                              = 6720 yd³

Volume of pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Height})[/tex]

                                = [tex]\frac{1}{3}(28\times 12)(20)[/tex]

                                = 2240 yd³

Volume of the shaded space = 6720 - 2240

                                                  = 4480.0 yd³

Answer: 34.64

Step-by-step explanation: you multiply 10 and 2 and that gives you 20 and then u square root 20 and 3 and you get your answer.

Answer:

b

Step-by-step explanation:

Answer:

ok

Step-by-step explanation

part b

Answer:

x = total pencils = 400 pencils

Step-by-step explanation:

Let

x = total pencils

Pencils sold in the morning = 3/5x

Remaining pencil = x - 3/5x

= 5x-3x/5

= 2/5x

Pencils sold in the afternoon = 1/4 of the remainder

= 1/4 * 2/5x

= 2/20x

= 1/10x

Pencils sold in the afternoon = 1/10x

3/5x + 200 = 1/10x

3/5x - 1/10x = 200

(6x-x)/10 = 200

5/10x = 200

1/2x = 200

x = 200 ÷ 1/2

= 200 × 2/1

x = 400 pencils

x = total pencils = 400 pencils

Answer:

C

Step-by-step explanation:

Answer:

Question 1. x>4

Question 2.  x<9

Answer:

11. 8/30

Step-by-step explanation:

add all the marbles

you get 30 marbles

then the probability of yellow being taken out is 8

Answer:

Total surface area of this pyramid =665.6 in^2

Answer:

E) q / p

Step-by-step explanation:

Spanish

m% de p = pf / 100

m% de q = mq / 100

El recíproco se obtiene haciendo que el numerador sea el denominador y el denominador el numerador.

El recíproco de m% de p = 100 / mp

El recíproco de m% de q = 100 / mq

Divisor

100 / mp / 100 / mq

= 100 / mp * mq / 100

= mq / mp

= q / p

English

If the reciprocal of m% of p is divided by the reciprocal of m% of q, the result is: A) pq / 100 B) pq C) 1 / pq D) p / q E) q / p

m% of p= mp/100

m% of q= mq/100

The reciprocal is obtained by making the numerator the denominator and the denominator the numerator

The reciprocal of m% of p= 100/mp

The reciprocal of m% of q= 100/mq

Dividing

100/mp/ 100/mq

=100/mp* mq/100

= mq/mp

= q/p

Answer:

p * 48

Step-by-step explanation:

Lets break this down into something simpler

"The product"

answer to a multiplication problem

"of"

to multiply

"p"

an unknown value

"48"

factor

Answer:

42

Step-by-step explanation:

We know that 10x + 6y = 7, and so

6(10x + 6y) = 6(7) = 42

Answer:

Part A

The first transaction which is to write a check of $8.50 is a debit transaction which carries a negative sign while

The second transaction which states that she wrote it as a deposit carries a positive sign because deposit means to add

Part B

The absolute value of a number is never negative.

|-8.50| = 8.50

Step-by-step explanation:

Part A: Which point represents each of Shelby's transaction on the number line below? Explain the difference between these two transactions.

The firsts transaction says:

She wrote a check for $8.50 to rent a video game.

Writing a check of $8.50 is a debit to her bank account. This is a negative value because $8.50 is taken from the money in her bank account.

Mathematically this means, -$8.50

The second transaction states that:

She mistakenly recorded it in her checkbook as an $8.50 deposit.

Mathematically, a deposit means a positive action, where money is added to the money in her bank account.

Hence,

+$8.50

Part B: Use absolute value to explain how a debt of $8.50 and a deposit of $8.50 are similar.

In mathematics it is important to note that:

The absolute value of a number is never negative.

Hence,

Debt of $8.50 = -8.50

Deposit of $8.50 = +8.50

Hence,

|-8.50| = 8.50

Answer:

Step-by-step explanation:

I am not gonna give the exact answer but remember how to find the volume of the certain object first figure out what kind of object then figure out the formula..

Answer:

PE = 51.45 Joules

Step-by-step explanation:

PE = mgh

= (7.0 kg)(9.8m/s^2)(0.75 m)

= 51.45 Joules

Answer:

C

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{285}{360}[/tex]

    = 2π × 18 × [tex]\frac{19}{24}[/tex]

    = 36π × [tex]\frac{19}{24}[/tex] ( cancel 36 and 24 by 12 )

    = 3π × [tex]\frac{19}{2}[/tex]

    = [tex]\frac{57\pi }{2}[/tex] → C