Is the discriminant of f positive, zero, or negative?

Answer:

y = 2[tex](x - 3)^{2}[/tex] - 1

Step-by-step explanation:

y = 2[tex]x^{2}[/tex] - 12x + 16  

y = 2([tex]x^{2}[/tex] - 6x + 8)        ( Factor out 2 )

y + 9= 2([tex]x^{2}[/tex] - 6x + 9) + 8 ( Complete the square [tex](\frac{-b}{2} )^{2}[/tex] ) Add 9 both sides  

y + 9 = 2 [tex](x - 3)^{2}[/tex] + 8      (Subtract 9 each side)  

y = 2 [tex](x - 3) ^{2}[/tex] - 1         ( simplify )

Answer:

The expected value is an expression of the weighted average and can be taken as the (arithmetic) mean

As the number of trials is increased in a binomial experiment, the expected values obtained, in each of the set of trials continuously tend to the theoretical expected value

Step-by-step explanation:

Answer:

i dont see a diagram ?

Step-by-step explanation:

Answer:

AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.

Answer:

[tex]Sets = 27[/tex]

Step-by-step explanation:

Given

[tex]Coin = 1[/tex]

[tex]Toss = 5[/tex]

Required

Number of outcomes with at most 3 heads

First, we list out the sample space of a toss of coin 5 times

[tex](HHHHH)[/tex], [tex](HHHHT)[/tex], [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], [tex](THHHH)[/tex], [tex](HTHTH)[/tex], [tex](THTHT)[/tex], [tex](HHTHH)[/tex], [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](HHHTH)[/tex], [tex](TTTHT)[/tex]

Next, we list out all outcomes with at most 3 heads

, , [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], , [tex](HTHTH)[/tex], [tex](THTHT)[/tex], , [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](TTTHT)[/tex]

So, the number of set is:

[tex]Sets = 27[/tex]

Answer:

the answer is 3x2-10x+6=0

Answer:

His average speed is

12 km/hr

.

Step-by-step explanation:

Remember the triangle of Speed, Distance and Time. If you remember it, you'll ace these kinda questions.

I had trouble with these formulas but the triangle helped me a LOT! Anyways, let's get back to the question. The formula for average speed is pretty much the same as the formula for just speed. The average speed formula is

Average speed

=

Total Distance

Total Time

So......

48 km

4 hr

=

12 km/hr

My source

I hope this explanation helps you!

Step-by-step explanation:

The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,

[tex]\implies 2x -y +6=0\\\\\implies 2x + 3y -6=0[/tex]

On subtracting the given equations we have,

[tex]\implies -y - 3y +6 -(-6) = 0 \\\\\implies -4y = -12 \\\\\implies y = -12/-4\\\\\implies y = 3 [/tex]

Put this value in any equation , we have ,

[tex]\implies 2x -3 +6 =0\\\\\implies 2x = -3 \\\\\implies x =\dfrac{-3}{2} \\\\\implies x =-1.5 [/tex]

Hence the lines will Intersect at ,

[tex]\implies\underline{\underline{ Point=(-1.5, 3)}}[/tex]

for the first one x = 1/2 y-3" and y = 2 x + 6 and for the other one is x =  − 3 /2  y+ 3  and y= − 2 /3  x + 2

how i did this Step 1: Add -3y to both sides.

Step 2: Add 6 to both sides.

Step 3: Divide both sides by 2.

Answer:

39.48

Step-by-step explanation:

1/2(5.3+13.5)(4.2)

Answer:

think it is D

Step-by-step explanation:

look at the X axis and the number at the Y axis

The equation best models the relationship between x and y is y=-5x+125.

We have given that,

John reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks.

We have to determine the equation best models the relationship between x and y.

The three main ways to represent a relationship in math are using a table, a graph, or an equation.

The X-axis and the number at the Y-axis.

Therefore, The equation best models the relationship between x and y is y=-5x+125.

To learn more about the graph visits:

https://brainly.com/question/4025726

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Answer:

hope it helps.

Answer:

A) 60%

Step-by-step explanation:

24/40

= 0.6

0.6*100

= 60%

I really hope this is right and it helps.

Answer:

C

Step-by-step explanation:

Since it's the product, the two numbers must be multiplied together. -3 * x will equal 21, so -3x=21. By dividing both sides by -3, we see that x=-7

Answer:

Volume of paint required is 3.125 litres.

Step-by-step explanation:

It would be noted that each side walls would have the shape of a trapezium. So that the areas of each wall can be determined as:

wall 1 = [tex]\frac{1}{2}[/tex](a + b) h

         =  [tex]\frac{1}{2}[/tex](0.5 + 1.5)2

        = 2 [tex]m^{2}[/tex]

wall 2 = [tex]\frac{1}{2}[/tex](a + b) h

          = [tex]\frac{1}{2}[/tex](1 + 3)2

          = 4 [tex]m^{2}[/tex]

wall 3 = [tex]\frac{1}{2}[/tex](a + b) h

         =  [tex]\frac{1}{2}[/tex](0.5 + 1.5)2

        = 2 [tex]m^{2}[/tex]

wall 4 = [tex]\frac{1}{2}[/tex](a + b) h

          = [tex]\frac{1}{2}[/tex](1 + 3)2

          = 4 [tex]m^{2}[/tex]

Total area of the walls = 2 + 2 + 4 + 4

                            = 12 [tex]m^{2}[/tex]

Area of the bottom base = l x b

                          = 1 x 0.5

                          = 0.5 [tex]m^{2}[/tex]

Total area to be painted = 12 + 0.5

                           = 12.5 [tex]m^{2}[/tex]

But to paint one square meter of a gap surface, we need 0.25 litres of a green paint color. Thus, to paint 12.5 [tex]m^{2}[/tex] of the gap surface:

12.5 x 0.25 = 3.125

The litres of paint required is 3.125.

Answer:

The correct answer is -2 , -4

Step-by-step explanation:

if x = -2 and y = -4

-5x-3y=22

so :

-5(-2)-3(-4)=22

10+12=22

22=22

end.

Answer:

34 should be added to it to make it 20

Answer:

[tex] \frac{1}{4}x[/tex]

Step-by-step explanation:

take the reciprocal of 4 which is 1/4

=============================================================

Explanation:

Choice B has the GCF x we can factor out like so

10x^4-5x^3+70x^2+3x = x(10x^3-5x^2+70x+3)

Showing that choice B is not prime. If a polynomial can be factored, then we consider it not prime. It's analogous to saying a number like 15 isn't prime because 15 = 3*5, ie 15 can be factored into something that doesn't involve 1 as a factor.

In contrast, we consider 7 prime because even though 7 = 1*7, there aren't any other ways to write this integer as a factorization if we don't involve 1.

-----------------------------------

Choice C is a similar story. This time we can factor out 3

3x^2 + 18y = 3(x^2 + 6y)

So we can rule this out as well.

-----------------------------------

Choice D is a bit tricky, but we can use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

where in this case a = x and b = 3y^2

Note how b^3 = (3y^2)^3 = 3^3*(y^2)^3 = 27y^(2*3) = 27y^6

All of this means choice D can be factored and it's not prime either.

------------------------------------

We've ruled out choices B through D. The answer must be choice A.

If you let w = x^2, then w^2 = x^4

The polynomial w^2+20w-100 is prime because setting it equal to zero and solving for w leads to irrational solutions. I'm assuming your teacher wants you to factor over the rational numbers.

Because w^2+20w-100 can't be factored over the rational numbers, neither can x^4+20x^2-100. This confirms that choice A is prime.

Answer:

96 green pens

Step-by-step explanation:

Super simple. You do: 14x+15x+24x=212 which is 53x = 212 and x=4

Green = 4*24=96

Answer:

1. LM < PN

2. AD < DC

3. m<CAB < m<CBA

4. m<1 = m<2

Step-by-step explanation:

Recall: an angle measure is relative to the length of the opposite side. That is, the longer the side opposite to an angle, the larger the measure of that angle and vice versa.

1. LM is opposite to <LNM,

PN is opposite to <NLP

m<LNM is less than m<NLP, therefore,

LM < PN

2. AD is opposite to <ABD

DC is opposite to <DBC

m<ABD is less than m<DBC, therefore,

AD < DC

3. m<CAB is opposite to CB

m<CBA is opposite to CA

CB is less than CA, therefore,

m<CAB < m<CBA

4. The side opposite to <1 is congruent to the side opposite to <2.

Therefore,

m<1 = m<2

Answer:

1. a. (ii) 1/27

Step-by-step explanation:

1st one is already given, I will give you the answer to the second one,

³√27/9²

= 3/81

= 1/27

Answered by GAUTHMATH

Answer:

17/42 or in decimal 0.405

Step-by-step explanation:

Add: 1 4/7+2/3- 1 5/6= 47/21- 1 5/6

Subtract: 47 - 1 5/6 = 17/42

Simplify: 17/42

Hello,

The conic is a parabola ,

vertex (-1,3)

focus : (-1,-2)

directrix: y=8

equation: y= - 1/20x²-1/10*x+59/20

solution in picture

The vertex is v(-1,3) , focus is f(-1,8) and the equation of directrix is          y = -2.

A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. The equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix (x + a = 0).

For the given situation,

The standard form of equation of parabola is given by, [tex]y=\frac{1}{4p}(x-h)^{2}+k[/tex]

The vertex is given by [tex]v(h,k)[/tex]

The focus is given by [tex]f(h,k-p)[/tex]

The equation of directrix is given by [tex]y=k+p[/tex]

The given equation is [tex](x+1)^{2} =-20(y-3)[/tex]

On rearranging the given equation in standard form,

⇒ [tex](x+1)^{2} =-20y+60[/tex]

⇒ [tex](x+1)^{2} -60=-20y[/tex]

Divide by 20 on both sides,

⇒ [tex]\frac{(x+1)^{2}}{20} +4 = y[/tex]

⇒ [tex]y=\frac{-1}{(4)(5)} (x+1)^{2} +3[/tex]

On comparing the above equation with the standard form,we get

[tex]p=-5, h=-1, k=3[/tex]

⇒ [tex]k-p=3-(-5)\ =8[/tex]

Hence we can conclude that the vertex is v(-1,3), focus is f(-1,8) and equation of directrix is y=-2.

Learn more about a parabola here

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Answer:

115 degree

Step-by-step explanation:

x + 65 = 180 (Sum of angles in a straight line = 180 [Also known as Linear pair])

x = 180 - 65

x = 115 degree

Answer:

option C

Step-by-step explanation:

2, 4, 6

i don't know whether it is correct or not...

hmm...let me think a little bit

Step-by-step explanation:

hmmm ..... i dont know so sorry

i am very very sory

Answer:

400 in.²

Step-by-step explanation:

Surface area of the triangular prism = bh + L(s1 + s2 + s3)

Where,

b = 8 in.

h = 15 in.

s1 = 17 in.

s2 = 15 in.

s3 = 8 in.

L = 7 in.

Plug in the values

S.A = 8*15 + 7(17 + 15 + 8)

S.A = 120 + 7(40)

S.A = 120 + 280

S.A = 400 in.²