add one line to each of the diagrams below so that the resulting figure has rotational symmetry but no line symmetry.

Liesl is correct, if the discriminant is a perfect square, then we can factorize the quadratic equation.

For a quadratic equation:

y = a*x^2 + b*x + c

The discriminant is:

D = b^2 - 4ab

Notice that for the equation:

0 = a*x^2 + b*x + c

The solutions are given by:

[tex]x = \frac{-b \pm \sqrt{D}}{2a}[/tex]

If D is a perfect square, then we know that the square root has solutions, so there are two values:

[tex]x_1 = \frac{-b + \sqrt{D}}{2a}\\\\x_2 = \frac{-b - \sqrt{D}}{2a}[/tex]

Now with these solutions, we can factorize our equation as:

[tex]y = a*(x - ( \frac{-b + \sqrt{D}}{2a}))*(x - ( \frac{-b - \sqrt{D}}{2a}))[/tex]

So Liesl is correct, if the discriminant is a perfect square, we can factorize the quadratic equation.

If you want to learn more about factorization, you can read:

https://brainly.com/question/11579257

Answer:

4 pi/3

Step-by-step explanation:

960 degrees in standard position is the same thing as 960-360 = 600 degrees in standard position because rotating the second line 360 degrees just brings it back to where it started.

Do it again to get 600 - 360 = 240

240 degrees would end up in the same spot as 600 degrees and 960 degrees, so they are all coterminal.

Convert 240 degrees to radians:

240 * pi/180 = 4pi/3.

Answer:

B.) x = 16

Step-by-step explanation:

Answer:

6 people

Step-by-step explanation:

Answer:

a) 1/16

b) 7/16

Step-by-step explanation:

a) The area of the outside circle is π (8")² = 64π in².

The area of the center circle is π (2")² = 4π in².

So the probability is (4π / 64π) = 1/16.

b) The area of the outside strip is π [(8")² − (6")²] = 28π in².

So the probability is (28π / 64π) = 7/16.

Answer:

c

Step-by-step explanation:

The equation =( denominater * derivative of numerator - numerator * derivative of denominator) / denominator ^2

so the qstn is (x^2 + 3x +2) / (x+3)

apply the values as the above eqtn states

ie,[ (x+3) * derivative of (x^2 +3x + 2)] - [( x^2 +3x + 2) *derivative of (x+3)] /

(x+3)^2

derivative of numerator, (x^2 +3x + 2) is 2x+3

" of denominator, (x+3) is 1

so we get

[(x+3)* (2x + 3 ) - (x^2 +3x + 2) *1 ] / (x+3)^2

open the brackets

[ 2x^2 + 3x + 6x + 9 - x^2 +3x + 2 ] / (x+3)^2

subtract similar terms and we get the final answer in option c

Answer:

3 ×-2 - (2×1) + 2

-6 - 2 + 2

= -6

Answer:

10

Step-by-step explanation:

[tex]| 3(-2)-2(1)|+2\\[/tex]

Solve inside the absolute value(Between the two lines).

[tex]|3(-2)-2(1)|+2\\|-6-2|+2\\|-8|+2\\8+2=10[/tex]

Quick Tip...

Anything between absolute values will result in positive form.

Such as -3=-3 but |-3|=3 or |-9+1|=|-8|=8 where positive over-rides(Not sure if I spelled that right) negative.

Or |4|=4.

Answer:

The other 2 had 96 pieces of candy combined.

Step-by-step explanation:

5 + 19 = 24

so, 120 candies - 24candies = 96 candies left

Answer:

3,000 + 1 = 3,001

Step-by-step explanation:

Just add it vertically.

3,000

+      1

3,001

Answer:

3,000+1=3,001

Step-by-step explanation:

Just simple logic

Answer:

m = -3/5

Step-by-step explanation:

-5m = 3

Divide each side by -5

-5m/-5 = 3/-5

m = -3/5

Answer:

C, $769 per week

Step-by-step explanation:

There are 52 weeks in a year. To find the answer to this question, divide $40,000 by 52 to get $769.230769231, rounded to $769.

Answer:

Exact form: -4/3

Decimal form: -1.3

Mixed number form: -1 1/3

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

1/2 ÷ 2/3

1/2 * 3/2

1 * 3/ 2 * 2

3/4

Please mark me the brainliest!?!

Answer:

the skater needs to get a score of 97  [or more ]

Step-by-step explanation:

[ 83 + 88 + 92  + M  ] / 4   ≥  90      multiply both sides by  4

83 + 88 + 92  + M ≥   360     simplify

263 + M ≥ 360           subtract  263 from both sides

M ≥  97      →  the skater needs to get a score of 97  [or more ]

Answer:97

Step-by-step explanation:

83+88+92+97=360

360/4=90

Answer:

per ounce is $5.92

Step-by-step explanation:

All you gotta do is 53.28 divided by 9 $5.92!

Mark me brainliest!!

Answer:

a isosceles triangle because it has two sides that are paarrelell

Step-by-step explanation:

Answer:

40 because you multiply 4x10

Answer:

Hi I think the answer would be D

Step-by-step explanation:

Why is because it starts in the negative and ends in the positive.

Does this help if so please mark me brainlest

Answer:

see explanation

Step-by-step explanation:

If (5, - 4) is a solution to the system then both equations will be true when (5, - 4) is substituted into them.

Substitute (5, - 4) into the left side of the equations and if equal to the right side then (5, - 4) is a solution.

3(5) - 2(- 4) = 15 + 8 = 23 = right side

2(5) + (- 4) = 10 - 4 = 6 = right side

Then (5, - 4) is a solution to the system of equations.

or by solving

3x - 2y = 23 → (1)

2x + y = 6 → (2)

Multiplying (2) by 2 and adding to (1) will eliminate the y- term

4x + 2y = 12 → (3)

Add (1) and (3) term by term to eliminate y, that is

7x = 35 ( divide both sides by 7 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (2)

2(5) + y = 6

10 + y = 6 ( subtract 10 from both sides )

y = - 4

Solution is (5, - 4 )

Using the concept of simultaneous equation, the solution to the system of equations is (5, - 4)

Given the system of linear equations :

From (2) :

Substitute (3) into (1)

3x - 2(6 - 2x) = 23

3x - 12 + 4x = 23

7x = 23 + 12

7x = 35

Divide both sides by 7 to isolate x

x = 35 / 7

x = 5

From (3)

y = 6 - 2(5)

y = 6 - 10

y = -4

Therefore, the solution to the system of equation is (5, - 4)

Learn more : https://brainly.com/question/15165519

Answer:

x=-3

Step-by-step explanation:

-3x-2y=9

-3x-2(0)=9

-3x-0=9

-3x=9

x=-3

Step-by-step explanation:

A man by the name of Luigi Fonti wrote this. I hope it can guide you, as it did for me! "The set of rational numbers is closed for all the four operations, so x+y, x-y, x*y and x/y are rational too. And it is easy to demonstrate. A rational number can be expressed as a fraction of two integers. So, x can be expressed as a/b and y as c/d. Hence x+y = a/b + c/d = (ad+bc)/bd, which, as fraction of two integers, is rational."

Answer:

Let's define:

A = distance traveled before deploying the landing gear

B = distance traveled after deploying the landing gear.

We must have that the sum of those two distances must be equal to 600 yards.

A + B = 600 yd.

And we know that:

" the plane will travel half the distance with the landing gear than without the landing gear."

Then we have that:

B = A/2.

Now we can replace this last equation in the first one:

A  + B = 600yd

A + A/2 = 600yd.

(3/2)*A = 600yd.

A = (2/3)*600yd = 400yd.

Ohama should deploy the landing gear 400 yd into the runway.

Answer:4,2

Step-by-step explanation: is u divide both side with 2 that will be your answer

Answer:

Your answer is: Midpoint =  (0.5, -0.5)

Step-by-step explanation:

(xa+xb/2 , ya+yb/2)

Plug the points ---> (5,2)(-4,-3)

= (1/2 , -1/2)

In decimal form it would be: (0.5,-0.5)

Hope this helped : )

Answer:

1020 cm²

Step-by-step explanation:

The area of a trapezoid is given by:

Area=(big base+small base)/2 ×h

So,

Area=(TR+PA)/2 ×h

Area=(54+31)/2 ×24

Area=85/2 ×24

Area=42.5×24

Area=1020 cm² or Area=0.102 m²

Answer:

d = (-9/13)

Step-by-step explanation:

13d + 8 = -1

       -8     -8

13d = -9

÷13    ÷13

d = ( -9/ 13 )

I hope this helps!

Answer:

d = -9/13

Step-by-step explanation:

13d +8= -1

Subtract 8 from both side

13d +8-8= -1-8

13d = -9

Divide 13 from both side

13d/13 = -9/13

d = -9/13

Answer:

AA

Step-by-step explanation:

ΔCSR and ΔMDR share ∠CRS

Since lines [tex]n[/tex] and [tex]k[/tex] are parallel, ∠C ≅ ∠M and ∠S ≅ ∠D. These are corresponding angles.

Either of these sets of angles could be used along with ∠CSR to prove that ΔCSR and ΔMDR are similar because of AA.

Answer:

value of h makes the equation true is -3.5

Step-by-step explanation:

=> 4h = -14

multiply both side by h

=> [tex] \frac{4h}{4} = \frac{ - 14}{4 } \\ [/tex]

=> [tex]h = \frac{ - 14}{4} [/tex]

divide -14 by 4

÷> h = - 3.5

Answer:the answer would be 20

Step-by-step explanation:

because it is use the most

Step-by-step explanation:

Let the first number be x and the second y

x+y=100

(x-12)+y

Answer:

y > x + 2

Step-by-step explanation: