Determine the maximum or minimum value of the quadratic function from its equation.

Answer: [tex]-6,13[/tex]

Step-by-step explanation:

Given

The sum of the two numbers is 20

and the difference of the two is -6

Suppose, the numbers are x and y

[tex]\therefore x+y=20\quad \ldots(i)\\\Rightarrow x-y=-6\quad \ldots(ii)\\\text{Solving} (i)\ \text{and}\ (ii)\ \text{we get}[/tex]

[tex]\Rightarrow 2x=14\\\Rightarrow x=7[/tex]

[tex]\therefore y=13[/tex]

Therefore, the numbers are [tex]-6,\ \text{and}\ 13[/tex]

Answer:

240,000

Step-by-step explanation:

standard form means the way you would write it

Answer:

6912 / 823,543 or approximately 0.8%

Step-by-step explanation:

4 black

3 red

7 total

P(B) = 4/7

P(R) = 3/7

4/7 x 3/7 x 4/7 x 3/7 x 4/7 x 3/7 x 4/7 = 6912 / 823,543

Answer:

x = 19

Step-by-step explanation:

5x - 26 = x + 50

Subtract x on both sides of the equation.

4x - 26 = 50

Add 26 on both sides.

4x = 76

Now, divide by 4 on both sides.

x = 19

Answer:

x = 19

Step-by-step explanation:

5x-26=x+50

5x = 76 +x

4x = 76

x = 19

Given:

The equation is:

[tex]270=3e^{2.4K}[/tex]

To find:

The solution for the given equation to the nearest hundredth.

Solution:

We have,

[tex]270=3e^{2.4K}[/tex]

Divide both sides by 3.

[tex]\dfrac{270}{3}=e^{2.4K}[/tex]

[tex]90=e^{2.4K}[/tex]

Taking ln on both sides, we get

[tex]\ln (90)=\ln e^{2.4K}[/tex]

[tex]\ln (90)=2.4K[/tex]                  [tex][\because \ln e^x=x][/tex]

Divide both sides by 2.4.

[tex]\dfrac{\ln (90)}{2.4}=K[/tex]

[tex]\dfrac{4.4998}{2.4}=K[/tex]           [tex][\because \ln (90)\approx 4.4998][/tex]

[tex]1.874916667=K[/tex]

Round the value to the nearest hundredth (two decimal place)

[tex]K\approx 1.87[/tex]

Therefore, the value of K is 1.87.

Let the original price = x

An increase of 10 % = 18.15

Multiply x by (1 + percent increase) which is 1.1x = 18.15

Now to find x divide both sides by 1.1:

X = 16.50

The original price was 16.50

Answer:

£16.50

Step-by-step explanation:

Let cost price be x

Now, create a formula:

x + 10x / 100 = 18.15

'or'

110x / 100 = 18.15

'or'

x = (18.15*100) / 110

x = 16.5

Answer:

y = 6

Step-by-step explanation:

Answer:

i helped

Step-by-step explanation:

Answer:

(-2, -4)

Step-by-step explanation:

y = f(x) = ax²+bx +c

given the vertex is (3, -4)

=> the symetry axis: x = 3

x = -b/2a = 3

so, -b = 6a => b = -6a

the function f(x) = x²-6x + 5

g(x) = f(x+5)

g(x) = (x+5)²-6(x+5)+5

g(x) = x²+10x+25-6x-30+5

g(x) = x²+4x

=> a=1, b=4

find the vertex of the function g :

the symetry axis: x= -4/2(1) => x = -2

y = g(-2) = (-2)²+4(-2)= 4-8 = -4

so, the vertex is (-2, -4)

Answer:

Step-by-step explanation:

Vertex form of a quadratic function:

We have (h, k) = (3, -4)

The function f(x) is:

The function g(x) is:

g(x) = f(x + 5) =

         (x + 5 - 3)² - 4 =

         (x + 2)² - 4

Vertex of g(x) is:

Answer:

y = 1/3 x - 1

Step-by-step explanation:

use slope formula then substitute an x and y and the m to find b

y=mx+b

Answer:

Step-by-step explanation:

Answer:

20a

Step-by-step explanation:

26a+4a-10a=30a-10a=20a

Answer:

20a

Step-by-step explanation:

26a+4a-10a

since they are like terms u can add and subtract them

=30a-10a

=20a

Answer:

[tex]a_{n} = 600/2^{n-1}[/tex]

This the correct answer

Answer: 1. equal to - having the requisite qualities for; "equal to the task"; "the work isn't up to the standard I require" adequate to, up to, capable.

Step-by-step explanation:Glad Too Help :))

Answer:

B

Step-by-step explanation:

Answer:

22 grams

Step-by-step explanation:

loses 50% of it's mass per 22 years

so after 22 years the mass would be 44 grams

22 years later would leave 50% of 44 grams = 22 grams

Answer:

gdfhddfdhgbg

Step-by-step explanation:

Answer:

785.4

Step-by-step explanation:

The formula to find the surface area of a cylinder is

2* pi* radius* height + 2* pi* 2radius.

2( 3.14) (5) (20)= 628

2 (3.14* 5*5)= 157

628+ 157= 785.

Answer:

Step-by-step explanation:

a=4 square units

b=9 square units

sqrt (4+9)

(sqrt(13))^2

c= 13 square units

Answer:

3

Step-by-step explanation:

tan 60 = root(3)

tan² 60 = {root (3)}²

tan² 60 = 3

Answer:

Step-by-step explanation:

The answer is B.

It's a line that shows every point that satisfies the equation

y = 3x + 4  which is what I think you meant (but I'm not sure). If I am correct then there are a million possible points that could be the answer to this question.

If I am not correct, leave a comment that tells me so, and I'll revise my answer.

Never mind the question has the right equation. And my answer remains as given.

Given:

The image of a lens crosses the x-axis at –2 and 3.

The point (–1, 2) is also on the parabola.

To find:

The equation that can be used to model the image of the lens.

Solution:

If the graph of polynomial intersect the x-axis at c, then (x-c) is a factor of the polynomial.

It is given that the image of a lens crosses the x-axis at –2 and 3. It means (x+2) and (x-3) are factors of the function.

So, the equation of the parabola is:

[tex]y=k(x+2)(x-3)[/tex]          ...(i)

Where, k is a constant.

It is given that the point (–1, 2) is also on the parabola. It means the equation of the parabola must be satisfy by the point (-1,2).

Putting [tex]x=-1, y=2[/tex] in (i), we get

[tex]2=k(-1+2)(-1-3)[/tex]

[tex]2=k(1)(-4)[/tex]

[tex]2=-4k[/tex]

Divide both sides by -4.

[tex]\dfrac{2}{-4}=k[/tex]

[tex]-\dfrac{1}{2}=k[/tex]

Putting [tex]k=-\dfrac{1}{2}[/tex] in (i), we get

[tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex]

Therefore, the required equation of the parabola is [tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex].

Note: All options are incorrect.

Answer: 187

Step-by-step explanation:

negative cancels negative so that will turn to positive. (-) x (-) = +

100- (-87)

=

100 + 87

= 187

Answer:

187

Step-by-step explanation:

100 - (-87)

100 + 87

187

PLZ MARK as BRAINLIEST

Answer:

5

Step-by-step explanation:

3*4=12

4*3=12

6*2=12

but 12 is not factor of 5

Answer:

Step-by-step explanation:

Answer:

third side = 4

Step-by-step explanation:

third side is hypoenuse as it is opposite to 90 degree.

using pythagoras theorem

(perpendicular)^2 + (base)^2 = (hypotenuse)^2

2^2 + (2[tex]\sqrt{3[/tex] )^2 = hypotenuse^2

4 + 4*3 = hypotenuse^2

16 = hypotenuse^2

[tex]\sqrt{16}[/tex] = hypotenuse

4 = hypotensue

Answer:

B. (1,4)

Step-by-step explanation:

If you go over to the right by 1 and up by 4 the point will land inside the blue, hence it is the answer since the rest do not land inside the blue.

Answer:

0.0152 probability

Step-by-step explanation:

first there are 12 marbles: odds are 2/12 = 1/6

Then, there are 11 marbles: odds are 1/11

So the odds of both of them being blue are: 1/6 * 1/11 = 0.0152

Please give brainliest thanks!

Answer: $6335.76

Step-by-step explanation:

you would do 3,000 times 105% = 3450

then you would do 3450 times 105% = 3967.5 then you would do 3967.5 times 105% = 4562.62 then you would do 4562.62 times 105% = 5247.01 next you would do 5247.01 times 105% = 6034.06 finally you would do 6034.06 times 105% = 6335.76