which of the following statement is true?​

Given:

A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8).

To find:

The corresponding quadratic expression.

Solution:

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

A quadratic function has x-intercepts 2 and 6. It means (x-2) and (x-6) are two factors of the required quadratic function.

The function is defined as:

[tex]P(x)=a(x-2)(x-6)[/tex]                    ...(i)

Where, a is a constant.

The vertex of the quadratic function is (4,8). It means the point (4,8) will satisfy the function.

Substituting x=4 and P(x)=8 in (i).

[tex]8=a(4-2)(4-6)[/tex]

[tex]8=a(2)(-2)[/tex]

[tex]8=-4a[/tex]

Divide both sides by -4.

[tex]\dfrac{8}{-4}=a[/tex]

[tex]-2=a[/tex]

Putting [tex]a=-2[/tex] in (i), we get

[tex]P(x)=-2(x-2)(x-6)[/tex]

[tex]P(x)=-2(x^2-6x-2x+12)[/tex]

[tex]P(x)=-2(x^2-8x+12)[/tex]

[tex]P(x)=-2x^2+16x-24[/tex]

Therefore, the correct option is B.

Answer:

56.3 =c

44.1 =a

Step-by-step explanation:

Using the law of sines

sin 102        sin 28

----------  = ----------

c                 27

Using cross products

27 sin 102 = c sin 28

Divide by sin 28

27 sin 102

------------   = c

sin 28

56.25470702= c

Rounding to the nearest tenth

56.3 =c

To find a

We need Angle A

A = 180 - 102 -28

A = 50

sin 50        sin 28

----------  = ----------

a                 27

Using cross products

27 sin 50 = a sin 28

27 sin 50

------------   = a

sin 28

44.0563425= a

Rounding to the nearest tenth

44.1 =a

Answer:

150 degrees

Step-by-step explanation:

8x-10=3x+90

solve for x in calculater

x = 20

Substitute:

3(20)+90 = 150

Answer:

Step-by-step explanation:

8x - 10 = 3x + 90

5x - 10 = 90

5x = 100

x = 20

8(20) - 10 = 160 - 10 = 150

Answer:

-1,024

Step-by-step explanation:

4×2=8

8×2=16

and so on repeating 7 times

Answer:

I hope This will Help u.. Plz mark me as Brilliant please

Step-by-step explanation:

Before you get started, take this readiness quiz.

Simplify: 

If you missed this problem, review (Figure).

Solve Equations with Constants on Both Sides

In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.

Our strategy will involve choosing one side of the equation to be the “variable side”, and the other side of the equation to be the “constant side.” Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.

By doing this, we will transform the equation that began with variables and constants on both sides into the form  We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.

Solve: 

Solution

In this equation, the variable is found only on the left side. It makes sense to call the left side the “variable” side. Therefore, the right side will be the “constant” side. We will write the labels above the equation to help us remember what goes where.



Since the left side is the “”, or variable side, the 8 is out of place. We must “undo” adding 8 by subtracting 8, and to keep the equality we must subtract 8 from both sides.

Use the Subtraction Property of Equality.Simplify.Now all the variables are on the left and the constant on the right.

The equation looks like those you learned to solve earlier.Use the Division Property of Equality.Simplify.Check:Let .

Solve: 



Solve: 



Solve: 

Solution

Notice, the variable is only on the left side of the equation, so we will call this side the “variable” side, and the right side will be the “constant” side. Since the left side is the “variable” side, the 9 is out of place. It is subtracted from the , so to “undo” subtraction, add 9 to both sides. Remember, whatever you do to the left, you must do to the right.

Answer:

Division property of equality

Step-by-step explanation:

[tex] - 2m = 40[/tex]

[tex]m = - 20[/tex]

Answer:

Nope, this is because the angles in a triangle add up to 180, whereas these values added are equal to 200 degrees

No, the angles with measures 80°, 55°, and 65° cannot form angles on a line.

In geometry, angles on a line are also known as "linear angles" or "straight angles." A straight angle measures 180°, and it is formed by two rays that point in opposite directions and share a common endpoint, creating a straight line. To determine if the given angles can form a straight angle, we need to add their measures.

Let's calculate the sum of the given angles:

Sum = 80° + 55° + 65°

       = 200°

Since the sum of the given angles (200°) is not equal to 180°, it means that the angles cannot form a straight line. Instead, they form a shape that is not a straight angle, such as a triangle or a polygon.

In this case, the given angles form a triangle since they satisfy the triangle inequality theorem. The sum of any two sides of a triangle is always greater than the third side. Mathematically, for a triangle with sides of lengths a, b, and c, the inequality holds: a + b > c, b + c > a, and c + a > b.

Therefore, the angles with measures 80°, 55°, and 65° cannot form angles on a line but rather form a triangle with a sum of 180°, satisfying the triangle inequality.

To know more about Linear Angles here

https://brainly.com/question/13045673

#SPJ2

Answer:

0

Step-by-step explanation:

37 + (-37)

open the bracket

remember when u multiply the bracket - sign and + sign also gets multiplied and (-) * (+) is( -) . So

37 - 37

0

Answer:

2

Step-by-step explanation:

Answer:

8 feet, 256 ft^2

Step-by-step explanation:

The function of the area can be graphically rapresented with a parabola that opens downwards

in this specific case the vertex is the maximum point of the parabola.

(X) Vertex = -64/-8 = 8 feet

(Y) Vertex = -4(64) + 512 = -256 + 512 = 256 ft^2

Answer:

Maximum Width = 8 feet.

Maximum area = 256 ft^2.

Step-by-step explanation:

Part A.

A = -4w^2 + 64w

Finding the derivative:

dA/dw = -8w + 64 = 0  for maxm/minm, so

-8w  = -64

w = 8

The second derivative is -8 so w = 8 gives a maximum.

Part B.

The maximum area = -4(8)^2 + 64*8

= -256 + 512

= 256 ft^2.

Answer:

(fog)(x)=6x-3

Step-by-step explanation:

In this problem, we are looking to find f of g of x. Simply put, we just have to plug g(x) into f(x). Whereever there is an x in f(x), we will replace with g(x).

[tex](fog)(x)= 2(g(x))-7\\(fog)(x)=2(3x+2)-7\\(fog)(x)=6x+4-7\\(fog)(x)=6x-3[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

2604

Step-by-step explanation:

Answer:

2600 as a estimate but it is 2604

Step-by-step explanation:

Answer: 20 laps

Step-by-step explanation:

Given

Roger just ran 5 laps and completes 20% of his goal

Suppose his goal is x laps

So, 20% of x must be equal to 5

[tex]\Rightarrow 20\%\times x=5\\\Rightarrow 0.2x=5\\\\\Rightarrow x=\dfrac{5}{0.2}\\\\\Rightarrow x=\dfrac{50}{2}\\\\\Rightarrow x=25\ \text{laps}[/tex]

So, he needs 20 more laps to complete his goal.

Answer:

18 muffins

Step-by-step explanation:

Amount of flour Maggie used

Total amount of flour she bought - Amount of flour left over.

= 45oz - 14.72 oz

= 30.28 oz of flour

She used 17.5 oz to make a loaf of bread, and 0.71 oz for each muffin.

Hence,

Let the number of muffins = x

17.5 + 0.71x = 30.28

0.71x = 30.28 - 17.5

0.71x = 12.78

x = 12.78/0.71

x = 18 muffins

Therefore, Maggie made 18 muffins

Answer:

[tex]A: (-3,1)[/tex]

[tex]B:(-1,-1)[/tex]

[tex]d=\sqrt{(-3-(-1)^{2} +(-1(-1))^{2} }[/tex]

[tex]=\sqrt{(-2)^{2}+(2)^{2} }[/tex]

[tex]=\sqrt{4+4}=\sqrt{8}[/tex]

[tex]=2\sqrt{2} =2.8[/tex]

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

hope it helps..

have a great day sis ^_^!!!

Answer:

Coordinates of :-

A= (-3,1)

B= (-1,-1)

Distance AB= [tex]\sqrt{-2+3)^{2}+(-1-1)^{2} }[/tex]

OAmalOHopeO

Answer:

x = -2 ±√(13/2)

Step-by-step explanation:

Answer:

[tex]9+y[/tex] ≤ [tex]16[/tex]

Step-by-step explanation:

The sum of [tex]9[/tex] and [tex]y[/tex] which is [tex]9+y[/tex] is less than or equal to 16, which is ≤ [tex]16[/tex]

Hope this is helpful.

Answer:

x = 100

Step-by-step explanation:

365.12 x = 36512

36512 / 365.12 = x

x = 100

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The answer will be 2a×3=6a

Answer:

i think A

Step-by-step explanation:

sorry if im wrong

Answer:

The answer is option c

Step-by-step explanation:

Product means we have to multiply

[tex](3x - 4y) \times ( - 2x + 5y - 6) \\ 3x( - 2x + 5y - 6) - 4y( - 2x + 5y - 6) \\ - 6x {}^{2} + 15xy - 18x + 8xy - 20y { }^{2} + 24[/tex]

You then group like terms

[tex] - 6x {}^{2} + 15xy + 18xy - 20y {}^{2} + 24 \\ 6x {}^{2} + 23xy - 20y {}^{2} + 24[/tex]

And there's your answer

Answer:

8.34 ×10^4 as in sceintific notation so in normal

8.39×10^4 = 83900

and 3.84 × 10^-3 = 0.00384

Hope it helps

Answer and Step-by-step explanation:

Convert the numbers into improper fractions.

[tex]\frac{25}{6} ,\frac{28}{5}[/tex]

Now, multiply the numbers.

[tex]\frac{700}{30}[/tex]

Finally, simplify.

[tex]\frac{70}{3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

9514 1404 393

Answer:

  7+(7–7) ÷(7+7•7)= 7

Step-by-step explanation:

The difference 7 - 7 provides an opportunity to zero out everything to its right. That's what we've done in this version:

  7 +(7 -7) ÷ (7 +7×7) = 7 . . . our version of the equation

  7 +0 ÷ (7 +49) = 7 . . . . . multiplication inside parentheses first

  7 +0 ÷ 56 = 7 . . . . . . . . parentheses first

  7 +0 = 7 . . . . . . . . . . . . division before addition

They are the same amount. neither is greater or lesser than the other.

Answer:

1=68 (Vertically opposite angles are equal)

2= 112 (sum of angles on a straight line gives 180°)

3=112 (vertically opposite angles are equal)

Answer: D

Step-by-step explanation:

I’m like 90% sure it’s D ‍♀️

Answer:

D

Step-by-step explanation:

Domain is how far the graph goes left to right.

The left arrow goes left into -infinity forever

The right arrow goes down and to the right forever, into infinity