Which of the following represents this function written in standard form?

y=2(x+1)(x-6)

a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12
Which of the following represents this function written in standard form?

y=2(x+1)(x-6)

a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12

The reference angle for an angle whose measure is -440 is  80.

Reference angle--

It is the angle which is made from the terminal side of the given angle and it is always made by taking x-axis as a reference.

Here we are given a angle whose measure is:

   -440.

This means that the angle covers more than one rotation and ends in the fourth quadrant.

Hence, the reference angle is:

-440+360=80

Answer with explanation:

In a triangle sum of two sides , should always be greater than the third side.

Sides of the given triangle are, 3 x cm, 7 x cm and h cm.

1.

3 x + 7 x > h

→ 10 x > h

2.

3 x+ h > 7 x

→h > 7 x -3 x

→h> 4 x

3.

7 x + h > 3 x, which will be always true.

Combining 1, 2 and 3 we get

→4 x < h < 10 x

Option A

Final answer:

To calculate the minimum amount of burgers you will need, count the number of individuals who will be eating and multiply it by 2. The Total burgers needed is 50 .

Explanation:

To calculate the minimum amount of burgers you will need, you need to count the number of individuals who will be eating. Let's count:

1 Grandfather

1 Grandmother

2 Fathers

2 Mothers

4 Children

3 Grandchildren

1 Brother

2 Sisters

2 Sons

2 Daughters

1 Father-in-law

1 Mother-in-law

1 Daughter-in-law

Adding all of these individuals, we get a total of 25 people. Since every person will be eating 2 burgers, we can calculate the minimum amount of burgers we will need by multiplying the total number of people by 2:

Total burgers needed = 25 people * 2 burgers per person = 50 burgers

Answer:

1/32

Step-by-step explanation:

You're welcome

The angle of repose is calculated using the equation θ = cot-1(r/h). For a pile with a height of 19 feet and a base diameter of 30 feet, the angle of repose is approximately 38.03 degrees. Using this angle and the base diameter of 104 feet, we can find that the height of the new pile is approximately 77.07 feet.

The angle of repose θ is related to the height h and base radius r of the conical pile by the equation θ = cot-1(r/h).

Given a pile with a height of 19 feet and a base diameter of 30 feet, we can find its base radius by dividing the diameter by 2, which gives us a radius of 15 feet.

Now, we can substitute the given values into the equation to find the angle of repose θ.

θ = cot-1(15/19)

Using a calculator, we find that the angle of repose is approximately 38.03 degrees.

Next, we can use the height of the new pile and the known angle of repose to find its base radius.

Given a base diameter of 104 feet, the radius is half of the diameter, so the radius is 52 feet.

Now, we can use the equation θ = cot-1(r/h) and solve for h to find the height of the new pile.

h = r / tan(θ)

Substituting the known values, we get:

h = 52 / tan(38.03)

Using a calculator, we find that the height of the pile with a base diameter of 104 feet is approximately 77.07 feet.

The correct translation of the function is,

⇒ Four units to the right and three units up from 3√x

Option B is true.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The parent function is,

⇒ f (x) = 3√x

And, the translation of the function is,

y = 3√x- 4 + 3

Now, We get;

The parent function is,

⇒ f (x) = 3√x

After translated Four units to the right we get;

⇒ f (x) = 3√x - 4

And, After translated three units up from 3√x;

f (x) = 3√x- 4 + 3

Thus, The correct translation of the function is,

⇒ Four units to the right and three units up from 3√x

Option B is true.

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The first 20 digits of pi are 3.1415926535897932384. It's an irrational number used in many mathematical calculations and its decimal representation never ends or repeats.

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The probability that Pam will not purchase either car A or car B is 0.20.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Probability that she will purchase car A = 0.46

Probability that she will purchase car B = 0.34

The probability that she will purchase either car A or car B is

⇒ [tex]0.46+0.34[/tex]

⇒ [tex]0.80[/tex]

Thus the probability that she will not purchase either car A or car B is

⇒ [tex]P(A)=1-0.80[/tex]

⇒ [tex]P(A)=0.20[/tex]

Hence we can conclude that the probability that Pam will not purchase either car A or car B is 0.20.

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We want to find the g'(0) by knowing that:

g(x) + x*sin(g(x)) = x^2

We will get:

g'(0) = 0

First, we can see that:

g(0) is given by:

g(0) + 0*sin(g(0)) = 0^2

g(0) = 0.

Now let's derive this, we can rewrite:

g(x) = x^2 - x*sin(g(x))

Now we just differentiate to get:

g'(x) = 2*x - sin(g(x)) - x*cos(g(x))*g'(x)

Now we need to move all the terms with g'(x) to the left side:

g'(x) + x*cos(g(x))*g'(x) = 2x - sin(g(x))

g'(x)*(1 +  x*cos(g(x)) =  2x - sin(g(x))

g'(x) = ( 2x - sin(g(x)) )/(1 +  x*cos(g(x))

Now we just need to evaluate this in x = 0, so we get:

g'(0) = (2*0 - sin(g(0)))/(1 + 0*cos(g(0)) = -sin(g(0))

And remember that g(0) = 0 then:

g'(0) = -sin(0) = 0

g'(0) = 0

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Option: D is the correct answer.

          D. The graph would shift 5 units to the left.

We know that the transformation of a function f(x) to f(x+a) is a shift of the function either to the left or to the right by a units depending on the sign of a i.e.  if a>0 then the shift is a units to the left

and if a<0 then the shift is a units to the right.

Here we have:

          [tex]y=x^2+5x-2[/tex] is converted to:

[tex]y=(x+5)^2+5(x+5)-2[/tex]

Here we have a=5>0

            Hence, the shift is 5 units to the left.

Step-by-step explanation: A balance sheet is a statement of financial condition at a point in time. It includes assets, liabilities, and equity. The balance sheet demonstrates the overall health of a company. It can be used to obtain loans and more financing.