Rewrite the function in intercept form y=x^2+8x+15

Final answer:

To find the number of baskets of peaches sold on Saturday, we can set up a system of equations and solve it using elimination or substitution. The answer is 15 baskets Option Dof peaches.

Explanation:

To solve this problem, we need to use a system of equations. Let's call the number of baskets of strawberries x and the number of baskets of peaches y. We can set up the following equations:

20x + 18y = 430 (equation 1)

x + y = 23 (equation 2)

We can solve this system of equations using substitution or elimination. Let's use elimination:

Multiply equation 2 by 18 to make the coefficients of y in both equations cancel:

18x + 18y = 414 (equation 3)

Subtract equation 3 from equation 1 to eliminate y:

(20x + 18y) - (18x + 18y) = 430 - 414

2x = 16

Divide both sides of the equation by 2:

x = 8

Substitute x = 8 into equation 2 to find y:

8 + y = 23

y = 23 - 8

y = 15

Therefore, 15 baskets of peaches were sold on Saturday.

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.

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 required number is 6.

The process of subtracting one number from another is known as subtraction.

Let the number be x.

Given that, 5 added to 2 times the number, x, is equal to 7 less than 4 times the number, which is:

2x + 5 = 4x - 7

2x - 4x = -7 - 5

-2x = -12

x = 12/2

x = 6

Hence, the required number is 6.

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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

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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Answer:

1/32

Step-by-step explanation:

You're welcome

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.

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.