Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).
f(x) = -x^2+6x-5
f'(x) =

Answer:

it will take appr 3.8 seconds to hit the ground

Step-by-step explanation:

h = -16t^2 + 60t + 3

at ground level , h = 0

16t^2 - 60t - 3 = 0

t = (60 ± √3792)/32

t = 3.799.. or t = a negative

Answer:

it is in fact 3.80

Step-by-step explanation:

I know the other person said that but I was just backing them up

Answer:

The values of y are 1 , 2 , 5 , 10 ⇒ answer B

Step-by-step explanation:

* We will use the substitution method to solve the problem

- The quadratic equation is y = x² + 4x + 5

- The values of x are -2 , -1 , 0 , 1

- We will substitute the values of x in the equation to find the

  values of y

# At x = -2

∵ y = x² + 4x + 5

∵ x = -2

∴ y = (-2)² + 4(-2) + 5  = 4 - 8 + 5 = 1

∴ y = 1

# At x = -2

∵ y = x² + 4x + 5

∵ x = -1

∴ y = (-1)² + 4(-1) + 5  = 1 - 4 + 5 = 2

∴ y = 2

# At x = 0

∵ y = x² + 4x + 5

∵ x = 0

∴ y = (0)² + 4(0) + 5  = 0 + 0 + 5 = 5

∴ y = 5

# At x = 1

∵ y = x² + 4x + 5

∵ x = 1

∴ y = (1)² + 4(1) + 5  = 1 + 4 + 5 = 10

∴ y = 10

* The values of y are 1 , 2 , 5 , 10 ⇒ from left to right

Answer:

the answer is B.

Step-by-step explanation:

It makes the problem solve smoother.

Answer:

Choice d. [tex]l:x = 7[/tex] is parallel to the line [tex]x = 4[/tex].

Step-by-step explanation:

Refer to the diagram attached. (Created with GeoGebra)

The line [tex]x = 7[/tex] is made of all the points on a cartesian plane that meet the requirement [tex]x = 7[/tex]. In other words, this line consists of points with x-coordinate [tex]7[/tex]. That includes:

That line is perpendicular to the x-axis (the horizontal axis) and intersects the x-axis at the point [tex](7,0)[/tex].

Now, consider the lines in the choices.

The first line [tex]3y =7[/tex] requires only that the y-coordinates of its points be 7/3. This line accepts any x-values. Points on this line include:

As a result, this line is parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].

Similar to the first, the second line [tex]y = 7[/tex] is also parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].

The third line [tex]x = y[/tex] requires that the x- and y- coordinates of all its points be equal. Points may include:

This line is slant.

The last line [tex]x = 4[/tex] is similar to the given line [tex]x = 7[/tex]. This line is also perpendicular to the x-axis. The difference is that this line is three units to the left of the line [tex]x = 7[/tex].

Answer:

990 feet

Step-by-step explanation:

Fabricator 4 recieved what's left after the rest were distributed

= 5,840 - 2,500 - 1,200 - 1,150 = 990

Answer:

990 feet.

Step-by-step explanation:

To calculate the feet of metal that the last fabricator will sell, you just have to substract from the total feet needed the amount of metal that have been already ordered to the other fabricators.

Total metal duct work= Fabricator 1+ Fabricator 2+ Fabricator 3+ Fabricator 4

If you clear the equation it would be:

F4= Total- F1- F2- F3

F4= 5840- 2,500- 1,200- 1150

F4= 990 ft.

Answer:

yea its pi not pie, but he is right

Step-by-step explanation:

Answer:

Cube

Step-by-step explanation:

Im not sure what the option choices are but a cube has 6 faces. :)

Answer:

hexahedron

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Given

Mean= μ=60

and

Standard Deviation= σ=5

In order to calculate the percentage of students between 55 and 65, we have to calculate z-score for both

z-score for 55=(55-60)/5  

=(-5)/5

=-1

The area to the left of z-score -1 is 0.1587

z-score for 65=(65-60)/5  

=5/5

=1

The area to the left of z-score 1 is 0.8413

Area between z-scores of 55 and 65=0.8413-0.1587

=0.6826

Converting into percentage

=0.6826*100

=68.26%

Option C is the correct answer ..  

Answer:

c. 68

Step-by-step explanation:

The empirical rule states that, if a population is approximately normal then 68% of the observations will fall within 1 standard deviation of the mean.

Going by this definition, 65 is one standard deviation to the right of the mean while 55 is one standard deviation to the left of the mean. Therefore, the percent of students who have scored between 55 and 65 points will be about 68%.

The question requires an approximation, About what percent, not exact computation. Thanks

Answer:

The answer isc

Step-by-step explanation:

C

Answer:

B. n = 65; p = 0.8

Step-by-step explanation:

Look at the equations and see if the statements are true.

Company 1 and 4 do not charge the same rate per mile, company one charges 0.5 per mile and company 4 charges 0.06 per mile.

Company 2 and 3 do not charge the same.

Company 2 has an x in the equation so is not just a flat fee.

Company 3 does not have an x in the equation, so only charges a flat fee.

The correct answer is the last one.

Answer:

If you mean 2 and 3 it would be (x-2)(x-3)=0

Step-by-step explanation:

(x-2)=0

x-2=0 move the two on the other side to get positive

x=2

(x-3)=0

x-3=0 move the three on the other side to get positive

x=3

The standard deviation of the binomial distribution with n = 1000 and p = 0.94 is calculated using the formula σ = √(npq) and turns out to be approximately 7.51.

To calculate the standard deviation of a binomial distribution, we use the formula σ = √(npq), where n is the number of trials, p is the probability of success on a single trial, and q is the probability of failure (q=1-p).

Given the values of n = 1000 and p = 0.94, we can first calculate q:

q = 1 - p = 1 - 0.94 = 0.06.

Now, using the standard deviation formula:

σ = √(npq)

= √(1000 × 0.94 × 0.06).
We carry out the calculation:

σ = √(1000 × 0.94 × 0.06)

= √(56.4)

≈ 7.51.

Therefore, the standard deviation of the binomial distribution is approximately 7.51.

Answer:

-2+sqrt(3)

Step-by-step explanation:

When cos(angle)=sqrt(3)/2

then sin(of that angle)= + or - 1/2 depending on the quadrant

Anyways 330 degrees is in the 4 quadrant.  Cosine is positive there while sine is negative.

so sin(330)=-1/2

Formula for tan(x/2)=(1-cos(x))/sin(x)

Therefore  tan(165)=tan(330/2)=(1-cos(330))/sin(330)=(1-sqrt(3)/2)/(-1/2)

Multiply top and bottom by 2 to get

tan(165)=(2-sqrt(3))/-1

tan(165)=-2+sqrt(3)

Enter the given values into the equation and solve.

5800 = 4100e^(k*40)

Divide both sides by 4100 and simplify:

58 / 41 = e^(k*40)

Remove e by taking the logarithm of both sides:

ln(58/41) = k *40

Divide both sides by 40:

k = ln(58/41)/40

k = 0.00867

Now for the population to double set up the equation:

2*4100 = 4100e^kt

The 4100 cancels out on both sides:

2 = e^kt

Take the logarithm of both sides:

ln(2) = k*t

Divide both sides by k

t = ln(2) /k

replace k with the value from above:

t = ln(2) / 0.00867

t = 79.95

Rounded to the nearest tenth = 80.0 hours to double.

Answer:

Step-by-step explanation:

To answer the question, we first need to find the constant k, using the given information and the expression.

[tex]P=4100e^{kt} \\5800=4100e^{k(40)} \\\frac{5800}{4100}=e^{40k}\\e^{40k}=1.41\\lne^{40k}=ln1.41\\40k=0.34\\k=\frac{0.34}{40}\approx 0.0085[/tex]

Now that we have the constant. We can find the time it would take to double the population which would be 11600:

[tex]P=4100e^{kt}\\11600=4100e^{0.0085t}\\\frac{11600}{4100}= e^{0.0085t}\\e^{0.0085t}=2.83\\lne^{0.0085t}=ln2.83\\0.0085t=1.04\\t=\frac{1.04}{0.0085}\approx 122.35[/tex]

Therefore, it would take around 122 hours to double the population.

Answer:

1. The median.

Step-by-step explanation:

First arrange in ascending order:

5.8  6.1  6.1  6.2  6.2  6.2  6.3  6.8  6.8 7

The median = 6.2. On the box plot the median is marked at 6.3 so that is incorrect. All the others are correct

Answer:

[tex]Rateofchange=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where x₁ and x₂ are values in the interval [x,y] respectively

Step-by-step explanation:

Well, first to determine the average rate of change of a function, you should have the interval of the values of x for the function.

So lets assume you have a function;

[tex]f(x)=x^3-4x[/tex]

And the interval as [1,3]

Then the average rate of change for the function f(x) will be;

[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where x₁ and x₂ are the interval coordinates x,y respectively. In this case x₁=1 and x₂=3

To find the average rate of change in this example will be;

[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\\\=f(x_2)=f(3)=3^3-4(3)=27-12=15\\\\=f(x_1)=f(1)=1^3-4(1)=1-4=-3\\\\\\=x_2-x_1=3-1=2\\\\\\=\frac{15--3}{2} \\\\=\frac{18}{2} =9[/tex]

Answer:

Elsa's error was adding (4r+r) instead of subtracting (4r-r)

Step-by-step explanation:

we have

[tex](3b+4r)+ (-2b-r)[/tex]

step 1

Eliminate the parenthesis

[tex]3b+4r-2b-r[/tex]

step 2

Group terms that contain the same variable

[tex]3b-2b+4r-r[/tex]

step 3

Combine like terms

[tex]b+3r[/tex]

therefore

Elsa's error was adding (4r+r) instead of subtracting (4r-r)

Answer:

Ella' s error was adding (4r+r) instead of subtracting (4r-r)

Step-by-step explanation:

Answer:

The correct answer option is D. 168 units³.

Step-by-step explanation:

We are given a prism with known side lengths and we are to find its volume.

We know that the volume of a prism is given by:

Volume of prism = area of base × height

Here the base is a triangle so the base area will be:

Base area = 1/2 × base × height = 1/2 × 6 × 8 = 24  units²

Volume of prism = 24 × 7 = 168 units³

For this case we have that by definition, the volume of a prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

The base of the prism is a triangle, then:

[tex]A_ {b} = \frac {6 * 8} {2} = 24 \ units ^ 2[/tex]

Thus, the volume is:

[tex]V = 24 * 7\\V = 168 \ units ^ 3[/tex]

Now, the prism volume is [tex]168 \ units ^ 3[/tex]

Answer:

Option D

Answer:

The function has a domain of all real numbers.

The function is a reflection of y =³√x.

Step-by-step explanation:

1. The function is always increasing. - False

(Taking a cube root makes the number smaller so the domain of the function should be decreasing)

2. The function has a domain of all real numbers. - True

The cube root of real number is also real so the minus sign would not result in an imaginary number as it is outside the radical.

3. The function has a range of {y |– ∞ < y < ∞ }. - False

4. The function is a reflection of y =³√x. - True

5. The function passes through the point (3, –27). - False

(these coordinates do not satisfy the function)

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

===================================

f(x) = x²

w(x) = (x - 7)² = f(x - 7) → shift the graph of f(x) 7 units to the right

Answer:

c. pi/2

Step-by-step explanation:

The answer is the option c. pi/2.

You must know that y = sin(x) is an odd function and also that y = cos(x) is an even function.

Also, you should know that sin(x + pi/2) = cos(x).

You can show it using the definition of the functions sine and cosine in the unit circle or using the formula of the sine of a sum: sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B).

When you substitute B with pi/2 you get sin (A + pi/2) = sin(A)*0 + cos(A)*1 = cos(A).

Then, given that cos(A) is even sin(A+pi/2) is even.

Answer:

option b

Step-by-step explanation:

We are given that [tex]y=sin \frac{1}{2}(x-C)[/tex] be an even function

We have to find the value of C for which given function is even function

We know that sin x is odd function and cos is even function

Odd function : when f(x)[tex]\neqf(-x) [/tex] then the function is called an odd function.

Even function : When f(x)=f(-x) then the function is called an even function.

Sin(-x)=-Sin x

Cos (-x)= Cos x

When we take C=[tex]2\pi[/tex]

Then , y=Sin[tex]\frac{x}{2}-\frac{2\pi}{2}[/tex]

y=[tex]sin(\frac{x}{2}-\pi)[/tex]

[tex]y=-sin\frac{x}{2}[/tex]  ( [tex]sin (x-\pi)=-sin x[/tex])

When x is replace by -x

Then, we get [tex]y=-sin(-\frac{x}{2})=sin\frac{x}{2}[/tex]

[tex]f(-x)\neq f( x)[/tex]

Hence, option a is false.

b.C=[tex]\pi[/tex]

[tex]y= sin (\frac{x}{2}-\frac{\pi}{2})[/tex]

[tex] y=-sin(\frac{\pi}{2}-\frac{x}{2})[/tex]

[tex]y=-cos \frac{x}{2}[/tex]

When x is replaced by -x then we get

[tex] y=-cos (-\frac{x}{2})=- cos \frac{x}{2}[/tex]

f(x)=f(-x) , Therefore, function is even,hence option b is true.

c.C=[tex]\frac{\pi}{2}[/tex]

[tex]y=sin (\frac{x}{2}-\frac{\pi}{4})[/tex]

[tex]Sin (A-B)=Sin A Cos B- Sin B Cos A[/tex]

[tex][y= sin \frac{x}{2} cos {\frac{\pi}{4}-cos\frac{x}{2} sin\frac{\pi}{4}[/tex]

[tex] sin\frac{\pi}{4}= cos \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]

[tex]y=\frac{1}{\sqrt2}(sin \frac{x}{2}- cos \frac{x}{2})[/tex]

When x is replaced by -x then we get

[tex]y=\frac{1}{\sqrt2}(-sin\frac{x}{2}-cos \frac{x}{2})[/tex]

[tex]f(x)\neq f(-x)[/tex]

Hence, function is odd .Therefore, option c is false.

To graph the equation y = 3x + 1 - 2, find the slope and y-intercept. Plot the y-intercept and use the slope to find additional points. Connect the points to get the graph.

To graph the equation y = 3x + 1 - 2, we need to find the slope and the y-intercept. The slope, represented by m, is 3 in this equation. The y-intercept, represented by b, is -1. We can plot the y-intercept on the graph first, which is the point (0, -1). From there, we can use the slope to plot additional points and draw a line through them. Since the slope is 3, we can move up 3 units on the y-axis and 1 unit to the right on the x-axis to find another point. By connecting these points, we will have the graph of y = 3x + 1 - 2.

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Answer:

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

Remember that the solution of a linear system of equations is shown by the interception point between those lines.

In this case, the interception point is at (2,3).

Also, the horizontal line is [tex]y=3[/tex]. Notice that the solution are is below this line, that means the inequality that represents that part is [tex]y\leq 3[/tex].

Now, the other line has y-intercept at -1, that means [tex]b=-1[/tex].

Then, we use two points (0,-1) and (2,3) to find its slope.

[tex]m=\frac{3-(-1)}{2-0}=\frac{4}{2}=2[/tex]

So, the equation that represents that line is [tex]y=2x-1[/tex].

Notice that the area of solution is above this line, that means the inequality is

[tex]y>2x-1[/tex]

Therefore, the sytem that represents the graph is

[tex]y>2x-1\\y\leq 3[/tex]

Notice that we used [tex]\leq[/tex] for the solid line and [tex]>[/tex] for the not solid line.

Final answer:

The most helpful form to determine the time for the ball to hit the ground is Option A, h(t) = -16(t - 3)(t + 1), as it is already in factored form, making it easy to find the positive root, which represents the time when the ball would hit the ground.

Explanation:

When attempting to determine the time required for the ball to hit the ground in a quadratic model, we are essentially looking for the time when the height of the ball, h(t), is zero. To find this, we need to find the roots of the quadratic equation. Function A, h(t) = -16(t - 3)(t + 1), is already factored, which makes finding the roots straightforward. When dealing with quadratic equations, remember that negative time values do not make sense in this context, so we are only interested in the positive root.

The most helpful form for this task would therefore be Option A, h(t) = -16(t - 3)(t + 1), as the roots can be easily read from the factored form, which directly gives the times when the ball reaches the ground level without further calculation. In this case, the positive root t = 3 seconds represents the time when the ball would hit the ground. Ignoring the root t = -1 because time cannot be negative.

Answer:

- 120

Step-by-step explanation:

-2 x² + 8 x = 0

x = - 6

Substitute x = - 6 into -2 x² + 8 x = 0

- 2 x² + 8 x = 0

- 2 × ( - 6² ) + 8 × ( - 6 ) = 0

( - 2 × 36 )  + ( 8 × -6) = 0

- 72 + ( - 48 ) = - 120

Answer:

the answer is B. They are perpendicular because their slopes are negative reciprocals.

Step-by-step explanation:

Answer:

(10 x 13) + (10 x 12) + (12 x 5 / 2) + (12 x 5 / 2) + (10 x 5)

360

Answer: Fourth option is correct.

Step-by-step explanation:

Since we have given that

56 is 14 more than a number.

Let the number be 'p'.

So, the equation would be

[tex]14+p=56\\\\p=56-14\\\\p=42[/tex]

Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.

Hence, Fourth option is correct.

Answer: Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56

__________________________________________________________

Hence, (d) is correct.

Step-by-step explanation:

edge2023

Answer:

5x - 3x = 10

2(2x - 1) = 46

6x - 15 = 75

x+(x - 10) = 26

Step-by-step explanation:

5x - 3x = 10

2x = 10  Divide by 2

x=5

2(2x - 1) = 46   Distribute the 2

4x - 2 = 46  Add 2

4x = 48  Subtract by 4

x = 12

6x - 15 = 75  Add 15

6x = 90  Divide by 6

x=15

x + x - 10 =26  Add the x's together and the 10

2x = 36  Divide by 2

x = 18

Increasing order of the x-values that make them true are,

Solve each equations,

5x - 3x = 10

Simplifying the equation, we get

2x = 10

(Divide by 2)

x = 10/2

x = 5

2(2x - 1) = 46  

Divide both sides by 2

[tex]\frac{2(2 x-1)}{2}=\frac{46}{2}[/tex]

Simplify

[tex]$$2 x-1=23$$[/tex]

Add 1 to both sides

[tex]$$2 x-1+1=23+1$$[/tex]

Simplifying the equation, we get

[tex]$$2 x=24$$[/tex]

Divide both sides by 2

[tex]\frac{2 x}{2}=\frac{24}{2}[/tex]

Simplify

[tex]$$x=12$$[/tex]

6x - 15 = 75

Add 15 to both sides

[tex]$$6 x-15+15=75+15$$[/tex]

Simplifying the equation, we get

[tex]$$6x=90$$[/tex]

Divide both sides by 6

[tex]\frac{6 x}{6}=\frac{90}{6}[/tex]

Simplify

[tex]$$x=15$$[/tex]

x + x - 10 =26

Add similar elements:

x + x = 2x

[tex]$2 x-10=26$[/tex]

Add 10 to both sides

[tex]$2 x-10+10=26+10$[/tex]

Simplifying the equation, we get

[tex]$2 x=36$[/tex]

Divide both sides by 2

[tex]\frac{2 x}{2}=\frac{36}{2}[/tex]

Simplify

x = 18

Hence,

Increasing order of the x-values that make them true are,

To learn more about Equations in increasing order refer to:

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