Find all critical points of the function f(x) = x^3 + 5x^2 - 7x - 3.The critical point(s) is(are) =

To find the inflection points the first step we have to follow is to find the second and third derivatives of the function:

Now, find the values of x for which the second derivative is 0:

Evaluate the third derivative at this values of x, if the third derivative is different from 0, then that value is an inflection point:

It means that there is an inflection point at x=3.

Okay, here we have this:

Considering the provided operation, we are going to perform it, so we obtain the following:

Let us remember that when two terms with the same base are multiplied, then the base is preserved and the exponents are added, in this case we have:

Finally we obtain that the operation is equal to a^10.

Use the elimination method to solve the given system of equations.

To do so, multiply the first equation by -3 so that the coefficient of x in the first equation becomes the additive inverse of the coefficient of x in the second equation:

Then, the system is equivalent to:

Add both equations to eliminate the variable x and to obtain an equation in terms of the variable y only:

Replace y=2 into the first equation to find the value of x:

Replace y=2 and x=5 into the second equation to confirm the answer:

Therefore, the solution to the system of equations is x=5, y=2.

The correct list is

This is option F

The probability of a 6 being drawn in one pick is

For 4 drawings, the probability would be

From the given side lengths, let's find the measures that will form a right triangle.

Apply Pythagorean Theorem:

Where:

• a ,and ,b, are lengths of the legs

• c is the length of the hypotenuse.

Now, let's start from the first measures in option a.

• 48m, 64m, and 85m

The measures in option a will NOT form a right triangle since the left side of the equation does not equal the right side.

• 27 yd, 36 yd, 45 yd

The measures in option B will form a right triangle because the Equation is true.

ANSWE

(x - h)^2 = 4p(y - k)

(-1 - 3)^2 = 4p(8 - 0.5)

(-4)^2 = 4p(7.5)

16 = 30p

p = 16/30

p = 8/15

(x - 3)^2 = 16/15(y - 0.5)

15(x^2 - 6x + 9) = 16y - 8

15x^2 - 90x + 135 = 16y - 8

16y = 15x^2 - 90x + 135 + 8

y = 15/16 x^2 - 90/16 x + 143/16

f(x) = 15/16 x^2 - 90/16x + 143/16

Solution

For this case we can do the following:

We can understand 7/2 as the reciprocal of 2/7 and we can create the following diagram

Answer:

  (d)  b = 7

Step-by-step explanation:

You want the solution to b³ = 343.

The equation can be written in standard form and factored according to the factoring of the difference of cubes:

  b³ -343 = 0

  (b -7)(b² +7b +49) = 0

The solutions to this are the values of b that make the factors 0.

  b -7 = 0   ⇒   b = 7

  b² +7b +49 = 0   ⇒   b = -3.5 ± i√36.75 . . . . . complex solutions

The one real solution to the equation is b = 7.

__

Additional comment

Every cubic has 3 solutions. Here, two of them are complex. When the only terms in the equation are the cubic term and the constant, there will always be only one real root.

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The equation b^3 = 343 has two valid real solutions: b = 7 and b = -7. Both values satisfy the equation and meet the given condition. Option B.

To determine the value of b, we can solve the equation b^3 = 343.

Taking the cube root of both sides, we get:

b = ∛343

The cube root of 343 is 7, since 7 * 7 * 7 = 343. Therefore, one solution to the equation is b = 7.

However, it's important to note that the cube root function has a real and complex solution. In this case, b = 7 is the real solution, but there are two additional complex solutions.

Using complex numbers, we can express the other two solutions as follows:

b = -∛343

b = -7

So the complete set of solutions for b is b = 7, -7.

In summary, the equation b^3 = 343 has two real solutions: b = 7 and b = -7. These solutions satisfy the equation and fulfill the condition. So Option B is correct.

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ANSWER:

EXPLANATION:

Given:

To find:

The area of the training field

We can see that the two semicircles will form a circle with a diameter(d) of 60 m, so the radius(r) of the circle will be;

r = d/2 = 60/2 = 30 m

Given pi as 3.14, we can go ahead and determine the area of the circle as seen below;

Answer:

move B to true then everything is right ✅

The fraction for the amount of honey each jar holds is 2/3.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, Daniel fills 24 equal sized jars with honey and he brings a total of 16 cups of honey to sell at the farmers' market.

The amount of honey will be:

= Number of cups / Number of jars

= 16 / 24

= 2/3

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Answer

Option C is correct.

The area of the triangle = 18 square units

Explanation

The area of a triangle is given as

Area of the triangle = ½ × B × H

where

B = Base of the triangle = 6 units (From -3 t

The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.

It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.

Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.

Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;

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a.

Noah put marbles on a bag, each color marble represents that the battery of the toy died before 15 hours (red marbles) or that the battery lasted after 15 hours (green marbles)

There are 4 batteries on the toy, for each battery there are two possible outcomes, each one represented by a red and green marble.

So, for each battery, he has to put two marbles. There will be 4 red marbles and 4 green marbles in the bag.

b.

To estimate the probability that at least one battery will die within 15 hours, you have to calculate the expected value.

A lollypop have a circular shape

Diameter D is the line in a circumference that divides it in half

then calculate directly π• D

to the nearest tenth

π•D = 3.14 x 2 = 6.28

then nearest number is 6.3 , or 6.30. Option C)

The discount rate of the digital player is 22%

From the question, we have the given parameters:

List price = $249.99

Sales price = $194.99

Start by calculating the change in the price.

This is calculated as follows

Change = List price - Sales price

So, we have

Change = $249.99 - $194.99

Evaluate the difference

Change = $55

The discount rate of the digital player is then calculated as

Discount = Change/List price x 100%

This gives

Discount = 55/249.99 x 100%

Evaluate

Discount = 22%

Hence, the discount rate is 22%

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the sum of the internal angles of a triangle is equal to 180, then

so

answer:

angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°

angle 2 = 5x = 5(23) = 115°

angle 3 = 12°

Given,

The coordinates of the points shown in the graph is:

Here, the given mapping is:

On comparing the coordinates then x = 6.

Hence, the value of x is 6.

The perimeter is the sum of all sides, therefore:

The factors of 3 that sum to 4 are 3 and 1. So:

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

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

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

[tex](x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\[/tex]

The slope of line A is 7

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

Now let's find the slope of line B.

[tex](x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\[/tex]

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

Now onto line C.

[tex](x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\[/tex]

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

Lastly we have line D.

[tex](x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\[/tex]

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

Here's a summary of the slopes we found

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}[/tex]

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

The total of all the present values of the payments is $2,973,483.

The present value is the future cash flows discounted to the present day's values.

The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.

The total present value is a function of the summation of the four present values.

Since the present values are given, computing the total involves the mathematical operation of addition.

1st payment    $320,640

2nd payment    $787,116

3rd payment    $878,611

4th payment    $987,116

Total PV      $2,973,483

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Answer:

The correct answer is $878,611 for plato users

Step-by-step explanation:

Answer:

draw a line from the top left to the bottom right going through the centre

Step-by-step explanation:

because m=-1 (gradient)

and b=0 (y intercept)

Area of a circle is

If a square foot cost $ 1.25

Answer:

A'(0,4)

B'(-3,6)

C(-4,3)

Step-by-step explanation:

A glide reflection is the combination of a translation with a rotation.

In this question:

T(-1,1): This means that the translation is given by:

(x,y) -> (x-1,y+1)

Rotation: Around the y-axis. This means that:

(x,y) -> (-x,y)

The triangle has the following coordinates:

A(1,3), B(4,5), C(5,2)

Applying the translation:

(x,y) -> (x-1,y+1)

A(1,3) -> (1-1,3+1) = (0,4)

B(4,5) -> (4-1,5+1) = (3,6)

C(5,2) -> (5-1, 2+1) = (4,3)

Rotation over the y-axis:

(x,y)->(-x,y)

A'(0,4)

B'(-3,6)

C(-4,3)

Those are similar triangles, which means, they are related by a ratio

For example in this case,

7: 10

to find x

10 / 7 = x/3

x= 10*3 /7

x= 30/ 7

x= 4.29

____________

4a)

Looking at the figure,

AD and BE are parallel lines

AE and BD are transversals

Thus,

angle DAE is congruent to angle BEA because they are alternate angles(They lie in similar positions but on alternate sides of the transversal

Also,

angle ADB is congruent to angle EBD because they are alternate angles(They lie in similar positions but on alternate sides of the transversal.

Angle ACD is congruent to angle BCE

Recall, 2 triangles are similar if at least, 2 of their corresponding angles are congruent. In this case, 3 corresponding triangles are congruent. Thus,

triangle ADC is similar to triangle EBC by AA(angle angle) postulate

4b) If 2 triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,

AD/EB = DC/BC = AC/ CE

From the information given,

AD = 2

AC = 4

EB = 5

Thus,

2/5 = 4/CE

By cross multiplying,

2 * CE = 5 * 4

2CE = 20

CE = 20/2

CE = 10

Part A:

Let:

T(h)= Total Number of bacterias as a function of time

h = Number of hours

B = Initial number of bacterias

Since the number of bacteria increases by 25 every hour, we can defined the equation as:

Part B:

B = 5

h = 6

Evaluate the previous equation for those values:

there will be 155 baterias after 6 hours

Part C

Let's graph the equation: