The base of a regular pyramid is a hexagon.

Answer:

1. [tex]\bold{S=f(P) = 0.07P}[/tex]

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be [tex]P[/tex].

And sales tax be [tex]S[/tex].

As per the given statement:

[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]

Writing it in the function notation:

[tex]\bold{S=f(P) = 0.07P}[/tex]

2. To find the value of x such that [tex]f(x) = 14[/tex] and

[tex]f(x) = \dfrac{1}4x + 10[/tex]

Putting the value of [tex]f(x) = 14[/tex]

[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

[tex]\bold{S=f(P) = 0.07P}[/tex]

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

[tex]y=f(x) = \dfrac{1}4x + 10[/tex]

x is the independent variable and y is the dependent variable.

Answer:

2 pi

Step-by-step explanation:

The radius is 2

The area of a circle is

A = pi r^2

We have 1/2 of a circle so

1/2 A = 1/2 pi r^2

         =1/2 pi ( 2)^2

         =1/2 pi *4

      = 2 pi

Answer:

4,500 Codes

Step-by-step explanation:

Given that, the access code consists of 4 digits.

Since, the First digit cannot be zero, and the last digit has to be even.

Therefore, Locks can only use numbers (0-9), which means the first digit has 9 possible outcomes ( 1-9),

the 2nd has 10 possible outcomes (0-10),

the same with the 3rd (0-10) and

finally the 4th has only 5 possible outcomes (0,2,4,6,8),

which we assume that zero is not excluded.

Finally, Mulitply 9 x 10 x 10 x 5 = 4,500.

Answer:

Step-by-step explanation:

to solve an equation by completing the square in a quadratic formula

f(x)=ax²+bx+c

example :x²-6x-16=0

first rearrange if necessary, move the constant to one side .

x²-6x=16

second you find a new term to complete the square which is (b/2)², and add the term to both sides.(6/2)²=3²=9

x²-6x+9=16+9

x²-6x+9=25

third  factorize : find the common factor between 6 and 9 which is 3

x²-6x+9=25

(x-3)²=25

last solve for x: (x-3)²=25

x-3=√25

x=3±5

x=3+5=8 or 3-5=-2

Answer: 1320; 495

Step-by-step explanation:

Explanation is in the attachment file

Answer: 75 u²

Step-by-step explanation:

1/2(5)((14)+(16))

Add in parenthesis

1/2(5)(30)

Multiply

1/2(150)

Multiply

75

Hope it helps <3

Answer:

135.5

hope this helps :)

Answer:

9 pencils

Step-by-step explanation:

Answer:

'll tell you where the problem lies - it is IMPOSSIBLE to form triangles like this.

If the perimeter of the smallest triangle is 6 and one side is 3, then the sum of the other two sides can only be 6 - 3 = 3

One property to enable you to form a triangle is that NO ONE SIDE can be greater or equal to the sum of the other two sides. In the smallest triangle 1 side of length 3 equals the other two sides.

In the middle triangle one side of length "4" equals the sum of the other two sides and

In the large triangle one side of length "5" equals the other two sides.

Therefore when I say "triangle" above I am not actually correct because it is IMPOSSIBLE to form triangles with those dimensions of 1 side and with those perimeters

Answer:

nine added to seven times a number.

Step-by-step explanation:

''x'' is the unknown number which is being multiplied by 7. Than 9 is added to it.

Answer:

M(2, −4), N(−2, 4)

Step-by-step explanation:

Transformation is the movement of a point from one place to another. If an object is transformed, all the points of the object are being changed. There are different types of transformation which are: Reflection, rotation, translation  and dilation.

Reflection of a point is the flipping of a point. If a point A(x, y) is reflected across the x axis, the new point is A'(x, -y). If a point B(x, y) is reflected across the y axis, the new point is A'(-x, y).

The coordinates of point L on a coordinate grid are (−2, −4), if Point L is reflected across the y-axis to obtain point M, the coordinates of M is at (2, -4).

if Point L is reflected across the x-axis to obtain point N, the coordinates of N is at (-2, 4).

Answer: M(2, −4), N(−2, 4) So D can i get branliest

Step-by-step explanation:

Answer:

The correct option is;

B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy

Step-by-step explanation:

The given requirements are;

Volume of air and water to be filtered by the robot = 343 liters

The amount of energy consumed by the robot < 49 joules

The number of minutes the robot filters air and water to filter more than 343 liters = 12A + 8W > 343

The number of minutes the robot filters air and with less than 49 Joule of energy = 3A + 4W < 49

Given that filtering air takes 20 minutes, filtering water takes 15 minutes, we have;

To filter more than 343 liters, we have

12*20 + 8*15 = 360 > 343

The robot meets the amount of air and water requirement

To filter with less than 49 joules we have

3*20 + 4*15 = 120 > 49

Therefore, the robot does not meet the energy requirement

The correct option is the robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.

Answer:

After 32 minutes the two pools will have the same amount of water.

There will be 1,366 liters in each pool when they have the same amount of water.

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

The first pool contains 720 liters of water, and it’s being added at a rate of 19.25 liters per minute.

First Pool = 720 +19.25 m

Where m is the number of minutes.

The second pool is empty, and Water is being added at a rate of 41.75 liters per minute

Second pool = 41.75m

Since both pools must have the same amount of water:

720 +19.25 m = 41.75m

Solving for m:

720 = 41.75m-19.25 m

720 = 22.5m

720/22.5 = m

32 = m

After 32 minutes the two pools will have the same amount of water.

Finally, we replace m=32 on any equation:

41.75m = 41.75 (32) = 1,336 liters

There will be 1,366 liters in each pool when they have the same amount of water.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

The probability that the first card is a Heart and the second card is a Spade is 0.064.

Step-by-step explanation:

A standard deck of 52 cards is shuffled and two cards are drawn without replacement.

The denominations of the cards are as follows:

Spades (S) = 13

Hearts (H) = 13

Diamonds (D) = 13

Clubs (C) = 13

Compute the probability of selecting a Heart first as follows:

[tex]P(H)=\frac{13}{52}=0.25[/tex]

Compute the probability of selecting a Spade second as follows:

[tex]P(S)=\frac{13}{51}=0.255[/tex]

Since the two cards are selected without replacement the second draw is independent of the other.

Then the probability that the first card is a Heart and the second card is a Spade is:

[tex]P(1st\ H\cap 2nd\ S)=P(H)\times P(S)[/tex]

                            [tex]=0.25\times 0.255\\=0.06375\\\approx 0.064[/tex]

Thus, the probability that the first card is a Heart and the second card is a Spade is 0.064.

Answer:

1/6

Step-by-step explanation:

using this formula

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

You get 0.1666666666666666666666666666666666666666

which is 1/6

Hope this helped, if it did, please consider giving me brainliest it will help me a lot

Have a good day! :)

k = b + 13

k - 19 = b - 6

k = b + 19 - 6

k = b + 13

Answer:

[tex]\boxed{k=b+13}[/tex]

Step-by-step explanation:

[tex]k-19=b-6[/tex]

Add 19 on both sides.

[tex]k-19+19=b-6+19[/tex]

[tex]k=b+13[/tex]

Answer:

C

Step-by-step explanation:

Answer:

La máquina llenó:

6 baldes

Step-by-step explanation:

Por regla de tres:

4 baldes son a 30 minutos

M baldes son a 45 minutos

M = 45*4/30

M = 180/30

M = 6

Step-by-step explanation:

[tex]A[/tex]- all of the chosen balls are white [tex]E_{i}-[/tex] result of the die roll is [tex]i, \quad i \in\{1,2,3,4,5,6\}[/tex]

Probabilities:

since the die is fair:

[tex] P\left(E_{i}\right)=\frac{1}{6} \quad \text { for } \quad i \in\{1,2,3,4,5,6\} [/tex]

If the die rolls [tex]i[/tex] we choose a combination of [tex]i[/tex] balls, among 10 black and five white balls, therefore

\[ \begin{array}{c}

P\left(A \mid E_{1}\right)=\frac{\left(\begin{array}{c} 5 \\

1 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 1 \end{array}\right)}=\frac{5}{15}=\frac{1}{3} \\ P\left(A \mid E_{2}\right)=\frac{\left(\begin{array}{c} 5 \\ 2 \end{array}\right)}{\left(\begin{array}{c} 15 \\ 2

\end{array}\right)}=\frac{10}{105}=\frac{2}{21} \\

P\left(A \mid E_{3}\right)=\frac{\left(\begin{array}{c} 5 \\ 3

\end{array}\right)}{\left(\begin{array}{c} 15 \\ 3

\end{array}\right)}=\frac{10}{455}=\frac{2}{91} \\

P\left(A \mid E_{4}\right)=\frac{\left(\begin{array}{c} 5 \\ 4

\end{array}\right)}{\left(\begin{array}{c} 15 \\ 4

\end{array}\right)}=\frac{1}{273} \\

P\left(A \mid E_{5}\right)=\frac{\left(\begin{array}{c} 5 \\ 5

\end{array}\right)}{\left(\begin{array}{c} 15 \\ 5

\end{array}\right)}=\frac{1}{3003} \\

P\left(A \mid E_{6}\right)=\frac{\left(\begin{array}{c} 5 \\ 6

\end{array}\right)}{\left(\begin{array}{c} 15 \\ 6

\end{array}\right)}=0

\end{array} \]

Answer:

See explanation

Step-by-step explanation:

if multiply the 3 factors together you get

(x² - x - 2)(x - 3) - trinomial x binomial

x³ - 3x²- x² + 3x - 2x + 6 - polynomial

x³ - 4x² + x + 6, this is the polynomial with those factors.

Poly means many so it could be a bigger polynomial with more factors but if it is limited to only these factors than there is just the one polynomial.

The polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3)

A polynomial is the defined as mathematical expression that have a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 12 -2 = 10

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

Given that ,

P(x) has three factors (x-2), (x+1), and (x-3).

Multiplying the 3 factors together, we get

⇒ (x-2)(x+1)(x-3)

⇒ [x(x-3) - 2(x+1)](x-3)

⇒ (x² - x - 2)(x - 3)

⇒ x³ - 3x²- x² + 3x - 2x + 6

Rearrange the terms likewise and apply arithmetic operations

⇒ x³ - 4x² + x + 6

Hence, the polynomial is x³ - 4x² + x + 6 with factors (x-2), (x+1), and (x-3).

Learn more about polynomial here:

https://brainly.com/question/11536910

#SPJ2

Answer:

Option (4) and Option (5)

Step-by-step explanation:

By calculating the second difference, if the second difference in a table is equal, table will represent the quadratic relationship.

In the given option, we analyze that table given in Option (4) will represent the quadratic relationship.

x             y             Ist difference [tex](y_2-y_1)[/tex]         IInd difference

0            4                      -                                             -

1            -4             -4 - (4) = -8                                     -    

2           -4             -4 - (-4) = 0                              0 - (-8) = 8

3            4              4 - (-4) = 8                                  8 - 0 = 8

Second difference of the terms in y are the same as 8.

Therefore, table of Option (4) represents the quadratic relationship.

Similarly, in Option (5) we will calculate the second difference of y terms.

x            y            Ist difference     IInd difference

0          -4                    -                            -

1           -8             -8 - (-4) = -4                 -

2          -10           -10 - (-8) = -2        -2 - (-4) = 2      

3          -10           -10 - (-10) = 0        0 - (-2) = 2

Here the second difference is same as 2.

Therefore, table of Option (5) will represent the quadratic relationship.

Answer:

Option 5 is wrong

Step-by-step explanation:

Answer:

a) Multiplica la variable independiente por -7 y luego resta 7

Step-by-step explanation:

Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:

1) Multiplica la variable por 7.

2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).

3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.

Por ende, la opción correcta es a).

Answer:

4x² -14x - 8

Step-by-step explanation:

(2x - 5)² + 3(2x-5) - 18

Expand brackets.

(2x-5)(2x-5) + 6x -15 - 18

2x(2x-5)-5(2x-5) + 6x - 33

4x² - 10x - 10x + 25 + 6x - 33

Combine like terms.

4x² -14x - 8

Answer:

4x^2 -14x -8

Step-by-step explanation:

( 2x-5)^2 + 3( 2x-5) -18

Foil

(2x-5)(2x-5) = 4x^2 -10x-10x +25 = 4x^2 -20x+25

Distribute

3( 2x-5) = 6x -15

( 2x-5)^2 + 3( 2x-5) -18

Replace with the foil and distribute

4x^2 -20x+25 +6x -15 - 18

Combine like terms

4x^2 -14x -8

Answer:

d) -3

Step-by-step explanation:

The equation of a parabola in vertex form is given as:

y = a(x - h)² + k. Where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (4,-3) i.e h = 4 and k = -3.

The equation of the parabola is given as:

y = a(x - 4)² + (-3)

y = a(x² - 8x + 16) - 3

y = ax² - 8ax + 16a - 3

Given that when x = 5, y = -6. i.e:

-6 = a(5)² - 8a(5) + 16a - 3

- 6 = 25a - 40a + 16a - 3

-6 + 3 = a

a = -3

Answer:

Step-by-step explanation:

A term, loosely defined, is a product of numbers and variables. Terms are separated from one another with a + or a - sign. So we have 2 terms here.

The degree of the polynomial, because it is just in terms of x and no other variable, is the highest degree'd term.  Our highest degree of x is 3, so this is a third degree polynomial.

It is classified by its number of terms:

1 term is a monomial, 2 terms is a binomial, 3 is a trinomial, and anything higher is just called a "polynomial". This has 2 terms so it is a binomial.

The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Now, [tex]\sf{14x^3+x^2}[/tex] has 2 terms so it's a binomial; the highest exponent is 3.

Answer:

The error was made when they factored out the i, so this would be the distributive property they did not do correctly.

Factoring out the i was never needed.

Answer:

She shouldn't have factored out the i.

Step-by-step explanation:

In both parentheses, only one of the two additives had an "i" in it, so only one of them could have i factored out of it. If she wanted to factor out the i, the equation would look like this:

(4/i + 5)i + (-3/i + 7)i.

If anything, she should have done:

5i+7i + 4-3=

12i + 1.

Factoring out the i was unnecessary.

Hope this helps!

Answer:

Step-by-step explanation:

cosine law

a²=b²+c²-2(bc)cos44  (c=20, b=15)

a²=15²+20²-2(15*20)cos44

a=√15²+20²-2(15*20)cos44

a=13.91

Answer:

Katie is correct. You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80

Step-by-step explanation:

Answer:

The solution is

Step-by-step explanation:

x - 3y = 6 ............ Equation 1

2x + 2y = 4 ............ Equation 2

Make x the subject in equation 1 and substitute it into equation 2

That's

x = 6 + 3y

2( 6 + 3y ) + 2y = 4

Expand and simplify

12 + 6y + 2y = 4

8y = - 8

Divide both sides by 8

y = - 1

Substitute y = - 1 into x = 6 + 3y

That's

x = 6 + 3(-1)

x = 6 - 3

x = 3

x = 3 y = - 1

( 3 , - 1)

Hope this helps you

Answer:

B. ( 3 , - 1)  

Step-by-step explanation:

x - 3y = 6 Equation 1

2x + 2y = 4  Equation 2

x = 6 + 3y

2( 6 + 3y ) + 2y = 4

12 + 6y + 2y = 4

8y = - 8

y = - 1

x = 6 + 3(-1)

x = 6 - 3

x = 3

x = 3 y = - 1

( 3 , - 1)

Answer:

[tex]\boxed{-i}[/tex]

Step-by-step explanation:

[tex]-i^5[/tex]

Use identity : [tex]i^5 =i[/tex]

[tex]-(i)[/tex]