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[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+9 \end{array}}[/tex]

Volume of the aquarium is 27 [tex]s^{3}[/tex]

The total number of cubic units that a cube totally fills up is referred to as its volume. An object with six square faces that is three dimensional is called a cube. The amount of space an object takes up in total is known as its volume. Space would be taken up by an object having a larger volume.

Depending on the inputted inputs, many formulas can be used to determine the volume of any cube. You may figure it out by measuring the diagonal of the cube or its sides.

Given that : Carlos bought a cube shaped aquarium with side 3s

As the aquarium have cube shape so the volume will be

Volume of cube is V =[tex]a^{3}[/tex]

a = 3

V = 27 [tex]s^{3}[/tex]

Hence ,Volume of the aquarium is 27 [tex]s^{3}[/tex]

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Answer:

x=12

Step-by-step explanation:

The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.

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Explanation:

Let's go over an example. We'll have these two sets

A = {1,2}

B = {3,4}

The cartesian product is this set of ordered pairs

A x B= {(1,3), (1,4), (2,3), (2,4)}

Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.

If we swap the order of set A and B then we have

B x A = {(3,1), (4,1), (3,2), (4,2)}

We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.

Side note: Two sets are equal when they are subsets of each other.

The answer as a simplified fraction in the box is -1/6

Given the expression

[3-|-5/6 -2(-1/3)|] ÷ (-17)

Using PEDMAS

P is for parenthesis

[3-|-5/6+2/3)|] ÷ (-17)

[3-|2/3 - 5/6)|] ÷ (-17)

[3-|(4-5)/6)|] ÷ (-17)

[3-|-1/6)|] ÷ (-17)

Since the modulus of a negative number is equal to a positive number, the result will give:

[3 - 1/6] ÷ (-17)

[(18-1)/6] ÷ (-17)

17/6  ÷ (-17)

Next is to carry out the division operation

17/6  × (-1/17)

= -1/6

Hence, The answer as a simplified fraction in the box is -1/6

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Answer:

44.38%

Step-by-step explanation:

Becuase of 365 days a year, 162 out of 365 is 44.38% meaning that if he would selwcted a fay the probability would be 44.38% chance.

Answer:

43

Step-by-step explanation:

From the graph we can conclude:

The function is increasing for the following interval:

Answer:

(-∞,0), (2,∞)

Answer: B

Step-by-step explanation: i got it because i

SOLUTION

The image below will help in answering the following questions

Now, from the graph, the parts above the horizontal line represents profit, while the part below the horizontal line represents loss.

(a) Maximum profits are earned when there are 4 clerks working.

From the graph, we can see that this statement is CORRECT. The maximum profit is at 400 thousand dollars and takes place at 4 on the horizontal axis, this 4 represents 4 clerks working

(b) The store earns profits when no clerks are working.

No clerks are working when we consider 0 on the horizontal plane. From the picture above, tracing 0, it shows us something below the horizontal line which represents loss. So, this statement is INCORRECT. When no clerks work, there is a loss not profit

(c) Maximum profits are earned when there are 7 clerks working.

Tracing 7 from the graph, it doesn't fall on the top part of the curve which indicates maximum profit. Hence, this statement is INCORRECT.

d) The store earns about $400,000 in profits on its best days.

From the image above, we can see that this is correct.

(e) The store loses money when 8 or more clerks are working.

When we traced 8 from the horizontal line, it fell to the part of the graph which indicated loss.

Hence this is CORRECTstatement .

So you will select the 1st, 4th and 5th options

Answer:  9 boys

Reason:

The multiples of 13 are

13, 26, 39, 52, ...

We only need to focus on the first two since they are smaller than 35

So we focus on 13 and 26

The second option has more girls than boys, so that must mean there are 26 girls and 9 boys.

Answer:

2x (2x³ + 1)

Step-by-step explanation:

To get the answer factor 2x^1 / 2x of ( 4x^4 + 2x )

When you factor an expression, you are looking for a number which can perfectly divide into another number.

Remember that the numerical timetable states that (2 x 2 = 4).

And we already know that (2 divided by 4 = 2), as well as, that any rational number divided by itself is equal to 1

Therefore the value 2x is divisible by itself and is also divisible by 4x^4 exactly two times

Note: the reason why (4x^4 ÷ 2x ) becomes (2x³), is that you have to subtract the exponents of each term from each other after you finish dividing.  So ( X^4 - X^1 = X^3) -

Always remember that any term in a polynomial expression which doesn't have a visible power attached to it is already at the first power

Find the number line that dotted only the numbers 5,- 2, 1, -4, which is clearly the last option.

SOLUTION:

Case: Circle equations

Metho:

Given:

Final answer:

Center (-11, 6)

radius, r= 3

The ratio of the simplest form of 2 nickels to 1 quarter is 2:5.

For the given question;

The two monetary values are given as;

2 nickles and 1 quarter.

We know that;

1 nickles = 0.2 quarter.

For 2 nickles multiply both side by 2.

2 nickles = 2×0.2 quarter.

2 nickles = 0.4 quarter.

Find the ratio;

2 nickels to that of 1 quarter

2 nickels/ 1 quarter

Put the value of 2 nickle.

2 nickels/ 1 quarter = 0.4 quarter/1 quarter

2 nickels/ 1 quarter = 2/5

2 nickels: 1 quarter = 2:5

Thus, the ratio of 2 nickels to that of 1 quarter is found as 2:5.

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Answer:

56

Step-by-step explanation:

[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]

Answer:

12 and 8; 16 and 6; 24 and 4

Step-by-step explanation:

Answer:

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

Convert the mixed fractions into decimal and find the sum as follows:

Answer: x=4

Step-by-step explanation:

First find the smallest x which would be 5x and subtract that from the 9x. So now it should be 4x-4=12. Then, move 4 and add that to the twelve which should now be 4x=16. Then, divide it by four and you get x=4.

Answer:

x = 4

Step-by-step explanation:

We start from

9x - 4 = 5x + 12

We move the "5x" to the left side of the "=" sign by changing it's sign from 5x which can be seen as +5x to -5x

9x - 4 - 5x = 12

Now we move the "4" to the right side of the "=" sign by applying the same principle as above, so -4 turns to +4

9x - 5x = 12 + 4

We than solve the subtraction and addition

4x = 16

Then we divide both sides of the equation by 4 and we get

x = 4

The length of one side of the poster, when the area of a square poster is 31 square inches is

Part A = 6 inch (To the nearest whole of an inch)

Part B = 5.6 Inch (To the nearest tenth of an inch)

As given in the question,

Area of square poster = 31 sq. inches

Let 'l' be the length of the square poster

Now according to formula

Area of square poster = Length * Length

Substitute the values in the formula we get,

31 = l × l

⇒ l² = 31

⇒ l = √31

⇒ l = 5.568

Length = 5.568

Hence, the length of one side of the poster, when the area of a square poster is 31 square inches is

Part A = 6 inch (To the nearest whole of an inch)

Part B = 5.6 Inch (To the nearest tenth of an inch)

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Answer:

1.50/3 Apples=0.5

That means each apple cost 0.5. If it's in rands gonna be R0.5 or 50 Cents per apple.

y4 - 9y3 +4

Step-by-step explanation:

solo tienes que ordenarlo de mayor a menor de las variables

The number of ways in which three digits can be written is 720 ways.

The number of ways in which 3 letters can be written is 15600.

From the information, the subject identification numbers in a certain scientific research project consist of two digits followed by four letters and then two more digits.

The ways in which three digits can be written will be:.

= 10P 3

= 10! / (10-3)!

= 10 × 9 × 8

= 720 ways

The number of ways in which 3 letters can be written will be:

= 26P3

= 26! / ( 26 - 3)!

= 26! / 23!

= 26 × 25 × 24

= 15600

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When the polynomial is divided by the linear expression we get the quotient k² -5k +8 and the remainder -8.

Polynomials are used in many areas of mathematics. For example, they are used in arithmetic and mathematical methods to approximate other functions. They are also used to describe linear combinations, which are encountered in a variety of situations, from basic physics and biology to economics and science.

From straightforward word problems to intricate scientific conundrums, polynomial equations are utilised to represent a wide range of topics. Algebraic varieties and polynomial rings, two essential concepts in algebra and computational geometry, are constructed in mathematics using harmonics.

The simplest way to do the long division is:

[tex]\begin{array}{r}k^2-5k+8\phantom{)} \\x+5{\overline{\smash{\big)}\,k^3-17k+32\phantom{)}}}\\\underline{-~\phantom{(}(k^3+5k^2)\phantom{-b)}}\\-5k^2-17k+32\phantom{)}\\\underline{-~\phantom{()}(-5k^2-25k+40)}\\ -8\phantom{)}\end{array}[/tex]

Hence the division will give quotient quotient k² -5k +8 and the remainder -8.

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Answer:

????

Step-by-step explanation:

The answer to the given question is option A that is only the first equation is an identity.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

Sin θ = 1/Csc θ or Csc θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ

RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ

Thus LHS = RHS and it is given above so 1st equation is an identity.

2) LHS:  11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ

and RHS : 11 cosec^2 θ

since LHS ≠ RHS because the second equation us not an identity.

thus the correct option is A that is Only the first equation is an identity.

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The value of the variable 'A' which is a consecutive digit in the card is: 6

What is consecutive digits?

In mathematics, the consecutive digits are those digits whose difference between the two terms are constant. And the pattern of the terms should be continuous. It is used for the calculation based problems.

According to the question, the given data states that the 14 digits of a credit card has sum of the three consecutive digits is 18.

Therefore, at the end the blank box between 8 and 4 can be written as:

8 + m + 4 = 18 ⇒ m = 18 - 12 = 6 ⇒ m =6

Now, the pattern for the last three digits be: 864.

The pattern is repeating and the whole IN  number is 64864864864864.

Hence, the value of the variable 'A' which is a consecutive digit in the card is: 6

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