during a lunch seminar chocolate caramel and strawberry toppings were available how many two-topping

Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.

The equation of two-degree polynomial having one variable is called quadratic equation.

The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.

given equation, x² = 6x -10

                x²-6x +10 =0

This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.

we know that standard form of a quadratic equation is given by

ax² + bx +c = 0

where a is the coefficient of x², b is the coefficient of x and c is the constant.

the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a

Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1

                                                                     x = 6 ± √ (36 -40) / 2

                                                                x = 6 ± √-4 / 2

                                                   as        √-4 = √-1 ×2

                                                            x = 6 ± 2 √-1 /2  

                                        divide both numerator and denominator by 2

                                              x = 3± i     as √-1 = i

this is the solution in (a + bi) form a = 3 and b = 1

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The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

Answer:

(-9,0)  and (1,0)

Step-by-step explanation:

The coeficient of x^3+y^4 in the algebraic expression is the number 2

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

2x^3+ 2y^4

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.

2 is the coefficient of x^3+y^4

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Answer:

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

The width of the space for computer stations is:

Each computer station has a space of:

On applying the midpoint theorem the values of x, y, and z are 2, 10 and 8 respectively.

What is the mid-point theorem?

According to the midpoint theorem, the line segment connecting any two triangle sides' midpoints is parallel to and equal to half of the third side.

The outer triangle is ABC and the inner triangle is DEF.

It can be seen that sides AB, BC and AC are equally divided such that AD=DB,

BE=EC and

CF=FA.

So, this proves that point D, E and F are the middle points of AB, BC and AC respectively.

Now, according to the midpoint theorem -

DF = 1/2(BC)

Plugging in the values -

x = (5x-6)/2

2x = 5x-6

2x-5x = -6

-3x = -6

x = 2

Now, for side DE -

DE = 1/2(AC)

Plugging in the values -

12 = (2z+8)/2

24 = 2z+8

24-8 = 2z

16 = 2z

z = 8

Now, for side EF -

EF = 1/2(AB)

Plugging in the values -

y = 20/2

y = 10

Therefore, the values obtained are x=2, y=10 and z=8.

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Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer: 102.4

Given ratio 5:8

Let's assume the answer to be x

5÷8 should be equal to 64÷x

∴ x= (64×8) ÷ 5

=102.4

The number that has the same ratio to 64 as 5:8 is gotten as; 40

How to Calculate Ratio?

We have the ratio 5:8.

Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;

x/64 = 5/8

Cross multiply to get;

x = 64 * 5/8

x = 40

Answer:

[tex](x,y)\rightarrow(0,2)[/tex]

Step-by-step explanation:

[tex]\displaystyle \left \{ {{x+y=2} \atop {y-x=2}} \right.\\[/tex]

Combine system of equations on both sides:

[tex](x+y)+(y-x)=2+2\\2y=4\\y=2[/tex]

Thus,

[tex]x+y=2\\x+2=2\\x=0[/tex]

(x, y) <=>(0, 2)

Step-by-step explanation:

[tex]x + y = 2 \\ y - x = 2 \\ \\ x + (x + 2) = 2 \\ y = x + 2 \\ \\ 2x + 2 - 2 = 2 - 2 \\ y = x + 2 \\ \\ 2x = 0 \\ y = x + 2 \\ \\ x = 0 \div 2 \\ y = x + 2 \\ \\ x = 0 \\ y = 0 + 2 \\ \\ x = 0 \\ y = 2[/tex]

Elimination is a method used to solve systems of linear equations with two or more variables. One possible method to solve a equation with 3 variables using elimination is solving algebraically.

To use elimination to solve a system of equations with three variables, you can follow these steps:

1. Write the system of equations. For example, if you have the equations:

3x + 2y - z = 5

2x - 4y + 2z = 6

5x - 2y + 3z = 10

2. Multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say y in two of the equations.

3. Next, you can multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say x in two of the equations.

4. Now substitute this value of z in the first or the second equation to solve for x

5. Now substitute this value of x and z in the second equation or any other equation to solve for y

This is one possible way to use elimination to solve a system of equations with three variables. Depending on the specific problem, there may be different ways to eliminate variables, but the general idea is to use scalar multiplication and addition or subtraction to create a new equation with one variable having the same coefficient but with opposite signs. One can also use Gaussian elimination or matrix inversion method.

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On solving the provided question we can say that the rectangular form of the equation is y = -1

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Ф = [tex]\pi[/tex]/2

y = - 1

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Answer:

2x + 2

Step-by-step explanation:

Combine all the like terms:

-5x + 7x -12 + 14 = 2x + 2

Answer:

2x + 2

Step-by-step explanation:

(- 5x - 12) + (14 + 7x) ← remove parenthesis

= - 5x - 12 + 14 + 7x ← collect like terms

= (- 5x + 7x) + (- 12 + 14)

= 2x + 2

If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of  inequality is [tex]x > 1[/tex] .

The inequality that Line is solving is [tex]15-x < 14[/tex] ,

the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;

we have to find the value of x for which the given inequality expression is true ,

Case(i) , let us take [tex]x > 1[/tex] ,

So , putting x = 2 , in the inequality ,

we get ; [tex]15-2 < 14[/tex]

= 13 < 14 , that is TRUE .

Case(ii) , let us take [tex]x < 1[/tex] ,

So , putting x  = 0 in the inequality ,

we get ; [tex]15-0 < 14[/tex]

= 15 < 14 , that is FALSE .

Therefore , the solution of the inequality is x > 1 .

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Hassan can paint maximum 11 bookcases with 10 gallons of paint.

A fraction represents a numerical value, which defines the parts of a whole.

Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction.

Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.

Given,

Hassan has 10 gallons of paints.

1 bookcase requires 7/8 gallons of paint

Let Hassan paints x bookcases.

According to the question

7/8x = 10

7x = 80

x = 80/7

x = 11.43

But no. of bookcases should be in whole.

Number of bookcases painted with 10 gallons of paint = 11.

Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint

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Answer:

4[tex]q^{3}[/tex]( q³ + 2)

Step-by-step explanation:

4[tex]q^{6}[/tex] + 8q³ ← factor out 4q³ from each term

= 4q³ (q³ + 2)

Answer:

4q^3(q^3 + 2)

Step-by-step explanation:

The GCF of the exponents is 3, and the GCF of the bases is 4q. So divide both numbers by 4q ^ 3 and get

4q ^ 6 / 4q ^ 3 = q ^ 3

8q ^ 3 / 4q ^ 3 = 2

so you get

4q^3 (q ^ 3 + 2)

Answer:

The answer is 679

Step-by-step explanation:

A significant figure is a number greater than zero so to 3 significant figures just count 3 from the front then round up 9 and it becomes 1 then add it to 8 to become 9 which equals 679

Hope it helps

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The slope of the line on the given coordinate plane is equal to 1.

In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the graph, we have the following data points on the line:

Points on x-axis = (-1, 0).

Points on y-axis = (0, 1).

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (1 - 0)/(0 - (-1))

Slope, m = 1/(0 + 1)

Slope, m = 1/1

Slope, m = 1

In conclusion, we can logically deduce that the slope of this line is equal to 1.

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If point P(2k, k) is equidistant from A(-2, 4) and B (7,-5), the numerical value of k is 3.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

The distance between P(2k, k) and A(-2, 4) is:

d = √((2k - (-2))² + (k - 4)²)

d = √((2k +2)² + (k - 4)²)

The distance between P(2k, k) and B(7, -5) is:

d = √((2k - 7)² + (k - (-5))²)

d = √((2k - 7)² + (k + 5)² )

Since the distances are equal, we can set the two equations for d equal to each other and solve for k.

√((2k +2)² + (k - 4)²) = √((2k - 7)² + (k + 5)² )

Square both sides

(2k +2)² + (k - 4)² = (2k - 7)² + (k + 5)²

(2k +2)² + (k - 4)² = 5k² - 18k + 74

5k² + 20 = 5k² - 18k + 74

Collect like terms

5k² - 5k² + 18k = 74 - 20

18k = 74 - 20

18k = 54

k = 54/18

k = 3

Therefore, the value of k is 3.

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Answer:

x=

y=31

Step-by-step explanation:

hope this helps

A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.

Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.

This means that the supplement of ABC = 82º is given as follows:

180º - 82º = 98º.

Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.

This means that the supplement of ABC = 90º is given as follows:

90º - 32º = 58º.

Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.

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Answer:

[tex]y=\sqrt{10}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]y=\sqrt{(2)(5)}=\sqrt{10}[/tex].

For acceptable x values of √12(x-1)+√√2(x-1)², the option is equivalent to the quotient given here (x-1) ² is [tex]$2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex] .

The equivalent of the quotient displayed above for allowable x values is

[tex]$\sqrt{1} \cdot 2(x-1)+\sqrt{\sqrt{2}}(x-1)^2$[/tex]

[tex]$2(x-1)+\sqrt[2 \cdot 2]{2}(x-1)^2$\\[/tex]

[tex]\$2(x-1)+\sqrt[4]{2}(x-1)^2$\\$(2 x-2)+\sqrt[4]{2}\left(x^2+2 x(-1)+(-1)^2\right)$\\$(2 x-2)+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x-2+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x+\sqrt[4]{2}\left(x^2-2 x+1\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-\sqrt[4]{2} \cdot 2 x+\sqrt[4]{2}\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}\right)-2$\\$2 x+\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}-2$[/tex]

[tex]$f(x)=\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\frac{d}{d x}\left(\sqrt{12(x-1)}-\sqrt{2(x-1)^2}\right)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$[/tex]

[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]

[tex]$\sqrt{12(x-1)}=2 \sqrt{3} \sqrt{x-1}$[/tex]

[tex]$\sqrt{2(x-1)^2}=\sqrt{2}(x-1)$\\$=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex]

Values that might result in a fraction's denominator being equal to zero are excluded. Finding these omitted values is crucial for resolving a rational statement because you cannot divide by 0.

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Step-by-step explanation:

[tex] = {x}^{2} \div {x}^{2} + 3x - 5x + 6 - 10 \\ = 1 - 2x - 4 \\ = - 2x - 4 + 1 \\ = - 2x - 3 \\ = - 1(2x + 3)[/tex]

HI,HOPE THAT IS HELPFUL.

Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

A trader can create their own automated trading strategies in forex by writing a script or program in a programming language, such as MQL4 or Python. This script will contain instructions to execute trades according to specific criteria defined by the trader. They can then backtest the strategy to see how it performs.

1. Decide on a trading strategy. This could include things like setting entry and exit points, calculating position sizes, and setting stop losses and take profits.

2. Choose a programming language that is compatible with the trading platform you are using, such as MQL4 or Python.

3. Write the script or program that will contain the instructions for the trading platform to follow in order to execute the trading strategy.

4. Test the script or program to make sure it works properly.

5. Run a backtest to see how the trading strategy performs.

6. If the results of the backtest are satisfactory, you can deploy the trading strategy on the trading platform.

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The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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expression h-9 is represented as statement 'h decreased by 9'.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".

Given expression

h-9

Here h is a variable, 9 is constant and - is the symbol of subtraction.

the phrase "decreased by" tells us to use subtraction.

Statement for the above expression

h decreased by 9.

Hence, the statement 'h decreased by 9' represents expression h - 9.

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The numerical figures are used to write numbers more than 100.

What is numbers?

An arithmetic value known as a number is used to represent a quantity and perform calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.

To represent numbers greater than 100, use numeral figures; however, whole numbers, such as 300 or 1,000, should be written out.

When representing non-whole numbers like 1,239 or 603, use numerals.

Except for whole numbers combined with hundred, thousand, hundred thousand, million, billion, and beyond, the Chicago Manual of Style advises spelling out numbers from zero to one hundred and using figures after that (e.g., two hundred; twenty-eight thousand; three hundred thousand; one million).

Hence, the numerical figures are used to write numbers more than 100.

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Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

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

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line