the value of y varies directly with x. if y = 20 and x = 30, what is the value of y if x = 1?
A. 200
B. 2/3
C. 110/3
D. 9/2

Answer:

x = 3 ± 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

x² - 6x = 15

to complete the square on the left side

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 15 + 9

(x - 3)² = 24 ( take square root of both sides )

x - 3 = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± ([tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] ) = ± 2[tex]\sqrt{6}[/tex]

add 3 to both sides

x = 3 ± 2[tex]\sqrt{6}[/tex]

then

x = 3 - 2[tex]\sqrt{6}[/tex] , x = 3 + 2[tex]\sqrt{6}[/tex]

Answer: the answer for the second is b^x= bxb^y and b^y= b^6xb^x

For the first the answer is b^x=b^3/b^y and b^y= b^3/b^x

Step-by-step explanation: First we must get the x or the y alone. When completing this I believe you have to take into account the exponent rules if you're trying to simplify it fully.

An expression to represent the perimeter is P = 2m + 2(m² + 11m + 28)/m

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We are given that;

The expression m² + 11m + 28

Now,

Let's assume that the length of the rectangle is "m" and the width is "n".

The formula for the area of a rectangle is A = l × w. We are given that the area of the rectangle is m² + 11m + 28, so we can write:

A = m² + 11m + 28

Substituting the formula for the area, we get:

m² + 11m + 28 = m × n

We can rearrange this equation to solve for n:

n = (m² + 11m + 28) / m

The perimeter of a rectangle is given by the formula P = 2(l + w). Substituting the values of l and w, we get:

P = 2(m + n)

Substituting the value of n, we get:

P = 2(m + (m² + 11m + 28) / m)

P = 2m + 2(m² + 11m + 28) / m

Therefore, by the given area of rectangle perimeter will be 2m + 2(m² + 11m + 28) / m

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The factorizations of the following are x²+3x-4 = (x+4)(x-1),x²-2x-3 = (x-3)(x+1) and x²+2x-8 = (x+4)(x-2).

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]betab = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

We are given that;

a) x²+3x-4

b) x²-2x-3

c) x²+2x-8

Now,

a) To factorise x²+3x-4, we need to find two numbers whose product is -4 and whose sum is 3. Those numbers are 4 and -1, so we can write:

x²+3x-4 = (x+4)(x-1)

b) To factorise x²-2x-3, we need to find two numbers whose product is -3 and whose sum is -2. Those numbers are -3 and 1, so we can write:

x²-2x-3 = (x-3)(x+1)

c) To factorise x²+2x-8, we need to find two numbers whose product is -8 and whose sum is 2. Those numbers are 4 and -2, so we can write:

x²+2x-8 = (x+4)(x-2)

Therefore, by factorization the answers will be x²+3x-4 = (x+4)(x-1),x²-2x-3 = (x-3)(x+1) and x²+2x-8 = (x+4)(x-2).

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when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

[tex]\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}[/tex]

Hope this helps : -)

- Jeron

Formula a = (v = 2 * pi * r / t)

Formula b = (v2 = g * m_central / r)

The scenario in context to formula a and formula b is given below:

Formula a = (v = 2 * pi * r / t)

It is used to calculate the velocity (v) of a circular object moving with a constant speed around a circle of radius (r) in time (t).

Example scenario: if you want to find the velocity of a moving object in a circular path, use formula a.

Suppose you want to find the velocity of a car moving in a circular path on a race track. The radius of the track is "r" and the time taken for the car to complete one lap is "t".

Using the equation (v = 2 * pi * r / t), we can calculate the velocity as follows:

Let's say the radius of the track is 100 meters and the time taken for the car to complete one lap is 60 seconds. Then, the velocity can be calculated as follows:

v = 2 * pi * (100 m) / (60 s)

v = 31.42 m/s

So, the velocity of the car moving in a circular path on the race track is 31.42 m/s.

Formula b = (v2 = g * m_central / r)

It is used to calculate the velocity squared (v^2) of an object moving under the influence of a central force (g * m_central) and is related to the radius (r) of its orbit.

Example scenario: If you want to find the velocity squared of an object under the influence of a central force, use formula b.

Suppose you want to find the velocity squared of a planet moving in a circular orbit around a star (a central force). The mass of the star is "m_central" and the distance of the planet from the star is "r".

Using the equation (v²  = g * m_central / r), we can calculate the velocity squared as follows:

v² = (6.67 x 10^-11 N m² /kg² ) * (m_central) / (r)

Let's say the mass of the star is 2 x 10^30 kg and the distance of the planet from the star is 1.5 x 10^11 m.

Then, the velocity squared can be calculated as follows:

v²  = (6.67 x 10^-11 N m² /kg² ) * (2 x 10^30 kg) / (1.5 x 10^11 m)

v²  = 2.22 x 10^20 m² /s²

So, the velocity squared of the planet moving in a circular orbit around the star is 2.22 x 10^20 m² /s² .

At, last we can say if you want to find the velocity of a moving object in a circular path, use formula a. If you want to find the velocity squared of an object under the influence of a central force, use formula b.

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The box plot that represents the data-set is given as follows:

Option C.

From left to right, the five features of the box and whisker plot are listed as follows

The minimum and maximum values are given as follows:

The median is of 34 concerts for each (middle value of the ordered data-sets), hence the plot is given by option C.

The quartiles are the mean of each half of the ordered data-sets.

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In a right angled triangle, the angles are given by the fοrmula:

Angle A + Angle B + Angle C = 180°Therefοre, x° = 131°.

Angle is a geοmetrical figure fοrmed by twο rays with a cοmmοn endpοint. It is measured in degrees οr radians and is used tο describe the amοunt οf turn between twο lines. It can alsο be used tο measure the size οf an angle in a triangle, the amοunt οf rοtatiοn οf a 3D οbject, and mοre. Angles are impοrtant in bοth mathematics and science as they're used tο calculate the amοunt οf fοrce needed tο mοve an οbject οr the amοunt οf energy needed tο keep an οbject in mοtiοn.

In a right angled triangle, the angles are given by the fοrmula:

Angle A + Angle B + Angle C = 180°

Given that FHG = 49°, we can calculate the οther angles:

Angle A = 180° - 49° = 131°

Angle B = 180° - 131° - 49° = 0°

Angle C = 180° - 131° - 0° = 49°

Therefοre, x° = 131°.

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The intersection of the labor supply and demand curves determines the equilibrium wage rate and quantity of labor.

The labor supply and demand curves are used to analyze the market of labor, where the demand is the amount of labor that employers are willing to hire at a given wage, and the supply is the amount of labor that individuals are willing to supply at a given wage. The labor supply curve is upward sloping and shows the quantity of labor supplied at different wages. Mathematically, this is represented as the equation: Qs = a + bw, where Qs is the quantity of labor supplied, a is a constant, b is the elasticity of labor supply, and w is the wage. The labor demand curve is downward sloping and shows the quantity of labor demanded at different wages. Mathematically, this is represented as the equation: Qd = c – dw, where Qd is the quantity of labor demanded, c is a constant, d is the elasticity of labor demand, and w is the wage. The intersection of the labor supply and demand curves determines the equilibrium wage rate and quantity of labor.

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The equation of the perpendicular bisector that goes through a segment with endpoints (2,1) and (6, -3) is y = x - 5.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

An equation of the line that passes through the points (2,1) and (6, -3) is,

y - 1 = (-3 - 1)/(6 - 2)(x - 2)

y - 1 = -1(x - 2)

y - 1 = -x + 2

y = -x + 3

The slope of the perpendicular bisector that goes through the line y = -x + 3 is,

= -(1/-1)

= 1

And the required line passes through (2 + 6/2, 1-3/2) = (4, -1) and have slope 1,

So, the equation of the line is,

y + 1 = 1(x - 4)

y = x - 5

Therefore, the equation is y = x - 5.

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By using the method of Normal Distribution, Marques made 4 three point shots and 4 free throws.

Let's denote the number of three point shots that Marques made as x and the number of free throws he made as y.

According to the problem, Marques made a total of 8 shots, so we have:

x + y = 8

And he scored a total of 12 points, which can be expressed as:

3x + y = 12

We now have a system of two equations with two unknowns:

x + y = 8

3x + y = 12

We can solve this system by either substitution or elimination. Here, we'll use the elimination method.

Multiplying the first equation by 3, we get:

3x + 3y = 24

Subtracting the second equation from this, we get:

2y = 12 - 3x

Dividing by 2, we get:

y = 6 - (3/2)x

We can substitute this expression for y into the first equation:

x + (6 - (3/2)x) = 8

Simplifying, we get:

(1/2)x = 2

x = 4

So Marques made 4 three point shots. We can substitute this value into either of the original equations to find y:

4 + y = 8

y = 4

So Marques made 4 free throws.

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Answer:

CFGGFF

Step-by-step explanation:

CGDF

Answer:

number of glasses he bought = 60

Step-by-step explanation:

Let the variable x represent the number of glasses he bought

Total cost of x glasses at Rs. 12 each = 12x

5 glasses broke so remaining number of glasses = x- 5

He sold this quantity of glasses for Rs. 16 each

Total sale price of (x - 5) glasses = 16(x - 5)

Total profit = Total sales - Total cost = 160

=> 16(x - 5) - 12x = 16

Expand brackets for 16(x - 5): 16x - 16 x 5 = 16x - 80

Therefore we get

16x - 80- 12x = 160

4x - 80 = 160

Add 80 on both sides:

4x -80 + 80  = 160 + 80

4x = 240

x = 240/4 = 60

The value of (gof)(-7) is 3√6.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x) = x² + 6 and g(x)=√x-1

We need to find the value of  (gof)(-7).

Let (gof)=g(f(-7))

=g( (-7)² + 6)

=g( 49 + 6)

=g(55)

=√55-1=√54

=√9×6

=3√6

Hence, the value of (gof)(-7) is 3√6.

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The requried, for a user who uses 4 gigabytes of data in a month, the plan from Company C would be less expensive.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The monthly cost of using 4 gigabytes of data on Company C's plan can be calculated using Rule C:

C(4) = $10 + $15 × 4 = $10 + $60 = $70

The monthly cost of using 4 gigabytes of data on Company D's plan can be calculated using Rule D:

D(4) = $80

So, in this case, C(4) is less than D(4), meaning that the monthly cost of using 4 gigabytes of data on Company C's plan is less than the monthly cost of using 4 gigabytes of data on Company D's plan.

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|t+4| ≤ 48 is the inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.

Here, we have

Given: Henry's bread recipe calls for 3 cups of flour, with a variation of up to 4 tablespoons depending on the humidity level. There are 16 tablespoons in 1 cup.

We have to find inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

= 3×16 = 48

= |t+4| ≤ 48

Hence, |t+4| ≤ 48 is the inequality that is used to find t, the number of tablespoons of flour actually used in a recipe.

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The result of dilating a rectangle using a scale factor of 1/2 through point B will be a new rectangle with half the length and width of the original rectangle, centered around point B.

When a rectangle is dilated using a scale factor of 1/2, it means that the size of the rectangle is reduced by half.

This can be achieved by multiplying the dimensions of the rectangle by the scale factor. In the case of a dilation through point B, the new rectangle will be centered around point B and its length and width will be half of the original dimensions.

In mathematical terms, let's assume that the original rectangle has length "l" and width "w". The new rectangle after the dilation with a scale factor of 1/2 will have a length of (1/2)l and a width of (1/2)w.

To find the new coordinates of the rectangle, we need to subtract (1/4)l and (1/4)w from the original x and y coordinates respectively.

If the original rectangle has a length of 4 and a width of 2, then the new rectangle after the dilation with a scale factor of 1/2 will have a length of 2 and a width of 1.

The new x and y coordinates will be x-1 and y-0.5 respectively.

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The amount of water required to produce 1% sugar syrup from 12g sugar is 1.2L.

Volume is the amount of space occupied by an object, whereas capacity is the ability of an object to hold a substance, such as a solid, liquid, or gas.

The amount of water that must be added for a given weight of solution is expressed as weight by volume solution (w/v).

w/v (weight by volume percentage):

The grams of solute in 100 milliliters of solution are defined as the percent weight per volume.

This method determines the concentration of the solution.

The concentration given is 1%.

The sugar weight is 12g.

Solvent volume = weight/concentration

Volume  = 12/1 = 12 x 100 mL

Volume = 1.2 L

Hence, 1.2l of water is required to produce 1% sugar syrup from 12g of sugar

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Answer:

Step-by-step explanation:

A

[tex]x!/10^{(6x)}[/tex] diverges as x approaches infinity.

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be as simple as a single number or variable, or they can be complex combinations of multiple variables and operations.

Examples of expressions include:

3 + 5

x - 2y

(a + b) * (c - d)

2x^2 + 3x - 5

sin(x) / cos(x)

Expressions can be evaluated to obtain a numerical value or simplified to make them easier to work with. For example, the expression 2x^2 + 3x - 5 can be simplified by factoring as (2x - 5)(x + 1) or by completing the square as 2(x + 3/4)^2 - 49/8.

Expressions are an important part of algebra and other branches of mathematics, where they are used to represent mathematical relationships and solve equations. They are also used in computer programming and other areas of science and engineering to represent mathematical models and calculations.

According to given condition :

The expression [tex]x!/10^{(6x)}[/tex] is a mathematical function that represents the factorial of x divided by 10 to the power of 6 times x. This expression diverges as x becomes large because the factorial function grows much faster than the exponential function.

As x increases, the value of x! grows very rapidly because x! is the product of all integers from 1 to x. In contrast, the value of 10^(6x) grows much more slowly because it is an exponential function with a fixed base of 10.

Therefore, as x gets larger, the value of [tex]x!/10^{(6x)}[/tex] grows very rapidly, eventually becoming much larger than any fixed value. This means that the expression diverges to infinity as x approaches infinity.

To see this more formally, we can use Stirling's approximation, which states that n! is approximately equal to [tex](n/e)^n * sqrt(2pin)[/tex] for large values of n. Substituting this into the expression for [tex]x!/10^{(6x)}[/tex], we get:

[tex]x!/10^{(6x)} ≈ [(x/e)^x * sqrt(2pix)] / 10^{(6x)}[/tex]

Taking the logarithm of both sides, we get:

[tex]ln(x!/10^{(6x)}) ≈ x * ln(x/e) + 0.5 * ln(2pix) - 6x * ln(10)[/tex]

As x approaches infinity, the first two terms on the right-hand side dominate, and the expression grows without bound.

Therefore, [tex]x!/10^{(6x)}[/tex]diverges as x approaches infinity.

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Answer:

A. 1&3 are vertical

C. 1&3 are supplementary angles

Step-by-step explanation:

Hello, So use the function p, to find the output

[tex]p(3) = - (3 - 4) {}^{2} + 10 = - 39[/tex]

[tex]p(5) = - (5 - 4) {}^{2} + 10 = 9[/tex]

Since p(4)>p(5) and p(3), p(4) is the maximum.

Also p is written in vertex form which is

[tex]a(x - h) {}^{2} + k[/tex]

Since a is negative, we will have a maximum vertex.

The answer is

Oriya has reasoned the vertex is a maximum because p(4) is the highest points compared to points near it such as p(3) and p(5).

Using the slope intercept form of the line, cost per night (m) is 75 and the initial fee (b) that the cabin charges is 50.

Equation of a line in slope intercept form is

y = mx + b

Here m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

The cabin that Jake and his friends are staying at charges an initial fee plus the cost per night.

Given graph is a linear relationship between the total cost, y, and number of nights, x.

Let initial fee be b and cost per night be m.

So the equation will be of the form,

Total cost = Initial fee + (cost per night × number of nights)

y = b + mx

Comparing this with slope intercept form, initial fee is the y intercept and cost per night is the slope.

From the graph, we have a point (0, 50).

y intercept = 50

So initial fee = 50

Consider (0, 50) and (2, 200).

Slope = (200 - 50) / (2 - 0) = 75

So cost per night = 75

Hence cost per night is 75 and the initial fee is 50.

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The number of rhinestones per square centimeter on the surface of a disco ball is 448/274.167.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

Given;

A disco ball has a circumference of 16.558 centimeters

448 rhinestones on its surface.

Now,

2pi*r=16.558

r=8.279/pi

Surface area of sphere=4pi*r^2

=4*68.541841

=274.167

Here, 448/274.167

Therefore, the surface area per square cm will be 448/274.167.

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[tex]\begin{cases} x = -3 &\implies x +3=0\\ x = 2 &\implies x -2=0\\ x = 4 &\implies x -4=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{ ( x +3 )( x -2 )( x -4 ) = \stackrel{0}{y}}\implies (x+3)(x^2-6x+8)=y \\\\\\ x^3-6x^2+8x+3x^2-18x+24=y\implies \boxed{x^3-3x^2-10x+24=y}[/tex]

Answer:

x = ± √20

or if you want an approximate solution correct to the nearest hundredth:

x = -4.47, 4.47.

Step-by-step explanation:

4x^2-80=0

This a quadratic equation and will have 2 solutions.

Add 80 to both sides of the equation:

4x^2 = 80

Divide both sides by 4:

x^2 = 20

Take the square root of both sides:

x = ± √20.

Answer:9

Step-by-step explanation:

3/8=x/24

3/8=x/3*8

[tex]\frac{3}{8} =\frac{\frac{x}{3} }{8}[/tex]

3=x/3

x=9

Answer:

First, we evaluate the amount that the portion has been multiplied by. We want to determine how many number 8's fit in to the number 24 because the bottom of the portion is 24.

The solution would be 3, because eight multiplied by 3 equals 24. Also because the bottom of the fraction has been multiplied by three, the top, known as the numerator, also needs to be multiplied by three. As a result, the top becomes 3 multiplied by 3, which equals 9. As a result, the portion is 9/24.

Step-by-step explanation:

3/8=?/24

3/8*3/3=9/24

9/24

____     =/8

3/3

Answer:

Step-by-step explanation:

To solve the expression "5 (5/2) + 2 (3/5)", we'll first simplify each term inside the parentheses, then add them up:

5 (5/2) = 5 * (5/2) = 5 * 2.5 = 12.5

2 (3/5) = 2 * (3/5) = 2 * 0.6 = 1.2

Now we can add the two terms:

12.5 + 1.2 = 13.7

So the expression "5 (5/2) + 2 (3/5) = 13.7".

Answer:

   [tex]\frac{137}{10}[/tex]  /  13[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

5 [tex]\frac{5}{2}[/tex] +2 [tex]\frac{3}{5}[/tex]

= [tex]\frac{11}{2}[/tex] + [tex]\frac{13}{5}[/tex]

do cross multiplication

= [tex]\frac{137}{10}[/tex]

further simplify ⇒ mixed fraction= 13[tex]\frac{7}{10}[/tex]

The number of cereal boxes in total is 48.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, cereal boxes fill 3/4 of each of 8 shelves at a grocery store.

Now, number of boxes in each shelve = 3/4 ×8

= 6

Thus, the number of boxes in 8 shelves

= 8×6

= 48

Therefore, the number of cereal boxes in total is 48.

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Since Nina made her career planning timeline in the year 2005, the year which Nina's timeline should start is: B. 2005.

A timeline can be defined as a list of important events or activities that are arranged in a chronological sequence, which is the order in which they happened (occurred).

we know that,

Chronology can be defined as the logical arrangement of events based on the order of their occurrence.

In this context, we can reasonably infer and logically deduce that the year which Nina's timeline should start is 2005 because Nina made her career planning timeline in the year 2005.

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