What is 426 divided by 12?

The expression tan(arcsec(x/3)) can be written   \(1/3 \sqrt{x^2-9}\)  in algebraic form.

The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.

The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to \(1/3 \sqrt{x^2-9}\).

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Answer:

$200

Step-by-step explanation:

money he has now is 150% of what he had in the beginning

300 = 1.5x

x = 200

if he had $200 in the beginning, you add half of that to itself (200 + 100 = 300)

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:3/20

Step-by-step explanation:

Answer: 80

Step-by-step explanation:

Answer: The correct answer is 80

Step-by-step explanation:

in parentheses 3x4 = 12 - 4 = 8

6 + 4 = 10

10 x 8 = 80

Step-by-step explanation:

This is mean domain is all real numbers

Answer:

.20x = 72, so x = 360

.30(360) = 108

x: number of tickets it takes to ride a roller coaster

y: number of tickets it takes to ride the bumper cars

Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times, that is,

4x + 2y = 16

Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times, that is,

2x + 3y = 12

Answer:

-25

Step-by-step explanation:

The required solution for the profits in the year 2020 is $10452958.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

In 1990, the profit of the Gamma company was $11,218,614.

profits fell by $12,189 on average.

According to given question we have

Initial profit P(x)= $11900848

Fall rate= $48263 per year

The year in between  1990<x<2020

The Equation is

P(x)= 11900848 - (x-1990)*48263,

P(2020)= 11900848- 30*48263

= $10452958

Therefore, the required solution for the profits in the year 2020 is $10452958.

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Assume that the number of granola bars is x and the number of bottles is y

Since they decided to purchase at least 50 bottles

At least means greater than or equal, so

Since the cost of 1 bar = $0.50, then

The cost of all bars = 0.50x

Since the cost of 1 bottle = $0.75, then

The cost of all bottles = 0.75y

Since their budget is $75

They can not exceed that, then

The solution will be in the common part of the two colors

The red represents the second inequality

The blue represents the first inequality

Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

Answer:

y=-x-2

Step-by-step explanation:

The slope is negative 1 and the y intercept is -2

Answer:

Sum of 8 = 13.8888... ≈ 14

Two 6's = 2.7777... ≈ 3

Sum of 8 and two 6's = 0.3858... ≈ 0

Sum of 8 or two 6's = 16.6666... ≈ 17

Step-by-step explanation:

Create a sample space for the sum of rolling two dice (where x are the die):

\(\begin{array}{|c||c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x& \textbf{1} &\textbf{2} &\textbf{3} &\textbf{4} &\textbf{5} &\textbf{6}\\\cline{1-7} \textbf{1}&2 &3 & 4& 5&6 &7 \\\cline{1-7} \textbf{2}& 3& 4& 5& 6& 7&8 \\\cline{1-7} \textbf{3}&4 &5 & 6&7 & 8&9 \\\cline{1-7} \textbf{4}&5 &6 &7 & 8&9 &10 \\\cline{1-7} \textbf{5}& 6 &7 & 8&9 &10 & 11\\\cline{1-7} \textbf{6}&7 & 8&9 &10 & 11&12\\\cline{1-7} \end{array}\)

Therefore, there are 36 possible outcomes.

Let Event A be getting a sum of 8.

Let Event B be getting two 6's.

From inspection of the the sample space diagram:

    \(\sf P(A) = \dfrac{5}{36}\)

    \(\sf P(B) = \dfrac{1}{36}\)

Therefore:

\(\implies \sf P(A)\;and\;P(B)=\dfrac{5}{36} \times \dfrac{1}{36}=\dfrac{5}{1296}\)

\(\implies \sf P(A)\;or\;P(B)=\dfrac{5}{36} +\dfrac{1}{36}=\dfrac{6}{36}=\dfrac{1}{6}\)

Given the two dice are tossed 100 times.

Number of times you will get a sum of 8 from 100 tosses of two dice:

\(\implies 100 \times \dfrac{5}{36}=13.8888...\)

Number of times you will get a two 6's from 100 tosses of two dice:

\(\implies 100 \times \dfrac{1}{36}=2.7777...\)

Number of times you will get a sum of 8 and two 6's from 100 tosses of two dice:

\(\implies 100 \times \dfrac{5}{1296}=0.385802...\)

Number of times you will get a sum of 8 or two 6's from 100 tosses of two dice:

\(\implies 100 \times \dfrac{1}{6} = 16.6666...\)

Answer:

Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes from boys? If 55 were girls then there were 123-55 = 68 boys. Thus the ratio would be 55 girls to 68 boys, or 55/68.

Answer:

60

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

5 – 3(2x – 7) = 12 – 5(x – 2)

Substitute x=2

5 – 3(2*2 – 7) = 12 – 5(2 – 2)

5 – 3(-3) = 12 – 5(0)

5 - 3*(-3) = 12

5+9 = 12

14=12

This is false so it is not a solution

5 – 3(2x – 7) = 12 – 5(x – 2)

Substitute x=5

5 – 3(2*4 – 7) = 12 – 5(4 – 2)

5 – 3(8-7) = 12 – 5(2)

5 - 3*1 = 12-10

5-3 = 2

2=2

This is true so it is  a solution

Answer:

Blank = 17/12

Step-by-step explanation:

Blank = 2/3 + 3/4

Blank = 8/12 + 9/12

Blank = 17/12

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

12

Step-by-step explanation:

Following the Pythagorean theorem, c^2 - b^2 = a^2.

If they are similar, b will be 16 and c will be 20.

20^2 - 16^2 = 144

144 = 12^2 so x=12

In linear equation, S = x2 + 36/x  the surface area S of the box as a function of the length x of one of the sides.

What in mathematics is a linear equation?

Let x = length of the sides of the base, and h = the height.  The volume is given as 9 m3

Volume = area of base * height

9 = x2*h

So 9/x2 = h

The surface area, S, of the box is:

S = (Area of Base) + 4*(Area of a Vertical Side)

S = x2 + 4 * (xh)

Substitute 5/x2 in place of h:

S = x2 + 4 * x * (9/x2)

S = x2 + 36/x

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Check the picture below, recall that the radius of a circle is always the same length in the circle.

The length of the arc CD is 14.13 centimeters.

Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:

L  = (a/360°)*2*pi*R

Where pi = 3.14

Here the angle is a = 45°

And R = 18cm, so we can replace that in the formula above to find the length.

L = (45°/360°)*2*3.14*18cm = 14.13cm

That is the length of the arc CD.

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The side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

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The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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The value of LO if RU is 6 inches is solved to be 30 inches

This is a term used in geometry to mean that the respective sides of the polygons are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the polygon are congruent then the side should be in proportions

Examining the figure when LM is 45 inches, and RS is 9 inches

the constant of proportionality from quadrilateral RSTU to quadrilateral LMNO is 5

9 * 5 = 45

when RU = 6 inches

6 * 5 = 30 inches

hence LO is 30 inches

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Answer:

I think is higher

Step-by-step explanation:

Answer:4:1

Step-by-step explanation: