Find the length of side � x in simplest radical form with a rational denominator. 30° 60° x 2

[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -3 ) = \stackrel{0}{y}}\hspace{4em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{5em}1( x +2 )( x -3 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-x-6=y \end{array}}~\hfill[/tex]

The inverse of the function is y = (-3x + 50)/4.

The domain of the inverse function are {4, 5, 6, 10}.

The range of the inverse function are {5, 8, 9, 13}.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

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

Where:

At point (5, 10), an equation of the line f(x) can be calculated by using the point-slope form:

y - 10 = (6 - 10)/(8 - 5)(x - 5)

y - 10 = -4/3(x - 5)

y = -4x/3 + 20/3 + 10

y = -4x/3 + 50/3

y = (-4x + 50)/3

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

x = (-4y + 50)/3

3x = -4y + 50

4y = -3x + 50

y = (-3x + 50)/4

Read more on inverse function here: brainly.com/question/23626757

#SPJ1

Therefore , the solution of the given problem of  unitary method comes out to be  x = (ab)c = a(bc) .

The job can be finished by multiplying the variable information obtained using this kind of nanosection alongside the results of the two people who used the unilateral approach. In essence, this mean that whenever a desired item happens, either the chosen entity is described or the tone of both commercial manufacturing is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.

Here,

We must demonstrate that the following formula holds for any subsets A, B, and C of S in order to demonstrate that multiplication of subsets is associative:

=> (AB)C = A(BC)

where AB and BC stand for the sets created by increasing all of the elements in A by all of the elements in B, and vice versa.

We must demonstrate that every element on the left-hand side is also an element on the right-hand side and vice versa in order to demonstrate that (AB)C = A(BC).

Let x represent any one of the (A*B)C elements. If a, b, and c are all in A, then x can be expressed as

=> x = (ab)*c by definition. * being associated with S gives us:

=> x = (ab)c = a(bc)

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

Answer:

Set the height equal to (1/2)gt^2 and solve for t.

h = (1/2)gt^2

t = (2h/g)^1/2

Plug in the numbers and get your answer in seconds:

h = 81 ft

g = 32 ft/s^2

Step-by-step explanation:

Answer: To estimate the mean score for all the students in the district, we can use a confidence interval. We are given that the sample size is 400, the sample mean is 110, the population means is 100, and the population standard deviation is 15. We are asked to find a 99% confidence interval for the population mean.

The formula for a confidence interval for the population mean with known population standard deviation is:

Confidence interval = sample mean ± z*(σ/√n)

where:

sample mean = 110 (given)

σ = 15 (given)

n = 400 (given)

z = the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.

Substituting the values, we get:

Confidence interval = 110 ± 2.576*(15/√400)

Confidence interval = 110 ± 1.92

Therefore, the 99% confidence interval for the population mean score is (110 - 1.92, 110 + 1.92), or (108.08, 111.92). We can be 99% confident that the true population mean score for all the students in the district falls between 108.08 and 111.92.

Step-by-step explanation:

Answer:

the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.

Step-by-step explanation:

Let the length of the corral be x, and the width be y. We know that the area of the corral is 117, so:

xy = 117

We also know that the corral is divided by a fence into two sections. Let the length of one section be L, and the width be y. Then, the length of the other section will be x - L, and the width will still be y. The total fencing cost will be:

10(2x + 2y) + 6(L + 2y)

Simplifying this expression, we get:

20x + 32y + 6L

Using the area equation, we can rewrite this as:

20x + 32(117/x) + 6L

To minimize the cost, we need to take the derivative of this expression with respect to L, and set it equal to zero:

d/dL [20x + 32(117/x) + 6L] = 6 = 0

Solving for L, we get:

L = x/2

Therefore, the two sections of the corral will have equal length. Substituting this value of L into the expression for total fencing cost, we get:

20x + 32y + 3x

Simplifying this, we get:

23x + 32y

Using the area equation to substitute for y, we get:

23x + 32(117/x)

Taking the derivative of this expression with respect to x, and setting it equal to zero, we get:

23 - 3744/x^2 = 0

Solving for x, we get:

x = sqrt(3744/23) ≈ 17.91

Substituting this value of x into the area equation, we get:

y = 117/x ≈ 6.54

Therefore, the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.

The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Let's call the length of the rectangle "l" and the width "w".

We can write two equations based on the given information -

Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)

Area equation: A = 3lw (since the field is divided into 3 equal parts)

We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.

We can use the perimeter equation to solve for one of the variables in terms of the other -

2l + 4w = 600

2l = 600 - 4w

l = 300 - 2w

Now we can substitute this expression for "l" into the area equation -

A = 3lw

A = 3(300 - 2w)w

A = 900w - 6w²

To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -

dA/dw = 900 - 12w = 0

12w = 900

w = 75

So the width of each of the smaller rectangular plots is 75 feet.

We can use the perimeter equation to find the length -

2l + 4w = 600

2l + 4(75) = 600

2l = 300

l = 150

Therefore, the dimensions value are obtained as 150 feet by 75 feet.

To learn more about area from the given link

brainly.com/question/25292087

#SPJ1

Answer:

Step-by-step explanation:

Let the age of the son be $s$ and the age of the father be $f$. From the first equation, we have $2s + f = 56$, and from the second equation, we have $f + 2s = 82$. Solving this system of equations, we get $s = 12$ and $f = 32$, so the son is 12 years old and the father is 32 years old.

Let the two-digit number be $10t+u$, where $t$ is the tens digit and $u$ is the units digit. We are given that $t+u=13$ and $2t-u=1$. Solving this system of equations, we get $t=7$ and $u=6$, so the two-digit number is $76$.

Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit. We are given that $2(10+x+y) = 27(10x+y)$, or $20+2x+2y = 270x+27y$. Simplifying this equation, we get $268x-25y = 10$. Since $y$ is a digit, we know that $0 \leq y \leq 9$. We can check that $x=1$ is too small, so we try $x=2$. Plugging in $x=2$, we get $536-25y=10$, which gives $y=21/5$, which is not a digit. Thus, there is no solution for a two-digit number.

The experimental probability of rolling a number less than or equal to 4 is 0.7.

The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).

Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.

Given that, the trial was run 10 times.

Thus,

P(B) = (number of times B occurred) / (total number of trials)

= 7 / 10

= 0.7

Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.

Learn more about conditional probability here:

https://brainly.com/question/30144287

#SPJ1

Answer:

The simplified expression is -13/12.  (are you sure you don't have a typo somewhere), double checked.

Step-by-step explanation:

First, let's simplify the expression inside the absolute value bars:

5/6 - 17/12 = 10/12 - 17/12 = -7/12

Next, we can simplify the expression outside the absolute value bars:

| -7/12 | - | 5/3 |

= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)

= 7/12 - 20/12

= -13/12

The simplified expression is -13/12.

_______________________

Simplify the following:

abs(5/6 - 17/12) - abs(5/3)

Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:

abs(((2×5)/12 - 17/12)) - abs(5/3)

2×5 = 10:

abs(10/12 - 17/12) - abs(5/3)

10/12 - 17/12 = (10 - 17)/12:

abs(((10 - 17)/12)) - abs(5/3)

10 - 17 = -7:

abs((-7)/12) - abs(5/3)

Since 5/3 is a non-negative constant, abs(5/3) = 5/3:

abs(-7/12) - 5/3

Since -7/12 is a negative constant, abs(-7/12) = 7/12:

7/12 - 5/3

Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:

7/12 - (5×4)/12

4 (-5) = -20:

7/12 + (-20)/12

7/12 - 20/12 = (7 - 20)/12:

(7 - 20)/12

7 - 20 = -13:

Answer: (-13)/12

Answer: The theoretical probability of selecting a meat option is 7/9.

Step-by-step explanation:

5 beef + 3 pork + 6 chicken + 4 veggie = 18 options total

meat options = 18 (total) - 4 veggie = 14 meat options

14/18 = 7/9

The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.

The total number of items purchased by the customer = 10

The cost for 5 items = $1.60× 5 = $8

The cost of 3 items = $1.25×3 = $3.75

The cost of 2 items = $0.55×2 = $1.1

The total cost = 8+3.75+1.1 = $12.85

Therefore, the change of the customer when $20 bill is used = 20-12.85

= $7.15.

Learn more about cost price here:

https://brainly.com/question/26008313

#SPJ1

The area of the trapezoid is 176 square units.

What is a trapezoid?

A trapezoid, which is also referred to as a trapezium, is a flat, closed shape with four straight sides and one set of parallel sides.

A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the length of the parallel sides measured perpendicularly.

The height of the trapezoid is 4 units.

The parallel sides of the trapezoids are 17 units and (5+17+5) = 27 units.

The area of a trapezoid is half of the product of the height and the sum of parallel sides.

The area of the trapezoid is

1/2 × 4 ×(17+27)

= 176 square units

To learn more about area of trapezoid, click on the below link:

https://brainly.com/question/27142379

#SPJ1

Answer: Here is a table that models the sample space for this event:

            Scorpion Tarantula Centipede Wasp

First     S1          T1                 C1                 W1

Second     S2          T2                 C2                 W2

Each combination of two fun things is represented by a two-letter code. For example, "S1T2" represents grabbing the scorpion first and the tarantula second.

Here is the list of all possible outcomes:

S1S2

S1T2

S1C2

S1W2

T1S2

T1T2

T1C2

T1W2

C1S2

C1T2

C1C2

C1W2

W1S2

W1T2

W1C2

W1W2

And here is a tree diagram that shows the same information:

       |----S2

       |----T2

First --|----C2

       |----W2

       |

       |----S2

       |----T2

Second--|----C2

       |----W2

The branches on the left represent the first fun thing that is grabbed, and the branches on the right represent the second fun thing that is grabbed.

Step-by-step explanation:

Answer:

1.  8

2. 24

3.  15

4.  135

b. 135 x 1/9

5. the answer is 24

The equivalent expression is (x -2)/(x+4)(x + 6)

It is important to note that algebraic expressions are defined as expressions composed of coefficients, terms, variables, constants and factors.

They are also made up of arithmetic operations.

Also, equivalent expressions are defined as expressions that have the same solution but differs in the arrangement of the terms.

From the information given, we have the expression;

(x - 2)/x² + 10x + 24

Now, let's factorize the denominator, we have;

x² + 10x + 24. Find the pair factors of 24 that add up to 10, we get;

x² + 4x + 6x + 24

Factorize in pairs

x(x + 4) + 6(x + 4)

Then, substitute the expressions;

(x -2)/(x+4)(x + 6)

Learn about equivalent expressions at: https://brainly.com/question/15775046

#SPJ1

Using differentiation, 200 boats should be produced to incur minimum cost

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative.

Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables. The most typical illustration is the velocity, or rate of change of displacement with respect to time.

Minimum boats can be found by differentiating the given function,

[tex]C(x)=21000 - 40x+0.1x^2[/tex]

Differentiating with respect to x,

0 = 0.2x - 40

0.2x = 40

x = 200

∴ 200 boats should be produced to incur minimum cost.

To learn more about differentiation from given link

https://brainly.com/question/954654

#SPJ1

The length and the width of the model are Length = 2 and Width = 3x² + 5x + 6

The expression 6x cant be the length because 12 cannot divide 6x without becoming a radical expression

We have

Area = 6x² + 10x + 12

Factor out 2

Area = 2(3x² + 5x + 6)

This means that

Length = 2 and Width = 3x² + 5x + 6

Read more about area at

https://brainly.com/question/24487155

#SPJ1

The base length of the parallelogram found using the area formula is 4 units.

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.

A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.

Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.

Given,

The area of the parallelogram A =36 sq. units

The height of the parallelogram  h = 9 units

We are asked to find the base length b.

Now the formula for the area of the parallelogram is:

A = b * h

36 = b * 9

b = 36/9 = 4 units.

Therefore the base length of the parallelogram, found using the area formula is 4 units.

To learn more about the parallelogram, follow the link.

https://brainly.com/question/970600

#SPJ1

Using algebra, Marty can make 4 triangles from a rope with 7 knots.

Algebra, a branch of mathematics, facilitates the representation of situations or issues as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.

All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, employ algebra. Algebraically, 2x + 4 = 8 is a simple expression.

Now here in the question,

3 knots form the vertices of a triangle.

Remaining 4 knots out of the 7 can be distributed as:

4+0+0 .......(on 3 sides)

3+1+0

2+2+0

2+1+1

Therefore, Marty can make 4 triangles from the rope with 7 knots.

To know more about algebra, visit:

https://brainly.com/question/24875240

#SPJ1

Therefore , the solution of the given problem of triangle  comes out to be segments LM and MN have equal 10x measures.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

Given that RS and LM are the respective sides of the two triangles, if we set x as the length of RS, then LM's length is 5x and ST's length is 2x. The duration of MN is five times that of ST, which is ten times longer.

We can now calculate the length of RS using the tangent of angle R:

=> tan R=RS/ST

=> 5/2.5=2

We thus have:

=> RS = 2

=> ST = 2x

We can determine the length of RT using the Pythagorean theorem:

=> RT/ST = sin R

=> RT = ST sin R

=>  2.5 (2/29) = 4.337 sin R = 2.5

We can now determine the lengths of LM and MN using the similarity of the triangles:

=> RM = 5 (2x) LM = 5 = 10

=> MN = 5 ST = 5 (two times) = 10

As a result, segments LM and MN have equal 10x measures.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The values of LM = 12.5 and MN = 25

A triangle is a closed geometric figure consisting of three line segments or sides, connected to each other at three endpoints or vertices. Each side of a triangle intersects with exactly two other sides, and the vertices are the points where the sides meet.

From the given figures, both the triangles are right angle triangle.

[tex]tan R=\frac{5}{2.5} = \frac{ST}{RS}[/tex]

So, ST = 5 and RS = 2.5

Since, ΔRST is 5th to create ΔLMN,

its corresponding sides are 5 times the length LM corresponding sides of RS. So, its length

LM = 5×2.5 = 12.5

LM = 12.5

MN corresponding sides of ST. So, its length

MN = 5×5 = 25

MN = 25

Therefore, The values of LM = 12.5 and MN = 25.

To know more about triangle, visit:

brainly.com/question/2773823

#SPJ1

After answering the presented question, we can conclude that equation  Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex]

An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

To find f(x) + g(x),

[tex]f(x) = 8 - 4x - x^3\\g(x) = x^2 + 7x - 9\\f(x) + g(x) = (8 - 4x - x^3) + (x^2 + 7x - 9)\\f(x) + g(x) = -x^3 + x^2 + 3x - 1\\[/tex]

Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex][tex]-x^3 + x^2 + 3x - 1.[/tex]

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

According to the recipe, the ratio of flour to water is 4:0.5 or 8:1 (since 1/2 can be simplified to 0.5).

To determine how much water is needed for 5 cups of flour, we can use this ratio:

8:1 = 5:x

where x represents the amount of water needed.

To solve for x, we can cross-multiply:

8x = 5 * 1

8x = 5

x = 5/8

Therefore, you will need 5/8 cup of water for 5 cups of flour, using the given recipe.

Step-by-step explanation:

Answer:

45 degrees I think

Step-by-step explanation:

sorry if wrong

According to the question the option C is the correct answer that is 8 6/8 or 8 ¾ calculated by simplifying the fraction.

To represent a whole, every number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of a numerator to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

To add mixed numbers, we need to first convert any fractions to a common denominator. In this case, we can use 10 as the common denominator.

12 1/2 = 12 + 1/2 = 12 + 5/10 = 12 5/10

4 7/10 = 4 + 7/10

Now we can add the two mixed numbers:

12 5/10 + 4 7/10 = 16 12/10

Simplifying the fraction by dividing the numerator and denominator by their greatest common factor of 2, we get:

16 12/10 = 16 6/5

Therefore, the answer is C) 8 6/8 or 8 3/4.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

Answer:

53.06 ft^2

Step-by-step explanation:

Calculate semi perimeter and use Scalence triangle area formula

Semi perimeter: a+b+c/2

Area of Scalence triangle: √s(s-a)(s-b)(s-c). {where s=semi perimeter}

Answer: I don't know

The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).

The first one is:

(a). f: Z → Z, where f(x) = x^2.

g: Z → Z, where g(x) = |x|^2.

Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.

b)   f: Z × Z → Z, where f(x,y) = |x + y|.

g: Z × Z → Z, where g(x,y) = |x| +| y|.

These are different, if x = 1 and y = -1

f(1, - 1) = |1 - 1| = 0

g(1, -1) = |1| + |-1| = 2

c) B = {0, 1}

f: B × B → B × B, where f(x,y) = (1-y, 1-x)

g: B × B → B × B, where g(x,y) = (x,y)

This is clearly false, when x and y are 0 and 0 we have:

f(0, 0) = (1 - 0, 1 - 0) = (1, 1)

While g gives:

g(0, 0) = (0, 0)

These functions are different.

Learn more about functions at:

https://brainly.com/question/2328150

#SPJ1

Answer:

36∘

Step-by-step explanation:

Decagon has ten sides and ten angles. All these sides and angles are equal to each other. Therefore, the measure of each exterior angle of a regular decagon is 36∘

Answer:

Answer:

0.050

Rounded to the nearest 0.001 or

the Thousandths Place.

Step-by-step explanation:

Explanation

0.05__

You rounded to the nearest thousandths place. The _ in the thousandths place rounds down to 0 because the digit to the right in the ten thousandths place is _.

0.050

When the digit to the right is less than 5 we round toward 0.

0.05 was rounded down toward zero to 0.050