How do you find the length of the third leg of a triangle?

The value of x is 14.7224.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Sin 60° = x/17 ____(1)

Sin 60° = √3/2 _____(2)

From (1) and (2) we get,

√3/2 = x/17

x = 17√3/2

x = 17 x 1.73205 / 2

x = 14.7224

Thus,

The value of x is 14.7224.

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The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.

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

We have the interval from x = 1 to x = 2.

To find the function’s average rate of change over the interval from x = 1 to x = 2 is:

We interpreted the interval in the coordinate form.

The curve from (1, 2) to (2, 0) is a straight line.

And the slope of the line is the average rate of change of the function.

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

then the equation of line is

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

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = (0-2) / (2-1)

m = -2/1

m = -2

Therefore, the average rate of change is -2.

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Answer:

240

Step-by-step explanation:

The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday

Answer:

278

Step-by-step explanation:

average = sum/count

count = 7 (7 days)

monday = 150

tuesday = 250

wednesday = 200

thursday = 250

friday = 350

saturday = 450

sunday = 300

sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950

mean = 1950/7 = 278.571428571 ≈ 278

Answer: Let x be the number of $13 books that Auggie bought and y be the number of $24 books. Then we can represent the given information in the following system of linear equations:

x + y = 8 (the total number of books Auggie bought is 8)

13x + 24y = 159 (the total amount of money Auggie spent is $159)

This system of linear equations represents the given situation. We can use this system to find out how many books Auggie bought of each price by solving the system of equations.

The equation (1) represents the number of books that Auggie bought is 8, and equation (2) represents the amount of money he spent $159. This system of equations is a valid representation of the given situation because the values of x and y that satisfy the system of equations will be the number of $13 books and the number of $24 books that Auggie bought.

Step-by-step explanation:

16<x+y<19,60<xy<84,10/7<y/x<12/6,3<y-x<6

smallest with the smallest biggest with the biggest, biggest with smallest, smallest with biggest

Answer:I know why your father never came back

Step-by-step explanation: So when he got the milk he got stuck in traffic for a long time which caused the milk to expire and so he went back to grab new milk and on his way home he was stuck in traffic again and the milk got expired so he repeats the process and the same thing happens over and over and over, so hes stuck in an infinite loop until he passes away.

For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal.

The length of the house on the map is calculated using equality in proportions as follows

The required proportion is

= height of the house / length of the house

= 6 / 4.5

= 4/3

Using this proportion, the length of the house in the drawing is

= 30 mm / 4/3

= 22.5

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Answer:c/π=d

Step-by-step explanation: the d and π was multiply with the d and if we want separate with it, we need to use the opposite way to get it.

Answer:

2

Step-by-step explanation:

look at where it intersects the line that goes straight up

Answer:

C. 2%

Step-by-step explanation:

(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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The three ways of finding the x-intercept are:

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that a table for showing the relation between length and width of a field;

                Width (w)                                     Length (l)

                       0                                                   50

                     100                                                 150

                     200                                                250

                     300                                                350

We see, that, width is 50 less than the length.

Therefore, the function (w) to represent the length of the field will be =

w = l-50

Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

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The function in the attached graph is nonlinear

The function is negative where x < 0 and where x > 0.

There is an extrema.

The maximum is located at x = 0.

As the x-value decreases the y-value decreases for x < 0

As the x-value increases the y-value decreases for x > 0

The function is not a straight line graph, because of this, it is a non linear function

The extrema refers to points of maximum or minimum values. The function on the graph has a maximum value at (0, 0)

The end behavior of the function is described as

x ⇒ ∞ f(x) ⇒ - ∞

x ⇒ -∞ f(x) ⇒ -∞

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The values of k are 3 and −1.

Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0

Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.

⇒b2−4ac=0

[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]

For given equation, a=4,  b=2(k+1),c=(k+1)

(2(k+1))^2 −4.4(k+1)=0

⇒(2k+2)^2−16(k+1)=0

⇒4k2+8k+4−16k−16=0

⇒4k2−8k−12=0

⇒4(k2−2k−3)=0

⇒k2−2k−3=0

⇒k2−3k+k−3=0

⇒k(k−3)+1(k−3)=0

⇒(k−3)(k+1)=0

⇒k−3=0   and   k+1=0

⇒k=3   and  k=−1

So, the values of k are 3 and −1.

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Answer:

Step-by-step explanation:

Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

What is a Ratio?

This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.

Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Answer:

Step-by-step explanation:

the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning

There are two steps of solving the equation -3(2x+6)=12.

The steps are given below.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given equation:

-3(2x+6)=12

The first step:

Solving the parenthesis first,

-6x -18 = 12

Adding 18 to both sides,

-6x = 30

Divide by -6,

x = -5

The alternate step:

-3(2x+6)=12

Divide by -3,

2x + 6 = -4

2x = -10

x = -5

Therefore, x = -5 is the solution of the equation.

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Answer:

Y=7x+67

Step-by-step explanation:

The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

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The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

The probability that Mr. Espinoza will select the middle toll booth on Monday and Tuesday is 8%.

Probability refers to the odds of Mr. Espinoza selecting the middle toll booth on Monday and Tuesday when he could have selected toll booths 1, 2, 4, or 5.

The chances of selecting one out of five toll booths = 1/5 or 0.2

The likelihood of Monday and Tuesday out of the five working days = 2/5 or 0.4

The probability of selecting the middle toll booth on Monday and Tuesday = 1/5 x 2/5

= 0.2 x 0.4

= 0.08

= 8%

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Using graphical method, the solution to the system of linear inequality (x, y) are (1, 5)

A mathematical statement called a linear inequality depicts the relationship between two different variables, typically on a graph. A line or border that divides the area of all the points that fulfill the inequality from the areas of the points that do not constitutes the graph of a linear inequality. A set of lines in the coordinate plane that represent the equations of a system of linear inequalities is called a graph. The region of the coordinate plane where each of the inequalities holds can be seen by joining these lines to create a graph.

The inequality given are;

This can be solved using a graphing calculator;

The point of intersection shows the solution to the graph

The solution to the linear inequalities (x, y) are (1, 5)

The broken lines in the graph is from the greater than inequality, while then straight unbroken lines is the inequality with greater than or equal to sign.

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Answer:

N = Pd - 2

Step-by-step explanation:

P = N + 2/d

Pd = N + 2

Pd - 2 = N

N = Pd - 2

The graph of y is a straight line parallel to the x−axis through the point (0,1)

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The equation is Y = 1

A straight line in slope (m) and intercept (c) form is:

y = mx + c

y is a straight line of slope 0 and y- intercept of 1

y = 0.x + 1

y = 1

Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)

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Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet

Now, According to the question:

Board lengths that should be accepted

From the question, we have the following parameters that can be used in our computation:

Length = 16 ft

Percent error = 1.5%

This means that the acceptable lengths are

Acceptable = Length ± Percent error * Length

Substitute the known values in the above equation, so, we have the following representation

Acceptable = 16 ± 1.5% * 16

So, we have

Acceptable = 16 ± 0.24

Evaluate

Acceptable = 15.76 to 16.24

Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet

Board lengths that should be rejected

In (a), we have

Acceptable = 15.76 to 16.24

Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet

The intended lengths of the boards

Here, we have

Lengths = 10, 12 and 14 feet

Length too long = 2.3 inches

Convert to inches

Length too long = 0.19

So, we have

Intended lengths = (10, 12 and 14 feet) + 0.19

Evaluate

Intended lengths = 10.19, 12.19 and 14.19 feet

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4-6 = -2

x/7-6

Substitute

28/7-6

PEMDAS

28/7 = 4

4-6 = -2

(If you're looking for the expression, it's 4-6. But if straight answer, -2)

Answer:

[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]

Step-by-step explanation:

Given information,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: x = 28[/tex]

Now the value of expression is,

[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]

[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]

[tex] \sf \rightarrow \: 4 - 6[/tex]

[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]

Therefore, the answer is -2.

(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.

To solve the problem, recall the factor theorem.

Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0

The given function is:

f(x) = x³ - 3x² + 4x - 12

To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).

Substitute x = 3 into f(x):

f(3) =3³ - 3(3)² + 4(3) - 12

f(3) = 27 - 27 + 12 - 12

f(3) = 0

Since f(3) = 0, then x -3 is a factor of  x³ - 3x² + 4x - 12

Your question is incomplete, but most probably your question was:

Is x - 3 a factor of the polynomial  x³ - 3x² + 4x - 12?

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Answer: x = a/b - c

Step-by-step explanation:

First divide by b on each side to get the x by itself.

Then subtract c from both sides to make x the subject of the formula.

Step-by-step explanation:

a = bx + c

the goal is to get to a form with "x = ...".

a - c = bx

(a - c)/b = x

done.

The Fraction for the given word problem is x/y = 9/11

A fraction, which derives from the Latin word fractus, meaning "broken," is a portion of a whole or, more broadly, any number of equal parts. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in everyday speech.

Let the fraction be x/y

The numerator of a fraction is 2 minus its denomination.

⇒ x = y - 2 .....(i)

When 3 is subtracted from numerator and from denomination the new fraction obtained is 3/4

⇒ x - 3/y - 3 = 3/4

Can also be written as

⇒ 4(x + 3) = 3(y - 3)

⇒ 4x - 12 = 3y - 9

⇒ 4x - 3y = -9 + 12

⇒ 4x - 3y = 3 .....(ii)

Substitute the value of (i) in (ii)

⇒ 4x - 3y = 3

⇒ 4(y - 2) - 3y = 3

⇒ 4y - 8 - 3y = 3

⇒ y - 8 = 3

⇒ y = 3 + 8

⇒ y = 11

Putting the value of y in (i).

⇒ x = y - 2

⇒ x = 11 - 2

⇒ x = 9

Hence, Fraction = x/y = 9/11

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The correct equation which represent an identity will be;

⇒ 4(5x+2) = 20x+8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the equations are,

1) 2x + 1 = 3x + 4

2) 4x - 3 = 2(2x + 7)

3) 6x + 3 = 2x + 10

4) 4(5x + 2) = 20x + 8

Now,

Solve each equation and find an identity as;

1) 2x + 1 = 3x + 4

⇒ 1 - 4 = 3x - 2x

⇒ - 3 = x

⇒ x = -3

Thus, It is not represent an identity.

2) 4x - 3 = 2(2x + 7)

⇒ 4x - 3 = 4x + 14

⇒ - 3 ≠ 14

Thus, It shows no solution.

3) 6x + 3 = 2x + 10

⇒ 6x - 2x = 10 - 3

⇒ 4x = 7

⇒ x = 7/4

Thus, It is not represent an identity.

4) 4(5x + 2) = 20x + 8

⇒ 20x + 8 = 20x + 8

⇒ 20x - 20x = 8 - 8

⇒ 0 = 0

Clearly, '0' is an additive identity.

Thus, This equation shows an identity.

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