Solve for x to the nearest tenth.
Answer:

The length of the diagonal of the right triangle is 21.2 units.

The game is played on a square court divided into four smaller squares that meet at the centre.

A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite side = 15 feet

hypotenuse side = 15 feet

The hypotenuse side is the diagonal.

Hence,

sin 45° = 15 / h

cross multiply

h = 15 / sin 45

h = 15 / 0.70710678118

h = 21.2132034356

h = 21.2 units

Therefore,

length of diagonal = 21.2 units

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The equation of the graph in slope intercept form is y = x + 2

The equation of a graph can be represented in slope intercept form as follows:

y = mx + b

where

Hence, let's find the slope using (1, 3) and (2, 4)

Therefore,

slope = 4 - 3 / 2 - 1

slope = 1 / 1

slope = 1

Let's find the y-intercept using (1, 3)

y = x + b

3 = 1 + b

b = 3 - 1

b = 2

Therefore, the equation is y = x + 2

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The predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

The given results of regression:

y = –0.693x + 28.802

The formula for regression equation is:

y = ax + b

So, given that:

a = –0.693

b = 28.802

r2 = 0.571536

r = 0.756

Back to the given results of regression:

y = –0.693x + 28.802

In this case, y represents the number of sit-ups a person can do, and x represents the hours of TV watched per day.

Thus, the predicted number of sit-ups for a person who watches x = 6 hours of TV is:

y = –0.693x + 28.802

y = –0.693 * 6 + 28.802

y = –4.158 + 28.802

y = 24.644

Hence, the predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

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1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :

What is rational coefficients?

A coefficient is a number that is placed in front of a variable. A variable and a rational number are preceded by a rational coefficient, which may be an integer, decimal, or fraction.

(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32

1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisfices the given conditions. The leading coefficient here is 1, we call this a monic polynomial.

2. There may be something missing in the question here

3. We can use the factoring techniques to find the roots :

x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :

(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)

We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :

Y = (x-5)(x²+9)

This is the maximum we can do on R, but on C the set of complex we can still factor again.

x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9

Δ < 0, Δ = - 36

Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i

Y = (x-5)(x-3i)(x+3i)

So the solution is S = {5, 3i, -3i} the three roots of the function.

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The absolute maximum is 1.29, which occurs at x= 9

What is absolute extrema?

An absolute extremum  of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.

Main body:

Given =

f(x) = [tex](x^{2} -64)^{1/11[/tex]

f' (x) = derivative of function f(x)

f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]

   =  2x/11[tex](x^{2} -64)^{-10/11[/tex]

putting f'(x) = 0

2x/11[tex](x^{2} -64)^{-10/11[/tex]  = 0

       [tex](x^{2} -64)^{-10/11[/tex]  = 0

         [tex]x^{2} -64[/tex]            = 0

x² = 64

x = ±8

We are given interval [-8,9].

Hence, calculating f(x) at -8, 8, 9.

f(-8) =  0

f(8) = 0

f(9) = [tex]17^{1/11[/tex]

     = 1.29

Hence, absolute maximum value is 1.29 at x=9.

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Answer:

Rhs

Step-by-step explanation:

angle N (R)

pq=mq ( h)

Nq (s)

Answer:

#4 is one, and #5 is two.

Step-by-step explanation:

In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].

What is function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]

[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]

By putzes method

[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]

here [tex]$r_1=2, m_0=I$[/tex]

[tex]$$m_1=A-2 I $$[/tex]

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Thus, 18 weeks are needed for the population of beetles to reach 183. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will take place.

The number of possible outcomes is divided by the total of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event but by probability that it won't.

For instance, how many heads would appear if you throw a coin 100 times? Assuming a probability of 1/2, we can anticipate 50 heads. However, when we actually attempt it, we might just get 48 heads, 55 heads, or anything else, but most of the time it will be close to 50.

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Answer:

10(-x + 1)

Step-by-step explanation:

-2x - 8x + 20

-10x + 20

10(-x + 1)

20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms

Explanation:

4 +2 + 6 + 8 = 20.

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The slopes of the linear equations are:

a) -1

b) 0

c) undefined, it is a vertical line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

1) The points are (3, 5) and (2, 6), so the first slope is:

a = (6 - 5)/(2 - 3)  =1/-1 = -1

2) The points are (-3, 2) and (7, 2)

Notice that this is a horizontal line of the form y = 2, so the slope is zero.

3) The points are (6, 8) and (6, -2)

This is a vertical line of the form x = 6, so the slope is undefined.

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                                    [tex]\large\boldsymbol{\rm{Slope}}[/tex]

[tex]\bf{Intro}[/tex]

To find the slope of a line, given that it passes through two points, use the slope formula:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{6-5}{2-3}}[/tex]

[tex]\bf{m=\dfrac{1}{-1}}[/tex]

[tex]\bf{m=-1}[/tex]  {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{2-2}{7-(-3)}}[/tex]

[tex]\bf{m=\dfrac{0}{7+3}}[/tex]

[tex]\bf{m=\dfrac{0}{10}}[/tex]

[tex]\bf{m=0}[/tex]    {slope}

[tex]\rule{250}{1}[/tex]

Substitute the known values and simplify:

[tex]\bf{m=\dfrac{-2-8}{6-6}}[/tex]

[tex]\bf{m=\dfrac{-10}{0}}[/tex]

[tex]\bf{m=not\:de fined}[/tex]

✦ Therefore, the slopes are: -1, 0, not defined.

The pros and cons regarding the methods of the polynomial include:

Graphing the related system eliminates the need to rewrite the equation in order to set it equal to 0. It is simpler because you can graph each side of the equation separately.

It can be difficult to locate the system's intersection point at times. You may need to zoom in or learn how to resize the window. Using the related function allows you to find the points by focusing on the x-axis.

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

The formula is ax² + bx + c = 0, where a and b are coefficients, c is a constant, and the polynomial degree is 2. A trinomial equation is a polynomial with three variable terms. It is also known as a cubic equation. To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.

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Answer:

(a) 6.33 miles per hour

(b) $4.33 per hour

(c) $0.68 per mile

Step-by-step explanation:

Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]

[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]

(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]

(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]

[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]

If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that the triangle has two equal sides which makes the triangle as isosceles.

In an isosceles triangle the two sides will be always equal and the angles will be also equal.

One angle of the triangle is 67 degrees

We need to find the ∠2.

As we know that the equal sides make equal angles.

∠2=67 degrees

and from given ∠2=10x+7

Now equation 67 with the 10x+7 to find the value of x.

So 67=10x+7

subtract 7 from both sides

67-7=10x+7-7

60=10x

Divide both sides by 10

x=60/10

x=6

Hence, the value of x is 6.

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electricity consumed:28 units

charge upto 20 units : 20 * Rs 3 : Rs 60

charge from (21 to 28) : 8 * Rs 6.50 : 52

total charge including service charge : Rs 60 + Rs 52 + Rs 50 : Rs 162

The number of shirts Samuel can fold in 2 minutes is 12

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

Number of Shirts 3 6 ?

Time (minutes) 0.25 0.50 2

Represent the missing value with x

So, we have the following representation

Number of Shirts 3 6 x

Time (minutes) 0.25 0.50 2

From the above table of values, we have the following equation

6 : x = 0.5 : 2

Multiply the second ratio by 12

So, we have

6 : x = 6 : 12

By comparison, we have

x = 12

Hence, the number of shirts is 12

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Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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For the given equation, 1/x + 2/x+10 = 1/3,

1)The least common denominator is x+10. Option c is correct.

2)The equation will have 2 valid solutions. Option a is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is,

1/x + 2/x+10 = 1/3

[tex]\frac{1}{x}+\frac{2}{x+10}=\frac{1}{3}[/tex]

Cross-multiply the given equation,

[tex]3\left(x+10\right)+6x=x\left(x+10\right)[/tex]

The obtained value of x after simplifying the equation is,

[tex]\\\ x=5,\:x=-6[/tex]

Thus, for the given equation, 1/x + 2/x+10 = 1/3, the least common denominator is x+10. Option c is correct and the equation will have 2 valid solutions. Option a is correct.

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Answer:

width is 2.75 and $6.60

Step-by-step explanation:

first divided by 132 by 12 which gives you 11 then divided 11 by 4 and you get 2.75.

Dubble Check: to chock multiply 12 x 4 x 2.75 which gives you 132.

Cost: Multiply 132 times 5 and you get 660 then place a decimal point between 6 and 6 to get $6.60

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

-25

Step-by-step explanation:

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

Equation in terms of k about the average age is:

(2k + 61) / 5 = 17

After solving the equation, k = 12 years

Step-by-step explanation:

Age of Roxanne = k years

Age of the sister = (k + 8) years

Age of brothers = 21, 18 and 14 years

Total number of siblings = 5

Average age of siblings = [k + (k + 8) + 21 + 18 + 14] / 5

or, 17 = [2k + 61] / 5

or, 85 = 2k + 61

or, 24 = 2k

or, 12 = k

So, k = 12 years

The set A ∩ (/B ∪ C) is given as { 1, 6 }

From the information given, we have the sets as;

U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {1, 2, 4, 6}

B= {3, 7}

C= {1, 3, 6, 7, 8}

Note that;

B∪C = { 1, 3, 6, 7, 8}

A ∩ (/B ∪ C) = { 1, 6 }

Hence, the set is { 1, 6 }

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a) The percentage of $680 which is $490 is 72.06%.

b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.

The percentage is the ratio of a value to another.

Percentages are depicted as fractional values expressed over 100.

To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.

The result is then multiplied by 100.

For instance:

$490 of $680 is 72.06% ($490/$680 x 100)

Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.

Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.

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Answer:

-80x + 28y -56

4(-20x + 7y -14)

Step-by-step explanation:

The first answer is distributing the 8 through the whole expression.  The second answer is when you factor out a 4.