Solve for x. Round to the nearest tenth, if necessary.

in option A and B a right triangle is formed when three squares are joined at their vertices, the area of the largest square is the same as the combined area of the two smaller squares.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

A) From the given figure, side of a largest square is 17 inches, side of a larger square is 15 inches and the area of a smaller square is 64 square inches.

We know that, the area of a square is side².

The side(c) of a smaller square is side²=64

Then, c=8 units

By using Pythagoras theorem, we get

17²=15²+c²

289=225+8²

289=289

B) From the given figure, area of a largest square is 169 square inches, area of a larger square is 144 square inches and the side of a smaller square is 5 inches.

We know that, the area of a square is side².

The side(a) of a largest square is side²=169

Then, a=13 inches

The side(b) of a larger square is side²=144

Then, b=12 inches

By using Pythagoras theorem, we get

13²=12²+5²

169=144+25

169=169

Therefore, in option A and B a right triangle is formed when three squares are joined at their vertices, the area of the largest square is the same as the combined area of the two smaller squares.

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Check the picture below.

From the combination of 251 textbook, 92 sociology and 159 biology textbook were sold.

Let the number of biology textbook be x. So, the number of sociology textbook = 251 - x. The difference between the number of two books is 67. Representing this as equation.

Number of biology textbook = number of sociology textbook + 67

Keep the values in formula -

x = 251 - x + 67

Rewriting the equation

x + x = 251 + 67

Performing addition on both sides of the equation

2x = 318

x = 318/2

Performing division

x = 159

Number of biology textbook = 159

Number of sociology textbook = 251 - 159

Number of sociology textbook = 92

Thus, 92 sociology and 159 biology textbook 1ere sold.

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The complete question is -

A textbook store sold a combined total of 251 biology and sociology textbook in a week. The number of sociology textbook old was 67 less than the number of biology textbook sold. How many textbook of each type were sold?

The values of b for the function f(x) = x² + bx + 1  has

(a) two real roots is |b| > 2 .

(b) has only one real roots is b = ±2  .

(c) has no real roots is  b < -2 or b > 2.

A Quadratic Function of the form f(x) = x² + bx + 1 has two real roots if and only if its discriminant (b² - 4ac) is positive, where a = 1, c = 1 .

So ,the discriminant can be written as ⇒ b² - 4 × 1 × 1

⇒ b² - 4.

Part (a) ; the two roots are real if and only if b² - 4 > 0,

⇒ b² > 4.

⇒ |b| > 2 .

Part (b) : function has only one real root if and only if its discriminant =0 .

⇒ b² - 4 = 0  ;

⇒ b² = 4  ;

which implies ⇒ b = ±2  .

Part (c) : function has no real root if and only if its discriminant < 0 .

⇒ b² - 4 < 0  ;

⇒ b² < 4  ;

which implies ⇒  b < -2 or b > 2.

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Answer:

2*7*7

Step-by-step explanation:

Answer: 2*7^2

Step-by-step explanation:

98=2*49

and 49=7^2

so 98=2*7^2

The dependance on experience is reflected in the syntactic distinction between prior probability statements.

syntax refers to alphabet, while semantics refers to meaning. Syntax is the set of rules demanded to insure a judgment is grammatically correct; semantics is how one's wordbook, grammatical structure, tone, and other rudiments of a judgment coalesce to communicate its meaning. syntax is the arrangement or order of words, determined by both the pen's style and alphabet rules. consisting of or noting coinages that are combined in the same order as they would be if they were separate words in a corresponding construction The word blackberry, which consists of an adjective followed by a noun, is a syntactic emulsion.

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Answer: Reduce the fraction to the simplest form.

Hope this helps :)

Step-by-step explanation:

8/10

/ 2

4/5

When the angle of elevation from a point on the structure to its top is 40°, the building has a height to the nearest foot of 758 feet.

Offered that it has sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with the endpoints A, B, and C. When the three points are not collinear, a unique rectangle and triangle in Trigonometry are discovered. Triangles are polygons because they have three sections and three corners. The points where the four sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

Using the triangles OBD and OAD and the SOH CAH TOA identity

OAD in triangle

Divide the two resulting equations to obtain the value of "x" for the triangle OBD.

The building's height must then be determined to the closest foot.

Just to refresh your memory, H = xtan50 H = 636tan50

H = 636(1.1918)

H = 757.96 feet.

Consequently, the building is 758 feet tall to the nearest foot.

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Answer: y = -6x + 1

Step-by-step explanation:

An equation for a line written in slope-intercept form is written as y = mx + b, with m being the slope and b being the y-intercept.

Within 100 feet of a bridge, viaduct, tunnel, intersection, or railroad grade crossing.

In contrast to crossing over or under using an overpass or tunnel, a level crossing is an intersection where a railway line crosses a road, path, or (in rare circumstances) an airport runway at the same level. The phrase also applies when a light rail line crosses a road in a similar manner but has a separate right-of-way or reserved track.

Other terms include road through railroad, criss-cross, train crossing, and RXR. They also include railway level crossing, railroad crossing (mostly international), grade crossing, or railroad crossing (primarily American) (abbreviated).

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As per the differential equation, the value of k for which the constant function is 1.

The term called differential equation in math is defined as an equation which contains one or more terms and the derivatives of one variable

Here we know that the differential equation is

=> 4t³ dx/dt + 2x - 2 = 0

Here we have also know that x(t) = k is a solution of the differential equation.

Which means the t the value of x' = 0.

Then the value of 4t³ dx/dt = 0.

So, here we have rewritten the equation like the following,

=> 0 + 2x - 2 = 0

Here we know that the value of x = k, then we get the equation like the following,

=> 2k - 2 = 0

=> k = 1

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The number of bicycle  store needs to sell each month to break even is, 55

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

A bicycle store costs ​$3850 per month to operate

The store pays an average of ​$75 per bike

The average selling price of each bicycle is ​$145

The number of sells to break even = ?

Suppose, the number of sales is x

So, it can be written as,

For break even condition

75x + 3850 = 145x

145x - 75x  = 3850

70x = 3850

    x = 3850/70

    x =  55

Hence, the number of sales is 55

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Answer:The box plots for Theo’s math scores and language arts scores.

2 box plots. The number line goes from 50 to 100.

For math, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80.

For language arts, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70.

About 50% of Theo’s scores are in which range for each subject?

60 to 85 for math; 60 to 80 for language arts

55 to 90 for math; 50 to 90 for language arts

55 to 60 for math; 50 to 60 for language arts

85 to 90 for math; 80 to 90 for language arts

Step-by-step explanation:

the whiskers range from 55 to 90 =>   ( min 55 , max 90  , range = 90-55 = 45)

the box ranges from 60 to 85.  =>  (Q₁ = 60 and Q₃ = 85)

A line divides the box at 80   => (Q₂ = Median = 80)

For language arts,

the whiskers range from 50 to 90 => ( min 50 , max 90  , range = 90-50 = 40)

the box ranges from 60 to 80.  =>  (Q₁ = 60 and Q₃ = 80)

A line divides the box at 70.  => (Q₂ = Median = 70)

50% of Theo’s scores lies between Q₁ and Q₃

The point on the curve with a slope of −93–√2 is (2, 0.43)

Given x(t) = 2 sin(8t) and y(t) = −9 cos(8t)

We are asked to determine the points on the curve with a slope of −93–√2.

Now, x/2 = sin(8t)   --(1)

       -y/9 = cos(8t)   --(2)

Squaring and adding equations (1) and (2)

               (x/2)² + (-y/9)² = sin²(8t) + cos²(8t)

                   x²/4 + y²/81 = 1

Differentiating both sides

                 x/2 + (2y/81) (dy/dx) = 0

Given slope = dy/dx = −93–√2

                 (2sin(8t))/2 + (2(−9 cos(8t))/81)(-93 - √2) = 0

                   sin(8t) + (2/9)cos(8t)(93 + √2) = 0

Solving for t and taking care of 0 ≤ t <π/8

                 we get t = 11.59°, 34.09°, 79.09°......

But only t within the given range is t = 11.59°.

Now, x = 2sin(8 x 11.59°) = 2

and y = -9 cos(8 x 11.59°) = 0.43

Hence, the point on the curve with a slope of −93–√2 is (2, 0.43)

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The worth at the end of the third​ year is 15,400.

Depreciation:

The purchase value of an asset is the amount that it is purchased for. The value of the asset after a certain number of years is the difference between the purchase value and the accumulated depreciation.

There is a general formula to calculate Depreciation:

Depreciation Method = (Cost of an Asset – Residual Value)/Useful life of an Asset.

Given that Cost of an Asset=25000

Residual Value=2600

The useful life of an Asset=7

Now plug the given values in the above formula:

(25,000-2,600)/7=22,400/7=3,200

DM=3,200 which is calculated annually.

For the 3 years worth:

25,000-3,200*3

25,000-9,600=15,400.

At the end of the third year, the worth is 15,400.

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Tiana' laptop originally cot $250, but the tore offered a 20% off discount, the final place of the laptop is $216.

Let the Laptops original price be $250

But he tore the offer of 20% discount, after getting a 20% discount,

(100 - 20)% x 250

= 200

Tiana then paid also a 8% tax on this price so,

= (100+8)% x 0.8(250)

=1.08 x 200

=216

So final price be ,

P = L (0.8)(1.08)

P = 250 x 0.8 x 1.08

P = $216

A tax is a mandatory financial charge or other type of levy imposed by a government organization on a taxpayer (an individual or legal entity) to cover costs associated with running the country and other public expenditures.

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Answer:

Step-by-step explanation:

The expression representing the area covered by the pavilion can be found by multiplying the length by the width:

A = (x + 8) * (x - 4)

where A represents the area and x is the length of one of the sides.

The probability that a state is occupied by an electron at

i)1kt:0.5

ii) 3kt: 0.7

ii)5kt: 0.9

The probability that a state is occupied by an electron at any given temperature above the Fermi level is calculated using the Fermi-Dirac statistics. This equation states that the probability of a state being occupied is equal to 1/(1+exp(-(E-EF)/KT)), where E is the energy of the state, EF is the Fermi level energy, and KT is the product of Boltzmann's constant and the temperature in Kelvin.

Thus, for a temperature of 1kt above the Fermi level, KT = 1. By plugging these values into the equation, we can calculate that the probability of a state being occupied is 0.5. For a temperature of 3kt and 5kt above the Fermi level, KT = 3 and 5, respectively. Using these values, the probability of a state being occupied at 3kt and 5kt above the Fermi level is 0.7 and 0.9, respectively.

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Answer: 0.6

Step-by-step explanation:

3 divided by 5 is 0.6

0.6 x 5 = 3

3/5 = 0.6

The probability that a randomly selected set of 3 will include 1 a and 2 b is 45/182.

Probability

The probability is equal to the variety of possible outcomes.

For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12.

the total number of outcomes that could occur.

there are total 4 types of probability,

1- Classical

2- Empirical

3- Subjective.

4- Axiomatic

There are 66 equally likely outcomes, or C(9+5,3) =C(14,3)= 364 possible outcomes.

Only C(9,1) * C(5,2)= 90 of these contain 1A and 2B. thus, the likelihood is 90/364.

The value of the solution is 90/364 or 45/182.

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Answer:

c. m<-15/8

Step-by-step explanation:

solve

m + 1/4 < -13/8 = m< -15/8

Answer: ill explain

Step-by-step explanation:

the form for linear equations are f(x) = mx+b

b is the y-intercept (otherwise known as the place where the line crossed the y-axis)

since there is no b, the y-intercept is 0. The line with cross the point (0,0)

your problem is f(x) = x/1

x/1 is equal to 1x/1.

to graph linear functions, you do rise over run (rise/run)

in this case, you rise (go up) one unit, and run (go right) one unit since your digits are 1 and 1

Answer:

Step-by-step explanation:

The sum of two supplementary angles is 180

Let A be the larger angle and B be the smaller angle

A+B=180

Given A=5B-18

5B-18+B=180

6B=180+18=198

B=198/6=33

A=180-B=180-33=147

Hence A=147, B=33

After solving the equation P = [tex]$ \frac{ry}{r+y}[/tex], y is equal to [tex]\dfrac{rp}{(r- p)}[/tex].

What is equation?

An equation is a mathematical statement that expresses the equality of two expressions by showing that they have the same value. Equations can be used to describe a variety of physical, chemical and biological processes.

They are often used to solve problems in a variety of fields, including engineering, finance and physics. Equations are typically written in standard form, with the equal sign being used to indicate the equality of two expressions.

The two expressions can be written in a variety of forms, including algebraic equations, differential equations, calculus equations and trigonometric equations. The solutions to equations can be found by using a variety of techniques, including solving equations graphically or analytically.

Given

P = [tex]$ \frac{ry}{r+y}[/tex]

Solve for y

⇒ pr + py = ry

⇒ pr = y(r−p)

⇒ y = [tex]\dfrac{rp}{(r- p)}[/tex]

Thus, after solving the equation P = [tex]$ \frac{ry}{r+y}[/tex],y is equal to [tex]\dfrac{rp}{(r- p)}[/tex].

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Complete question:

The missing values in the ratio table are:

The equivalent ratios in the order they appear in the table are:

Ratios that are the same when compared are referred to as equivalent ratios. To determine whether two or more ratios are equivalent, they can be put side by side.

An equivalent ratio is, for instance, 1 : 2 and 2:4.

Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

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The probability of Tabria randomly selecting a peanut butter cookie and then an oatmeal cookie is 8/35 or 8 in 35 chance

The probability of selecting a peanut butter cookie first is 8/29, since there are 8 peanut butter cookies and 29 total cookies of all variety in the bag. Then, the probability of selecting an oatmeal cookie after eating a peanut butter cookie is 8/28, since there are now only 28 cookies remaining in the bag and 8 of them are oatmeal cookies. To find the combined probability, we multiply the individual probabilities:

8/29 × 8/28 = 8/35.

This means there is an 8 in 35 chance that Tabria will randomly select a peanut butter cookie and then an oatmeal cookie.

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The nurse asks the patient about their ability to stand when preparing to measure their height and weight because it is the most accurate way to measure these physical characteristics. By asking about their ability to stand, the nurse can determine if alternative methods of measurement need to be used, and can also identify any underlying health issues that need to be addressed

When a patient is admitted to a healthcare facility, one of the first things the healthcare provider does is gather information about the patient's physical characteristics. This includes measuring the patient's height and weight.

As part of the preparation process for measuring height and weight, the nurse may ask the patient about their ability to stand. There are several reasons why this is important.

First, the most accurate way to measure height is to have the patient stand upright, with their head facing forward and their feet together. If the patient is unable to stand, the nurse may have to use alternative methods to measure height, such as a measuring tape, which may not be as accurate.

Second, standing is also the most accurate way to measure weight. If the patient is unable to stand, the nurse may have to use a bed scale, which may not provide an accurate measurement of the patient's weight.

Finally, asking the patient about their ability to stand helps the nurse to determine if there are any underlying health issues that need to be addressed. For example, if the patient is unable to stand, it may indicate that they have a mobility issue that needs to be addressed.

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A. In a case whereby Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $1000 worth of shoes  his commission is  $22.50

B. The percentage markup was  $30

C.In a case whereby  aTyler’s brother earns $14 per hour. The store offers him a raise—a 5% increase per hour the amount Tyler’s brother make per hour is 12.60

The concept that will be used here is commision and percentage.

A. Therefore, a commission is often a percentage of a sale. Suppose, for illustration, that I own a cookie company. I take you on as a seller and inform you that you will receive a 10% commission for each box you sell. Given that the box of cookies costs $5.00,

you would get $5.00 * (.10), or $0.50, for each successful box you sell. Therefore, if you sell 200 boxes in a week and earn $0.50 per box, your total commission would be $0.50 * 200 = $100!

Thus, Tyler's brother sold shoes valued a total of $900. In the event that he earns a 2.5% commission, his reward will be [ $900 * (0.025) ]= $22.50 for his work.

B. The Markup on the shoe =Amount sold - purchase price

Markup = [$80 - $50]

= $30

Percentage Markup is :$30/50  *100 =  60%

C. 5% of 12  can be calculated as 5/100*12=  0.60

[12 + 0.60 ]

= 12.60

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