Evaluate the expression.

(13+9)+37
=

The value of x would be √2.

What is the 45-45-90 triangle?

A 45-45-90 triangle is a special type of right triangle where the angles measure 45 degrees, 45 degrees, and 90 degrees. The sides of the triangle are in a specific ratio to each other. The hypotenuse, or the longest side of the triangle, is the same length as the other two sides (the legs). This side length is also equal to the square root of 2 times the length of either leg. The legs of the triangle are congruent to each other. This triangle is also known as an "isosceles right triangle".

In the given figure, we can apply a 45-45-90 triangle,

side opposite to 45 = 1/√2 * Hypotenuse

x = 1/√2 * 2

x = √2

Hence, the value of x would be √2.

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An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is always the same.

This common difference is called the common ratio of the arithmetic progression. The general form of an arithmetic progression is a, a + d, a + 2d, ..., where a is the first term and d is a common difference.

The nth term of an arithmetic progression can be found by using the formula: a_n = a + (n-1)d, where a is the first term, d is a common difference, and n is the position of the term in the progression.

If a, b, and c are in arithmetic progression, then the common difference is (b-a) = (c-b).

If d, e, and f are also in arithmetic progression, then the common difference is (e-d) = (f-e).

If a, d are the same and b, e are the same, then c = f.

so the common difference between both progressions is the same, and c = f

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let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is the common difference

The relative frequency of Selena's friends who speak more than one language is 3/16 or 0.1875

To create a relative frequency distribution, we first need to find the total number of responses by summing up the number of languages spoken by Selena's friends. In this case, the total number of responses is 2 + 1 + 1 + 1 + 2 + 3 + 1 + 2 + 1 + 1 = 16.

Next, we need to find the relative frequency for each category, which is the number of responses in that category divided by the total number of responses. To find the relative frequency of her friends who speak more than one language, we need to add up the number of responses in categories 2, 3, and above.

In this case, the number of responses in category 2 is 2, the number of responses in category 3 is 1, and there are no responses above 3.

So the relative frequency would be (2+1)/16 = 3/16 or 0.1875

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The given series in sigma notation is [tex]\sum_{k=1}^{88} 2.5(1.2)^{k-1}[/tex].

A geometric series is the summation of an infinite number of terms that have a constant ratio between consecutive terms.

This is an infinite geometric series with a first term of 2.5, a common ratio of 1.2, and 87 terms. It can be written as:

2.5 + 2.5(1.2) + 2.5(1.2)^2 + ... + 2.5(1.2)^87 = 2.5 × (1 + 1.2 + 1.2^2 + ... + 1.2^87)

If we look at the power, it is always one less the term, i.e., for the first term, the value of k = 0.

So, the series in the form of summation is as follows:

[tex]\sum_{k=1}^{88} 2.5(1.2)^{k-1}[/tex]

Hence, the correct answer is D.

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--The given question is incorrect; the correct question is

"what is this series written in sigma notation 2.5 + 2.5(1.2)+2.5(1.2)^2+...+2.5(1.2)^87"--

The equation of the inverse of y = x + 3 is y = x - 3.

The theory used in this question is the concept of inverse relationships. In mathematics, an inverse relationship is a relationship where two variables are related in such a way that when one variable increases, the other decreases.

In this case, the relationship between x and y is represented by the equation y = x + 3.

To find the inverse of this equation, we need to switch the coordinates in each ordered pair, which is done by subtracting 3 from the output (y) for each ordered pair.

This gives us the equation y = x - 3, which is the inverse of y = x + 3.

y=x+3

Input (x) Output (y)

3   6

-1   2

5   8

Inverse of y=x+3

Input (x) Output (y)

6   3

2   -1

8   5

The equation of the inverse of y = x + 3 is y = x - 3.

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The angle denoted by the letter x is an inscribed angle created by the intersection of the chords AC and BD, as can be seen.

Corner, whether it be a protruding element or a section of an enclosed space. the pattern created by two lines that diverge from the same point.

a measurement of an angle or the degree of rotation necessary to parallelize or align two angled lines or planes.

An angle in planar geometry is a form created by two rays or lines that have a common termination. The English word "angle" derives from the Latin word "angelus," which means "corner."

The vertex, which serves as the joint terminus of two rays, and the two rays are known to as the sides of an angle and an angle, respectively.

Our goal is to determine the size of the angle denoted by the x:

We may use the chord theorem formula because we can see that the angle denoted with x is an inscribed angle created by the intersection of the chords AC and BD.

x = BC + AD / 2

By replace BC with 39 and AD with 62, we get:

x = 39 + 62/2

x=50.5°

Therefore, measure of the angle marked x=50.5°

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Answer: If your simplifying it's: 2x (power of 3) + x (power of 2) + 3x + 12x +2. Dividing would be 2x (power of 2) − 3x + 9 − 6/x+2. Have a nice day ;)

y = 4x is the only function that represents the proportionality.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given there are Few functions, we need to find which of the given function is proportional:

Since, We know that only the linear functions that pass through the origin are proportional.

So only function that provides the value of y at x = 0 is 0 will shoe properties of proportionality

Therefore, only function that is proportional is y = 4x.

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The quotient for the given division of fractions [tex]5\dfrac{2}{3} \div 4[/tex]  is 17/12.

We are given the equation - [tex]5\dfrac{2}{3} \div 4[/tex]

First we will convert the mixed fraction 5\dfrac{2}{3} in to improper fraction as follows -

[tex]5\dfrac{2}{3}[/tex]   [tex]= \frac{3*5+2}{3}[/tex]

[tex]5\dfrac{2}{3}[/tex]   [tex]= \frac{17}{3}[/tex]

Now we will divide the fraction as follows -

[tex]5\dfrac{2}{3} \div 4[/tex]

= 17/3 ÷ 4

taking the reciprocal of 4 and changing the divide sign into multiplication we get,

= 17/3 x 1/4

= 17*1 / 3*4

= 17/12

Hence, the quotient for the given division of fractions is 17/12.

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Poisson's ratio v can get close to 1, but never reach it 1/2. G/B = 3(1-2v)/(2(1+v)) limits it.

The right hand side must be positive because the shear G and bulk B moduli must both be positive since else an elastic material would spontaneously deform. This results in -1 v 12.

Because of those  symbols, equality is not possible; consequently, G/B cannot be zero. The elasticity formulas are invalid because any substance with G = 0 is a fluid.

Keep in mind that v = 12 is the typical model for rubbers. Since the ratio G/B is greater than 6000 for gum rubbers, this estimate is only a rough guide. This presumption has the effect of ignoring any volumetric distortion.

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It's important to note that even if the sample is random, there's still a chance that the sample may not be representative of the population, this is known as sampling error.

The fundamental act of thinking about anything logically and sensibly is best described as reasoning.

It depends on how the teacher choose the class members. Because every student had an equal chance of being chosen, the sample, if the students were chosen at random, is likely to be indicative of the class' performance on the quiz. However, the sample would not be indicative of the class's performance on the quiz if the teacher arbitrarily chose the students, for instance, by selecting only the best or the worst performers.

In general, if a sample is large enough and random, it is thought to be representative of the population. The likelihood that the sample is representative of the population rises with greater sample sizes. Since only 8 students were chosen in this instance, it's possible that the results don't accurately reflect how the entire class did on the quiz.

The term "sampling error" refers to the possibility that a sample, even one drawn at random, may not be representative of the population as a whole.

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Answer:

C

Step-by-step explanation:

When a > 0, the graph opens upward

When a < 0, the graph opens downward

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

The quadratic function y = mx²

The variable represents the leading coefficient

i.e. a = m

As a general rule:

Equations with negative leading coefficients open downwards, while other open upwards

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Answer:

Without exponents: a * a * a * a * a

Fill in the blank: [tex]a^5[/tex]

Step-by-step explanation:

We have to use exponent rules:

[tex]x^y * x^y = x^{y+y} \\= x^{2y}[/tex]

So for this problem, we can apply that rule here:

[tex]a^3 * a^2 = a^{3+2}[/tex]

= [tex]a^5[/tex]

^ This will be the answer to the second question.

Now, to find the equation without exponents, we can use the information we have from above. We need to use this rule: [tex]x^2 = x * x[/tex]

Since our equation is [tex]a^5[/tex], we can rewrite it as a * a * a * a * a.

1 hour and 12 minutes is the time that will it take her to develop 8 rolls of film.

According to the question,

Tara develops 2 rolls of film in about 18 minutes.

Tara develops 1 roll of film in about  = (18 ÷2) minutes

                                                                = 9 minutes (using division)

Tara develops 8 rolls of film in about = ( 8 × 9) minutes

                                                                   = 72 minutes

we know that, 1 hour = 60minutes

Tara can develop 8 rolls of film in about = (72 ÷ 60)

                                                                   = 1 hour 12 minutes

So, Tara can develop 8 rolls of film in about 1 hour and 12 minutes.

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The radical form for each expression is given as follows:

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

To obtain the radical form, we have that:

Hence the radical form of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

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The required simplified value of the m is given as -37. as of the given information.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
According to the question, we have variable m, and 35 less than m is -72

m - 35 = -72

Add 35 on both sides
m = -72 + 35
m = -37

Thus, the required simplified value of the m is given as -37.

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∠XBC is 55 degrees because it is corresponding to ∠AXY..

The angle ∠BXC is 70 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines.

XB = XC

ΔXBC is an isosceles triangle.

Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.

Let's find ∠BXC.

Therefore, the base angles of an isosceles triangle are congruent.

Hence,

∠XBC = ∠BCX = 55 degrees

Therefore,

55 + 55 + ∠BXC = 180

110 + ∠BXC = 180

∠BXC = 180 - 110

∠BXC = 70 degrees

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The perimeter of the floor of the office building  which was given as 127.5 feet is equal to 42.5 yards.

Perimeter of the floor in an office building is equal to 127.5 feet.

Convert perimeter of the floor of the given office building in feet into yards:

Number of feet in one yard = 3 feet

3 feet = 1 yard

⇒ 1 feet = ( 1 / 3 ) yard

⇒ 127.5 feet = ( 127.5 ) ×   ( 1 / 3 ) yards

⇒127.5 feet = ( 127.5 / 3 ) yards

⇒127.5 feet = ( 42.5 ) yards

Therefore, the perimeter of the floor of the given office building is equal to 42.5 yards.

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Step-by-step explanation:

you did not provide an expression. only fragments, I suspect.

I can give you the basic rules.

always remember the order of operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

a fraction is a division.

e.g. 2/3 = 2 divided by 3

e.g. (a/b)⁵ = a⁵/b⁵

(a×b)⁵ = a⁵×b⁵

e.g. a^-b = 1/(a^b)

e.g. a^(c/b) =

[tex] \sqrt[b]{ {a}^{c} } [/tex]

I think that is all about exponents and fractions.

The amount that Brian and Jamie have to plan on spending should be: $4859.

The security deposit is equal to 1 month's rent, which is $1350.

The first and last month's rent is also $1350, so that's a total of $2700 for the first and last month's rent and the security deposit.

The broker's fee is 12% of the yearly rent, which is $1350 x 12 = $16,200.

12% of $16,200 is $1944.

So in total, they will have to pay $150 application deposit + $15 credit report + $2700 + $1944 = $4859.

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Answer:

x = 7 , y = 4

Step-by-step explanation:

the triangle on the right has 3 congruent angles and is therefore equilateral with 3 congruent sides, so

3x - 5 = 5y - 4 → (1)

the triangle on the left has 2 congruent angles and is therefore isosceles with the 2 legs being congruent, so

3x - 5 = y + 12 → (2)

we have 2 equations with 3x - 5 on the left side so equate the right sides

5y - 4 = y + 12 ( subtract y from both sides )

4y - 4 = 12 ( add 4 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

Then

5y - 4 = 5(4) - 4 = 20 - 4 = 16 , so

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Gwen is correct. The expression 43 + 3 can be written as 43/1 + 3/1

In most cases, something is said to be equivalent if two of them are the same. Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning. The two expressions, however, produce the identical outcome when the values are inserted into them.

Gwen is correct. The expression 43 + 3 can be written as 43/1 + 3/1. To simplify, you can add the numerators (43 + 3) and keep the denominator the same (1). So the simplified expression is 46/1, which is equal to 46.

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Answer:

To convert inches to feet, we divide the number of inches by the number of inches per foot. One foot is equal to 12 inches.

So, to convert 5 inches to feet:

5 inches / 12 inches/foot = 5/12 feet

The answer can be simplified as a proper fraction.

5 inches = 5/12 feet

At the height of 2500 m, the temperature will be T = 16 ℃.

Given is that air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃.

2 ℃ for every 500 m of elevation.

Then, for 1 m of elevation, it will change by (2/500) or (1/250) ℃

We can write the function as -

T{x} = 26 - {x/250}

Now, for T = 16 ℃, we can write -

26 - {x/250} = 16

26 - 16 = x/250

10 = x/250

x = 2500 m

Therefore, at the height of 2500 m, the temperature will be T = 16 ℃.

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The radius of circle for the given length of rod is found as 1.65 ft

Perimeter of circle = 2 π r

In which,

When the length of the rod is bent to form the circle.

Length of rod = Perimeter of circle

10.38 = 2 π r

r = 10.38 /  2 π

r = 1.65

Thus, the radius of the circle for the given length of rod is found as 1.65 ft.

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The expression that is equivalent is options D. (-g - 3h)(-6) and E. -2(-3g + 9h)

Factorization is a process in which a given term is reduced to its lowest form by comparing common divisible number, or alphabet.
Considering the given expressions, that one that will be equivalent to 6g - 18h can be determined by;

i. 6g - 18h

factor out 6 to have;

6g - 18h = (g - 3h)6

             = (-g - 3h)(-6)

ii. 6g - 18h

The common divisor is 2, so that;

6g - 18h = 2(3g - 9h)

minus sign can be factor out

2(3g - 9h) = -2(-3g + 9h)

So that on expansion, the initial expression in the question can be gotten.

Therefore, the expression that are equivalent are (-g - 3h)(-6) and -2(-3g + 9h)

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The  sign of r is positive and  there is a positive and weak correlation.

What is Statistics ?

In statistics, association is any statistical relationship, whether causal or not, between two random variables or bivariate data.  One is independent and other is dependent variable.  

In the broadest sense correlation is any statistical association, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.

Examples are exercise and sickness are negatively correlated.

Study hours and marks are positively correlated

When correlation is nearer -1 or +1 there is a strong correlation.  When correlation is nearer to 0 than to 1 or -1 we say that there is a negative correlation.

Hence, The  sign of r is positive and  there is a positive and weak correlation.

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The percentage decrease from the August price to the September price = 20%

Here, In July the price of a holiday is £500.

And in August the price increases by 25%.

Let 'p' represents the price of a holiday.

First we need to find the value of the 25 percent of £500.

25% of £500

= 500 × (25/100)

= £125

so, the value of p would be,

p = £500 + 25% of £500

p = £500 + £125

p = £625

In September the price drops to £500 again.

i.e., p = 500

So, the decrease in price is: 625 - 500 = 125

Now we find the percentage decrease from the August price to the September price.

(125/625) × 100 = 20%

the percentage decrease in price = 20%

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