Answer: An inequality for the expected population, p, next year can be written using the information provided. Since the population is expected to grow between 5% and 8% per year, we can represent that as a range of growth rates: 0.05 <= growth rate <= 0.08
To find the expected population next year, we can use the formula:
p = population * (1 + growth rate)
where "population" is the current population of 50,000 and "growth rate" is the percentage increase. Since the growth rate is expected to be between 0.05 and 0.08, we can write the inequality as:
50,000 * (1 + 0.05) <= p <= 50,000 * (1 + 0.08)
This inequality represents the expected range of population next year, with the lower bound being the population if it grows by 5% and the upper bound being the population if it grows by 8%.
Simplifying the inequality:
52,500 <= p <= 54,000
So the expected population next year, p, is between 52,500 and 54,000.
Step-by-step explanation:
Buddy walks 5000 feet due North, then turns and walks 4000 feet due East. What is the direction and magnitude of the resultant vector?
The direction and magnitude of the resultant vector are:
i. Magnitude = 6403
ii. Direction = 51.3^o
What is a resultant vector?A resultant vector is just a single vector which represent two or more vectors acting at a point in both magnitude and direction.
To determine the magnitude of the resultant vector, we have;
let the resultant vector be represented by R, so that;
/Hyp/^2 = /Opp/^2 + /Adj/^2
R^2 = 5000^2 + 4000^2
= 25000000 + 16000000
R^2 = 41000000
R = (41000000)^1/2
= 6403.12
The resultant of the two vectors is 6403.
ii. To determine the direction (θ) of the vector,
Tan θ = y/ x
Tan θ = 5000/ 4000
θ = Tan^-1 1.25
= 51.341
θ = 51.3^o
The direction of the resultant vector is 51.3^o.
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Consider the quadratic function y = mx².
When a > 0, the graph
When a < 0, the graph
When a > 0, the graph opens upward
When a < 0, the graph opens downward
How to complete the statementsFrom 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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A surveyor measures the lengths of the sides of a triangular plot of land. what is the measure of the angle of the triangular plot at which the surveyor stands? approximate to the nearest degree. cos–1(0.75) = 41° cos–1(0.125) = 83° cos–1(0.563) = 56° cos–1(0.15) = 89°
The measure of the angle of the triangular plot at which the surveyor stands is cos(0.125) = 83°
Since we have given that the lengths of the sides of triangle from figure :
a = 300 m
b = 250 m
c = 200 m
We need to find the measure of angle i.e. A
As we know the "Law of Cosine rules ":
Cos A = b^2 + c^2 - a^2 / 2bc
= 250^2 + 200^2 - 300^2 / 2.250.200
= 125 / 1000
= 0.125
therefore , A = 82.81° approximate and close to 83°
Hence second option is correct.
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The perimeter of the floor in an office building is 127. 5 feet. What is the perimeter of the floor in the office building in yards?
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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What kind of sequence is this?
139, 126, 113, 100, ...
This is an example of a decreasing sequence. In this case, each number is 13 numbers less than the previous.
What is a sequence?A sequence is a term to refer to a group of numbers that have some characteristics in common. For example, in this case these numbers are more than 100 and the value of difference between them is 13.
How to calculate the difference?To calculate the difference between these numbers we have to substract one of the number with the next number:
139 - 126 = 13
126 - 113 = 13
Accprding to the above, this sequence is characterized for a difference of 13 numbers between each value.
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Select the correct answer.
What is this series written in sigma notation?
2. 5 + 2. 5(1. 2) + 2. 5(1. 2)2 +.
2 +. 2. 5(1. 2)87
ОА.
87
2. 5(1. 2)*
OB.
2. 5(1. 2)*1
O c.
2. 5(1. 2)*
OD.
2. 5(1. 2)*–1
=1
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"--
Question What is the radical form of each of the given expressions? Drag the answer into the box to match each expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The radical form for each expression is given as follows:
[tex]5^{\frac{2}{3}} = \sqrt[3]{5^2}[/tex][tex]5^{\frac{1}{2}} = \sqrt{5}[/tex][tex]3^{\frac{2}{5}} = \sqrt[5]{3^2}[/tex][tex]3^{\frac{5}{2}} = \sqrt{3^5}[/tex]How to obtain the radical form of each expression?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:
a is the radicand.n is the exponent.m is the root.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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To predict the performance of her first period class on their next quiz, á teacher randomly selects eight students from the class and takes the mean of their scorés on the last quiz. Is this sample representative of the class's performance on the quiz? Explain your reasoning.
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.
What does reason mean?
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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Order of operations with fractions and exponents
Evaluate the expression.
Do not round your answer.
2
3²
Stuck? Review related articles/videos or use a hint.
Report a problem
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.
(3x + 12 + 2x³ + x²)/(x + 2)
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 ;)
26. In the diagram below, what must be the
measure of the angle marked x?
39
62
Please help
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.
What is meant by angle?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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let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is ?
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 inverse of a relationship can be found by
switching the coordinates in each ordered pair. Complete the table for three
input and output values of y = x + 3 and its inverse. Then use the table to
write an equation of the inverse of y = x + 3.
y=x+3
Input (x)
Output (y)
Inverse of y=x+3
Input (x)
Output (y)
The equation of the inverse of y = x + 3 is y = x - 3.
What is inverse relationship?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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A solid-state drive (SSD) is a piece of hardware used to store data, much like a hard-drive. However, SSDs are much faster and more reliable than traditional hard-drives, and therefore many new computers are built using SSD technology Suppose a company is producing SSDs and experimenting with different sizes of storage. The function f is such that f(s) represents the cost of producing an SSD that can store s Gigabytes (GB) of data. Use function notation to answer the following questions. The cost (in dollars) to produce an SSD with 4 TB of storage, given that there are 1024 Gigabytes (GB) in one Terabyte (TB). Hint: The cost of producing an SSD that stores 4 TB is not the same as the cost of producing 4 SSDs that each store 1 TB of data
The cost of producing an SSD that can store 4 TB of data can be represented by the function f(s), where s is measured in GB. Since there are 1024 GB in one TB, 4 TB is equal to 4 x 1024 = 4096 GB.
So, the cost of producing an SSD with 4 TB of storage can be represented by:
f(4096)
It is important to note that f(s) is the cost of producing an SSD with s GB of storage, not the cost of producing s SSD with 1 GB of storage.
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What expressions are equivalent to 6g - 18h?
Choose 2 answers
A: (g - 3) x 6
B: 2 x (3g - 18h)
C: 3(2g - 6h)
D: (-g - 3h)(-6)
E: -2 x (-3g + 9h)
The expression that is equivalent is options D. (-g - 3h)(-6) and E. -2(-3g + 9h)
What is factorization?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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Can someone help with this
y = 4x is the only function that represents the proportionality.
What is 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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what value of poisson's ratio characterizes deformation without change in volume? group of answer choices
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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The 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 ℃ ?
At the height of 2500 m, the temperature will be T = 16 ℃.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.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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For a set of data, r = 0.27. Which is true about the correlation of the variables?
• The variables have a strong positive correlation.
• The variables have a weak negative correlation.
The variables have no correlation.
O The variables have a weak positive correlation.
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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In July the price of a holiday is £500.
In August the price increases by 25%.
In September the price drops to £500 again.
Work out the percentage decrease from the August price to the September price.
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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PLEASE HELP let f(x) = 2x^2+x-3 and g(x) =x-1
find the domain
a x^2-4: domain; positive real numbers
b 2x^2-4 domain all real numbers
c x^2-4 domain all real numbers
d 2x^2-2 domain all real numbers
The correct options regarding the domain of the functions are given as follows:
b 2x^2-4 domain all real numbers
c x^2-4 domain all real numbers
d 2x^2-2 domain all real numbers
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
Quadratic functions have no restrictions, hence the domain for all of them is of all real values, and thus options b, c and d are the correct options.
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Amanda wants to showcase her favorite function: f(x)=1+sqrt(x+5). She has built a function machine that performs these operations on the input values. Her brother Eric is always trying to mess up Amanda's stuff, so he created the inverse of f(x), called it e(x), and programmed it into a machine.
b. What happens if the two machines are pushed together? What is e(f(-4))? Explain why this happens
Answer:
First find what f(-4) is, it is 2. Then substitute the 2 into x for e(x). Then is becomes e(2) which equals -4. The output is the same as the input because they are inverses. When putting the output of the original equation as the input of the inversed equation, the output of the inversed equation becomes the input of the original equation.
The function e(f(-4)) = -4. This happens because when two function machines are pushed together, the output of the first machine is used as the input for the second machine.
The inverse of a function f(x) is a function e(x) such that e(f(x)) = x for all x in the domain of f(x). To find the inverse of Amanda's favorite function, f(x) = 1 + sqrt(x + 5), we need to isolate x in the expression 1 + sqrt(x + 5) and call it y:
y = 1 + sqrt(x + 5)
Squaring both sides of the equation, we get:
y^2 = 1 + 2sqrt(x + 5) + (x + 5)
y^2 - 1 = 2sqrt(x + 5) + x + 5
Expanding the square on the left side, we get:
y^2 - y - 6 = x
So the inverse function, e(x), can be defined as:
e(x) = y^2 - y - 6
Finally, to evaluate e(f(-4)), we first need to find f(-4), then use the result as an input to the inverse function e(x):
f(-4) = 1 + sqrt(-4 + 5) = 1 + sqrt(1) = 1 + 1 = 2
e(f(-4)) = e(2) = 2^2 - 2 - 6 = 4 - 8 = -4
Therefore, e(f(-4)) = -4.
This happens because when two function machines are pushed together, the output of the first machine is used as the input for the second machine.
The inverse of Amanda's favourite function takes the output of the first machine and finds the original input that would have produced the same output. In this case, the original input was -4.
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Convert. Simplify your answer and write it as a proper fraction or as a whole or mixed
number.
5 inches = ? Feet
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
Han and Leia plan on renting a 1050SQFT apartment. In order to do this, they
have the following fees: $150 application desposit, $15 credit report, Security
deposit equal to 1 month's rent, Last AND first month's rent, Broker's fee that
is 12% of the yearly rent. If 1 month's rent is $1350, howmuch should Brian
and Jamie plan on spending when they sign their lease?
The amount that Brian and Jamie have to plan on spending should be: $4859.
How to solve for the amount that should be spentThe 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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Divide. Write the quotient in lowest terms. 5\dfrac{2}{3} \div 4 =5 3 2 ÷4=5, start fraction, 2, divided by, 3, end fraction, divided by, 4, equals
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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escribe two different ways to find the slope of a function and two different ways to find the y-intercept of a function
Frank was trying to simplify the following expression 43+3. Sarah said to add 3 to both the top and the bottom of the fraction. Gwen said to
just add three to the top of the fraction. Which person is correct? What is the value of the expression?
cor
correct. The value of the expression is
V
Gwen is correct. The expression 43 + 3 can be written as 43/1 + 3/1
What is an Algebraic Expression?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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35 less than a number m is -72
The required simplified value of the m is given as -37. as of the given information.
What are equation models?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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A barn is 40 feet wide by 100 feet long. Make a scale drawing of the barn that has a scale of 1/2 inch = 10 feet
As per the given measurement, the scale drawing of the barn is attached below.
The term scale drawing is defined as a real object with accurate sizes reduced or enlarged by a certain amount.
Here we have given that a barn is 40 feet wide by 100 feet long.
Here we have given in the question that if you draw a line that is 1/2 an inch on paper its proportional to 10 feet long on the house.
Which means that 1 inch would be 20, then 1.5 would be 30 feet, and then 2 inches would be 40.
Here we have given the proportion would be written as,
=> 2 in: 40 ft
As we know that if we make the ratios equal, then we have,
=> 1/20 = x/40
When we simplify this then we get the value of x as 2
Similarly, for the another one,
=> 1/20 = x/100
Now, we have to multiply both sides by 100:
=> 100/20 = x
Therefore, the value of x is 5.
Hence the scale drawing of the house would be 2 inches wide and 5 inches long.
And the drawing is attached below.
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PLEASE HELPPPPPPPP.
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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