The distance KT and angle of elevation of the pole's top, K, with respect to the ground, D, are;
KT is about 6.2 cm
DN = 30 m
The angle of elevation of K from D is 0.23°
What is an angle of elevation?The angle created between a horizontal line and the line of sight of a viewer gazing up at an object is known as the angle of elevation.
The two vertical poles are MT and NK
The height of MT = 8 cm
The height of NK = 12 cm
From the top of the pole MT, point T, to the top of the pole NK, point K, there is a 40-degree elevation difference.
The poles' height differences are 12 cm - 8 cm, or 4 cm.
The distance KT can be found as follows;
Therefore;
sin(40°) = 4/KT
KT = 4/(sin(40°)) ≈ 6.2
The distance KT is approximately 6.2 cm
According to the information in the question, the distance is DN = 30 m.
The base of the poles MT and NK is on the same level ground as point D.
ND=30m
Hence, the trigonometric ratio for tangent may be used to get the angle of elevation,, of the top of the pole NK, (point K), from D as follows;
tan(θ) = NK/ND
tan(θ) = (12 cm)/(30 m) = 0.12/30 = 0.004
θ = arctan(0.004) ≈ 0.23°
K is elevated from d at an angle of roughly 0.23°.
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Find m1 if m5 = 142 and m4 = 65
The angles measures are m∠1 is 103, m∠2 is 38, m∠3 is 77.
Describe Angles?In geometry, an angle is a measure of the amount of turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians.
A degree is a unit of measure for angles, where one full circle contains 360 degrees. A right angle, which forms a quarter of a circle, is 90 degrees. Angles that are smaller than a right angle are called acute angles, while angles that are larger than a right angle are called obtuse angles. Angles that add up to a straight line, which forms half of a circle, are called supplementary angles, while angles that add up to a full circle are called explementary angles.
A radian is another unit of measure for angles, where one full circle contains 2π radians. A right angle, which forms a quarter of a circle, is π/2 radians.
Here, m∠5 + m∠2 = 180 [ Supplementary Angles ]
142 + m∠2 = 180
m∠2 = 180 - 142 = 38
Now, m∠2 + m∠3 + m∠4 = 180 [ Angles in a Triangle ]
38 + m∠3 + 65 = 180
m∠3 = 180 - 103
m∠3 = 77
Again, m∠3 + m∠1 = 180 [ Supplementary Angles ]
m∠1 + 77 = 180
m∠1 = 180 - 77 = 103
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The complete question is:
What is the minimum value of f(x) = x^2 + 6x + 4
Answer:
-5
Step-by-step explanation:
You want the minimum value of f(x) = x² +6x +4.
Line of symmetryThe line of symmetry of a quadratic function f(x) = ax² +bx +c is given by ...
x = -b/(2a)
The line of symmetry passes through the extreme point. When a > 0, that extreme point is the minimum.
Here, we have a=1, b=6, so the line of symmetry is ...
x = -6/(2·1) = -3
ExtremeThe extreme point (minimum) is ...
f(-3) = (-3)² +6(-3) +4 = (-3 +6)(-3) +4 = -9 +4
f(-3) = -5
The minimum value of f(x) is -5.
Suppose you borrow $5000 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $325 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$5000
$4520.84
Question Help: Video
1.75% Interest
on Prior Balance
S
$74.81
Monthly Payment
$325
$325
$325
$325
Ending Balance
$
S
$5000
$4520.84
Answer:
Step-by-step explanation:
To fill in the table, we can use the following steps:
Calculate the interest for each month, which is the prior balance multiplied by the monthly interest rate (1.75%).
Subtract the monthly interest from the prior balance to get the new balance before the monthly payment.
Subtract the monthly payment from the new balance to get the ending balance.
Month Prior Balance 1.75% Interest on Prior Balance Monthly Payment Ending Balance
1 $5000 $87.50 $325 $4762.50
2 $4762.50 $83.39 $325 $4520.84
3 $4520.84 $79.06 $325 $4276.90
4 $4276.90 $74.50 $325 $4029.23
5 $4029.23 $69.69 $325 $3777.87
Therefore, after 5 months of making $325 payments, the remaining balance on the loan is $3777.87.
A dietitian was interested in the heights of 13-year-olds in the state. He gathered data from a random sample of 400 pediatricians in the state and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for the data?
Bar graph
Circle graph
Histogram
Line plot
Histogram would be the best for the data representation of the girls by dietitian.
What is histogram?Histogram, it is an approximate representation of the distribution of numerical data. The most popular graph for showing frequency distributions is a histogram. Though it also closely resembles a bar chart, there are significant differences. One of the seven basic quality tools is this useful gathering and analysing information tool.
Variable = the height of 13-year-olds in the state of Texas.
Where the height of each bar represents the frequency of observations.
[tex](2 - 2.5) feet\\\\(2.6 - 3) feet\\(3.1 - 3.5) feet\\(4.1 - 4.5) feet[/tex]
So, The best graphical representation of the dietitian's data would be a histogram.
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please help i need it rn (25points for answer)
Please give me an explanation on how to do these, I have more than just this one
Answer:33.34
Step-by-step explanation:
we'll use sinuses theorem for this which is,
[tex]\frac{x}{sina}=\frac{y}{sinb}\\\frac{27}{sin39} =\frac{x}{sin(90-39)} \\\frac{27}{sin39} =\frac{x}{sin51} \\x=\frac{sin51*27}{sin39}\\x=33.34[/tex]
Challenger Deep in the Pacific Ocean is the deepest point in Earth's oceans. It is 38 797 ft. below sea level. What is this depth to the nearest fathom? Is this depth greater than or less than 7 mi.? Explain.
Answer:
Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.
Step-by-step explanation:
One fathom is equal to 6 feet. To convert 38,797 ft. to fathoms, we divide by 6:
38,797 ft. / 6 = 6,466.17 fathoms
Rounding this to the nearest fathom gives us 6,466 fathoms.
One mile is equal to 5,280 feet. Seven miles would be:
7 mi. x 5,280 ft/mi = 36,960 ft.
Since 38,797 ft. is greater than 36,960 ft., we can conclude that Challenger Deep's depth is greater than 7 miles.
Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.
Find the volume of the region under the graph of f ( x , y ) = 3 x + y + 1 and above the region y 2 ≤ x , 0 ≤ x ≤ 9 .
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0 Mark this and return
Answer:
Listed below.
Step-by-step explanation:
(Let y be the length of the room and x be the width of the room.)
Because the width of the room is 5 feet less than the length of the room, we have:
x = y - 5.The area of the room can be solved by multiplying its length and width, so we have x × y or xy = 750.
Substituting x for y - 5 into this equation:
y (y - 5) = 750.If we expand the left side of the equation, we get:
[tex]y^{2}[/tex] - 5y = 750Subtracting 750 from both sides, we get:
[tex]y^{2}[/tex] - 5y - 750 = 0The equation [tex]y^{2}[/tex] - 5y - 750 = 0 can be factored into:
(y + 25) (y - 30) = 0Therefore, 3 equations you can use are:
y (y - 5) = 750[tex]y^{2}[/tex] - 5y - 750 = 0(y + 25) (y - 30) = 050 Points!!!!!!! Please help ASAP!!
Example of The Transitivity Property that follows
Premise:
Premise:
Conclusion:
Example of The Transitivity Property that follows
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
The transitivity property is a logical property that states that if a=b and b=c, then a=c. This property is commonly used in mathematics to make deductions and draw conclusions.
Example:
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
Explanation: By the transitivity property, we can substitute the value of y in the second premise with the value of x + 2 from the first premise to get z = (x + 2) - 1, which simplifies to z = x + 1. Then, we can substitute x = 3 to get z = 4.
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Members of a softball team raised $2252.25 to go to a tournament. They rented a bus for $1018.50 and budgeted $58.75 per player for meals.
Answer: 2252.25 - 1018.50 = P58.75
Step-by-step explanation:
Find the coordinates of the vertex and the equation of the axis of symmetry for the parabola given by the equation.
y=x²-x-6
vertex (x,y) = (1/2, -25/4)
axis of symmetry=
The equation of the axis of symmetry is [tex]x = 1/2.[/tex]
What sort of equation would that be?The definition of the an equation in algebra is a logical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What about the equation's meaning?A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equal. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equations.
To find the equation of the axis of symmetry for the parabola[tex]y = x^2 - x - 6,[/tex] we first need to find the x-coordinate of the vertex.
We can use the formula [tex]x = -b/2a[/tex] to find the x-coordinate of the vertex. In this case, a = 1 and b = -1, so:
[tex]x = -(-1) / 2(1) = 1/2[/tex]
So the x-coordinate of the vertex is [tex]1/2[/tex].
To find the y-coordinate of the vertex,
x = 1/2
[tex]y = (1/2)^2 - (1/2) - 6 = -25/4[/tex]
So the coordinates of the vertex are [tex](1/2, -25/4).[/tex]
[tex]x = 1/2[/tex]
Therefore, the equation of the axis of symmetry is [tex]x = 1/2.[/tex]
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Trig Identities---
1. Use the pythagorean identity
Find cotθ if cosθ = 1/7 and the value exists in the first quadrant.
I have a calculus exam tomorrow and have no idea how to solve this equation, please provide a detailed explanation. I'm slow.
Answer:
Let's first recall the Pythagorean identity:
sin²θ + cos²θ = 1
We can use this identity to find the value of sinθ, given that cosθ = 1/7 and θ is in the first quadrant. Since θ is in the first quadrant, both sinθ and cosθ are positive.
cosθ = 1/7
cos²θ = (1/7)² = 1/49
sin²θ + cos²θ = 1
sin²θ + 1/49 = 1
sin²θ = 1 - 1/49 = 48/49
sinθ = √(48/49) = (4/7)√3
Now we can use the definition of cotangent to find cotθ:
cotθ = cosθ/sinθ
Substituting the values we found for cosθ and sinθ, we get:
cotθ = (1/7)/[(4/7)√3] = √3/4
Therefore, cotθ = √3/4 when cosθ = 1/7 and θ is in the first quadrant.
2. A study by the Disney World in Orlando, FL revealed that 60% of the vacationers going
to the Magic Kingdom, 50% visit the Epcot Center and 25% visit both. What is the
probability that a vacationer will visit either the Magic Kingdom or Epcot Center?
As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
what is probability ?The measurement and study of random events are the focus of the mathematic branch known as probability. It is a means to express how likely an event or series of events are to occur. Probability is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. An occurrence that has a probability of 0.5 (or 50%) is equally likely to occur or not. In a variety of disciplines, including statistics, economics, engineering, and science, probability is used to evaluate and forecast the possibility of specific events in light of the information and presumptions at hand.
given
The formula for the union of two events must be used to determine the likelihood that a visitor will go to either the Magic Kingdom or Epcot Center:
P(A or B) equals P(A) + P(B) - P (A and B)
P(A) represents the likelihood that event A will occur, P(B) represents the likelihood that event B will occur, and P(A and B) represents the likelihood that both events will occur at the same time.
Let's describe event A in this scenario as a trip to the Magic Kingdom, and event B as a trip to the Epcot Center. We are aware of:
P(A) = 0.60 (the Magic Kingdom is visited by 60% of tourists)
P(B) = 0.50 (50 percent of tourists go to the Epcot Center)
P(A and B) = 0.25 (25% of tourists go to both places).
The result of the formula is:
P(A or B) is equal to P(A) + P(B) - P(A and B), which is 0.60 + 0.50 - 0.25 = 0.85.
As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
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what radian measure is equal to 315?
The radian measure for 315° is (7/4)π radians.
What exactly is a radian measure?
Radian measure is a unit of measurement for angles, where one radian is defined as the central angle subtended by an arc of a circle with a length equal to the radius of the circle. Therefore, to convert degrees to radians, we need to multiply the degree measure by pi/180.
Now,
To convert 315 degrees to radians, we can use the formula:
radians = degrees x π/180
So, we have:
radians = 315 x π/180
Simplifying this expression, we get:
radians = (7/4) x π
Therefore,
315 degrees is equal to (7/4) π radians.
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21. Brian took out a 48-month (4 years) loan for $1,800 at
an annual interest rate of 12%. Andy took out a
2-year loan for $4,200 at an annual interest rate of
10%. Who paid more in interest and how much more
did he pay?
A. Andy paid $34 more in interest.
B. Brian paid $34 more in interest.
C. Andy paid $24 more in interest.
D .Brian paid $24 more in interest.
Answer:
To find the total interest paid by Brian, we can use the simple interest formula:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.
For Brian's loan, we have:
I = 1800 * 0.12 * 4 = $864
So Brian paid a total of $864 in interest over the 4-year term.
For Andy's loan, we can use the same formula:
I = 4200 * 0.10 * 2 = $840
So Andy paid a total of $840 in interest over the 2-year term.
To find the difference in interest paid, we subtract the smaller amount from the larger amount:
864 - 840 = $24
Therefore, Brian paid $24 more in interest than Andy. The answer is option D.
Answer: the answer is C. Brian paid $24 more in interest than Andy.
Step-by-step explanation: To find out how much interest each person paid, we can use the formula:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the annual interest rate (as a decimal), and Time is the length of the loan (in years).
For Brian's loan:
Principal = $1,800
Rate = 0.12
Time = 4 years
Interest = $1,800 x 0.12 x 4 = $864
For Andy's loan:
Principal = $4,200
Rate = 0.10
Time = 2 years
Interest = $4,200 x 0.10 x 2 = $840
So Andy paid $840 in interest, while Brian paid $864 in interest. To find out how much more Brian paid than Andy, we can subtract:
$864 - $840 = $24
Find the value of x in the triangle shown below.
Using the Pythagorean Theorem 2 4 X
Answer: We are given a right triangle where the two legs have lengths 2 and 4, and we need to find the length of the hypotenuse (which is denoted by x in the question). We can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. That is,
hypotenuse^2 = leg1^2 + leg2^2
Plugging in the values we know, we get:
x^2 = 2^2 + 4^2
Simplifying the right-hand side, we get:
x^2 = 4 + 16
x^2 = 20
Taking the square root of both sides (and noting that x must be positive since it is a length), we get:
x = sqrt(20) = 2sqrt(5)
Therefore, the length of the hypotenuse is 2sqrt(5).
Step-by-step explanation:
A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.
The required answers are a) 6.5 m, b) Dimensions 8 m, 5 m c) square has the greater area.
How to deal with square and rectangle?(a) Let s be the length of a side of the square. The perimeter of a square is given by 4s. Since the piece of wire used to make the square has length 26 m, we have:
[tex]$\begin{align*}4s &= 26 \s &= \frac{26}{4} = 6.5 \text{ m}\end{align*}[/tex]
Therefore, the length of a side of the square is 6.5 m.
(b) Let l be the length of the rectangle. Then the width of the rectangle is l-3. The perimeter of a rectangle is given by 2(l+w). Since the piece of wire used to make the rectangle has length 26 m, we have:
[tex]$\begin{align*}2(l + (l-3)) &= 26 \2(2l-3) &= 26 \4l - 6 &= 26 \4l &= 32 \l &= 8 \text{ m}\end{align*}[/tex]
Therefore, the length of the rectangle is 8 m and its width is 8-3=5 m.
(c) The area of the square is given by [tex]$s^2$[/tex], which in this case is [tex]$6.5^2 = 42.25$[/tex] square meters. The area of the rectangle is given by lw, which in this case is [tex]$8\times5 = 40$[/tex] square meters. Therefore, the square has the greater area.
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Complete question;
A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.
(a) What is the length of a side of the square?
(b) What are the dimensions of the rectangle?
(c) Which shape has the greater area?
Solve the equation by completing the square
X^2 -2x=-3
What is 48.312 rounded to the nearest tenths?
Answer: 48.3
Step-by-step explanation:
Answer:
48.3
Step-by-step explanation:
Which shows one way to determine the factors of
The correct option is (d) i.e. by grouping x²(x + 11) -3(x +11).
What are Factors?
Factors are numbers or algebraic expressions that can be multiplied together to obtain a given product.
In algebra, factors are often used to factorize polynomials or other expressions, which involves expressing them as a product of simpler expressions.
One way to determine the factors of x³ + 11x² - 3x - 33 by grouping is:
x²(x + 11) - 3(x + 11)
We can see that the two terms have a common factor of (x + 11), so we can factor it out as follows:
= x³ + 11x² - 3x - 33
=x²(x + 11) -3(x +11)
= (x² - 3) (x+11).
The quadratic factor can be factored further using the difference of squares formula:
(x + 11)(x - √3)(x + √3)
So the factors of x³ + 11x² - 3x - 33 are (x + 11)(x - √3)(x + √3).
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Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
C-The upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
The statement that is most likely true is: "The data in Sample B is clustered around the center where Sample A is more spread out."
What is data set?A dataset is a collection of information, often represented in a tabular form, that contains one or more variables or pieces of data for a particular set of individuals or observations. Each individual or observation in the dataset is typically represented by a row in the table, while the variables are represented by columns. Datasets can be used to study a wide variety of phenomena, from social and economic trends to scientific experiments and medical studies. They can be collected through a variety of methods, including surveys, experiments, observations, and automated data collection systems, and can be analyzed using statistical methods to gain insights into the underlying patterns and relationships in the data.
Here,
This is because Sample A has a larger range than Sample B, indicating that the data points in Sample A are more spread out across the number line. Additionally, the median for both samples is the same (5), but the mean for Sample A is higher than the mean for Sample B, which could suggest that there are some larger values pulling the mean upward in Sample A. Taken together, these characteristics suggest that Sample A has more variability in its data points, while Sample B is more clustered around the center.
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A space shuftle orbits Earth at a rate
about 4 376 miles in 15 minutes At this rate how far does the space shattle travel around
Earth in 1 hour
I need help asap!
Answer:
17,500
Step-by-step explanation:
IRAs. You have $500,000 in your IRA (Individual Retirement Account) by the time you retire. You choose to invest this money in two funds: Fund A pays 5.2%/year and Fund B pays 7.7%/year. How should you divide your money between Fund A and Fund B to get an annual return of $34000?
Using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The amount in the IRA account = $500,000
Let the amount invested in fund A be x and fund B be y.
x + y = 500,000
The amount received annually for fund A = 0.052x
The amount received annually for fund B = 0.077y
This amount is given as:
0.052x + 0.077y = 34,000
Now we have a system of equations.
x + y = 500,000
0.052x + 0.077y = 34,000
Multiply the first equation by 0.052.
0.052x + 0.052y = 26,000
0.052x + 0.077y = 34,000
Subtracting,
-0.025y = -8000
y = 320,000
Then, x = 500,000 - y = 500,000 - 320,000 = 180,000
Therefore using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
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For what value of x is the square of the binomial x+1 one hundred and twenty greater than the square of the binomial x-3?
Answer:
x = -14
Step-by-step explanation:
(x+1)² + 120 = (x-3)²
expand each binomial:
x² + 2x + 1 + 120 = x² -6x + 9
combine 'like terms' to simplify:
8x = -112
x = -14
NEED THIS ASAP PLEASE
Answer:
d ≈ 4.5
Step-by-step explanation:
calculate AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (1, 0 ) and (x₂, y₂ ) = B (5, 2 )
d = [tex]\sqrt{(5-1)^2+(2-0)^2}[/tex]
= [tex]\sqrt{4^2+2^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= [tex]\sqrt{20}[/tex]
≈ 4.5 ( to the nearest tenth )
Write a polynomial equation with integer coefficients that has the given roots.
x =8, x = 7
The polynomial equation with the roots is P(x) = x^2 - 15x + 56
How to determine the polynomial equationFrom the question, we have the following parameters that can be used in our computation:
Roots: x = 8 and x = 7
Using the above as a guide, we have the following:
The equation can be represented as
P(x) = (x - root)
Substitute the known values in the above equation, so, we have the following representation
P(x) = (x - 8)(x - 7)
Evaluate the product
P(x) = x^2 - 8x - 7x + 56
This gives
P(x) = x^2 - 15x + 56
Hence, the equation is P(x) = x^2 - 15x + 56
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On a map, my house is 4.8 inches away from the school. If each inch represents two miles, how far away is my house from the school?
Which shows the expression Fifty-four decreased by a number squared
A. 54 - 2x
B. 45 - x 2square
C. 54 - x 2square
Answer:
C: 54-x^2
Step-by-step explanation:
54(decreased=minus)-number^2
help fast How many miles is 17,600 yards?
10 miles
7 miles
5 miles
4 miles
Answer:
10 miles
the first option
Work Shown:
[tex]17600 \text{ yards} = 17600 \text{ yards}\times\frac{3 \text{ feet}}{1 \text{ yard}}\times\frac{1 \text{ mile}}{5280 \text{ feet}}\\\\= \frac{17600 \times 3\times 1}{1 \times 5280\times 1} \text{ miles}\\\\= \frac{52800}{5280} \text{ miles}\\\\= 10 \text{ miles}\\\\[/tex]
Take notice in the jump from the 1st to 2nd lines, we have the "yards" and "feet" units cancel out.