a. The domain of a(r) is [tex]A(r)= 2\pi r^{2} + 16\pi r[/tex].
b. The radius r as a function of a is [tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex] .
What In Geometry Is a Cylinder?The three-dimensional solid shape of a cylinder is made up of two circular bases joined by a curving surface that is created by folding a rectangle. A cylinder's top and bottom faces are parallel to one another. There are 3 faces, 2 edges, and 0 vertices in all.
In this question, we must apply our understanding of cylinders to determine the function that most accurately captures its value:
[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]
The area domain of A can be represented as:
[tex]A(r)= 2\pi r^{2} + 16\pi r[/tex]
Let's divide the equation by 2π and write A(r) as just A to get:
[tex]r^{2} + 8r = \frac{A}{2\pi }[/tex]
So, after we sum on both sides we get,
[tex]r^{2} +8X +16 =\frac{A}{2\pi } + 16[/tex]
[tex](r+4)^{2} = \frac{A}{2\pi } +16[/tex]
By taking the square root of the previous equation and then figuring out r, we get:
[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]
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Since
∠
AOB
is a right angle, it is
90
∘
.
∠
AOB
is supplementary to
∠
BOC
, so
m
∠
AOB
+
m
∠
BOC
=
180
∘
. By the substitution property of equality,
90
∘
+
m
∠
BOC
=
180
∘
. Applying the subtraction property of equality,
m
∠
BOC
=
90
∘
.
What statement is missing from the proof?
A.
∠
AOB
and
∠
BOC
form a linear pair.
B.
∠
AOB
and
∠
DOC
are vertical angles.
C.
∠
COD
and
∠
AOD
form a linear pair.
D.
∠
DOA
and
∠
BOC
are vertical angles.
The missing piece of information in the proof is that m ∠ DOA and m ∠ BOC are vertical opposite angles.
What is meant by subtraction property of equality?According to the equality's subtraction property, equality is unaffected by removing the same amount from both sides of an equation. When the same quantity or value is removed from both sides of an equation, the resultant difference is also identical on both sides.
Both the equality's addition and subtraction properties are related. The same integer added to or subtracted from both sides of an equation maintains equality on both sides.
To prove that m ∠ BOC = 90°.
Given that m ∠ AOB exists a right angle triangle.
Therefore; m ∠ BOC must also be equivalent to 90°.
Since m ∠ BOC and m ∠ AOB are right angles, it follows that m ∠ DOA and m ∠ BOC are also vertical opposing angles and, as such, are equal.
So, the fact that m ∠ DOA and m ∠ BOC are vertical opposing angles is the crucial piece of information missing from the proof.
The complete question is:
Given: AOB is a right angle
Prove: m BOC = 90°
Since AOB is a right angle, it is 90°. AOB is supplementary to BOC,
so m AOB + m BOC = 180°. By the substitution property of equality,
90 + m BOC = 180°. Applying the subtraction property of equality,
m BOC = 90%. What statement is missing from the proof?
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How do you do this please help me
Step-by-step explanation:
you know how equations are transformed ?
by applying the same operation on both sides of the equation (so that the equality remains).
x + 38 = 79
to get "x = ...", we need to eliminate the "+ 38" in the x side.
clearly we need to subtract 38.
again, whatever e do, we have to do on both sides, otherwise the equality relation is destroyed.
so,
x + 38 - 38 = 79 - 38
x = 41
that is the height of the avocado tree : 41 in.
it is 38 in shorter than 79 in (the fig tree).
that's all that is to this. it is a really simple method.
the same applies to any operation you want to do (+, -, ×, ÷, ...).
6. jessie and bob are financing $425,500 to purchase a house. they obtained a 30/8 balloon mortgage at 6.55%. what will their balloon payment be? (3 points)
o $379,659.89
0 $637,130.99
o $357,491.39
o $380,040.19
So, on solving the provided question we can say their balloon payment will be $380,040.19.
What is balloon payment ?A balloon loan is a type of loan arrangement where only a portion of the original balance is repaid during the course of the loan's relatively short repayment term. When only a fraction of the initial debt is repaid during the duration of the loan's relatively short repayment term, the loan is referred to as a "balloon loan."
the monthly fixed payment. there is a formula
Pmt = (A * i * (1 + i)ⁿ) / ((1 + i)ⁿ - 1)
Pmt - monthly payment;
A is Loan amount;
i is periodic interest rate; and
n is number of periods.
Mortgage amount: $425,500
[tex]Term in years: 8 years[/tex]
Interest rate: 6.55%
Amortization period is - 30 years.
pmt=(425500*6.55*(1+6.55)^12)/((1+6.55)^12-1)
Balloon payment=[tex]$380,301.82.[/tex]
Total interest paid[tex]$211,630.52.[/tex]
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If you’re standing on the trail 220
feet from the bottom of the tree, you have to look up at a 60
degree angle to see the top. How tall is the tree? Round to the nearest whole number
The height of the tree is 381.05 ft.
The given distance between the man and the tree's base is 220 feet.
Let the tree's height be x feet.
A group of figures known as the trig ratios is characteristic of each angle.
They can be defined when the angle is in a right triangle.
as in this:
Angle's tangent (tan): (opposite leg) divided by (adjacent leg)
Angle's cotangent (cot): (adjacent leg) divided by (opposite leg)
To see the summit of the tree, we must now gaze up at a 60-degree angle.
in the form of a trigonometric ratio,
Tan60= perpendicular/base
√3=x/220 (Tan60 = √3)
x= 220×√3
x= 381.05 ft
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Which is the solution set for x2 − 5x − 14 = 0 ?
x2−5x−14=0
x2−7x+2x−14=0
x(x−7)+2(x−7)=0
(x−7)(x+2)=0
(x−7)(x+2)=0
x=7,−2
(x^2 - 5x - 14 = 0) has the solution set as F: "x = 7 , -2" .
Solve the equation by factorization method.
x^2 - 5x - 14 = 0
x^2 - 7.x + 2.x - 14 = 0
taking x common from the frist two terms and +2 common from the last two terms.
[ x(x - 7 ) PLUS (+) 2 (x -7) ] = 0
[( x - 7) . (x + 2)] = 0
x - 7 = 0 , & x + 2 =0
x = 7 , & x = -2
Thus the solution is x = 7 and x = -2.
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When conducting a significance test in practice, how should you choose the alpha level? A.Use a larger alpha when the consequences of mistakenly rejecting the null hypothesis are more serious. B.Always use alpha-0.05 since it's the most appropriate for every situation.C. Always use alpha-0.05 since it's the most commonly used one.D.Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious
Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.
When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.
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Scale is 1/4"=4'. What is the line's actual length?
Answer:
16x feet
Step-by-step explanation:
A scale of 1/4" = 4' means that every 1/4 inch on the drawing or map represents 4 feet in the actual measurement. To find the actual length of a line on the drawing or map, you need to multiply the length of the line in inches on the drawing by the denominator of the scale, and then divide by the numerator of the scale.
The formula is:
Actual length = (length on the drawing or map x scale denominator) / scale numerator.
In this case, the length on the drawing or map is x inches, and the scale is 1/4" = 4'.
So the actual length is: (x inches x 4') / 1/4" = 16x feet
Therefore, the actual length of the line on the drawing or map is 16x feet.
10 1/2 cup of flour are needed to make three lova of bread how many cup are needed
The offered statement states that 42 cups of grain are required to produce three loaves of bread.
Where did the loaves and fishes tradition start?As a completely volunteer hot meal service in 1983, Breads & Fishes quickly evolved into a pre-packaged shopping bag contribution program for locals. This nonprofit's first year's budget was $6,500, at which time the pantry supplied food to about 50 homes.
We know we need four times 10 1/2 cups of flour since 12 was 4 times higher than three (3 * 4 = 12).
We only have to calculate 10.5 * 4 = x but then just solve for x.
42 cups - grain (10.5 * 4)
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The complete question is-
10 1/2 cups of flour are needed to make 3 loaves of bread. How many cups are needed for 12?
The line l cuts the y-axis at (0,5).
l also passes through the point (2, 1).
find the equation of the line which is parallel to l and which passes through the point
(3,0).
The equation of the line is y = -5/2x + 5.
1. We know that the equation of a straight line is given by y = mx + c, where m is the slope of the line and c is the y-intercept.
2. We need to find the slope of line l. To find the slope, we can use the formula: m = (y2-y1)/(x2-x1). In this case, we have y2 = 1, y1 = 5, x2 = 2, and x1 = 0. Therefore, m = (1-5)/(2-0) = -4/2 = -2.
3. We now have the slope of line l, so we can find the equation of the line which is parallel to l and which passes through the point (3,0). To do this, we can use the formula y = mx + c, where m is the slope of the line and c is the y-intercept.
4. In this case, m = -2 and c is the y-intercept, which is the point at which the line intersects the y-axis.
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Using -1, -2, -1.68 as examples, describe where negative numbers are located on a number line, based on the locations of 0 and 1.
The location on negative integers will be on left side of zero.
What is Number system?A number system is defined as a system of writing to express numbers.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
On a number line the integers were represented.
Integers are collect of positive numbers, negative numbers and zero.
On the right side of zero the number are positive 1,2,3..
To the left side of zero there are negative integers -1,-2,-3...
Fom left to right the value of numbers be increases.
Hence, the location on negative integers will be on left side of zero.
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Given points F(3, 1), G( 8, 2), H(2, 4), and J(1, 6).
a. Find the slope of FG and the slope of HJ.
b. Explain if FG and HJ are parallel, perpendicular or neither.
Need to answer both for full credit
The FG slope is 1/5 and the HJ slope is -2. Because slopes are not connected to one another, they are neither parallel nor perpendicular.
What is slope?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). A slope is the steepness of a hill. The same is true for a line's steepness. The slope is defined as the ratio of the vertical change between two places, known as the rise, to the horizontal change between those same two points, known as the run.
Here,
F(3, 1), G( 8, 2), H(2, 4), and J(1, 6)
a. FG=2-1/8-3
=1/5
HJ=6-4/1-2
=-2
b. Since slopes are not related to each other it is neither parallel nor perpendicular.
The slope of FG is 1/5 and slope of HJ is -2. Since slopes are not related to each other it is neither parallel nor perpendicular.
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slove the equation 125(5²ˣ⁻¹) = 1
Step-by-step explanation:
5^(2x-1) = 1/125
5^2x = 5/125 => (1/25) = 5^2x
5^-2=5^2x
equating both sides
-2=2x
X=-1
hope this helps you.
when n 200, what is the probability that the propor- tion of couples in the sample who are racially or ethni- cally mixed will be greater than .10?
To calculate the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10, we can use a normal approximation to the binomial distribution.
First, we need to calculate the mean and standard deviation of the proportion of mixed couples in a sample of 200.
The mean is calculated as:
mean = n * p
where n is the sample size (200) and p is the proportion of mixed couples in the population (assumed to be .10).
So: mean = 200 * .10 = 20
The standard deviation is calculated as:
standard deviation = sqrt(n * p * (1-p))
where n is the sample size (200), p is the proportion of mixed couples in the population (assumed to be .10), and sqrt is the square root function.
So: standard deviation = sqrt (200 * .10 * .90) = sqrt (18) = 4.24
We can use the standard normal distribution to calculate this probability. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert our random variable X to a standard normal variable using the following formula:
Z = (X - mean) / standard deviation
So: Z = (X - 20) / 4.24
To find the probability that X is greater than .10, we can use a standard normal table or calculator to find the probability that Z is greater than (X - 20) / 4.24
This probability is 0.48, so the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10 is 48%.
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Hii can someone helpe with this plsss is urgent
Answer:
sorry, No answer I have no idea for this
Answer:
Step-by-step explanation:
As you see in the X coloum they have already given you the number for x. So what you do is plug in -2 for x. so it would be 6(-2)+3y=18. it will be -12+3y=18. Put like terms on the same side. Meaning you would add 12 to both sides. it will end up being 3y=30. Divide both sides by 3 so the variable can stay alone and that would mean y=10. So when x=-2, y=10. You can always plus it back in the equation to double check if the answer is right. 6(-2)+3(10)=18. Do the same thing for the remaining ones and youre all set!!! Hope th
Please help me ASAP I need it for homework that needs to be done! Also show me the solution as clear as possible cause thats what I need! Thank you! Btw the problem is in the image below!
Answer:
[tex]x=16y^2-5[/tex]
Step-by-step explanation:
Lets solve for x.
[tex]\frac{\sqrt{x+5} }{4} =y[/tex]
Multiply both sides of the equation by 4.
[tex]\sqrt{x+5}=4y[/tex]
Eliminate the square root on the left side raising both sides of the equation to the power of 2.
[tex]\sqrt{x+5}^2=(4y)^2[/tex]
The square root and the exponent on the left side cancel out leaving us with
[tex]x+5=(4y)^2[/tex]
Distribute the exponent on the right side.
[tex]x+5=4^2y^2[/tex]
Simplify.
[tex]x+5=16y^2[/tex]
Subtract 5 from both sides.
[tex]x=16y^2-5[/tex]
Helpppp - due tomorrow
Answer:
9.68
Step-by-step explanation:
x*(x-4)=55; x approximately equals 9.68
Find all values of n > 1 for which one can dissect a rectangle into n right triangles, and outline an algorithm for doing such a dissection.
If n=2k (means even value) is always possible to dissect a rectangle into n right triangles.
What is the dissect?Dissect means to separate a dead person's or animal's body into its component for closer examination.
Dissect is to consider or talk about the specifics of something in order to fully comprehend it.
To dissect is to separate into components.
For n=2, it is easy to show that it is possible (just insert the diagonal).
For n=3, it is not possible ( I tried on some examples but not able to do it).
For n=4, it is possible first make two rectangle from the original rectangle then use the case of n=2
So if n=2k (means even) then it is always possible.
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What is no solution called?
An inconsistent system is a set of equations that have no solution.
Consider the following as the lines' equation:[tex]p_1x+q_1y+a_1=0 , p_2x+q_2y+a_2=0[/tex]
We can start analyzing the equations of lines and evaluating their various properties now that we understand how to display points on a coordinate plane and graph linear equations. The common forms for writing linear equations and the characteristics of lines that can be inferred from their equations are covered in this section.
If both lines are parallel to one another, there is no answer because the lines never cross.
In such a circumstance, the pair of linear equations in two variables is considered to be inconsistent because algebraically, [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex].
For example, line of equations are
[tex]2x-y=4\\\\4x-2y=8[/tex]
[tex]\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{4}{8}=\frac{1}{2}[/tex]
Here, both equation has no solution so equation are called inconsistent equation.
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Which formula describes the range?
On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.
A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
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27 g^7 k^3 z^4 - 9 g^2 K^5 z
The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)
What are algebraic expressions?Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.
They are also described as expressions composed of arithmetic operations, such as;
DivisionBracketParenthesesAdditionMultiplicationSubtractionIt is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.
From the information given, we have the expression;
27 g^7 k^3 z^4 - 9 g^2 K^5 z
Subtract the coefficient
18(g⁷k³z⁴ - g²k⁵z)
Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)
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Ravi has 4 times the amount of marbles as sam.they have 630 marbles.How many marbles should ravi give to same so that they have the same amount of marbles ?
Answer: 126 marbles
Step-by-step explanation:
Let the marbles with Sam be x
so, marbles with Ravi will be 4x
we know total marbles are 630 which means
x + 4x = 630
x = 126
so marbles with Sam & Ravi will be 126 & 504.
To make marbles equal each should have 315 marbles.
So, Ravi has to give 315 - 126 = 189 marbles to Sam.
Select the parallel lines from the given pairs of lines :
Select one:
a.
y = x / 3 + 1, y = - x / 2 + 15
b.
y = 7x + 11, y = x / 2 + 11
c.
y = 3x + 21, y = − 3x - 8
d.
y = 5x / 2 + 1, y = 5x / 2 + 7
Answer:
d. y = 5x/2 + 1, y = 5x/2 + 7
Step-by-step explanation:
Both lines have the same slope (5/2) , so they are parallel.
Annabelle records the length, in inches, of a colored pencil over time. Review the table showing her data.
Which description best fits the regression model for the data?
Answer:
Option 2
Step-by-step explanation:
The data is not periodic, so the model is not is not a trigonometric equation.
Setting [tex]x=0[/tex] eliminates Option 1.
Therefore, Option 2 is the only remaining option
for breakfast bob has three options: cereal, eggs or fruit. he hasto choose exactly two items out of the three available.(a) describe the sample space of this experiment
According to the concept of probability, the sample space for the experiment is explained below.
The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.
Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.
Here let us consider that the sample space is B
And the the sample space is written as.
=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}
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-7x = 63 don’t type x = just type the numerical answer.
Answer:
-9
Step-by-step explanation:
-7x = 63
Divide both sides by -7.
-7x/-7 = 63/-7
Simplify.
x = -9
Follow directions and input only the -9
[tex]-7x=63[/tex]
1. Divide both sides by -7.
[tex]\frac{-7x}{-7} = \frac{63}{-7}[/tex]
[tex]x=-9[/tex]
-9 would be your answer.
A car travels the 200 miles along the M1 from London to Leeds. The car leaves London at 8am and travels at a constant speed of 60mph for the first 60 miles. The driver takes a break of 30mins at a motorway services before continuing the journey at a constant speed of 70mph a) Draw a distance-time graph of the journey
Answer:
The distance-time graph of the journey would be as follows:
From 8am to 8:01am, the car travels 0 miles (at 8am, it leaves London)
From 8:01am to 9:01am, the car travels 60 miles (at a constant speed of 60mph)
From 9:01am to 9:31am, the car travels 0 miles (the driver takes a break of 30mins)
From 9:31am to 12:51pm, the car travels 140 miles (at a constant speed of 70mph)
The graph would be a line with a slope of 60 for the first hour, a flat line for the 30 minutes break, and then a line with a slope of 70 for 2 hours and 20 minutes.
Note: Since we don't have a time-scale and time unit, this graph is just a representation of the pattern of the journey, and the actual values are not accurate.
(1 point) a math professor finds that when he schedules an office hour for student help, an average of 2.6 students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is 1.
There is a 0.2209 = 22.09% probability that three students will arrive during a randomly chosen office hour.
What is probability ?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.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).
According to our question-
The number of successes is x.
The Euler number is e = 2.71828.
is the average over the specified range.
When a professor of statistics sets an office hour for student assistance, she discovers that on average, 3.3 students show up.
It follows that
Determine the likelihood that three students will arrive during a randomly chosen office hour.
So, P(X = 3).
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The length l of a pencil is 13cm to the nearest centimetre (cm) what number should go in the box to complete the error interval
The correct expression for the given error interval is; 12.5 cm ≤ l ≤ 13.4
How to find the error interval?Error intervals are defined as the limits of accuracy when a number has been rounded or truncated. These error intervals are the range of possible values that a number could have been before it was rounded or truncated.
Now, we can also say that Error interval is the range of values (between the upper and lower bounds) in which the precise value could possibly be.
Now, since the precise value is given as 13 cm after approximation to the nearest centimeter, then the lower bound will be 12.5 because it is the lowest number that can be approximated to 13. Meanwhile the upper bound will be 13.4 cm as it is the largest values that can be approximated to 13 cm. Thus, the inequality is;
12.5 cm ≤ l ≤ 13.4
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Find the length of the third side. If necessary, write in simplest radical form.
6
√11
The third side of the right angle triangle is 5 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore, using Pythagoras's theorem,
6² - (√11)² = b²
36 - 11 = b²
b² = 25
square root both sides of the equation
b = √25
b = 5 units
Therefore.
third side = 5 units.
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Find the possible dimensions of the sports field given if the width is at least 50 yards.
click the icon to view the sports field.
select all that apply.
a. width 70 yards, length 9-60 yards
ob. width 45 yards, length 14 - 10d yards
c. width 50 yards, length 13 - 9d yards
od. width 90 yards, length 7-5d yards
By finding the Greatest Common Factor we can conclude that the possible dimensions of the sports field are a width of 70 yards and a length 9-6d yards.
There are two theories needed to solve the problem:
Dimensions of an object are defined as a measure of length, width, or height extended in a certain direction.
The Greatest Common Factor (GCF) of two or more numbers is the largest number that can be evenly divisible by these numbers.
We can assume that the sports field is a rectangle since we know that:
- the width is at least 50 yards
- the area is (630-420d) yard square
To find the dimension of the sports field, we have to find the GCF of 490 and 210, by enumerating their prime factors and multiplying those factors both numbers have in common.
490 = 2 × 5 × 7 × 7
210 = 2 × 5 × 3 × 7
So the GCF is 2 × 5 × 7 = 70
This GCF depicts one of the dimensions of the sports field, which we denote as d₁.
By substituting the value of one dimension, the value of another dimension (d₂) can be obtained:
Area = d₁ x d₂
d₂ = Area / d₁
= (630-420d) / 70
= 9-6d
Thus we can conclude that the possible dimensions of the sports field are width 70 yards and length 9-6d yards.
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