Brian likes to go bird watching along the Harvest Park Trail in a nearby forestpreserve. He wants to calculate the area enclosed by the trail which is shownbelow. Based on the diagram, what is the closest approximation of the area insquare yards of the land enclosed by the trail?
Answers
Answer:
(B)138,000 square yards.
Explanation:
To determine the area of the land enclosed by the trail, we divide the diagram into two as shown below:
Therefore, the area will be:
[tex]\begin{gathered} \text{Area}=(800\times900)+(400\times1300) \\ =720,000+520,000 \\ =1,240,000\text{ square feet} \end{gathered}[/tex]We then convert it to square yards.
[tex]\begin{gathered} \text{9 square feet=}1\text{ square yard} \\ \text{Therefore:} \\ 1,240,000\text{ square feet}=\frac{1,240,000}{9}\text{ square yard} \\ \approx137777\text{ square yards} \end{gathered}[/tex]Therefore, the closest approximation of the area in square yards is 138,000 square yards.
Related Questions
Find the equation that results from completing the square into the following equation X squared -14 X +40 equals zero
Answers
Given:
The equation is
[tex]x^2-14x+40=0[/tex]Required:
Find the equation that results from completing the square into the given equation.
Explanation:
The given equation is:
[tex]x^{2}-14x+40=0[/tex]Subtract 40 on both sides.
[tex]\begin{gathered} x^2-14x+40-40=0-40 \\ x^2-14x=-40 \end{gathered}[/tex]Add 49 on both sides.
[tex]\begin{gathered} x^2-14x+49=-40+49 \\ x^2-14x+49=9 \end{gathered}[/tex]Use the following formula:
[tex]a^2-2ab+b^2=(a-b)^2[/tex][tex](x-7)^2=9[/tex]Final answer:
The second option is the correct answer.
What is the equation in standard form of the line that passes through the point (6,-1) and isparallel to the line represented by 8x + 3y=15?A 8x+3y=-45B 8x-3y = -51C 8x+3y=45D 8x - 3y=51
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The slope of the given line is:
[tex]s=-\frac{8}{3}\text{.}[/tex]Therefore, the slope of a parallel line to the given line must be -8/3.
Using the slope-point formula for the equation of a line we get:
[tex]y-(-1)=-\frac{8}{3}(x-6)\text{.}[/tex]Taking the above equation to its standard form we get:
[tex]\begin{gathered} y+1=-\frac{8}{3}(x-6), \\ 3y+3=-8(x-6), \\ 3y+3=-8x+48, \\ 8x+3y=48-3, \\ 8x+3y=45. \end{gathered}[/tex]Answer: Option C.
Simplify or expand each expression and then Classify it by its degree and number of terms
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2x^3 (7x^2 + 3x + 1) - 4x^4
multiply 2x^3 in
14x^5 + 6x^4 + 2x^3 - 4x^4
14x^5 + 2x^4 + 2x^3
3 terms, the degree is 5
terms are single expressions such as (2x^3)
the degree is the highest exponent
(6x - 2x^4 + 5x^6) + (7x^4 - 3x^6 + 9)
combine
6x - 2x^4 + 5x^6 + 7x^4 - 3x^6 + 9
simplify
2x^6 + 5x^4 + 6x + 9
4 terms, the degree is 6
(x^2 + 9)(x^2 - 9)
FOIL, (a + b)(c + d) -> ac + ad + bc + bd
x^2 * x^2 + x^2 * -9 + 9 * x^2 + 9 * -9
simplify
x^4 - 81
2 terms, the degree is 4
Find each measure measurement indicated. Round your answers to the nearest tenth. Please show work. Answer number 1.
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Let's redraw the given figure, to easily understood the problem:
The figure appears to be a triangle with the following given,
c = AB = 17 cm
a = BC = unknown
b = CA = 44 cm
θ = 125°
m∠B means it is the angle at vertex B of the triangle, it is also the only angle given in the figure.
Therefore, the measure of m∠B is 125°.
Michael says that 5 = 5 Is his answer correct? Explain. (1 O A. 00:00 Yes. Both expressions are equal to 625 СВ. 00:00 Yes Both expressions are equal to O C. 00:00 No. The first expression is equal to and the second expression is equal to 625 00:00 No. The first expression is equal to 625 and the second expression is equal to
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Michael says that
[tex]5\cdot(\frac{1}{5^3})=5(5^3)[/tex]We are asked whether he is correct or not?
Let us simplify the equa
Find the value of the logarithmic expression. log subscript 6 216log subscript 6 216=____?
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Solution
For this case we have the following:
[tex]\log _6(216)=3[/tex]The reason is because:
[tex]6^3=6\cdot6\cdot6=216[/tex]micah runs a lemonade stand.He sells large cups of lemonade for$0.50 and small cups of lemonade for$0.35.Create an expression represents how much money he could earn
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Answer:
The expression for the amount of money in dollars he could earn is;
[tex]0.50x+0.35y[/tex]Explanation:
Let x represent the number of cups of large cups of lemonade he sell and
y represent the number of cups of the small cups of lemonade he sell.
Given that;
He sells large cups of lemonade for $0.50
and small cups of lemonade for $0.35.
The amount he will male by selling x cups of large cups of lemonade and y cups of small cups of lemonade is;
[tex]0.50x+0.35y[/tex]The expression for the amount of money in dollars he could earn is;
[tex]0.50x+0.35y[/tex]Answer:
the dude above me is wrong this is the right answer 0.85(l + s)
Step-by-step explanation:
what's the answer please help
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Domain are the "x"'s in this example Domain = [-2, 2]
Range are the "y" in this example Range = [-3, 3]
The second choice is correct.
f(x) = -3x² + 6x + 1
find f(6)
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Step-by-step explanation:
this is a college question ? and you don't know how to do this ?
come on, remember ! I don't know how you ever made it into college, if you don't understand this.
with f(6) we say x = 6, and now we simply have to put 6 into all the places of x and calculate.
f(6) = -3×6² + 6×6 + 1 = -3×36 + 36 + 1 = -2×36 + 1 =
= -72 + 1 = -71
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.after constant its 6x squared -x-1
Answers
For polynomial 1: simplified form
[tex]6x^2-x-1[/tex]Name by Degree: Quadratic
Number of Terms: 3
Polynomial 2:
Simplified form is 3x+4
Name by Degree: Linear
Number of Terms: 2
Polynomial 3:
Simplified form: 2
Name by Degree: Number
Number of Terms: 1
[tex]3x+4[/tex]You have $28 to buy 7 goldfish for your new fish tank. Write and solve an inequality that represents the prices you can pay per fish.
Answers
If the price per each goldfish is p
The total cost of 7 goldfishes is 7p and it has to be less or equal to 28
The the inequality is:
7p <= 28
Solving for p:
7p <= 28
p <= 28/7 = 4
p <= 4
Answer:
You can pay up to $4 per each goldfish
Inequality: 7p <= 28
This is a 1st-grade math problem 12 + _____ = 13 + 7
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I'll say that the unknown number is "x", then our expression is
[tex]12+x=13+7[/tex]And we want to find out the value of "x"
To solve it, we will first do the sum on the right side:
[tex]12+x=20[/tex]Now, we want to have "x" alone on the left side, then, let's subtract 12 on both sides
[tex]\begin{gathered} 12-12+x=20-12 \\ \\ x=20-12 \\ \\ x=8 \end{gathered}[/tex]Then the value of x is 8, let's test it:
[tex]\begin{gathered} 12+8=13+7 \\ \\ 20=20 \end{gathered}[/tex]Correct! 12 + 8 is 20. Then, the unknown number is 8
Answer:
Step-by-step explanation:
12 + 1 = 13 + 7=20
Destiny needs a new coat for the winter and she found one at Old Navy for $48.88. The sale tax is 8%. How much will she pay for the sales tax? How much will she pay all together? SHOW ALL OF YOUR WORK.
Answers
Hello!
First, let's consider the value of $48.88 as 100%. Then, we have to find how many correspond to 8% of it. We can calculate it using the rule of three:
[tex]\begin{gathered} \frac{48.88}{x}=\frac{100}{8} \\ \\ \text{ multiplying across} \\ x\cdot100=8\cdot48.88 \\ 100x=391.04 \\ x=\frac{391.04}{100} \\ x\cong3.91 \end{gathered}[/tex]So, the sales tax is $3.91.
Now, we have to add the price of the coat with the sale tax:
$48.88 + $3.91 = $52.79
If she pays all together, the cost will be $52.79.
Jessica currently has $180 dollars in her bank account and will add an additional $15 each week. Nate has $120dollars in his account and will add $20 each week.A. After how many weeks will they have the same amount of money in their accounts?B. What is the amount, in dollars, that each person will have after this many weeks?
Answers
Answer:
(a)12 weeks
(b)$360
Explanation:
Part A
Let the number of weeks when they have the same amount of money in their accounts be x.
[tex]\begin{gathered} \text{Jessica's amount after x weeks }=180+15x \\ \text{Nate's amount after x weeks }=120+20x \end{gathered}[/tex]If the amount of money is equal:
[tex]180+15x=120+20x[/tex]Solve for x:
[tex]\begin{gathered} 180-120=20x-15x \\ 60=5x \\ \frac{60}{5}=\frac{5x}{5} \\ x=12 \end{gathered}[/tex]Therefore, they will have the same amount of money after 12 weeks.
Part B
The amount that each person will have, (Using Jessica's Equation)
[tex]\begin{gathered} \text{Amount}=180+15x \\ =180+15(12) \\ =180+180 \\ =\$360 \end{gathered}[/tex]The amount, in dollars, that each person will have after 12 weeks is $360.
help ! brainliest !!!
Answers
a, the reflexive property
Which expressions have the fewest significant Figures?A. 18.8 - 6.5B. 4350 - 2210C. 15.4 - 8.1D. 54.5 * 30.7
Answers
Answer
Option C is obviously the answer.
Explanation
It will be easy to answer this by providing the answers to the expressions.
Option A
18.8 - 6.5 = 12.3 (3 significant figures)
Option B
4350 - 2210 = 2140 (4 significant figures)
Option C
15.4 - 8.1 = 7.3 (2 significant figures)
Option D
54.5 * 30.7 = 1673.15 (6 significant figures)
Hope this Helps!!!
find the circumference to the nearest whole number the whole number is 14
Answers
Answer:
The circumference is 88 in
Explanation:
The circumference of a circle can be determined, using the formula:
[tex]C=2\pi r[/tex]Where r is the radius of the circle.
Given a radius of 14 in, then
[tex]\begin{gathered} C=2(14)\pi \\ =28\pi \\ =28\times3.14 \\ =87.92 \\ \approx88in \end{gathered}[/tex]Use the quadratic formula to solve for X.3x2 + 4x = 9Round your answer(s) to the nearest hundredth.Select all that apply.O x= 2.52x = 1.19x = -2.52x= -1.18O x = -20.00x = 20.00
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a = 3, b = 4, c = -9
[tex]x\text{ = }\frac{4\pm\text{ }\sqrt[]{4^2-4(3\times-9)}}{2\times3}[/tex][tex]x_1=2.52[/tex][tex]x_2\text{ = -1.1}8[/tex]To prepare an aquarium for use, you can clean it with saltwater solution.The amount of salt varies directly with the volume of the water.The solution has 3 teaspoons of aquarium salt for every 2 gallons of water.
Answers
teaspoons of water = y
gallons of water = x
• a)
y = k x
Where k is the constant of proportionality.
Replace x,y by the values given and solve for k:
3= k 2
3/2 = k
k= 1.5
Equation:
y= 1.5x
• b) replace x=10 and solve for y
y= 1.5x
y= 1.5 (10)
y= 15
15 teaspoons of aquarium salt
• c) replace y= 39 and solve for x
y=1.5x
39 = 1.5 x
39/1.5= x
x = 26
26 gallons of water
Which graph represents 7x+2y<8? four different graphs to chose from.
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we have the inequality
7x+2y < 8
the solution for this inequality is the shaded area below the dashed line 7x+2y=8
so
the slope of the dashed line is negative
the intercepts of the dashed line are
y-intercept is (0,4)
the x-intercept is (8/7,0)
therefore
the answer is option BUse add or sub formula to write as trig fun tho on
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The formula to write this function is going to be:
[tex]tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)*tan(b)}[/tex]Substituing:
[tex]\frac{tan(43)-tan(18)}{1+tan(43)tan(18)}=tan(43-18)[/tex]In this case a= 43 and b=18:
[tex]tan(43-18)=tan(25)=0.466\approx0.5[/tex]The answer is: tan(25).
wich of the following is the correct value of 0.22 0.4?
Answers
Answer:
The decimal place will be placed to the left by the total number of digits after the two numbers.
Explanation:
The multiplication we are asked to perform is
[tex]1.35\times4.2[/tex]which has a total of 3 digits after the decimal point.
Now we know that
[tex]135\times42=5670[/tex]therefore, to find 1.35 x 4.2 we just shift the decimal place in the above to the left by 3 units
therefore
[tex]1.35\times4.2=5.67[/tex]which is our answer!
The total revenue from the sale of a poplar book is approximately by the rational function Where x us the number of years since publication and r(x) is the total revenue in millions of dollars. Use this function to complete parts a through dFind the total revenue at the of the first year ?
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Find the surface area and volume of the figure .The surface area is _ft2.(Round to the nearest tenth as needed .)
Answers
Question:
Find the surface area and volume of the figure.
Solution:
1) The surface area:
This shape is composed of a cylinder and hemisphere. Now, we know that the surface area of the sphere is:
[tex]SA\text{ sphere = 4}\pi\text{ }r^2[/tex]So that, the surface area of the hemisphere would be:
[tex]SA\text{ hemisphere = }2\pi r^2[/tex]On the other hand, the area of the circle is:
[tex]A\text{= }\pi r^2[/tex]thus, the surface area of the cylinder would be:
[tex]SA\text{ cylinder = }2\pi rh[/tex]replacing the data given in the problem in the formulas of the surface area of the hemisphere, area of the circle, and surface area of the cylinder, we get:
[tex]SA\text{ hemisphere = }2\pi(9)^2\text{ = 162}\pi[/tex]and
[tex]SA\text{ cylinder = }2\pi(9)(12)\text{ = }216\pi[/tex]and
[tex]A\text{= }\pi(9)^2=\text{ 81}\pi[/tex]then, we can conclude that the surface area of the given figure is:
[tex]SA\text{ = 162}\pi\text{ + 216}\pi+81\pi\text{ = 459}\pi\approx1441.9\text{ }\approx1442[/tex]that is:
[tex]SA\text{ }\approx1441.9\text{ }\approx1442[/tex]
2) The volume
The volume of a cylinder is given by the following formula:
[tex]V_C=\pi r^2h[/tex]and the volume of a hemisphere is :
[tex]V_H=\frac{1}{2}(\frac{4}{3}\pi r^3)\text{ = }\frac{2}{3}\pi r^3[/tex]thus, the volume of the figure would be:
[tex]V=V_C+V_H=\text{ }\pi r^2h\text{+}\frac{2}{3}\pi r^3[/tex]Then replacing the data given in the problem in the above formula we get:
[tex]V=\pi(9)^2(12)\text{+}\frac{2}{3}\pi(9)^3\text{ = 972}\pi\text{+486}\pi=\text{ 1458}\pi\approx4580.4\approx4580[/tex]that is;
[tex]V\approx4580.4\approx4580[/tex]A.Find the equation of the line of best fit round one decimal place, if needed choose the correct answer
B.the correlation coefficient is
C. The predicted number of cars sold in year 10 is
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An equation for the line of best fit is equal to: D. y = 4.8x + 10.
The correlation coefficient, R² is equal to 0.988.
The predicted number of cars sold in year 10 is equal to 490 cars.
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of cars sold would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the number of years and cars sold in the table, a linear equation for the line of best fit is given by:
y = 4.8x + 10
Next, we would determine the predicted number of cars sold in year 10:
y = 4.8x + 10
y = 4.8(10) + 10
y = 480 + 10
y = 490 cars.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Below is the graph of a trigonometric function. It intersects its midline at (-1.7, -10) and again at(5.1, -10). What is the period
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you can get the Period graphically if you see the points A and B are the upper points of the graph. if you subtract them you get the period
in this case, let me see
Here they give you the points where the graph cross the midline, if you see, that is half of the period, so
Period= 2* (5,1-(-1,7))= 13,6
You have to subtract the points to know the distance between that points, and the graph is
when you subtract the points, you are getting the distance between (for example) the green point on my draw
And the period is the time it takes for one complete oscillation, after this, it repeats over and over
So between 3 of these green points we have a period
to know the value, we need to know the distance between them (in this case (5,1-(-1,7))= 6,8
each square have 1 period on it, and the value is 2 times the distance between the green points
Answer:
Period= 2* (5,1-(-1,7))= 13,6
The length of a rectangle is 1 inch shorter than twice the width (x).Which is the width (x) when the area (y) = 3321 square inches?
Answers
the width (x) of the rectangle = 41 inches
Explanation:
let the width = x
twice the width = 2x
The length of a rectangle is 1 inch shorter than twice the width (x) = 2x - 1
length = 2x -1
Area of rectangle = length × breadth
area (y) = 3321 square inches
y = x × 2x - 1 = x(2x - 1)
3321 = 2x² - x
2x² - x - 3321 = 0
We use factorisation to find x:
a = 2, b = -1, c = -3321
a × c = 2(-3321) = -6642
The factors which gives -1 when we sum together but gives -6642 when we multiply together are -82 and +81
2x² -82x + 81x - 3321 = 0
2x(x - 41) + 81(x - 41) = 0
(2x + 81) (x - 41) = 0
(2x + 81) = 0 or (x - 41) = 0
2x + 81 = 0
2x = -81
x = -81/2 inches
(x - 41) = 0
x - 41 = 0
x = 41 inches
Since we can't have a negative number as the width, the width (x) of the rectangle = 41 inches
Graph the function and then determine the asymptote of the function.
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We need to graph the following function:
[tex]y=\log _{1/2}(x)-4[/tex]We know that the domain of a logarithmic function can't be negative, then our domain is
[tex]x\in(0,\infty)[/tex]We need to analyze this function at its extremes to find the asymptotes.
Let's calculate the limit of this function at x = 0 and at infinity.
[tex]\begin{gathered} \lim _{x\to0}\log _{1/2}(x)-4=\infty \\ \lim _{x\to\infty}\log _{1/2}(x)-4=-\infty \end{gathered}[/tex]By definition, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. From our limits, we have an vertical asymptote at x =0 and no horizontal asymptotes.
This logarithmic function, comes from infinity at x = 0, an decays to minus infinity as x grows. We have the following graph:
The circumference of a circle is 37.68 meters, what is the radius?
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Here are the numbers of times 13 people ate out last month 7, 3, 4, 3, 6, 4, 7, 6, 5, 7, 3, 6,5Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, tap on "No mode."Explanation
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In statistics, the mode is the value that occurs most frequently in a data set. This goes in the form of a column when we find two modes, that is, two data that have the same maximum absolute frequency.
First, we are going to count how many times each number is repeated in the data set.
[tex]\begin{gathered} 7\to3\text{ times} \\ 3\to3\text{ times} \\ 4\to2\text{ times} \\ 6\to3\text{ times} \\ 5\to2\text{ times} \end{gathered}[/tex]The highest frequency in the data set as we can see is 3. That is, the mode will be all the numbers that have that frequency in this case 7, 3 and 6