Answers
From the question given, we have the following data;
Height of the tree = 80 feet
Angle of elevation to the top of the tree = 68 degrees
Distance from Corey to the tree = unknown
We shall now call the unknown variable x.
With that we shall have the following diagram;
We now have a diagram detailing the triangle and the dimensions showing Corey, the tree and the eagle at the tree top.
To get a better look, Corey moves several steps away from the tree and now determines his new angle of elevation to be 41 degrees.
This can now be illustrated as follows;
From triangle EDC, we shall calculate the distance from point C to point D using trigonometric ratios. The reference angle is at point C, which means the opposite side is side ED. The adjacent side is side CD (labeled x). Using trig ratios we have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]We cross multiply and we now have;
[tex]\begin{gathered} x=\frac{80}{\tan 68} \\ U\sin g\text{ a calculator, we have tan 68 as 2.475086}\ldots \\ x=\frac{80}{2.475086} \\ x=32.322109\ldots \\ \text{Rounded to the nearest hundredth of a foot;} \\ x=32.32ft \end{gathered}[/tex]Looking at triangle EDB;
The reference angle is 41 which makes the opposite side ED and the adjacent side BD. To calculate the distance BD, we'll have;
[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 41=\frac{80}{BD} \\ We\text{ cross multiply and we now have;} \\ BD=\frac{80}{\tan 41} \\ BD=\frac{80}{0.869286} \\ BD=92.02955\ldots \\ \text{Rounded to the nearest hundredth;} \\ BD=92.03 \end{gathered}[/tex]Take note that the distance Corey moved before he had a new angle of elevation is line segment CD which is indicated as y. Note also that
[tex]\begin{gathered} BC+CD=BD \\ CD=x=32.32ft \\ BC+32.32=92.03 \\ \text{Subtract 32.32 from both sides;} \\ BC=59.71 \end{gathered}[/tex]The distance Corey stepped back is indicated as y (line segment BC).
ANSWER:
Corey stepped back 59.71 feet
Related Questions
* The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically.
Answers
Solution
f(2) = 4 and f(3) = -1
g(2) = 6 and g(-3) = 7
From the info given we can see this :
x = 2 f(2) = 4 , g(2)= 6
x= 3 f(3)= -1 , g(3)= 7
And we can calculate the slope with the following formula:
[tex]m=\frac{-1-4}{3-2}=-5[/tex][tex]m=\frac{7-6}{3-2}=1[/tex]And for this case we can conclude that the lines are neither
Since m1 is different from m2
And m1*m2 is not -1
Compute the area of each triangle. Round to the nearest tenth.
Answers
The triangle ΔDEF has the following coordinates
[tex]\lbrace D(-1,6),E(-4,-6),F(3,-5)\rbrace[/tex]To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by
[tex]Area(\Delta ABC)=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]Using this formula for our problem, we have
[tex]Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))|[/tex]Solving this equation, we have
[tex]\begin{gathered} Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))| \\ =\frac{1}{2}|(-1)((-6+5)+(-4)(-5-6)+3(6_{}+6)| \\ =\frac{1}{2}|(-1)(-1)+(-4)(-11)+3(12)| \\ =\frac{1}{2}|1+44+36| \\ =\frac{1}{2}|81| \\ =\frac{81}{2} \\ =40.5 \end{gathered}[/tex]And this is our answer Area(ΔDEF) = 40.5
how do i solve the equation?
Answers
Answer: 7x=63 and 12x+9= 117
Step-by-step explanation:
add those two equations and set it to 180 degree
7x+12x+9=180
19x=171
x= 9
7x = 7 (9) = 63
12x+9 = 12 (9)+9 = 117
To produce a textbook, suppose the publisher spent $110,000 for typesetting and $7.50 per book for printingand binding. The total cost to produce and print n books can be written asC = 110,000+ 7.51a. Suppose the number of books printed in the first printing is 10,000. What is the total cost?The total cost is $b. If the average cost is the total cost divided by the number of books printed, find the average cost of producing10,000 textbooks.The average cost of producing 10,000 textbooks is $c. Find the cost to produce one more textbook when you have already produced 10,000 textbooks.If you have already produced 10,000 textbooks, it'll cost you $ to produce one more.
Answers
The given equation is
[tex]C=110000+7.5n[/tex]a)
The number of books=10000
Substitute n=10000 in the given equation, we get
[tex]C=110000+7.5\times10000[/tex][tex]C=185000[/tex]The total cost is $185,000.
b)
[tex]\text{Average cost =}\frac{185000}{10000}=18.5[/tex]The average cost of producing 10,000 textbooks is $18.5.
c)
If we need to produce one more after producing 10000 books.
substitute n=10001 in the given equation, we get
[tex]C=110000+7.5(10001)=185007.5[/tex][tex]\text{One book cost after printed 10000 book=cost of 10000 books-cost of 10001 books}[/tex][tex]\text{One book cost after printed 10000 book=1}85000-185007.5=7.5[/tex]
If you have already produced 10,000 textbooks, it'll cost you $7.5 to produce one more.
Given that events A and B are independent with P(A) = 0.08 and P(B) = 0.25,determine the value of P(A and B), rounding to the nearest thousandth, ifnecessary.
Answers
To find: P(AandB)
P(AandB)=P(A)*P(B)
P(AandB)=0.08*0.25
P(AandB)=0.02
Thus the required answer is 0.02
Solve by using a proportion. Round answers to the nearest hundredth if necessary. 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles? 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours?
Answers
EXPLANATION
Let's see the facts:
rate ---> 3.6 miles / 30 minutes
The unit rate is:
Unit rate = 0.12 miles/minute
Now, dividing the needed 4.8 miles by the unit rate will give us our desired number:
Time= 4.8 miles/ 0.12miles/minute = 40 minutes
The answer is 40 minutes.
Find the tangent of the angle whose measure is pi/2....pi divided by 2.
Answers
We have the following:
[tex]\begin{gathered} \tan \theta=x \\ \tan \frac{\pi}{2}=x \end{gathered}[/tex]the value of pi / 2 is not defined
2. Graph the image of Parallelogram WXYZ under a translation 4 units to the left and 6 units up
Answers
Translation 4 units to the left transforms the point (x, y) into (x-4, y). Applying this rule to the parallelogram WXYZ, we get:
W(0, -2) → (0-4, -2) →W'(-4, -2)
X(2, -2) → (2-4, -2) → X'(-2, -2)
Y(2, -5) → (2-4, -5) → Y'(-2, -5)
Z(0, -5) → (0-4, -5) → Z'(-4, -5)
Translation 6 units up transforms the point (x, y) into (x, y+6). Applying this rule to the parallelogram W'X'Y'Z', we get:
W'(-4, -2) → (-4, -2+6) → W''(-4, 4)
X'(-2, -2) → (-2, -2+6) → X''(-2, 4)
Y'(-2, -5) → (-2, -5+6) → Y''(-2, 1)
Z'(-4, -5) → (-4, -5+6) → Z''(-4, 1)
Where the parallelogram W''X''Y''Z'' is the image of Parallelogram WXYZ translated 4 units to the left and 6 units up, as can be seen in the next graph:
List the angle measures of △VWX in order from smallest to largest. Assume that t is a positive number.
Answers
Explanation
To begin with, we will first have to obtain the length of side VX
[tex]VX^2=WX^2+VW^2-2\times WX\times VWcosw[/tex]In our case
[tex]\begin{gathered} WX=28t \\ VW=95t \\ w=94^0 \end{gathered}[/tex]Thus
[tex]\begin{gathered} VX^2=(28t)^2+(95t)^2-2\times(28t\times95t)cos94 \\ \\ VX^2=784+9025+371.104 \\ VX^2=100180.10 \\ \\ VX=100.90t \end{gathered}[/tex]Next, we will determine the angles at V and X
using sine rule
[tex]\begin{gathered} \frac{sin94}{100.9t}=\frac{sinV}{28t} \\ \\ sinV=\frac{28t\times sin94}{100.9t} \\ \\ sinV=0.27683 \\ \\ V=16.07^0 \\ \end{gathered}[/tex]Then, we will get the measure at X
[tex]180^0-16.07^0-94=69.93^0[/tex]Therefore, the order from smallest to largest angles will be
m
OR
m
At a local school, 164 students play soccer and 112 students play baseball. What is the ratio of soccer players to baseball players?41:2828:4113:2828:13
Answers
Given
The number of students who play soccer is 164.
The number of students who play baseball is 112
Explanation
To find the ratio of soccer player to baseball players .
Divide the number of soccer player by the number of baseball player.
[tex]\frac{164}{112}=\frac{41}{28}[/tex]Answer
Hence the ratio of soccer players to baseball players is
[tex]41:28[/tex]hello I just need help with these no need to explain just the answers please
Answers
The two pairs of angles are supplementary
Here, we want to complete the given sentence
We want to find the relationship between two parallel lines which are cut by a transversal
A figure showing the described relationship is given below;
Now, we want to find the relationship between the two marked angles
From what we have, the two marked angles are supplementary
What this mean is that both angles add up to 180 degrees
use the generic rectangle 3x-8)² and -7x⁴(3x-2) what's the product and sum?
Answers
In this case the answer is very simple .
Step 01:
Data:
eq1. (3x - 8)²
eq2. -7x⁴(3x-2)
Step 02:
Sum.
eq.1 + eq.2
(3x - 8)² + (-7x⁴(3x-2))
(9x² - 2*3x*8 - 64) + (-21x⁴ - 14x⁴)
9x² -
Ms. Morgan is the cafeteria manager. She keeps track of how many students select each type of drink. Today during breakfast, 32 children picked milk while 44 children picked juice. What is the ratio of the numbe of children who picked juice to those who picked milk?
Answers
Answer:
ratio of those who picked juice to milk
it refers to division
Express y in terms of x. Then find the value of y when x= -1-3 (x + 2) = 5yY in terms of x:Y=
Answers
LEt's express y in term of x:
[tex]\begin{gathered} -3(x+2)=5y \\ y=\frac{-3(x+2)}{5} \end{gathered}[/tex]Therefore:
[tex]y=-\frac{3}{5}x-\frac{6}{5}[/tex]Now, if x=-1, then we have:
[tex]\begin{gathered} y=-\frac{3}{5}(-1)-\frac{6}{5} \\ =\frac{3}{5}-\frac{6}{5} \\ =-\frac{1}{5} \end{gathered}[/tex]Therefore, if x=-1 then y=-1/5
heyy could you help me out with this problem I'm stuck
Answers
Since congruent angles are equal
Therefore the two figures are similar
we have
9 / 9 = 2x / x + 4
introduce cross multiplication
9 (2x) = 9(x + 4)
18x = 9*x + 9*4
18x = 9x + 36
collect the like terms
18x - 9x = 36
9x = 36
divide boths sides by 9
9x / 9 = 36/9
x = 4
The first missing variable is 2x
2 x 4
= 8
The second is x + 4
we have 4 + 4
= 8
m
What is 13.496 rounded to the nearest tenth?A.13B.13.4C.13.5D.14
Answers
1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.
2) Note this number:
We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.
3) Thus, we can round it off to:
[tex]13.5[/tex]A random number generator is used to select an integer from 1 to 100 (inclusively). What is the probability of selecting the integer 730?
Answers
If a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.
Here a random number generator is used to select an integer from 1 to 100.
Therefore the range of the outcome = 1 to 100
Here we have to find the probability of selecting the integer 730
The probability = Number of favorable outcomes / Total number of outcomes.
Here a random number generator is used to select an integer from 1 to 100, but the given number is 730 which is out of range. Therefore the probability is zero
Hence, if a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.
Learn more about probability here
brainly.com/question/11234923
#SPJ1
Write a relation consisting of five ordered pairs that satisfies the following conditions. The relation is a function. Switching the x- and y-coordinates of each ordered pair results in a relation that is not a function.
Answers
Answer:
Step-by-step explanation:
If each value of x only has one corresponding value of y, it is a function. You can test this just by eye or by graphing and doing the vertical line test by rolling a pencil or other straight object across to make sure only one point is on the line at a time
plant A produced 3 times as many panels as plant b. two percent of the panels from plant A and 5% of the panels from plant b were defective. how many panels did plant b produce if the two plants together produced 990 defective panels
Answers
let x the number of panels that Plant A produced
y the number of panels that Plant B produced
then, we have
x = 3y
0.02x + 0.05y = 990
and solve the system:
[tex]\begin{gathered} 0.02(3y)+0.05y=990 \\ 0.06y+0.05y=990 \\ 0.11y=990 \\ \frac{0.11y}{0.11}=\frac{990}{0.11} \\ y=9000 \end{gathered}[/tex]answer: plant b produced 9000 panels
have $100 to spend on Halloween candy. A pack of M&Ms cost $3.50. 15 Twix bars cost $7.00. 9 Hershey Bars cost $3.00. If I need 15 M&M packs, 17 Twix bars and 9 Hershey bars how much will it cost? How much money will I have left?
Answers
Answer:
Assuming this is rounding to the nearest cent, $36.51
Step-by-step explanation:
1 ) Find the cost of each individual candy.
M&Ms are given at $3.50 per pack.
To find the cost of one Twix bar, divide $7.00 by 15. This makes Twix equal $0.47 per bar.
You don't need to find the individual price of the Hershey's bars because 9 bars cost $3.00 and you need 9 bars in the equation.
2 ) Now that you have the prices you need, multiply.
For M&Ms 15 x $3.50 = $52.50
For Twix 17 x $0.47 = $7.99
For Hershey's, it is given that 9 bars are $3.00
3 ) Add all of these up to get the total spent on candy.
$52.50 + $7.99 + $3.00 = $63.49
4 ) Subtract this from the budget to get the total amount left over.
$100 - $63.49 = $36.51
y = (x+3)^3 find the zeros of each function
Answers
Given,
[tex]y=(x+3)^3[/tex]We have,
[tex]y=0[/tex]when,
[tex]\begin{gathered} x+3=0 \\ \Rightarrow x=-3 \end{gathered}[/tex]The zeros of the function are x=-3,-3,-3
can you explain this to me what you are supposed to do this
Answers
Solution
If we see the two tirangles given BAC and A'B'C' we can conclude that we have the following congruent angles
< CAB = < C'A'B'
< BCA = < B'C'A'
< ABC = < A'B'C'
Area of a sector A sector with a radius of \maroonD{8\,\text{cm}}8cmstart color #ca337c, 8, start text, c, m, end text, end color #ca337c has an area of \goldE{56\pi\,\text{cm}^2}56πcm
Answers
To find the angle of the sector, follow the steps below.
Step 01: Find the total area of the circle.
The area (A) of a circle with radius r is:
[tex]A=\pi r^2[/tex]Knowing that r = 8 cm, then the area is:
[tex]\begin{gathered} A=8^2\pi \\ A=64\pi\text{ cm}^2 \end{gathered}[/tex]Step 02: Find the central angle.
To find the angle, use proportions.
Knowing that:
When angle = 2π, A = 64π,
Then when angle is x, A = 56π
[tex]\begin{gathered} \frac{x}{2\pi}=\frac{56\pi}{64\pi} \\ \\ \text{ Multiplying both sides by 2}\pi: \\ \frac{x}{2\pi}*2\pi=\frac{56\pi}{64\pi}*2\pi \\ x=\frac{56*2}{64}\pi \\ x=\frac{112}{64}\pi \\ \\ \text{ Dividing both the numerator and the denominator by 16:} \\ x=\frac{\frac{112}{16}}{\frac{64}{16}}\pi \\ x=\frac{7\pi}{4} \end{gathered}[/tex]Answer: The central angle measure is:
[tex]\frac{7\pi}{4}[/tex]hector recorded the amount of rainfall in the desert each month over a period of two years. the list shows the number of inches fell for each month for year 1 and year 2 year 1: 2,2,0,0,0,1,2,2,3,2,2,2year 2:1,1,0,0,0,0,2,2,2,1,2,1 whats the difference in rain fall between the mean of the rain fall in two years hurry its a test
Answers
ANSWER
The difference is 0.5
EXPLANATION
We have to find the mean of the rain fall for each year. To do this we have to add all the data and then divide by the total number of data.
Year 1: number of data = 12:
[tex]\bar{x_1}=\frac{2+2+0+0+0+1+2+2+3+2+2+2}{12}=\frac{18}{12}=\frac{3}{2}=1.5[/tex]Year 2: number of data = 12:
[tex]\bar{x_2}=\frac{1+1+0+0+0+0+2+2+2+1+2+1}{12}=\frac{12}{12}=1[/tex]The difference is:
[tex]\bar{x}_1-\bar{x}_2=1.5-1=0.5[/tex]Ashley‘s Internet service is terribly unreliable in fact on any given day there’s a 60% chance that her Internet‘s connection will be lost at some point that day what is the probability that her Internet service is not broken for seven days in a row inner a fraction or round your answer to four decimal places if necessary.
Answers
Let the event that her internet will be broken be A
The event that her internet will not be broken be B
Therefore:
[tex]\begin{gathered} P(A)=60\%=0.60 \\ P(B)=1-0.60=0.4 \end{gathered}[/tex]Thus, the probability that her internet is not broken for 7 days in a row:
[tex]P(B\text{ for 7 days\rparen=P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}[/tex]Substitute the value:
[tex]P(B\text{ for 7 days\rparen=0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4=0.001634}[/tex]Round to four decimal places is 0.0016
Answer: 0.0016
The half-life of a radioactive kind of iodine is 21 hours. How much will be left after 42 hours,if you start with 19,296 grams of it?In grams
Answers
The half-life of a radioactive material is the time that it takes to reduce to half
In this case, the half-life is 21 hs, and since 42hs is twice the half-life, the material will reduce to half after 21 hours and then to half again.
one half of one half is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Then we multiply by the initial amount:
[tex]19,296\cdot\frac{1}{4}=4824gr[/tex]The amount left after 42 hours is 4824 grams.
You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.
Answers
The given figure is a square that measures 12 foot by 12 foot. please see illustration below;
The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.
In the triangle ADC, using Pythagoras' theorem;
[tex]\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}[/tex]The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).
Jack scored 80 out of 85 points on a recent test. What is his score as a percent, rounded to the nearest whole percent?
Answers
jack scored = 80
total point = 85
so the percentage is,
[tex]=\frac{80}{85}\times100[/tex][tex]\begin{gathered} =\frac{8000}{85} \\ =94.11\text{ \%} \end{gathered}[/tex]thus, the nearest whole percentage is 94 %
help me pleaseeeeeeeee
Answers
The values of given functions f(-2), f(0) and f(7) when f(x) = 1-6x are 13, 1 and -41 respectively.
According to the question,
We have the following function:
f(x) = 1-6x
Now, we can find the values of each function by putting the numbers in place of x.
Now, in order to find the value of f(-2), we will put -2 in place of x in the given function.
f(-2) = 1-6*(-2)
f(-2) = 1+12
f(-2) = 13
Now, in order to find the value of f(0), we will put 0 in place of x in the given function.
f(0) = 1-6(0)
f(0) = 1-0
(We know that when a number is multiplied with 0 then the result is always 0.)
f(0) = 1
Now, in order to find the value of f(7), we will put 7 in place of x in the given function.
f(7) = 1-6*7
f(7) = 1-42
f(7) = -41
Hence, the values of f(-2), f(0) and f(7) are 13, 1 and -41 respectively.
To know more about values here
https://brainly.com/question/13581879
#SPJ1
Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method.
Answers
We have the following:
[tex]s^2+7s+6[/tex]solving:
[tex]\begin{gathered} \text{step 1} \\ s^2+s+6s+6 \\ \text{step 2} \\ s\mleft(s+1\mright)+6\mleft(s+1\mright) \\ \text{step 3} \\ (s+1)(s+6) \end{gathered}[/tex]