A tree on a hillside casts a shadow c = 215 ft down the hill. If the angle of inclination of the hillside is b = 23° to the horizontal and the angle of elevation of the sun is a = 53, find the height of the tree. (Round your answer to the nearest foot.)
Answers
This is the figure, roughly. We want h.
Using smaller triangle, we can write:
[tex]\begin{gathered} \text{Cos}23=\frac{x}{215} \\ x=215\cdot\cos 23 \\ x=197.9 \end{gathered}[/tex]Also,
[tex]\begin{gathered} y=215\cdot\sin 23 \\ y=84 \end{gathered}[/tex]Now, taking the larger triangle:
The angle is 53 (30 + 23).
Let the larger side (right side) be m, which is basically:
m = h + y
Let's find m:
[tex]\begin{gathered} \tan 53=\frac{m}{x} \\ \tan 53=\frac{m}{197.9} \\ m=197.9\cdot\tan 53 \\ m=262.62 \end{gathered}[/tex]Now, we want height, h, which is:
m = h + y
262.62 = h + 84
h = 262.62 - 84
h = 178.62
Rounded to nearest feet
h = 179 feet
Related Questions
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you'll find out. Consider AABC, whose vertices are A (2,1), B (3, 3), and C (1,6) ; let AC represent the base of the triangle. Part A Find the equation of the line passing through B and perpendicular to AC.
Answers
Answer: y = x/5 + 12/5
Explanation:
The first step is to find the equation of line AC
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept.
The formula for calculating slope of a line is expressed as
m = (y2 - y1)/(x2 - x1)
Considering line AC with points, A(2, 1) and C(1, 6),
x1 = 2, y1 = 1
x2 = 1, y2 = 6
m = (6 - 1)/(1 - 2) = 5/- 1 = - 5
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5
Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5
We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have
3 = 1/5 * 3 + c
3 = 3/5 + c
c = 3 - 3/5
c = 12/5
By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is
y = x/5 + 12/5
I have an image can I show it to you?
Answers
Answer:
Rhombus
Explanation:
Looking at the given figure, the correct option is a Rhombus because the figure is a quadrilateral and all of its sides have the same length, opposites sides are parallel and opposite angles are equal.
What is the height of a parallelogram with an area of 50 square meters
and a base length of 5 meters?
Answers
The height of a parallelogram with an area of 50 square meters and a base length of 5 meters is 10 meters
What is a parallelogram?The word "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bounded by parallel lines." As a result, a quadrilateral that is bound by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides. Square, rectangle, and rhombus are the three primary varieties of parallelograms, and each one has distinct characteristics. If a quadrilateral's opposite sides are parallel and congruent, it will be a parallelogram. So a quadrilateral with both pairs of opposite sides being parallel and equal is known as a parallelogram.
Various forms of parallelograms can be distinguished from one another based on their unique characteristics. It can be broadly classified into three distinct types:
RectangleSquareRhombusArea = 50
Base = 5
Area of ║gm = base (height)
50 = 5(X)
x = 10
To know more about parallelogram ,visit:
brainly.com/question/16287616
#SPJ13
Perform the following matrix row operation and write the new one.
Answers
Given: A matrix
[tex]\begin{bmatrix}{1} & {-3} & {2} \\ {3} & {9} & {5} \\ {} & & {}\end{bmatrix}[/tex]Required: To perform the following matrix row operation
[tex]-3R_1+R_2[/tex]Explanation: The operation is to be applied on the first row of the given matrix. Hence the second row will be same as that of the initial matrix.
The elements of the first row are first multiplied by 3 and then added with second row to give the required matrix.
Hence,
[tex]\begin{bmatrix}{-3+3} & {9+9} & {-6+5} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]which gives
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Final Answer: The required matrix is
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]One thousand Charity raffle tickets are sold for $1 each. Winning tickets will be drawn in order,1st,2nd,3rd. First prize is $500. Second prize is $300. Third prize is $150. Tickets are replaced after each drawing so the probability of being draw for each prize is 1/1000. What is the expected value? I am stuck on this question and need help
Answers
Answer:
-$0.05
Explanation:
The expected value can be calculated as the sum of each possible prize multiplied by its probability. You will buy a ticket for $1 and there is a probability of 1/1000 to win the $500, a probability of 1/1000 to win $300, and a probability of 1/1000 to win $150, then the expected alue is
[tex]\begin{gathered} E=-1+500(\frac{1}{1000})+300(\frac{1}{1000})+150(\frac{1}{1000}) \\ E=-1+0.5+0.3+0.15 \\ E=-0.05 \end{gathered}[/tex]Therefore, the expected value is -$0.05.
Write the equation of a line containing (3,-7) that is parallel to the line given by the equation -4x+8y=3
Answers
Two lines are parallel is they have the same slope. In this case:
[tex]-4x\text{ + 8y = 3}[/tex]Solving the equation for y, and obtaining the slope-intercept equation for the line equation, we have:
[tex]8y\text{ = 3 + 4x}[/tex][tex]y\text{ = }\frac{3}{8}\text{ + }\frac{4}{8}x[/tex]Then,
can someone please help me find the value of x?
Answers
Since we have a right triangle, we can relate the angle 28 with x and side 34 by meand of the sine function, that is,
[tex]\sin 28=\frac{34}{x}[/tex]where x is the hypotenuse. By moving x to the left hand side, we have
[tex]x\cdot\sin 28=34[/tex]and by moving sin28 to the right hand side, we get
[tex]x=\frac{34}{\sin 28}[/tex]since sin28=0.4694, we have
[tex]x=\frac{34}{0.4694}[/tex]then, x is given by
[tex]x=72.42[/tex]by rounding down, the answer is option D: x=72.4
Please help. I've been trying to answer this question but I haven't been successful.
Answers
Equations
It's required to find the value of x that satisfies the conditions of the figure.
We have an equilateral triangle. We know it's equilateral because all of its interior angles have the same measure (look at the tick mark on each angle).
Recall the sum of the interior angles of any triangle is 180°.
If all the interior angles have the same measure, then each angle measures 180/3 = 60°.
One of the angles is assigned an expression of x. We can equate it to 60:
5x - 18 = 60
Adding 18:
5x = 78
Dividing by 5:
x = 78/5
x = 15.6
Answer: I do believe the answer is 15.6. Hope this helps! ^w^
1. Sketch the graph of y = x that is stretched vertically by a factor of 3. (Hint: Write the equation first, then graph) Sketch both y = x and the transformed graph.
Answers
ANSWER and EXPLANATION
We want to stretch the graph of:
y = x
A vertical stretch of a linear function is represented as:
y' = c * y
where c is the factor
The factor from the question is 3.
So, the new equation is:
y' = 3 * x
y' = 3x
Let us plot the functions:
The shaded triangle has an area of 4 cm?Find the area of the entire rectangleBe sure to include the correct unit in your answer.
Answers
Given:
Area of a shaded region of a rectangle is given.
[tex]\text{Area of the triangle=}4cm^2[/tex]Area of the rectangle is twice the area of the triangle given.
[tex]\begin{gathered} \text{Area of a rectangle=2}\times Area\text{ of a triangle} \\ =2\times4 \\ =8cm^2 \end{gathered}[/tex]A group of 38 people are going to an amusement park together. They decide to carpool to save fuel. If seven people can fit in each car, how many cars do they need to take on the outing? [?] cars 3
Answers
So, the number of people = 38
7 people can fit in a one car
so, to find the number of cars divide 38 by 7
So, the number of cars = 38/7 = 5.4
But the number of cars must be integer
so, the number of cars = 6 cars
The answer is 6 cars
Use log, 20.356, log, 3 0.503, and log, 5 0.835 to approximate the value of the given logarithm to 3 decimal places. Assume that b>0 and b + 1.
log, 625
X
A
Answers
Answer:
3.34
Step-by-step explanation:
625 is 5^4
Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],
log_b(5^4) = 4*log_b(5)
4*0.835 = 3.34
A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
Answers
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
Which choice is equivalent to the quotient shown here for acceptablevalues of x?25(x - 1) = 5(x - 1)?A.5(x - 1)B. 125(x - 1)C. V25(x - 1) -5(x - 1)?D. V5(x - 1)SUBMIT
Answers
Given the expression:
[tex]\sqrt[]{28(x-1)}\div\sqrt[]{8x^2}[/tex][tex]\frac{\sqrt[]{28(x-1)}}{\sqrt[]{8x^2}}[/tex]Let's determine the inequality that represents all the values of x.
Here, we are to find the domain.
Let's solve for x.
Set the radicand in the numerator and denominator to be greater or equal to zero.
We have:
[tex]\frac{28(x-1)\ge0}{8x^2\ge0}[/tex]For the numerator, we have:
[tex]\begin{gathered} 28(x-1)\ge0 \\ \text{Divide both sides by 28:} \\ \frac{28(x-1)}{28}\ge\frac{0}{28} \\ \\ x-1\ge0 \\ \text{Add 1 to both sides:} \\ x-1+1\ge0+1 \\ x\ge1 \end{gathered}[/tex]For the denominator, we have:
[tex]\begin{gathered} 8x\ge0 \\ x\ge\frac{0}{8} \\ x\ge0 \end{gathered}[/tex]Therefore, the possible x-values for which the quotient is defined is all positive integers greater or equal to 1.
Thus, we have:
[tex]x\ge1[/tex]ANSWER:
[tex]C.x\ge1[/tex]9) Find the slope of the line that passes through these two points. (0.3) and (4, -2)
Answers
To find the slope of the line that passes through points (0, 3) and (4, -2), we can use the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We have then:
(0, 3) ---> x1 = 0, y1 = 3
(4, -2) --->x2 = 4, y2 = -2
Therefore:
[tex]m=\frac{-2-3}{4-0}\Rightarrow m=\frac{-5}{4}\Rightarrow m=-\frac{5}{4}[/tex]Then, the slope of the line that passes through points (0, 3) and (4, -2) is m = -5/4.
Nguyen deposited $35 in a bank account earning 14% interest, compounded annually. How much interest will he earn in 72 months?
Answers
Given:
a.) Nguyen deposited $35 in a bank account.
b.) It earns 14% interest.
To be able to determine how much interest will he earn in 72 months, the following formula will be used for Compound Interest:
[tex]\text{ Interest Earned = P(1 + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex]Where,
P = Principal amount
r = Interest rate
n = No. of times the interest is compounded = annually = 1
t = Time in years = 72 months = 72/12 = 6 Years
We get,
[tex]\text{ Intereset Earned = (35)(1 + }\frac{\frac{14}{100}}{1})^{(1)(6)}\text{ - 35}[/tex][tex]\text{ = (35)(1 + }0.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}1.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}2.19497262394)^{}\text{ - 35}[/tex][tex]\text{ = 76.82404183776 - 35}[/tex][tex]\text{ = 41.82404183776 }\approx\text{ 41.82}[/tex][tex]\text{ Interest Earned = \$41.82}[/tex]Therefore, the interest he will be earning is $41.82
Graph the system below. What is the x-coordinate of the solution to the system of linear equations?y= -4/5x + 2y= 2/3x + 2A. -4B. 2C. 3D. 0
Answers
The solution is (x,y) = (0,2)
Find an equation of the line described. Write the equation in slope-intercept form.With slope of -2 through (0,4)the equation of the line is y=0
Answers
y = -2x + 4
Explanations:The equation of the line having a slope m, and passing through the point (x₁, y₁) is given as:
y - y₁ = m (x - x₁)
From the description given:
The line passes through the point (0, 4)
That is, x₁ = 0, y₁ = 4
The slope of the line, m = -2
Substitute x₁ = 0, y₁ = 4, and m = -2 into the equation y - y₁ = m (x - x₁)
y - 4 = -2 (x - 0)
y - 4 = -2(x)
y - 4 = -2x
y = -2x + 4
What is the slope of a line that is perpendicular to the line whose equation is 2x−y=7?A. −1/2B. 3/2C. −3/2D. 1/2
Answers
We have the following line:
[tex]\begin{gathered} 2x-y=7 \\ y=2x-7 \end{gathered}[/tex]and we must determine the slope of its perpendicular line.
Slopes of two perpendicular lines, m1 and m2, have the following property:
[tex]m_1\cdot m_2=-1[/tex]Given the slope of the first line (the coefficient that multiplies the x):
[tex]m_1=2[/tex]and using the formula above for the slope of its perpendicular line, we get:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{2} \end{gathered}[/tex]Answer
A. −1/2
Instructions: Complete the following table, computing each students' mean, median, mode, and range: Math Test Scores ( picture attached ) What is the mean score for Test 2? What is the mode of Test 7? ________What is the median score of Test 4? ________What is the range of Test 6? ________
Answers
The completed worksheet is the following:
This worksheet involves three measures of central tendency: Mean, Median, Mode and Range
Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)
Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.
For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).
Mode: The mode is the most repeated value of a dataset.
Range: The range is the difference between the biggest and smallest values of a dataset.
Use the information and diagram to complete the proof. Given: C is the midpoint of AD¯¯¯¯¯¯¯¯.∠BAC≅∠EDC Prove: △BAC≅△EDC Triangles A B C and D E C share vertex C, where C is between A & D and C is between B & E. Angles A & D are right angles.© 2016 StrongMind. Created using GeoGebra. Statements Reasons 1. ∠BAC≅∠EDC 1. Given 2. C is the midpoint of AD¯¯¯¯¯¯¯¯. 2. Given 3. C bisects AD¯¯¯¯¯¯¯¯. 3. Definition of midpoint 4. AC¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ 4. Definition of bisect 5. ∠ACB and ∠DCE are vertical angles. 5. Definition of vertical angles 6. ∠ACB≅∠DCE 6. Vertical Angle Theorem 7. △BAC≅△EDC 7. _[blank]_ Stephanie and Miranda disagree about which reason goes in the blank for Statement 7.Stephanie states that the missing reason is the ASA Congruence Theorem, but Miranda says the missing reason is the SAS Congruence Postulate.Answer the following two questions.Which student, if either, is correct? Why? Select two answers: one for Question 1 and one for Question 2.
Answers
Solution:
Given:
Stephanie is correct. Because:
[tex]\begin{gathered} \angle A\cong\angle D \\ \\ AC\cong DC \\ \\ \angle C\cong\angle C \end{gathered}[/tex]Thus, the proof shows that two pairs of corresponding angles and the included sides are congruent.
I need help creating a tree diagram for this probability scenario
Answers
We need to draw a tree diagram for the information given
The total is 400
120 in finance course
220 in a speech course
55 in both courses
Then we start for a tree for the given number
Then to make the tree for probability we will divide each number by a total 400
Then the probability of finance only is 65/400
The probability of speech only is 165/400
The probability of both is 55/400
The probability of neither is 5/400
The probability of finance or speech is 285/400
find the length of the gray arc in terms of pi
Answers
Given
a: angle
a = 60
r: radius
r = 3
Procedure
The length of an arc depends on the radius of a circle and the central angle θ
[tex]\begin{gathered} s=\theta r \\ s=\frac{1}{3}\pi\cdot3 \\ s=\pi \end{gathered}[/tex]The answer would be s = pi
If a cell disruptor is purchased with a frequency of 60Hz, what is the wavelength traveling through human tissue? (1540 m/s).
Answers
The wavelength traveling through human tissue when the velocity is 1540 m/s and frequency is 60Hz will be 25.67 m.
According to the question,
We have the following information:
Frequency of a cell disruptor = 60 Hz
Velocity of the cell disruptor = 1540 m/s
We know that the following formula is used to find the wavelength:
Wavelength = Velocity/frequency
Wavelength = 1540/60 m
(Note that when velocity is given m/s and frequency is given in Hz then the unit of wavelength is m. Every physical quantity has to be expressed with its units.)
Wavelength = 25.67 m
Hence, the wavelength traveling through human tissue is 25.67 m.
To know more about wavelength here
https://brainly.com/question/13533093
#SPJ1
are figures A and B congruent? explain your reason
Answers
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!!!!!
Answers
Answer:
Option 2
Step-by-step explanation:
hope this helps
Write the equation in standard form for the hyperbola with vertices (-9,0) and (9,0) and a conjugate axis of length 16
Answers
The given vertices are (-9,0) and (9,0).
Notice that they lie on the x-axis since they have 0 as their y-coordinate.
Hence, the hyperbola is a horizontal hyperbola.
Recall that the equation of a horizontal hyperbola is given as:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center and a>b.
As both vertices are equidistant from the origin, the center of the hyperbola is (0,0), and the equation becomes:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Note that the vertices are at (-a,0) and (a,0).
Compare with the given vertices (-9,0) and (9,0). It follows that a=9.
Substitute this into the equation:
[tex]\frac{x^2}{9^2}-\frac{y^2}{b^2}=1[/tex]Recall that the length of the conjugate axis is given as 2b, it follows that:
[tex]\begin{gathered} 2b=16 \\ \Rightarrow b=\frac{16}{2}=8 \end{gathered}[/tex]Substitute b=8 into the equation:
[tex]\begin{gathered} \frac{x^2}{9^2}-\frac{y^2}{8^2}=1 \\ \Rightarrow\frac{x^2}{81}-\frac{y^2}{64}=1 \end{gathered}[/tex]The required equation in standard form is:
[tex]\frac{x^2}{81}-\frac{y^2}{64}=1[/tex]An elevator car starts on the second floor of a building 27 feet above the ground. The car rises 4.2 feet every second on its way up to the 15th floor. Assuming the car doesn’t slow down or make any stops , how long will it take the car to reach a height of 102 feet above the ground?
Answers
17.86 seconds
Explanation:The starting point of the elevator car = 27 feet above the ground
The endpoint point of the elevator car = 102 feet above the ground
The total distance traveled by the elevator car = 102 feet - 27 feet
The total distance traveled by the elevator car = 75 feet
Time taken by the elevator car to rise 4.2 feet = 1 second
Time taken by the elevator car to rise 75 feet = 75/4.2 seconds
Time taken by the elevator car to rise 75 feet = 17.86 seconds
Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground
*Statistical question: Is the proportion of inner-city families living on a subsistence income: 20%? Two hundred families were randomly selected for the survey
and 38 were found to have income at the subsistence level. Use the formal critical value method at 5% level of significance.
List the assumptions pertaining to this procedure.
Answers
Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.
Hypothesis tested and critical valueAt the null hypothesis, it is tested if the proportion is of 20%, that is:
[tex]H_0: p = 0.2[/tex]
At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:
[tex]H_1: p \neq 0.2[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
Test statisticThe test statistic is given by the rule presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In the context of this problem, the parameters are given as follows:
[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]
z = -0.35.
|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.
More can be learned about the use of the z-distribution to test an hypothesis at https://brainly.com/question/13873630
#SPJ1
Write the expression as a sum and/or difference of logarithms. Express powers as factors.log7(343x)
Answers
Recall the product rule of logarithms
[tex]\log _b(xy)=\log _b(x)+\log _b(y)[/tex]Apply the product rule to the given and we get
[tex]\log _7(343x)=\log _7(343)+\log _7(x)[/tex]