3. juan lies on the ground 45 feet from his tent. the tent is 400 feet from the base of a tall cliff. both the top of the tent and the top of the cliff are in his line of sight. if juan's tent is 10 feet tall, how tall is the cliff?
Answers
The cliff is 98.89 feet tall.
In the attached diagram, we can there are two triangles forming. Small triangle involves Juan and tent and larger triangle involves Juan and cliff. As per the known fact, tan theta = perpendicular ÷ base. So, tan theta will be common for both the triangles. Hence, relating the components of tan theta, of both the triangles.
Smaller triangle :
tan theta = 10/45
Larger triangle :
tan theta = h/(400 + 45)
tan theta = h/445
Relating both the triangles as follows -
10/45 = h/445
Performing cross multiplication
10×445 = h×45
h = 4450÷45
h = 98.89 feet
Hence, the cliff is 98.89 feet tall.
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Related Questions
Обчислив площу поверхні Куба ребро якого дорівнює 4,2 м
Answers
Answer: I calculated the surface area of a cube whose edge is 4.2 m
Step-by-step explanation: hope this helps
B The table represents the location of QRST before and after a reflection. Use the table to
answer 3-5.
3. Give a verbal description of the transformation.
PRE-IMAGE
Q(-9,-8)
R(-9, -2)
S(-4,-2)
T(-4,-8)
IMAGE
Q'(9,-8)
R(9,-2)
S(4, -2)
?
4. Which best represents the transformation algebraically?
a. (x, y) b. (-x, y) c. (-x, -y)
d. (x + 18, y)
5. Find the location of T
Answers
3. The x-coordinate of the image is equal to the negative of that of the pre-image. The y-coordinate remains the same.
4. The transformation is best represented algebraically by (-x, y).
5. The location of the image of T is (4, -8).
3. The transformation makes the x-coordinate of the image equal to the negative of that of the pre-image. The y-coordinate remains the same.4. The transformation is best represented algebraically by (-x, y).5. The coordinates of the preimage of T are (-4, -8). On applying the transformation, the image of T becomes (-(-4), 8), i.e., (4, -8).To learn more about pre-image, visit :
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according to the rational root theorem, which function has the same set of potential rational roots as the function g(x)
Answers
Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
What are roots of an equation?Roots of an equation refer to the values that when put into the variable of the equation, satisfy the equation and give the required value as 0.
Given:
g(x) = 3x⁵ - 2x⁴ + 9x³ - x² + 12 = 0
To find: Function having same set of potential rational roots as g(x).
Finding:
Finding the rational roots of g(x):Let 'm' denote the rational roots of 12.=> Then, m = ±1, ±2, ±3, ±4, ±6
2. Let 'n' denote the rational roots of 3.
=> Then n = ±1, ±3
Hence, the rational roots [tex]\frac{m}{n}[/tex] will be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Now, in the Option A's equation: f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12,The rational roots will be taken of 12 and 3 in the same position as in g(x).
Hence, the rational roots of f(x) will also be given by: ±1, ±2, ±3, ±4, ±6, ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex].
Thus, Option (A)'s f(x) = 3x⁵ -2x⁴ - 9x³ + x² -12 has the same set of potential rational roots as the given function g(x).
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(COMPLETE QUESTION:
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
A).f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
B).f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
C).f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
D).f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48)
a ball is dropped from rest. after $t$ seconds, the ball has fallen a distance $d$. relative to this location, how much farther does it fall after another 5$t$ seconds?
Answers
The ball will fall 35d after 5t seconds.
Equation Of Motion is used to define the basic concept of motion of object at various interval of times.
There are three equation of motion
[tex](i) v=u+at\\ \\ (ii) s=ut+\frac{1}{2} at^{2} \\ \\ (iii)v^{2}=u^{2} +2as[/tex] (where s=distance, v=final velocity, u=initial velocity ,t=time, a=acceleration)
According to the given question
Given distance = d
time=t
Acceleration a=g( gravity)
Using second equation of motion
[tex]d=ut+\frac{1}{2} at^{2}[/tex] ( given u=0 as the ball was at rest, a=g , s=d)
[tex]d=\frac{1}{2} gt^{2}[/tex]........(1)
Using first equation of motion
Speed after t sec
[tex]v=u+at\\ \\ v=0+gt\\ \\ v=gt[/tex] ....... (2)
Using second equation of motion distance after 5t seconds
since ball is moving with velocity "v", t=5t.
[tex]s=ut+\frac{1}{2} at^{2}\\ \\ d=v(5t)+\frac{1}{2} g(5t)^{2}[/tex]
Substituting the value v=gt from equation (2)
[tex]d=(gt)(5t)+\frac{1}{2} g(5t)^{2}\\ \\ =5gt^{2} +\frac{1}{2} g(5t)^{2}[/tex]taking LCM as 2 and solving further we get
[tex]=35(\frac{1}{2}gt^{2} )[/tex]
using equation (1) we get
=35d
Therefore , The ball will fall 35d after 5t seconds.
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Find the point of intersection between the plane that contains the axis intercepts p(4, 0, 0)
Answers
The equation is 7x+11y+14z=33.
What is an equation?A mathematical statement made up of two gestures joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:
(x + 2y + 3z − 4) + k(2x + y − z + 5)=0(2k+1)x+(k+2)y+(3−k)z=4−5k ......(1)[tex]\frac{\mathrm{x}}{\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)}+\frac{\mathrm{y}}{\left(\frac{4-5 \mathrm{k}}{\mathrm{k}+2}\right)}+\frac{\mathrm{z}}{\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)}=1[/tex]It is assumed that the required plane's x-intercept is twice its z-intercept.
[tex]\left(\frac{4-5 \mathrm{k}}{2 \mathrm{k}+1}\right)=2\left(\frac{4-5 \mathrm{k}}{3-\mathrm{k}}\right)[/tex](4−5k) (3−k) = (4k+2) (4−5k)(4 − 5k) (3 − k − 4k −2) = 0(4 − 5k) (1 − 5k) = 04 − 5k = 0 or 1−5k = 0k = 4/5 or k = 1/5Substitute k = 4/5 in equation (1) as follows:
[tex]\left(2 \times \frac{4}{5}+1\right) x+\left(\frac{4}{5}+2\right) y+\left(3-\frac{4}{5}\right) z=4-5 \times \frac{4}{5}[/tex]7x + 11y + 14z = 15As a result, the required plane's equation is 7x+11y+14z=15.
Also,
7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.
7(x−2) + 11(y−3) + 14(z+1) = 07x + 11y + 14z = 33Therefore, the equation is 7x+11y+14z=33.
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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.
Ted works as a travel guide for a mountain resort, earning
$15.72 per hour. Ted is paid weekly, and works 40 hours in
one week. His current federal withholding per week is $69.
He works in a state with a flat-rate income tax of 4.63%. He
will receive a raise of 5% of his hourly rate. Determine the
change in Ted's net pay per paycheck, after taxes, if his new
federal withholding per week is $75.
Answers
Ted's net pay per week after the taxes is $559.09
Net Pay:
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Given,
Ted works as a travel guide for a mountain resort, earning $15.72 per hour. Ted is paid weekly, and works 40 hours in one week. His current federal withholding per week is $69. He works in a state with a flat-rate income tax of 4.63%. He will receive a raise of 5% of his hourly rate.
Here we need to find the Ted's net pay per paycheck, after taxes, if his new federal withholding per week is $75.
Through the given details we know that,
Per hour pay = $15.72
Total work per week = 40
So, the total amount for a week is
=> 15.72 x 40
=> $628.8
After federal withholding tax, then the amount is
=> $628.8 - 69
=> $559.8
Now the tax is 4.63%, then
=> $559.8 x 4.63%
=> $559.8 x (4.63/100)
=> $25.91
So, the remaining amount is
=> $559.8 - $25.91
=> $533.88
Now, he will receive 5% for his hourly rate,
Then,
=> $15.72 x (5%)
=> $15.72 x (5/100)
=> 0.78
So, the increased amount is
=> $16.5
Now, the net pay is,
=> (16.5 * 40) - (75 + 25.91)
=> 660 - 100.91
=> 599.09
So, Ted's net pay per paycheck, after taxes is $559.09.
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Approximate negative thirteen plus square root of seventy to the nearest tenth.
−8.4
−4.6
4.6
8.4
Answers
Answer:-4.6
Step-by-step explanation:
(Please Help) The vertex of a parabola is (−2,8) and its y-intercept is (0,4). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a solid line, and the exterior of the parabola is shaded.
What is the inequality represented?
(i got it graphed like what i have already but I don't know if its right even thought i gotten it)
Answers
Using the equation of the parabola, the inequality represented is:
y ≥ -(x + 2)² + 8.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (-2,8), hence:
h = -2, k = 8.
y = a(x + 2)² + 8.
The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:
4 = 4a + 8
4a = -4
a = -1.
Hence the parabola is:
y = -(x + 2)² + 8.
The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:
y ≥ -(x + 2)² + 8.
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Natalie's fifth grade classroom is 900 square feet. The length is 30 feet. What is the width of her classroom?
Answers
Answer:
30
Step-by-step explanation:
30*30 is 900
Answer:
30
Step-by-step explanation:
let x =width
900=(×)(30)
900=30×
900/30=30×/30
30=×
= 30 width
Find the coordinates of the midpoint of a segment with the given endpoints.
C(22,4), B(15,7)
Answers
The location of the midpoint of the line segment is (37 / 2, 11 / 2).
How to determine the location of the midpoint in a line segment
According to the statement, the position of the two endpoints of a line segment are known and we must determine where the midpoint is, that is, the point such that the line segment is divided into two parts of equal length. The location of the midpoint is found by means of the midpoint formula:
M(x, y) = 0.5 · B(x, y) + C(x, y)
Where M(x, y) is the midpoint.
If we know that B(x, y) = (15, 7) and C(x, y) = (22, 4), then the location of the midpoint is:
M(x, y) = 0.5 · (15, 7) + 0.5 · (22, 4)
M(x, y) = (15 / 2, 7 / 2) + (11, 2)
M(x, y) = (37 / 2, 11 / 2)
The location of the midpoint of the line segment is (37 / 2, 11 / 2).
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Help me help me help me please
Answers
Answer:
D. 24
Step-by-step explanation:
The area of a triangle is [tex]\frac{1}{2} (bh)[/tex].
The height is already given: 8
But we need to find the base and since the hypotenuse is given and it's a right triangle, we can use the pythagorean theorem. (Hypotenuse is longest, slanted side of a right triangle)
The pythagoren theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the sides, and c is the hypotenuse.
Plugging in the given values => [tex]8^2+b^2=10^2[/tex]
We have to solve for b. So, squaring 8 and 10 we get [tex]64+b^2=100[/tex].
Next, subtract 64 from both sides to get b by itself: [tex]b^2=36[/tex]
Square root both sides to get [tex]b=6[/tex].
Now that we have our base we can plug it in to the area of triangle formula: [tex]1/2(6*8)[/tex].
Multiply inside the parenthesis: 1/2(48) => 24
What is the result of adding these two equations?
Answers
The value of the linear equation after adding is -5x -8y = -5.
According to the statement
We have to find that the value of the linear equation.
So, For this purpose, we know that the
The linear equation, statement that a first-degree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant.
From the given information:
The given equations are:
4x-4y = -2
-9x-4y = -3.
Then
Now, add these equations then
4x-4y = -2 + -9x-4y = -3.
4x-9x-4y-4y = -2-3
-5x -8y = -5
After addition ,the value becomes -5x -8y = -5.
So, The value of the linear equation after adding is -5x -8y = -5.
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HELP 20 pointssss mathhhhh
Answers
the rainfall this year was 18.6 cm this is 3.2 cm less than half of the rainfall last year what was the rainfall
Answers
Answer: 43.6 cm
Step-by-step explanation:
18.6+3.2= 21.8
21.8*2= 43.6
what would be the value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 6.89? a. 19.32 b. 15.32 c. 18.43 d. 31.89
Answers
The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 25.32 and the sum of squares due to error (sse) is 31.89
What is regression?Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).
The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).
Linear regression determines the actual linear relationship between two variables based on a line of best fit. As a result, the slope of a straight line was used to depict linear regression indicating how altering one variable impacts modifying another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.
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Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile. Which statement is true?
Answers
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
What is a linear equation?
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let y be the total amount and x be the number of miles.
Samir can rent a moving truck from Company A for $35 plus $0.50 per mile. Then the equation will be
y = 0.5x + 35 ....1
Company B for $25 plus $0.70 per mile. then the equation will be
y = 0.7x + 25 ....2
For the same rent, the number of miles will be
0.7x + 25 = 0.5x + 35
0.2x = 10
x = 50 miles
Renting from Company B will be cheaper if Samir drives the truck 100 miles. Then the correct option is D.
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Samir can rent a moving truck from Company A for $35 plus $0.50 per mile or from
Which statement is true?
Company B for $25 plus $0.70 per mile .
A. Renting from Company A will always be cheaper.
B. Renting from Company B will always be cheaper.
C. Renting from both companies will cost the same if Samir drives the truck 50 miles.
D. Renting from Company B will be cheaper if Samir drives the truck 100 miles.
A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except ___________.
Answers
A research study variable that is believed to be related to the study's variable of interest is accurately described by each of the following terms except dependent.
What is a research variable?
Any variable employed in research that has a cause and effect relationship is referred to as a research variable (also known as a study variable) informally. An array of variables, including independent factors, dependent variables, and intervening variables, can be employed in a study, including research/study variables.
Independent and dependent variables are crucial in research since they provide the framework for a study to be carried out. Confounding factors, controlled variables, superfluous variables, and moderator variables are some other sorts of variables that could be used in a research.
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Choose the correct numbers in order to have the following output.
31
34
51
54
for numX in [3, +
for numy in [1,
#
print (numX, numy)
Answers
The correct number that represents the output of the print statement is 31
How to determine the correct output of the program segment?The program segment is given as
for numX in [3]
for numy in [1]
print (numX, numy)
The program flow of the above program segment is:
Iterate through the first listIterate through the second listPrint the values of both iterationsIn the above iterations, we have the following values
numX = 3
numY = 1
When both values are printed, we have the output to be 31
Hence, the correct number that represents the output of the print statement is 31
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Answer:
answer 1 = 3,5
answer 2 = 1,4
Step-by-step explanation:
All the data collected in a particular study are referred to as the? inference. variable. data set. population.
Answers
Inference is referred to as all the data collected in a particular study.
What is inference?Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.
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Helpppppp 20 pointssss mathhh
Answers
Solve for x. 4x + 6 = 2(2x + 3)
Answers
Answer:
True for all x/infinite solutions.
Step-by-step explanation:
[tex]4x+6=2\left(2x+3\right) < - Base Equation[/tex][tex]4x+6=4x+6 < - Expand-The-Equation-and-Simplify![/tex]
[tex]4x+6-6=4x+6-6 < - Subtract-Six-From-Both-Sides![/tex]
[tex]4x=4x[/tex]
[tex]4x-4x=4x-4x < - Subtract -4x- from- both -sides![/tex]
[tex]0=0[/tex]
________________________________________________________
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What is the volume of a rectangular prism with a base area of 32 cm and a height 7cm
Answers
Answer:
224 cm³
Step-by-step explanation:
Volume = Area of base x height
V = 32 x 7
V = 224 cm³
In this question, all the required information is given so we'll simply have to solve.
[tex]\large\boxed{\bold{V= \ base \ area× \ height}}[/tex]
Now, substitute the values according to the formula.
[tex]V= \ 32 × 7[/tex]
[tex]\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}[/tex]
The answer is a whole number so we won't have to round off.
Hence, the volume of the given rectangular prism is 224 cubic centimeters.
Find the value of the variable and YZ if Y is between X and Z. XY= 11d, YZ=9d-2, XZ=5d+28
Answers
Answer:
d = 2
YZ = 16
Step-by-step explanation:
X-Y-Z
so XY + YZ = XZ
11d + (9d -2) = 5d + 28
11d + 9d - 5d = 28 + 2
15d = 30
d = 30/15 = 2
YZ = 9d - 2 = 9(2) - 2 = 18 - 2 = 16
Ms. Hartman buys 4 pounds of potatoes for $12.76. How many pounds of potatoes could she get for $44.66?
Answers
Answer:
14
Step-by-step explanation:
44.66 / (12.76 / 4) = 14
5x - 2y. Could you please help me
Answers
neve has 12 full box of jars of slime and 7 lose jars of slime if neve has a total of 187 jars of slime which equation can be used to find the number of jars in each box
Answers
Solving a linear equation, we can see that each box has 15 jars.
Which equation can be used to find the number of jars in each box?
We know that Neve has 12 full boxes of jars of slime, and 7 jars of slime, then if each box has N jars, the total number of jars that Neve has is given by the linear equation:
12*N + 7
Now we know that Neve has 187 jars in total, then we can write:
12*N + 7 = 187
We want to find the value of N, which is the number of jars in each box, so we need to solve the linear equation:
12*N + 7 = 187
12*N = 187 - 7
12*N = 180
N = 180/12 = 15
We conclude that there are 15 jars in each full box.
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IMPORTANT HELPP
What type of transformation is this? Be specific
Answers
Answer:
Rotation
Step-by-step explanation:
Rotation at the origin (0,0) by 180*
write a two-column proof to verity each conjecture. If -3r+1/2=4, then r=-7/6
Answers
Answer:
7/6
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
6
Step-by-step explanation:
driver delight has 3 circluar go cart tracks. track 1 has a radius of 60 feet. track 2 has a radius of 85 feet. track 3 has a radius of 110 feet.
Compute the circumference of track 3.
Answers
The circumference of track 3 is 691.43 feet
What is the circumference of track 3 ?The circumference of a circle is the distance round the circle. It is the perimeter of the circle. The radius of a circle is a straight line that goes from the center of the circle to its circumference.
The circumference of a circle = 2πr
Where:
r = radius π = 22/72 x (22/7) x 110 = 691.43 feet
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