Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the base of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth. I watched the lesson but it all just went over my head, can someone simplify the explanation of how these problems work?
Answers
Suppose the dog is on the top vertex of the triangle while the cat is the rightmost corner of the triangle. The angle denoted as x° is the angle of depression. To determine this, we use the tangent function. The tangent of an angle is the ratio of its opposite side to its adjacent side.
tanx° = 16/4.5
x = 74.29°
Related Questions
What are the amplitude, period, and midline of f(x) = 3 cos(4x − π) + 2?
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Answer:
The amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=3\cos(4x-\pi)+2[/tex] .... (1)
The standard form of a Cosine function is
[tex]g(x)=a\cos(bx+c)+d[/tex] ... (2)
where, a is amplitude, period is [tex]\frac{2\pi}{b}[/tex] and d is midline.
From (1) and (2), we get
[tex]a=3,b=4,d=2[/tex]
The amplitude of the function is
[tex]a=3[/tex]
The period of the function is
[tex]\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
The midline of the function is
[tex]d=2[/tex]
Therefore the amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
When college students are asked to solve a puzzle problem independently, only about 10% solve it correctly. then, when students who did not solve the problem were allowed to discuss the problem together, 75% got it right. this illustrates the participants' _____?
Answers
The correct answer to fill in the blank is:
“Cognitive flexibility”
Cognitive flexibility refers to a person’s ability to adapt the mental processing strategies to face new and unexpected situations or problems. In this case, some of the students who initially did not solve the problem transformed their way of solving the puzzle after the discussion thus getting it right the next time.
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 3x + 2y = 6 x - y = 2
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Hope it helps.
You flip a coin and roll a number cube. What is the probability that you flip tails and roll a number less than five?
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Tail 1+T 2+T 3+T 4+T 5+T 6+T
Heads 1+H 2+H 3+H 4+H 5+H 6+H
So as you can see from about there are 12 different outcomes
There are 6 chances in getting a tails bit only 4 are less that 5 so you answer is 4/12
(You don't simplify probability)
Jack is building a deck that is 8 ft by 27.63 ft. He has the base built; he just needs to cover the surface with wood. When he gets to the hardware store he finds sheets of wood that are four ft by eight ft. Use estimation to determine how many sheets of wood he should buy to cover the surface of the deck.
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A ( deck ) = 8 * 27.63 = 221.04 ft²
The area of the sheet of wood:
A ( sheet ) = 4 * 8 = 32 ft²
221.04 : 32 = 6.9 ≈ 7 ( we need a whole number )
Answer: He should buy 7 sheets of wood to cover the surface of the deck.
What is the lateral surface area of the prism below?
1200 in2
2400 in2
1392 in2
2592 in2
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so, the lateral, sides, area, is just the area of the sides, well, the sides are just those three rectangles
now, the rectangle is the middle is length = 25 as well as the others, but we dunno the width, say width = c
[tex]\bf c=\sqrt{16^2+12^2}\implies c=\sqrt{256+144}\implies c=\sqrt{400}\implies c=20\\\\ -------------------------------\\\\ \textit{lateral area}\implies (25\cdot 16)+(25\cdot 12)+(25\cdot 20) \\\\\\ 400+300+500[/tex]
Jennifer is on a trip and travels a distance of 150 miles. she spends some of her time walking, and some of her time travelling by train. if she spends w hours walking and t hours travelling by train, what is the meaning of 3w in the equation below? 50t + 3w =150
Answers
In the equation 50t + 3w = 150, 3w represents the distance Jennifer travels by walking in 3 hours.
Explanation:In the equation 50t + 3w = 150, the term 3w represents the distance Jennifer travels by walking. Since w represents the number of hours she spends walking, 3w represents the distance she walks in 3 hours. This is because the rate of walking is constant, so if Jennifer walks for 1 hour and covers a certain distance, she would walk 3 times that distance in 3 hours.
What is the length of the third side of the right triangle?
( Best explained and correct answer gets brainliest. )
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6^2 + 3^2 = x^2
36 + 9 = x^2
45=X^2
X= sqrt(45) = 3squareroot5
answer is A
HELP PLEASE THANKS:(
Answers
4+3y=13
3y=9
y=3
The answer is B
In triangle def, FE = 13 and angle f equals 34. Find DF to the nearest tenth.
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When factored, the trinomials x^2-2x-15 and x^2-9x+20 have one binomial factor in common. What is this factor?
1. x-7
2. x+7
3. x-5
4. x+5
Answers
(x-5)(x+3)
Proof:
-5+3=-2
-5*3=-15
x^2-9x+20
(x-4)(x-5)
Proof:
-4-5=-9
-4*-5=20
Final answer: (x-5)
One week, Katie Hopper earned the following commissions: Monday, $124; Tuesday, $88; Wednesday, $62; Thursday, $137; Friday, $195. Find her total amount of commissions for the week
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This is the answer⬆️
add them together:
124 + 88 + 62 +137 +195 = $606 total
If BC = 4.5, CD = 7.7, and AD = 16.7, find AB to the nearest tenth.
A. 2.1
B. 28.6
C. 9.8
D. 2.2
Answers
[tex]9.8[/tex]
EXPLANATION
Triangle ABC is similar to triangle ADC,
therefore the corresponding sides sides are in the same proportion.
[tex] \frac{AB}{AD} = \frac{BC}{CD} [/tex]
We substitute the values to obtain,
[tex] \frac{AB}{16.7} = \frac{4.5}{7.7} [/tex]
We multiply through by
[tex]16.7[/tex]
to get,
[tex] AB= \frac{4.5}{7.7} \times 16.7[/tex]
This simplifies to give us,
[tex] AB= 9.75940259402....[/tex]
To the nearest tenth,
[tex] AB= 9.8[/tex]
The correct answer is C
Write 121 raised to the one-half power equals 11 as a logarithmic function
Answers
so
[tex]121^\frac{1}{2}=11[/tex] translates to [tex]log_{121}(11)=\frac{1}{2}[/tex]
What is the missing step in this proof?
Answers
¹²³⁴⁵⁶⁷⁸⁹⁰⁹⁸⁷⁶⁵⁴³²¹
₁¹₁¹₁
Answer:
Option C is correct.
The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].
Explanation:
Given ΔABC.
Prove that: The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]
Let A ,B and C forms a triangle [Given]
Parallel lines are those two lines that are always the same distance apart and never touch.
then, by the definition of parallel lines and labeling angles
DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.
Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.
Then,
[tex]\angle 1 \cong \angle 4[/tex] and
[tex]\angle 3 \cong \angle 5[/tex] [By Alternative Interior angle theorem]
Angles are always congruent if their measures in degrees are equal.
therefore,
[tex]m\angle 1 =m\angle 4[/tex] and
[tex]m\angle 3=m\angle 5[/tex] [By Congruent Angle have equal measure] ......[1]
Straight Angles states that angles on one side of a straight line always add to 180 degrees.
From the given figure;
By the addition angle and definition of straight angle we get;
[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex] ......[2]
Substituting equation [1] in [2] we get;
[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]
Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]
In the diagram, which two points are shown to be collinear?
Answers
In the given diagram, the points that are shown to be collinear are H and E.
Collinearity in geometry refers to the condition where three or more points lie on the same straight line. In this case, points H and E are collinear as they lie on the same straight line, which is represented by a vertical double-headed arrow passing through them.
The diagram consists of two parallelograms, labeled 'I M' and 'E P', with three points inside each. In the parallelogram 'I M', the points are labeled as I, H, and J from top to bottom. Similarly, in the parallelogram 'E P', the points are labeled as F, E, and G from top to bottom. Among these points, only H and E share the same straight line, making them collinear. The other points do not share this line and hence are not collinear with H and E. This concept is fundamental in understanding geometric relationships and properties.
can someone help me with this factoring problem? I forgot how to factor.
Factor completely −3x2 + 6x − 9.
−3(x2 − 2x + 3)
−1(x2 − 6x + 9)
−3x(x2 − 2x + 3)
−3(x2 + 2x − 3)
Answers
= -3(x^2 - 2x + 3)
answer
-3(x^2 - 2x + 3) first one
-3(x^2-2x+3)
To check, multiply what you took out by each term in the trinomial and make sure it's the same
-3*x^2=-3x^2
-3*-2x=6x
-3*3=-9
Express 257.36 multiplied by 10 in scientific notation
Answers
__________________________________________________________
Convert 7.2 ⋅ 10–3 to standard form.
72,000
7,200
0.0072
0.00072
Answers
................................
0.0072 hope that helped
If s is a sequence of consecutive multiples of 3, how many multiples of 9 are there in s? (1) there are 15 terms in s. (2) the greatest term of s is 126.
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[tex]\it a_{15} =126=3\cdot42 \\\;\\a_1=3n=? \\\;\\ 3, 6, 9, 12, ... , 3n, ..., 3\cdot42 [/tex]
[tex]\it 42-(n-1) =15 \Rightarrow n-1=42-15=27 \Rightarrow n=28 \Rightarrow \\\;\\ \Rightarrow a_1=3\cdot28= 84[/tex]
Now, we have the sequence :
[tex]\it a_1= 3\cdot28 = 84 \notin M_9 \\\;\\ a_2= 3\cdot29 = 87 \notin M_9 \\\;\\ a_3= 3\cdot30 = 90 \in M_9 \\\;\\ \vdots[/tex]
[tex]\it a_{15} =3\cdot42=126 \in M_9 \\\;\\ 90\leq9\cdot k\leq126 |:9 \Rightarrow 10\leq k\leq14 \Rightarrow k \in \{10, 11, 12, 13, 14\}[/tex]
It implies 5 multiples of 9
At a glance : {90, 99, 108, 117, 126}
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
Answers
[tex] \frac{-2x-1}{3} \leq x \leq 3[/tex]
this is what i understood from what you typed...
to the nearest whole degree, what angle measure has a sine of .9762
Answers
and if you just want the answer it is:
77.475 Degrees
and
it is 102.525 Degrees
05.02)
Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The other triangle has a vertical side of 10 and a horizontal side of 30.
Could the hypotenuses of these two triangles lie along the same line?
No, because they are not similar triangles
No, because one is larger than the other
Yes, because they are both right triangles
Yes, because they are similar triangles
Answers
Answer:
Yes, because they are similar triangles
Step-by-step explanation:
I got the answer right on the test
a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. He has 100 mice available. He randomly assigns 50 of them into ech group. He trains the first group to run the maze ar 9:00am and trains the sevond group to run the maze ar 9:00 pm. Each mouse is trained the same way, and the last 3 years run times are recored. Describe what is being measured in this experiment and what variable is being manipulated?
Answers
In this case, since the run times are the one being compared and recorded, therefore the data being measured in the experiment is the run times.
The difference of the two groups of mice is the time of the day that the mice run, day or night. Therefore the variable being manipulated is the time of the day.
Evaluate 9 y 1 − y 0 9y1−y0 if y=−8 y=−8 .
Answers
9y - y^0...when y = -8
9(-8) - 1......anything to the ^0 = 1
-72 - 1 =
-73 <==
Answer:
Step-by-step explanation:
Write the equation of the line that passes through the points (-2,3) and (-2,5)
Answers
Micah takes a job with a starting salary of $78,000 for the first year. He earns a 4% increase each year. How much does Micah make over seven years? $567,840 $616,067 $718,710 $718,499
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Fv=pmt [((1+r)^(t)-1)÷r]
Fv how much he made ?
PMT yearly salary 78000
R rate of increases 0.04
T time 7 years
Fv=78,000×(((1+0.04)^(7)−1)÷(0.04))
Fv=616,066.96 round your answer to get 616067
Answer:
b
Step-by-step explanation:
The height of the oversized container is 3 m it's diameter is 2 m what is its area?
Answers
i think
( 3.14×radius×radius) + (2×3.14×height)
thus,
(3.14×1×1) + (2×3.14×3)
=21.98 m
How to solve math problems with rules of exponents?
Answers
for example: 3^2 the answer would be 9 because it has to be 3 times 3
another example is 6^3 it would be 6 times 6 times 6 and that would be 216
Final answer:
When solving math problems with rules of exponents, it is important to understand key concepts such as multiplication of exponentials, taking square roots of exponentials, and dividing exponentials.
Explanation:
When solving math problems with rules of exponents, there are several key concepts to keep in mind:
Multiplication of Exponentials: Multiply the digit terms in the usual way and add the exponents of the exponential terms.Taking Square Roots of Exponentials: If necessary, decrease or increase the exponential term so that the power of 10 is evenly divisible by 2. Extract the square root of the digit term and divide the exponential term by 2.Dividing Exponentials: Divide the numbers out front and subtract the exponents.It is important to understand these rules and practice applying them to various problems in order to master solving math problems with rules of exponents.
how much would an 185 astronaut weigh on the moon?