Ollie has installed security lights on the side of his house that are activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m and the distance from B to C is 6 m. Angle AĈB is 15°.
Answers
Answer:
20.19°
Step-by-step explanation:
Find the diagram to the question attached. We are to look for <CAB
Applying sine rule on ΔABC:
[tex]\frac{4.5}{sin15^0} = \frac{6}{sin<CAB}[/tex]
cross multiply
[tex]4.5 * sin<CAB =6 sin15^0\\\\sin<CAB = \frac{6sin15^0}{4.5}\\ \\sin<CAB = \frac{6*0.2588}{4.5}\\ \\sin<CAB = \frac{1.5529}{4.5}\\\\sin<CAB = 0.3451\\\\<CAB = sin^{-1}0.3451\\[/tex]
[tex]<CAB = 20.19^0\\[/tex]
Hence the angle <CAB is 20.19°
The angle ∠CAB is 20.19° and the distance (d) Ollie is from the entrance to his house when he first activates the sensor is 5.77 m.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Ollie has installed security lights on the side of his house that is activated by a sensor.
The sensor is located at point C directly above point D.
The area covered by the sensor is shown by the shaded region enclosed by triangle ABC.
The distance from A to B is 4.5 m and the distance from B to C is 6 m.
The angle ACB is 15°.
The ∠CAB is ∠A.
We know that the sine rule
[tex]\dfrac{a}{\sin A} =\dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
We have
[tex]\dfrac{AB}{\sin C} \ \ = \dfrac{BC}{\sin A} = \dfrac{AC}{\sin B}\\\\\\\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} = \dfrac{b}{\sin B}[/tex]
From the first two, we have
[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{6}{\sin A} \\\\\sin A = \dfrac{6}{4.5} \times \sin 15^o\\\\A \ \ \ \ = 20.19^o[/tex]
We know that the sum of the angle is 180 degrees. Then we have
∠A + ∠B + ∠C = 180°
20.19° + ∠B + 15° = 180°
∠B = 144.81°
Then the value of b will be
[tex]\dfrac{4.5}{\sin 15^o} = \dfrac{b}{\sin 144.81^o}\\\\\\b \ \ \ = 10.02[/tex]
Then the distance (d) Ollie is from the entrance to his house when he first activates the sensor will be
d = b × sin 144.81°
d = 10.02 × sin 144.81°
d = 5.77 m
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Related Questions
PLEASE HELP
find area
Answers
Answer:
35.5?
Step-by-step explanation:
I am not 100 % but this is the answer I got
A manager drew this box-and-whisker plot to represent the ages of her 23 employees. Every employee is a different age.
Box-and-whisker plot ranging from 34 to 58 with ticks at increments of 1. Plot defined by points at 35, 42, 49, 54, 57.
How many employees are older than 54?
Enter your answer in the box.
employees
Answers
About 5 employees have ages that are older than 54 years.
What is a box plot?A box plot provides the summary of a data using the five number summary that is minimum, lower quartile, median, upper quartile and maximum.
From the diagram, the third quartile is 54 years. Hence 75% of the employees are between 35 to 57 years.
25% are older than 54 years, hence:
Employers older than 54 years = 25% of 23 employees = 5.75
About 5 employees have ages that are older than 54 years.
Find out more on box plot at: https://brainly.com/question/14277132
Answer:
5 is the answer
Step-by-step explanation:
A 2021 Toyota Rav4 Hybrid leases for $322/month for 3 years with a $2,101 down payment. What's the total that you will pay to lease this car? Round to the nearest cent
Answers
Answer:
13,693
Step-by-step explanation:
3 years x 12 months a year = 36 months.
322 per month x 36 months = 11,592
+
the 2,101 down payment
=
13,693
Work out the area of the triangle. Give your answer to 1 decimal place. 10cm, 13cm sides. Angle 105
Answers
Answer:
62.8
Step-by-step explanation:
So, keep in mind that the area of a triangle is equivalent to: 1/2(b)(h) with b being your base and h being your height.
We have our base: 10, and our angle: 105. Now we need to find our height. You don't just have to look at a triangle the way that it's oriented in the problem. Rotate it so that 10cm is at the bottom, and it will be much easier.
From there, you can create a right triangle and draw a line from the top of the triangle straight to the base. Then, you have a right triangle, where you can solve the height, and then plug your answer into the area formula. Further steps are detailed in the picture.
Which equation for g(x) represents the transformation of f(x) given that f(x) =x^2
g(x) = f(x) shifted right 2 units
Help!!
Answers
Answer:
g(x) = (x - 2)²
Step-by-step explanation:
If we want to shift a function to the right, we subtract the number we are asked to move to the right inside the function's argument:
⇒ To shift f(x) b units to right → f(x - b)
Similarly, in function notation, if we want to shift a function to the left, we add the number we are asked to move to the left inside the function's argument:
⇒ To shift f(x) b units to left → f(x + b)
Given function f(x) = x²
Shift 2 units to the right: f(x - 2) = (x - 2)²
Therefore, g(x) = (x - 2)²
----------------------------------------------------------------------
Additional info:
g(x) = (x - 2)²
= (x - 2)(x - 2)
= x² - 4x + 4
Given the definitions of f(x) and g(x) below, find the value of g(f(0))
f(x)= -x+9
g(x)=x^2 - 6x+9
Answers
Answer:
The value of g(f(0)) is 36
Step-by-step explanation:
g(f(x)) is a composite function, where f(x) is the value of x in g(x), which means substitute x in g(x) by f(x)
Let us use this rule to solve our question
∵ f(x) = -x + 9
∵ g(x) = x² - 6x + 9
→ Substitute x in g by f
∵g(f(x)) = g(-x + 9)
∴ g(f(x)) = (-x + 9)² - 6(-x + 9) + 9
→ Let us simplify it
∵ (-x + 9)² = (-x)(-x) + (-x)(9) + (9)(-x) + (9)(9)
∴ (-x + 9)² = x² + -9x + -9x + 81
→ Add the like terms (-9x + -9x)
∴ (-x + 9)² = x² + -18x + 81
→ Remember (+)(-) = (-)
∴ (-x + 9)² = x² - 18x + 81
∵ - 6(-x + 9) = -6(-x) + (-6)(9)
∴ - 6(-x + 9) = 6x + -54
∴ - 6(-x + 9) = 6x - 54
→ Substitute them in g(f(x))
∴ g(f(x)) = x² - 18x + 81 + 6x - 54 + 9
→ Add the like terms
∴ g(f(x)) = x² + (-18x + 6x) + (81 -54 + 9)
∴ g(f(x)) = x² + (-12x) + (36)
∴ g(f(x)) = x² - 12x + 36
→ Now substitute x by 0
∴ g(f(0)) = (0)² - 12(0) + 36
∴ g(f(0)) = 0 - 0 + 36
∴ g(f(0)) = 36
There is an easy way to find it quickly
Substitute x in f by 0
f(0) = -(0) + 9
f(0) = 9
Substitute x in g by 9
Find g(9)
g(9) = (9)² - 6(9) + 9
g(9) = 81 - 54 + 9
g(9) = 36
Which expression is equal to 3x? (1 point)
x + 3
x + x + x
x + x2
2x + 1
Answers
Answer:
x + x + x
Step-by-step explanation:
x + 3 can't be combined as they are two different terms
x + x + x = 3x (works)
x + x² can't be combined as they have different exponents
2x + 1 can't be combined as they are two different terms
20. Olivia translated triangle DEF 4 units vertically to form triangle GHJ.
If Olivia performed the translation correctly, what is the measure of angle H?
O 17.5°
O 43.0°
O 32.5°
O 28.0°
Answers
Answer:
Step-by-step explanation:
m∠E = m∠H
( 3x - 20 )° = ( x + 15 )°
3x - 20 = x + 15
3x - x = 15 + 20
2x = 35
x = 17.5
m∠H = 3(17.5) - 20 = 32.5 °
Find the value of x.
E
D
51°
G
(14x – 38)
F
Answers
Answer: 10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
will give brainliest
Answers
Answer:
third quadrant
Step-by-step explanation:
Under a clockwise rotation about the origin of 180°
a point in the first quadrant ( x, y ) → (- x, - y ) ← in the third quadrant
In a list of seven consecutive numbers a quarter of the smallest number is five less than a third of the largest number. If x is the smallest number, find expressions for:
a) “a quarter of the smallest number”
b) “five less than a third of the largest number”
Answers
Please see the solution.
Step-by-step explanation:[tex]Since\ x\ is\ the\ smavest\ number,\\ the\ Cavgent\ number\ equals\ to\ x+6.[/tex]
[tex]a)\frac{1}{4}x[/tex]
[tex]b)\frac{1}{3}(x+6)-5=\frac{1}{3}x+2-5=\frac{1}{3}x-3[/tex]
I hope this helps you
:)
is this true or false
Answers
Step-by-step explanation:
im not really sure because there is no question
Which of the following statements correctly uses the distributive property?
-2(15 - 3) = -2(15) + (-2)(3)
7(9 - 8) = 7(9) - 8
9(-7 + 6) = 9(-7) + 9(6)
-3(12 + 5) = -3(12) - (-3)(5)
Answers
Multiply the number outside the parentheses by each number inside.
Remember a negative x a negative becomes positive. A negative x a positive is negative.
The correct one is 9(-7 + 6) = 9(-7) + 9(6)
Answer:
The correct one would be 9(-7 + 6) = 9(-7) + 9(6)
Step-by-step explanation:
which of the following it true about √3x2
pls i need help its due tonight and i cant turn it in late bc my nine weeks will be over help pls
Answers
Answer:
B)
Step-by-step explanation:
Rational number: can be expressed as a ratio of two integersIrrational number: cannot be expressed as a ratio of two integers[tex]\textsf{2 is a rational number as }2=\dfrac21[/tex]
[tex]\sqrt{3} \textsf{ is an irrational number}[/tex]
[tex]2\sqrt{3} \textsf{ is an irrational number}[/tex]
Find the value of x
need help asap pls
will give brainliest
Answers
Answer: 10
Step-by-step explanation:
What is the surface area of this figure?
Answers
Answer:
582 ft²
Step-by-step explanation:
Area of a triangle = 1/2 x base x height
Area of a rectangle = width x length
Surface area = (5 x 15) + 2(15 x 8) + 2(5 x 8) + (15 - 11) x 5 + 2(1/2 x 11 x 7) + 2(9 x 5)
= 75 + 240 + 80 + 20 + 77 + 90
= 582 ft²
Answer: 582 ft
Step-by-step explanation: i took the test
Enrique is selling a drop leaf table and wants to include the area of the table when the leaves are down is his ad.
What is the area of the center section when the leaves are down? Explain how you found your answer. HELPPP
Answers
Answer:
drop-leaves 38 in "U SE 22 1 19 0 o Let the center of the table be O and the chord of length 38 in.be AB Drop a perpendicular from to AB meeting it at C. Since the diameter of the circle is 44 in., the radius of the circle must be 22 in. and thus, OA= = in. By the definition of the sine function, AC sin 500-Twice that gives ZAOB, so the area of OA sector AOB is about in and the area of AAOB is 1 OA. OB sin 20-in? Subtracting the area of the triangle from the area of the sector shows that the area of the segment bounded by chord AB is about in (Type integers or decimals rounded to four decimal places as needed.) 19 22 B 2
Step-by-step explanation: i really hope this is what your looking for, and helps!! love you have an amazing day:)) -marina mae
The area of the center section when the leaves are down is evaluated being of 932.84 in.²
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The simplified figure is attached below.
We need to find the area PQRS.
Area(PQRS) = 4(Area(DOQ) + Area(QOB)) (by symmetry.
The line OD and OT are perpendiculars on those 38 inch chords, and therefore D and T are bisecting them(by a theorem that perpendicular from center of a circle to its chords bisect them).
Finding Area of DOQ:Using Pythagoras theorem, we get:
[tex]|DO| = \sqrt{|OQ|^2 -|DQ|^2 } = \sqrt{22^2 - 19^2} = \sqrt{123}[/tex]
Thus, we get:
[tex]\text{Area DOQ} = \dfrac{1}{2} \times 19 \times \sqrt{123} \approx 105.36 \: \rm in^2[/tex]
Finding Area of QOB:Since angle ∠DQO and ∠QOB are alternate interior angle, they are of same measure.
From triangle DOQ, from the perspective of ∠DQO, we get the sine ration as:
[tex]\sin(m\angle DQO) = \dfrac{|DO|}{|OQ|}\\m\angle DOQ = \sin^{-1}\left( \dfrac{\sqrt{123}}{22}\right) \approx 30.27^\circ \: \text{(chose acute angle)}[/tex]
Thus, we get:
[tex]m\angle QOB \approx 30.27^\circ[/tex]
360 degrees cover full area of circle,
1 degree will cover full area /360 of the circle
Thus, we get:
Aera of the sector QOB = Area covered by central angle ∠QOB[tex]\approx 30.27 \times \dfrac{\pi (22)^2}{360} \approx 127.85 \: \rm in^2[/tex]
Thus, as we have:
Area(PQRS) = 4(Area(DOQ) + Area(QOB))
we get:
Area(PQRS) ≈ 4(105.36 + 127.85) ≈ 932.84 in.²
Thus, the area of the center section when the leaves are down is evaluated being of 932.84 in.²
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
On the track and field team, 38 of the members do the hurdles.
Of the members who do the hurdles, 45 also do the long jump.
If there are 40 members on the track team, how many do both the hurdles and the long jump?
Enter your answer in the box.
Answers
Answer:
your answer would be seven
Brianna graphed the equations y=2x+3.5 and y=2.5x−1 below and said the lines on the graph below are parallel and do not intersect, so the system has no solution. Is Brianna correct? Select the answer option that best explains why or why not.
PLEASE HELP URGENT
Answers
Answer:
Disagree because the slopes are different.
Step-by-step explanation:
When an equation is in y=mx+b form, answering these kinds of questions becomes easier. "M" is your slope, so if m for both equations match, then your lines will be parallel. This one shows the first equation as 2/1, so you would rise 2 and run 1. but the second is 2.5 or 5/2, so you would rise 5 and run 2. rise meaning y-axis and run being the x-axis. Whenever possible, I turn equations to the y=mx+b form because it makes everything a bit clearer, in my opinion.
how to do 630 divided by 8
Answers
Answer:
Use long division to get the answer of 78.75
Step-by-step explanation:
long division ends with this answer, ➗
please help me with problem 1 and 2 please and thanks.!
Answers
Answer:
ya no
Step-by-step explanation:
Answer:
Step-by-step explanation:
are you showing the entire question because that actually makes no sense
A photograph is enlarged to three times the size of the original. Which of the following statements is true? A. The area of the enlargement is three times the area of the original. B. The area of the enlargement is six times the area of the original. C. The area of the enlargement is nine times the area of the original. D. The area of the enlargement is twelve times the area of the original.
Answers
Answer:
A.
Step-by-step explanation:
Five swimmers are entered into competition. Four of the swimmers have had their turns. Their scores are 9.8s, 9.75s 9.79s and 9.81. What the score
Answers
9.80 -> 3
9.75 -> 1
9.79 -> 2
9.81 -> 4
The least decimal is 9.75. Now we must determine how 9.75 compare with the winning score.
The last swimmer must get a score less than 9.75 s in order to win.
9.75 -> 1
9.79 -> 2
9.81 -> 4
Hope this help if not comment so I can reply and help
Set A consists of the numbers 12, 15, 37, 10, and 11. Set B consists of the
numbers 3,58, 17, and 7. Which of the following is true?
Answers
Answer:
Both A and B are true,
Step-by-step explanation:
The median of set A equals the median of set B.
The mean of set A equals the mean of set B.
Hello people ~
Find the area of the square of side 13 cm.
Answers
Answer:
169 cm or 1.69 m
Step-by-step explanation:
the area of the square=length of any side^2
If a Realtor helps a family purchase a $160,000 house, and they earn a 3.5%
commission, how much will they earn from the sale of that house?
Answers
Answer:
5600
Step-by-step explanation:
160000 x 0.035= 5600
point p is on a unit circle. Solve for the coordinates of p
Answers
Answer:
I'm sorry I don't know how to do this but when I do i'll tell u :)
Step-by-step explanation:
Three side lenghts of 5.2,6.3, and 10.5 units will form exactly one unique triangle
Answers
True, the three sides will form exactly one unique triangle.
What is a triangle?A triangle is three dimensional shape, whose third length is less than the sum of the first and second length.
let the first length = alet the second length = blet the third length = k(b - a) < k < (b + a)
(6.3 - 5.2 ) < k (6.3 + 5.2 )
1.1 units < k < 11.5 units
The third length = 10.5 units which is greater than 1.1 units and less than 11.5 units.
Thus, the three sides will form exactly one unique triangle.
Learn more about conditions of a triangle here: https://brainly.com/question/22674890
Mr. steiner purchased a car for about $14,000. assuming his loan was
compounded monthly at an interest rate of 4.9% for 72 months:
p=
r=
n=
t=
a. how much will he have paid total?
b. how much more did he pay than the price of the car?
Answers
Using compound interest, it is found that:
a) He will have paid $18,774 in total.
b) He paid $4,774 more than the price of the car.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem, the parameters are:
[tex]P = 14000, r = 0.049, n = 12, t = \frac{72}{12} = 6[/tex].
Item a:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(6) = 14000\left(1 + \frac{0.049}{12}\right)^{12 \times 6}[/tex]
[tex]A(6) = 18774[/tex]
He will have paid $18,774 in total.
Item b:
18774 - 14000 = $4,774.
He paid $4,774 more than the price of the car.
More can be learned about compound interest at https://brainly.com/question/25781328
The greatest common factor of each term in the expression 60 a b minus 72 b is 12b. Which choice shows the expression written as a product?
12 b (5 a b minus 6 b)
12 b (5 a minus 6)
12 b (48 a minus 60)
12 b (48 a b minus 60 b)
Answers
Answer:
B--- 12 b (5 a minus 6)
Step-by-step explanation:
i took the quiz (edge 2021)