Answers
Answer:
b) [tex]\sin(B) = \frac{\sqrt 2}{2}[/tex]
e) [tex]\tan(B) = 1[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
The true statement about B
The given options show that we determine the correct trigonometry ratio of B.
So, we have:
[tex]\cos(B) = \frac{Adjacent}{Hypotenuse}[/tex]
This gives:
[tex]\cos(B) = \frac{a}{c}[/tex]
Where:
[tex]a = 3mm\\c = 3\sqrt 2 mm[/tex]
[tex]\cos(B) = \frac{3}{3\sqrt 2}[/tex]
3 cancels out
[tex]\cos(B) = \frac{1}{\sqrt 2}[/tex]
Rationalize
[tex]\cos(B) = \frac{1}{\sqrt 2}* \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\cos(B) = \frac{\sqrt 2}{\sqrt 2*\sqrt 2}[/tex]
[tex]\cos(B) = \frac{\sqrt 2}{12}[/tex]
Also:
[tex]\sin(B) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(B) = \frac{b}{c}[/tex]
Where:
[tex]b = 3mm\\c = 3\sqrt 2 mm[/tex]
[tex]\sin(B) = \frac{3}{3\sqrt 2}[/tex]
3 cancels out
[tex]\sin(B) = \frac{1}{\sqrt 2}[/tex]
Rationalize
[tex]\sin(B) = \frac{1}{\sqrt 2}* \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]\sin(B) = \frac{\sqrt 2}{\sqrt 2 * \sqrt 2 }[/tex]
[tex]\sin(B) = \frac{\sqrt 2}{2}[/tex]
Lastly:
[tex]\tan(B) = \frac{\sin(B)}{\cos(B)}[/tex]
This gives:
[tex]\tan(B) = \frac{\sqrt{2}/2}{\sqrt{2}/2}[/tex]
[tex]\tan(B) = 1[/tex]
Hence, (b) and (e) are true
Related Questions
2/6 = 1/2 1/3
which one is the answer
Answers
Answer:
1/3
Step-by-step explanation:
2+2+2=6
There are three 3's
Can you figure out the missing number
Answers
Answer:
Im not sure exactly what this is but it seems the answer is 6 because the only number 1-9 thats not there!
Step-by-step explanation:
Hope this helps!! :)
The missing number is 6
What are missing numbers?
Missing numbers are numbers omitted from a group or series of numbers.
The main purpose of finding a missing number is to determine the mechanism by which the numbers are arranged or encoded.
From the given information:
The number given is natural numbers from 1 - 9,The missing number in the series from 1 - 9 in the box is 6.Therefore, we can conclude that the missing number is 6.
Learn more about the missing numbers here:
https://brainly.com/question/11170254
A model rocket is launched with an initial upward velocity of 62/ms. The rocket's height h (in meters) after t seconds is given by the following.
h=62t-5t^2
Find all values of t for which the rocket's height is 29 meters.
Round your answer(s) to the nearest hundredth.
Answers
9514 1404 393
Answer:
t = 0.49, 11.91
Step-by-step explanation:
A graphing calculator can show you the answers quickly. The times are 0.49 seconds and 11.91 seconds.
__
We can write the equation as ...
h = 29
62t -5t^2 = 29 . . . . . substitute for h
-5(t^2 -12.4t) = 29
-5(t^2 -12.4t +6.2^2) = 29 -5(6.2^2) . . . . complete the square
-5(t -6.2)^2 = -163.2 . . . . . simplify
t -6.2 = ±√(-163.2/-5) = ±√32.64 . . . . divide by -5, take the square root
t = 6.2 ±5.71
t = 0.49, 11.91
The rocket has a height of 29 meters at t=0.49 seconds and t=11.91 seconds.
Please help me with this
Answers
Trust me bro
1 Remy has 4 monster trucks, 3 firetrucks, 1 ambulance, and 2 taxis. He will randomly choose. what is the probability that Remy will choose a taxi
A 1/10
B 1/5
C 2/4
D 1/3
Answers
Answer:
B) 1/5
Step-by-step explanation:
Remy has 2 taxis, and 10 cars in all. It is asking for the probability that Remy will choose a taxi. Divide the amount of taxis from the total amount of cars. Simplify the fraction:
2/10 = (2/10)/(2/2) = 1/5
B) 1/5 is your answer.
~
Answer:
Mmmmm maybe is A 1/10 por que se suman todas las posibilidades y luego se le coloca la cantidad que podria elegir
Pearl sent a box of 36 apples and oranges to her sister if 5/9 of shipments were apples how many apples did she send
Answers
Answer:
20 apples
Step-by-step explanation:
you do 36×5/9
36÷9=4
4×5=20
f(x) = 3x + 7. What is f(4) ?
Answers
Answer:
I believe the answer is 19.
I Need Help ;-; pls its timed
A rectangle is shown on a coordinate plane with vertices A(Negative 4, 8), B(1, 8), C(1, Negative 1), and D(Negative 4, Negative 1).
On a coordinate plane, a rectangle has 4 points. Point A is (negative 4, 8), point B is (1, 8), point C is (1, negative 1), point D is (negative 4, negative 1).
What are the dimensions of the rectangle?
The base is 4 units and the height is 9 units.
The base is 5 units and the height is 7 units.
The base is 5 units and the height is 9 units.
The base is 9 units and the height is 3 units.
Answers
Answer:
The correct answer is the third option
Step-by-step explanation:
I used a graphing calculator and also did L(W). But, the length (height) was 9 and (base) width 5
The _____ of a _____ can be found by dividing the area of the whole circle by ______.
Answers
Answer:
The area of the shaded region can be found by multiplying the area of the whole circle by three-fourths.
Step-by-step explanation:
Find the surface area of the prism.
Answers
Answer:
[tex]A=202\ cm^2[/tex]
Step-by-step explanation:
Given that,
The dimensions of the prism are 4 cm, 9 cm and 5 cm respectively.
The formula for the surface area of the prism is given by :
[tex]A=2(lb+bh+hl)[/tex]
Put all the values,
[tex]A=2(4(9)+9(5)+5(4))\\\\A=2(36+45+20)\\\\A=202\ cm^2[/tex]
So, the required surface area of the prism is equal to [tex]202\ cm^2[/tex].
A line goes through the points (-3,-6) and (6,9). Find the slope
Answers
Answer:
Slope = 5/3
-------------------
m = 5/3
Answer:
5/3
Step-by-step explanation:
Hello, to find the slope from two given points, you use this formula- y2-y1/x2-x1. In this problem, 9 would be y2, -6 would be y1, 6 would be x2, and -3 would be x1. The equation should look like this:
9-(-6)/6-(-3)
Since both are negatives, you would add it like this:
9+6/6+3= 15/9
Now, you need to simplify this fraction which is 5/3.
NO LINKS
Please help
Answers
Answer:
V≈1287.88
A≈1152.98
Step-by-step explanation:
9
3
The total length of the black-tailed jack rabbit is 24 inches.
3
The tail is 4 inches long.
8
How long is the rest of the body?
A
3
20- inches
8
5
B 20 inches
8
20 inches
1
D 20 inches
8
Answers
Answer:
20 inches
Step-by-step explanation:
24 inch total length - 4 inch tail length = 20 inch body length
write an equation for the nth term of the arithmetic sequence. Then find a40.
6,-1,-8,-15,....
Answers
Answer:
The next sequence will be -22 because they are subtracting 7
Plzz help will mark brainleast
Answers
Answer:
A-1 central nervous system
b- peripheral nervous
The following picture shows a saguaro cactus, a type of desert plant. Instead of leaves, this cactus has sharp needles. o How do sharp needles help a cactus survive in a desert?
A. They protect it from animals that want to eat it.
B. They attract Insects and birds that pollinate It
C. Thev help it get sunlight when it is dim or shadv.
Answers
A heavy piece of equipment has wheels on one side and legs on the other as shown in the diagram below.
Two people are trying to move the equipment. Each person grabs a handle and begins to lift. The first person imparts an upward force of 300 N and the second person imparts an upward force of 290 N. This is enough to lift the side of the equipment, but they also need to get it moving.
While maintaining the upward forces, the first person imparts a horizontal force of 185 N and the second person a horizontal force of 205 N. They maintain these forces while the equipment begins to move.
What is the total force in the horizontal direction?
____ N
What is the total force in the upward direction?
____ N
Determine the magnitude and direction of this resultant vector (the resultant vector from combining the forces of the two people).
Magnitude: ____ N
Direction: _____ °
Answers
9514 1404 393
Answer:
horizontal: 390 Nvertical: 590 N707.2∠56.5° NStep-by-step explanation:
The problem statement tells you the two horizontal forces are 185 N and 205 N. The total horizontal force is (185 +205) N = 390 N.
The vertical forces are said to be 300 N and 290 N. The total vertical force is (300 +290) N = 590 N.
The magnitude of the resultant is the root of the sum of the squares:
√(390² +590²) = √(152100 +348100) = √500200 ≈ 707.248
The angle of the resultant (relative to the horizontal) is ...
α = arctan(vertical/horizontal) = arctan(590/390) ≈56.53°
The resultant force is about 707.2 N at an angle of 56.5° above the horizontal.
Help me please! I will mark brainliest for whoever gets it right the fastest.
Answers
Answer:
274
Step-by-step explanation:
Identify whether the following equation has a unique solution, no solution, or infinitely many solutions.
3 + 6 = 3 – 4
A
unique solution
B
no solution
C
infinite solutions
Answers
Answer:
No solution
Step-by-step explanation:
3+6=9
3-4=-1
9 doesn't equal -1 therefore no solution.
7) You buy a notebook for $2.99 and a pack of erasers for $1.99. If you have a 25% off coupon for the whole order, how much will you have to pay for both items?
Answers
Answer:
i think it is $4.73
Step-by-step explanation:
Answer:
$3.73
Step-by-step explanation:
Notebook: $2.99
Pack of Erasers: $1.99
Add together to get the total amount before the coupon.
[tex]2.99 + 1.99 = 4.98[/tex]
Given 25% off coupon for the WHOLE ORDER. To make things easier, take 75% of 4.98.
[tex].75(4.98) = 3.735[/tex]
Or do the long way if you want.
[tex].25(4.98) = 1.245 = 1.25\\4.98 -1.25=3.73[/tex]
A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that: (a) Fewer than 14 of them have had a physical examination in the past two years. (b) At least 17 of them have had a physical exami- nation in the past two years
Answers
Answer:
a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.
b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.
Step-by-step explanation:
For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of adult women visit their doctors for a physical examination at least once in two years.
This means that [tex]p = 0.7[/tex]
20 adult women
This means that [tex]n = 20[/tex]
(a) Fewer than 14 of them have had a physical examination in the past two years.
This is:
[tex]P(X < 14) = 1 - P(X \geq 14)[/tex]
In which
[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916[/tex]
[tex]P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789[/tex]
[tex]P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304[/tex]
[tex]P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716[/tex]
[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]
[tex]P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068[/tex]
[tex]P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008[/tex]
So
[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079[/tex]
[tex]P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921[/tex]
0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.
(b) At least 17 of them have had a physical examination in the past two years
[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]
From the values found in item (a).
[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107[/tex]
0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.
12 6 12 24
Select one:
A. 240 square units
B. 252 square units
C. 180 square units
D. 216 square units
Answers
Answer:
B
Step-by-step explanation:
divide the given polygon into two (a square and a trapeziumarea of trapezium=1/2(a+b)×b 1/2(12+6)×12 ans 108square unitarea of a square=s×s 12×12 =144square unitadd 108+144=252square unitThe x-intercepts of a quadratic
(also called the zeros) occur
when the y-coordinate is [?].
Answers
Answer:
0
Step-by-step explanation:
The x-intercepts of a quadratic
(also called the zeros) occur
when the y-coordinate is [0].
That is why the x-intercepts are called zeros.
Answer:
0
Step-by-step explanation:
The x-intercepts of a quadratic
(also called the zeros) occur
when the y-coordinate is 0.
Solve the system of equations x + 2y = 8 and - 2x - 3y = - 7 by combining the equations.
Answers
Answer:
X+2Y = 8
-2X-3Y = -7
(X-2X+2Y-3Y)=8-7
-X-Y=1
The base of a triangle is 9/4 times of its height. If the area of triangle is 144 cm2. Find the height and the base.
Answers
Step-by-step explanation:
Given that the base of triangle is 9/4 times of its height . And area is 144 cm² . Let the height be h , then its base be 9h/4 .
• According to Question :-
[tex]\tt\to Area_{(\triangle)}=\dfrac{base\times height}{2}\\\\\tt\to 144cm^2 = \dfrac{9h\times h}{4\times 2 } \\\\\tt\to h^2 =\dfrac{12\times 12 \times 2 \times 2 }{3\times 3 }\\\\\tt\to h =\sqrt{\dfrac{12\times 12 \times 2 \times 2 }{3\times 3 }}\\\\\tt\to h =\dfrac{(12)(2)}{3} \\\\\tt\to \boxed{\orange{\tt h = 8 cm }}[/tex]
Therefore ,
Height = h = 8cm .Base ,= 9h/4 = 18cm .Please help!
First phtoto is the answer options for all questons
Second image is the Questions
Answers
Answer:
M is (-7,3)
N is (0,1)
I think p is (4,0) but the option isn’t there so I must’ve done something wrong though I can’t find what-
Please answer this quick!!
Answers
Please help! Tell me the numbers that I have to add to demostrate the answer
Answers
Simplify 12.856677878
Answers
Answer:
12.86
Step-by-step explanation:
this is rounded to the nearest hundredth
Due in 5 mins!! FIND THE MISSING LENGTHS!!!!!
Answers
Sqrt(169) = 13
So x = 13