The length οf the perpendicular is 2√2.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.
Step 1:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(30°) = p/8√2
We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:
1/2 = p/(8/√2)
Simplifying further, we can multiply bοth sides by 8/√2:
4/√2 = p
Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:
p = 4/√2 * √2/√2 = 4√2
Therefοre, the length οf the perpendicular is 4√2.
Step 2:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(45°) = p/4√2
We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:
√2/2 = p/(4/√2)
Simplifying further, we can multiply bοth sides by 4/√2:
2√2 = p
Therefοre, the length οf the perpendicular is 2√2.
To learn more about Trigonometry from the given link
https://brainly.com/question/24349828
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When 3(2x^2+4x+7)−(x^2−8x+11) is simplified, what is the coefficient of the x term?
Answer:
Step-by-step explanation:
when 3(2x^2+4x+7)−(x^2−8x+11) is solved you get
5x^2 + 20x + 10.
the x term is
−
2
+
√
2
,
0
)
,
(
−
2
−
√
2
,
0
)
[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]
On a circular playground, the distance from its center to the edge of the playground is 36 feet. What is the approximate circumference of the playground? (Use 3.14 for .)
A.
113.04 ft
B.
226.08 ft
C.
4,069.44 ft
D.
16,277.76 ft
Answer:
[tex]\fbox{\fbox{Circumference = 226.08 feet}}[/tex]
Step-by-step explanation:
Given:
distance from center to the edge(Radius) of playground = 36 feet
To find:
Circumference of playground=?
Solution:
we know that,
Circumference of circle = 2πr
substituting the radius value in above formula,
[tex]2 \pi r = 2 \times 3.14 \times 36 = 226.08 \: ft[/tex]
[tex]\fbox{\fbox{Circumference = 226.08 feet}}[/tex]
Thanks for joining brainly community!
Answer: 226.08ft
Step-by-step explanation: we are finding the circumference of a circle so we will make 3.14 times 2 times 36 as it is a radius I think .
3.14 ×2×36=226.08 and the units is feet . Hope it helps buddy
How do you convert 3 1/3 yards to inches? Use the drop-down menus to explain your answer.
Since, there are 36 inches in 1 yard, multiply 3 1/3 by 36
So, 3 1/3 yards = 120 inches
Answer:
120 inches
Step-by-step explanation:
To convert 3 1/3 yards to inches, you first need to figure out how many inches are in one yard. 1 yard=36 inches.
After this, you would turn your mixed fraction into an improper fraction and then multiply by 36 inches. It would look like this:
10/3 * 36/1
Here, you would cancel out the common factors by factoring 36 by 3.
12*3=36 ----> 10/3 * [tex]\frac{3(12)}{1}[/tex] ----->
Lastly, multiply 10 by 12 and your answer would be 120 inches.
NEED HELP!
What is the zero of the function?
f (x) = x2+x-42/x2+3x-28
Enter your answer in the box.
[tex]f(x)=\cfrac{x^2+x-42}{x^2+3x-28}\implies \stackrel{f(x)}{0}=\cfrac{x^2+x-42}{x^2+3x-28}\implies 0 = x^2+x-42 \\\\\\ 0=(x+7)(x-6)\implies x= \begin{cases} 6\\ -7 \end{cases}[/tex]
Pleaseee help!
What is 8^2+x^2=17
Answer:
6.856
Step-by-step explanation:
8² + x² = 17
8² - 17 = -x²
64 - 17 = -x²
-47 = -x²
x² = 47
x = 6.856
Use the compound interest formulas A = P1+
and A = Pert to solve.
Suppose that you have $11,000 to invest. Which investment yields the greater return over 9 years: 7.5% compounded
continuously or 7.6% compounded semiannually?
Answer:
7.5% compounded continuously yields the greatest return after 9 years
Step-by-step explanation:
Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.
7.6% compounded semiannually:
I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09
7.5% compounded continuously:
Since it is compounded continuously, we use the mathematical constant e.
I = 11000e = $29901.01
I took the Integrity Pledge.
Do I put True or False ?
True or False
What does integrity mean?
Answer:
a little confusing, but i think its a fake quiz that asks for your pledge so you put true, and integrity: the quality of being honest and having strong moral principles; moral uprightness
Step-by-step explanation:
What percent of 6y is 24?
Step-by-step explanation:
6y×100=24
600y=24
600y/600=24/600
y=4/100
y=0.04
Does anyone know all of these? (11th Grade Algebra)
Answer:
Step-by-step explanation:
17) In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠A + ∠D = 180
5x + 30 + x = 180
5x +x + 30 = 180 {Combine like terms}
6x + 30 = 180 {Now, subtract 30 from both sides}
6x + 30 - 30 = 180 - 30
6x = 150
Now divide both sides by 6
x = 150/6
x = 25
∠A = 5x + 30
= 5*25 + 30
= 125 + 30
= 155
In parallelogram, opposite angles are congruent.
∠C = ∠A
∠C = 155°
18)In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠A + ∠D = 180
3x + 4 + x = 180
3x +x + 4 = 180 {Combine like terms}
4x + 4 = 180 {Now, subtract 4 from both sides}
4x + 4 - 4 = 180 - 4
4x = 176
Now divide both sides by 4
x = 176/4
x =44
19) In parallelogram, adjacent angles are supplementary (add up to 180)
⇒∠GAC + ∠ACF = 180
125 + ∠ACF = 180
Now, subtract 125 from both sides
∠ACF = 180 - 125
∠ACF = 55
21) In parallelogram, adjacent angles are supplementary (add up to 180)
∠CFG + ∠ACF = 180
2w +30 + w + 15 = 180
2w +w + 30+ 15 = 180
3w + 45 = 180
3w = 180 - 45
3w = 135
w = 135/3
w = 45
∠ACF = w + 15
= 45 + 15
∠ACF = 60
21) In parallelogram, opposite sides are congruent.
GF = AC
4x - 14 = 2x + 2
4x = 2x + 2 + 14
4x = 2x + 16
4x - 2x = 16
2x = 16
x = 16/2
x = 8
22) In parallelogram, the diagonals bisect each other.
XC = GX
3y - 3 =2y + 2
3y = 2y + 2 + 3
3y = 2y + 5
3y - 2y= 5
y = 5
23) The length of the middle segment of trapezium is half the sum of the two parallel sides.
[tex]\dfrac{b_{1}+b_{2}}{2}=110\\\\\\b_{1}+b_{2}=110*2\\[/tex]
I WILL MARK YOU THE BRAINLIEST LINKS WILL BE REPORTED AND DELETED !
What is the value of 7p7 ?
A: 1
B: 14
C: 49
D: 5040
Answer:
the answer is D:5040
Step-by-step explanation:
The answer to your question would be D. 5040! Hope this helps - Have an amazing rest of your day :)
Gina made a
playlist of children's songs. In 1 hour,
how many more times could she play
"Row, Row, Row Your Boat" than "Twinkle,
Twinkle, Little Star"?
Here's li[tex]^{}[/tex]nk to the answer:
bit.[tex]^{}[/tex]ly/3HH[tex]^{}[/tex]Mdaf
simplify: -7/9-(-5/12)+1/3.
Step-by-step explanation:
please mark me as brainlest
Answer:
[tex]\sf -\dfrac{1}{36}[/tex]
Explanation:
[tex]\rightarrow \sf -\dfrac{7}{9} -(-\dfrac{5}{12} )+\dfrac{1}{3}[/tex]
remove parenthesis
[tex]\rightarrow \sf -\dfrac{7}{9} +\dfrac{5}{12} +\dfrac{1}{3}[/tex]
all the denominators has a common multiple of 108
[tex]\rightarrow \sf -\dfrac{7(12)}{108} +\dfrac{5(9)}{108} +\dfrac{1(36)}{108}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{-84}{108} +\dfrac{45}{108} +\dfrac{36}{108}[/tex]
join the fractions
[tex]\rightarrow \sf \dfrac{-84+45+36}{108}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{-3}{108}[/tex]
simplify
[tex]\rightarrow \sf -\dfrac{1}{108}[/tex]
Help picture below problem 6
Answer:
g is 37
Step-by-step explanation:
supplementary means two angles that add up to 180°
180-143=37
A right triangle has side lengths that are consecutive integers and a perimeter of 12 feet. What are the
angles of the triangle?
А. 30°, 60° and 90°
B. 33.47°, 56.53° and 90°
C. 36.87°, 53.13° and 90°
D. 40.16°, 49.84° and 90°
Answer:
option c
Step-by-step explanation:
Let the sides of the right angled triangle = x , (x +1) , (x +2)
Perimeter = 12 feet
x + x +1 + x + 2 = 12
x +x + x + 1+2 = 12
Combine like terms
3x+ 3 = 12
Subtract 3 from both sides
3x = 12- 3
3x = 9
Divide both sides by 3
x = 9/3
x = 3
x + 1 = 3 + 1 = 4
x + 2 = 3 + 2 = 5
The sides of the triangle are 3 , 4 ,5
The biggest side will be the hypotenuse.
So, hypotenuse = 5 ft. other legs are 3 and 4
[tex]\text {Sin \ $\theta$ = $\dfrac{opposite \ side \ of \ \theta}{hypotenuse}$ } \\\\\\ = \dfrac{4}{5}\\\\\\Sin \ \theta = 0.8\\\\\theta = Sin^{-1} \ 0.8\\\\\theta = 53.13 \ ^\circ[/tex]
another angle = 180 - [ 90 + 53.13]
= 180 - 143.13
= 36.87°
Help help help help math math
Answer:
the answer in the question mark that was in the green box ???
Adrian is 3 times as old as Anisah now. 4 years ago,Adrian was 28 years older than Anisah . How old will Anisah be in years' time?
Lets have Anisah be x right now.
4 years ago, Adrian was (x-4) + 28 = x+24
Right now, Adrian is 3x.
Knowing those two pieces of information, we can say that x+24 is equal to 3x-4. (This is because Adrian is 3x right now, and for 4 years ago, you subtract 4.)
x+24=3x-4
24=2x-4
28=2x
x=14
Right now Anisah is 14, and in 4 years he will be 14+4 = 18.
Use the digital text feature to complete the explanation: The 24th Amendment states that citizens of the United States will not be stopped from voting if
they are sick or elderly
Othey are guilty of a crime
Othey are in a political office
Othey do not pay their taxes
D or A not sure
The Twenty-fourth Amendment (Amendment XXIV) of the United States Constitution prohibits both Congress and the states from conditioning the right to vote in federal elections on payment of a poll tax or other types of tax.
Answer:
(D) they do not pay their taxes
Step-by-step explanation:
I got it correct on an exam I did.
Janie has $3. She earns $1.20d for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $13.50.
Write an inequality to determine the number of chores, c, Janie could do to have enough money to buy the CD.
Answer:
3+1.20c > 13.50
Step-by-step explanation:
hope this helps
Help picture below problem
Answer:
∠s = ∠v
Step-by-step explanation:
Supplementary angles add up to 180°
∠s + ∠v = 180
90 + ∠v = 180
∠v = 180 - 90
∠v = 90°
⇒∠s ≅ ∠v
Find the fraction suitable for the blank. Show the method how you found.
Answer:
3/5Step-by-step explanation:
Let the blank is x, solve the equation for x:
(4 1/2 - x) × 1 3/13 = 4 4/5(9/2 - x) × 16/13 = 24/59/2 - x = 24/5 × 13/169/2 - x = 39/10x = 9/2 - 39/10x = 45/10 - 39/10x = 6/10x = 3/5Let that be x
(9/2-x)×16/13=24/5(9-2x)/2=24/5×16/13(9-2x)/2=39/1090-20x=7820x=12x=12/20x=6/10x=3/5Jerry and Nadine had dinner at a Chinese restaurant. They left a 15% tip that was 2.70. How much did the meal cost before the tip?
Answer:
18 I believe
Step-by-step explanation:
when you do 2.70 divided by 15% you get 18 and if you do 18 times 15% you get 2.70 so I think it is 18
Hi can someone may help me with this problem I'm struggling with
ASSP
Answer:
see attached
cost = 33
Step-by-step explanation:
Kruskal's Algorithm is a "greedy" algorithm that adds the next minimum-weight edge to the tree, provided that it does not create a loop.
__
The minimum-weight edge in the graph is DF, with weight 1.
The next minimum-weight edge is GH, with weight 2.
The next minimum-weight edge is AB, with weight 3.
The next minimum-weight edge is EF, with weight 4.
Edge DE is the next lowest-weight, but it creates a loop (DEF), so we ignore it.
BC is the next edge we'll add to our tree.
FG is the next edge we'll add to the tree.
Edge DG creates a loop, so we ignore it.
Edge FH creates a loop, so we ignore it.
CF is the next edge we'll add to the tree. This completes the minimum spanning tree using Kruskal's Algorithm.
Included edges are AB, BC, CF, DF, EF, GF, GH.
The cost of the tree is 3+6+10+1+4+7+2 = 33.
11 18 The diagram shows an equilateral triangle. All measurements are in cm. NOT TO SCALE 2x+2 3x+4 3 OLTY а The perimeter of the triangle is 57 cm. Find the length of a.
Answer:
a = 7
Step-by-step explanation:
3x + 4 = 57 ÷ 3
3x + 4 = 19
3x = 15
x = 5
2x + 2 = 2(5) + 2 = 10 + 2 = 12
19 - 12 = 7
a = 7
hope this helps!! p.s. i really need brainliest :)
Solve 2 a 2 − 5 a − 25 = 0 by factoring. Enter your answers below a = or a =
Answer:
a=5, a=-2.5
Step-by-step explanation:
Given:
[tex]2 a^2 - 5 a - 25 = 0[/tex]
Solution:
[tex]a_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-25\right)}}{2\cdot \:2}[/tex]
[tex]a_{1,\:2}=\frac{-\left(-5\right)\pm \:15}{2\cdot \:2}[/tex]
[tex]a_1=\frac{-\left(-5\right)+15}{2\cdot \:2},\:a_2=\frac{-\left(-5\right)-15}{2\cdot \:2}[/tex]
[tex]a=5,\:a=-2.5[/tex]
~Lenvy~
The variables x and y have a proportional relationship: when x is 4, y is 11.
What is the constant of proportionality for this relationship?
Enter your answer, as a decimal, in the box.
Answer:
2.75
Step-by-step explanation:
When x = 4, y = 11
when x = 1, y = 2.75
k = 2.75
Please help me find x
|x+8|=x+8
square two sides
x+8=(x+8)2
x+8=x2+16x+64
x2+16x+64-x-8=0
x2+15x+56
then rule a2+-l
A boat, which moves at 29 miles per hour in water without a current , goes 825 miles upstream and 825 miles back again in 58 hours. Find the speed of the current to the nearest the the place.
Answer:
4 mph
Step-by-step explanation:
Travel time is proportional to distance and inversely proportional to speed. If c represents the speed of the current in miles per hour, an equation for the total trip time is ...
825/(29 -c) +825/(29 +c) = 58 . . . . . . hours travel time
825(29 +c) +825(29 -c) = 58(29 -c)(29 +c)
58c² -928 = 0 . . . . . . . rearrange to standard form
58(c -4)(c +4) = 0 . . . . factor
Values of c that satisfy this equation are 4 and -4. For the purpose here, we'll choose the positive solution.
The speed of the current is 4 miles per hour.
It takes Marty 1 1/4 hours to get ready for school. If 1/5 of that time is used to shower and 1/3 of that time is used to eat breakfast, how long does it take him to shower and eat breakfast?
Answer: 40 minutes
Step-by-step explanation:
First, break this down into minutes. 1 1/4 hours is 75 minutes. 75 divided by 5 is 15. he spends 15 minutes taking a shower. 75 divided by 3 is 25. he spends 25 minutes eating breakfast. 25 plus 15 is 40. he spends 40 minutes to shower and eat breakfast.
How many solutions are there to equation square root x = -16
A study population includes 320 freshmen 300 sophomoras, 500 juniors, and 510 seniors,
Which sample best represents the population
O 18 freshmen, 18 sophomores, 30 juniors, 30 seniors
O 18 freshmen, 18 sophomores, 18 juniors, 18 seniors
O 18 freshmen 30 sophomores, 18 juniors, 30 seniors
30 freshmen, 30 sophomores, 18 juniors 18 seniors
Answer:
18 freshmen, 18 sophomores, 30 juniors, 30 seniors
Step-by-step explanation:
Given ratio
freshman : sophomores : juniors : seniors
= 320 : 300 : 500 : 510
320 ≈ 300 and 500 ≈ 510
Therefore, 300 : 300 : 500 : 500
Ratio of 300 : 500 = 18 : 30
So 18 : 18 : 30 : 30 best represents the population
Given nos
320300500510Ratio:-
320:300:500:510Round out
300:300:500:50018:18:30:30Option A