Given the following information, find the length of the missing side. Leave your answer as a simplified radical.
Answers
Given:
A figure of a triangle, AD = 6 and DB = 2.
To find:
The length of AC.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
In triangle ACD,
[tex]\cos A =\dfrac{AD}{AC}[/tex]
[tex]\cos 30^\circ =\dfrac{6}{AC}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{6}{AC}[/tex]
[tex]\sqrt{3}\times AC=6\times 2[/tex]
[tex]AC=\dfrac{12}{\sqrt{3}}[/tex]
[tex]AC=\dfrac{12}{\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]AC=\dfrac{12\sqrt{3}}{3}[/tex]
[tex]AC=4\sqrt{3}[/tex]
Therefore, the length of AC is [tex]4\sqrt{3}[/tex] units.
Related Questions
an investment of 12,000 is losing value at a rate of 4% each year. what is the exponential function to model the situation after 9 years
Answers
Answer:
Amount after 9 year = 8,310 (Approx.)
Step-by-step explanation:
Given:
Amount invested = 12,000
Rate on decline = 4% per year = 0.04
Number of year = 9
Find:
Amount after 9 year
Computation:
A = P[1+r]ⁿ
A = 12,000[1-0.04]⁹
A = 12,000[0.96]⁹
A = 12,000[0.6925]
Amount after 9 year = 8,310 (Approx.)
In Ms. Chance's first period class, there are 9 students with hazel eyes, 10 with brown eyes, 7 with blue eyes, and 2 students with green eyes. Ms. Chance picks a student at random. Which color eyes is the student most likely to have?
Answers
Find an equivalent fraction 1/8 = x/56
Answers
Answer: I think it’s 1/8 = 7/56
The value of an equivalent fraction is,
⇒ 1/8 = 7/56
We have to given that,
A fraction to solve,
⇒ 1/8 = x/56
Now, We can simplify as,
⇒ 1/8 = x/56
Cross multiplication,
⇒ 56 = 8x
⇒ x = 56/8
⇒ x = 7
Therefore, The value of an equivalent fraction is,
⇒ 1/8 = 7/56
Learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ6
Help me please, please
Answers
Answer:
When used as a diacritic mark, the term dot is usually reserved for the interpunct, or to the glyphs 'combining dot above' and 'combining dot below' which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese.
Step-by-step explanation:
WILL GIVE BRAINLIEST IF SOLVED IN 10 MINS : Solve each equation with the quadratic :
Answers
Answer:
5. x = -1 or x = -3
6. b = -2 or b = 6
7. n = 5 or n = 4
Step-by-step explanation:
5. x² + 4x + 3 = 0
Factorize
x² + 3x + x + 3 = 0
x(x + 3) +1(x + 3) = 0
(x + 1)(x + 3) = 0
Set each of the factors equal to zero and solve for x
x + 1 = 0 or x + 3 = 0
x = -1 or x = -3
6. b² - 4b - 14 = -2
Put all terms on one side of the equation leaving zero on one side
b² - 4b - 14 + 2 = 0
b² - 4b - 12 = 0
Factorize
b² - 6b + 2b - 12 = 0
b(b - 6) +2(b - 6) = 0
(b + 2)(b - 6) = 0
Set each of the factors equal to zero and solve for b
b + 2 = 0 or b - 6 = 0
b = -2 or b = 6
7. n² = 9n - 20
Put all terms on one side of the equation leaving zero on one side
n² - 9n + 20 = 0
n² - 5n - 4n + 20 = 0
n(n - 5) -4(n - 5) = 0
(n - 5)(n - 4) = 0
Set each of the factors equal to zero and solve for b
n - 5 = 0 or n - 4 = 0
n = 5 or n = 4
How much money is needed to be invested now to obtain $12,100 8 years from now if this amount is invested at 7.25% compounded continuously?
Answers
Answer:
$6,911.92
Step-by-step explanation:
Given the following
Amount A = $12,100
Time t = 8yrs
Rate r = 7.25%
Required
Principal P
Using the compound interest formula;
A = P(1+r)^n
12,100 = P(1+0.0725)^8
12,100 = P(1.0725)^8
12100 = 1.7506P
P = 12,100/1.7506
P = 6,911.92
Hence the amount invested would have been $6,911.92
n+4=12 .step by step working please
Answers
[tex]n + 4 = 12[/tex]
Subtract sides minus 4
[tex]n + 4 - 4 = 12 - 4[/tex]
[tex]n = 8[/tex]
if d is 55 degrees then what is F and E degrees. Explain how you know
Answers
Answer:
F=55
E=70
Step-by-step explanation:
The total degree of a triangle is 180.
So we have 180-55*2
E=180-110
E=70
A summer movie club charges a $30
membership fee and then $5 per movie.
Which equation can be used to find y, the
total cost of the movie club, if x represents
the number of movies watched.
Is B right?
Answers
A robot packs boxes in a factory. it runs at a constant speed, and packs 10 boxes in 9 minutes. if the robot operated for 180 minutes on Monday, how many boxes did it pack
Answers
what scale factor is applied to shape b to make shape a? I need help asap please
Answers
Answer:
For shape B to make shape A all numbers in shape B would have to be divided by 1.5
Step-by-step explanation:
POSSIBLE POINTS: 6
Solve each equation and match the solution.
e+8=31
t−25=54
32=y −21
14=b−12
x+8.95=21.95
n +21 =32
Answers
Answers,
1. 23
2. 79
3. 53
4. 26
5. 13
6. 11
How I did this,
What I did was subtract 8 from 31 to get ( e ) by itself.
This subject will get harder so I reccomend you focus on school and learn how to do this.
What are the coordinates of point A
Answers
Answer:
The coordinates of point A are (-4, 3)
hope it helps
Answer:
The coordinates of point A is (-4,3)
Step-by-step explanation:
(x,y)
X= -4
Y= 3
The hanger image below represents a balanced equation. Write an equation to represent the image. PLEASE HELP ILL MARK U AS BRAINLIST OR WHATEVER o(*°▽°*)o
Answers
Answer:
i think its 3 in all the boxes but trying is better than not ig wait no nvm
the equation is (9+6)+4=(5+ blank)+4
Answers
Answer:
10
Step-by-step explanation:
(9 + 6) + 4 = (5 + x) + 4
15 + 4 = 5 + x + 4
19 = x + 9
19 - 9 = x
10 = x
B
7
25
с
24
А
Find sin(a) in the triangle.
Answers
Answer: 7/25
Step-by-step explanation:
got it correct on khan academy
What is the value of B?
Answers
Answer:
The value of B is 0 because going down from the middle is all negative and going up from point B is all positive so the answer is 0 degrees
Step-by-step explanation:
Answer:
in linear pair
90+a+24=180
a=180-90-24=66°
B°=90+a=90+66=156°
the value of B°=156°
5 divided by 1/4
go straight to the answer
Answers
Answer:
20
Step-by-step explanation:
On his last 5 math tests, Gilbert earned: 94, 72, 83, 94, 90. What was his average score? ( Report your answer to the tenths place).
Answers
Answer:
Average of Gilbert in last 5 test = 86.6
Step-by-step explanation:
Given:
Score earned by Gilbert in last 5 test = 94, 72, 83, 94, 90
Find:
Average of Gilbert in last 5 test
Computation:
Average value = Sum of all events / Total number of events
Average of Gilbert in last 5 test = Sum of all last results / Number of results
Average of Gilbert in last 5 test = [94 + 72 + 83 + 94 + 90] / 5
Average of Gilbert in last 5 test = [433] / 5
Average of Gilbert in last 5 test = 86.6
Brainliest goes to whoever explains the answer best pls help
Answers
Answer: (-2,9)
Step-by-step explanation: I did this not too long ago!
Solve equation [2] for the variable y
[2] y = 5x + 19
// Plug this in for variable y in equation [1]
[1] (5x+19) + 3x = 3
[1] 8x = -16
Solve equation [1] for the variable x
[1] 8x = - 16
[1] x = - 2
By now we know this much :
y = 5x+19
x = -2
Use the x value to solve for y
y = 5(-2)+19 = 9
Answer (-2,9)
im wasting my points pls answer
Answers
Answer:
1.
1 1/15
2.
1 7/15
3.
I think that the sister rode farther by 2/5
reason:
(the sister) 2/3 mile+4/5 mile=1 7/15
(you) 2/3 mile+2/5=1 1/15
1 7/15-1 1/15= 2/5(according to a website I used)
if supplementary angles add to 180, complementary angles add to 90, and angles A and B are complementary. Angle A measures 40 degrees, what is the measure of angle B
Answers
Answer:
∠ B = 50°
Step-by-step explanation:
complementary angles add to 90° , then
∠ A + ∠ B = 90° , that is
40° + ∠ B = 90° ( subtract 40° from both sides )
∠ B = 50°
The ordered pair (10,3) is in quadrant:
Answers
Answer:
1
Step-by-step explanation:
ordered pairs with both positive numbers are in Q1
Answer:
That would be the first quadrant, also known as the I quadrant and the top right quadrant.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3950 grams and a standard deviation of 374 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4473 grams. Round your answer to four decimal places.
Answers
Answer:
0.9192 = 91.92% probability that the weight will be less than 4473 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean weight of 3950 grams and a standard deviation of 374 grams.
This means that [tex]\mu = 3950, \sigma = 374[/tex]
Find the probability that the weight will be less than 4473 grams.
This is the pvalue of Z when X = 4473. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4473 - 3950}{374}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a pvalue of 0.9192
0.9192 = 91.92% probability that the weight will be less than 4473 grams.
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answers
HELPPP PLSSS
ANSWER ALL PLS HELP AND EXPLAIN HOW YOU GOT YOUR ANSWER
Answers
Answer:
1. 64
2. 36
3. 32
4. 20
5. 33
6. 30
Step-by-step explanation:
Sorry I can't see the symbols on questions 7-9
The function, f(x), is plotted below.
Evaluate the limits, if they exist. If not, write DNE.
Limit as x approaches negative 1 minusf(x) =
Limit as x approaches 3 plusf(x) =
Limit as x approaches 1 f(x) =
Answers
Answer:1 2 DNE
Step-by-step explanation:
Answer:
1
2
DNE
Step-by-step explanation:
How to show work on this one topic is angles formed by 2 chords and secants
Answers
Answer:
Step-by-step explanation:
giving brainliest !!!!!!
Answers
Answer:
216
Step-by-step explanation:
6*6*6= 216
btw i am not using the formula for volume. 6*6 because you need the area of one side. then multiply that by 6 because there are 6 sides of a cube so 6*6*6=216
Evaluate the algebraic expression for the given value(s) of the variable(s).
2x 2 - 7xy + 3y 2 ; x = -3, y = 4
Answers
Answer:
-18
Step-by-step explanation:
2x²-7xy+3y²
2(3²)-7(3)(4)+3(4²)
2(9)-84+3(16)
18-84+48
18+48-84
-18