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
38 POINTS FOR THIS
pls answer some of these questions or even all ty
Answers
Answer:
there are no questions
Step-by-step explanation:
but may i still please have a brainliest
if not then it is ok
write the questions in the comments
Answer:
What questions?
I don't see anything
Need help please help me if you know it
Answers
Answer:
I believe it's C... Not sure though...
The radius of the inside circle is 8 inches. The radius of the larger circle is 4 inches more than the radius of the small circle.
What is the area in square inches of the shaded area? Use 3.14 for π and round your answer to the nearest whole number.
Answers
Answer:
Area of shaded region=2 ×3.14×R -2×3.14×r(where R is lager radius and r is smaller radius.)
Therefore area of shaded region=2×3.14×12 -2×3.14×8
=2×3.14(12-8)
=6.18 ×4
=24.72 inc^2
Step-by-step explanation:
Dimensions of a building are 728 feet by 800 feet. If 1 inch represents 8 feet, what are the dimensions of the building on the drawing?
Answers
Answer:
91in by 100in
Step-by-step explanation:
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 590 hours. Find the probability of a bulb lasting for at most 605 hours. Round your answer to four decimal places.
Answers
Answer:
0.8413 = 84.13% probability of a bulb lasting for at most 605 hours.
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.
The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 590 hours.
This means that [tex]\sigma = 15, \mu = 590[/tex]
Find the probability of a bulb lasting for at most 605 hours.
This is the pvalue of Z when X = 605. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{605 - 590}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413 = 84.13% probability of a bulb lasting for at most 605 hours.
I need help with this question please
Answers
9514 1404 393
Answer:
y = -x -2
Step-by-step explanation:
The line crosses the y-axis at y = -2, so that is the y-intercept.
The slope is the ratio of "rise" to "run." The points on the graph show a "rise" of -3 for a "run" of 3.
m = rise/run = -3/3 = -1
Then the slope-intercept equation is ...
y = mx +b . . . . . slope m, y-intercept b
y = -x -2 . . . . . . . using m=-1, b=-2
Which of the following systems of linear inequalities is represented by the
solution graphed below?
O A. x>-1 and y 2-X
O B. y 2-1 and y<-X
O C. 2-1 and y> -X
OD. Y> -1 and ys-x
Answers
Answer:
B.
Step-by-step explanation:
i just solved it.
In this exercise we have to observe the graph informing and in this way identify the best alternative that represents this question, so we have to:
Letter B
So to start, we have to look at the graph axes separately, being the X axis first, then:
When we look at the area demarcated on the X axis, we realize that it is only about negative values, so X will always be less than zero.Now looking at the Y axis, we can see that it will always be values greater than or equal to -1.Thus, the alternative is found in the letter B, since:
[tex]Y\geq -1\\X\leq 0[/tex]
See more about graph at brainly.com/question/14375099
The length of a rectangle is 3 inches more than three times it's width. Write an equation relating the length, “, of the rectangle to its width, w.
Answers
Select the correct answer.
Which statement is true?
A.
The mean lies to the right of the median for a positively skewed distribution.
B.
The mean lies to the left of the median for a positively skewed distribution.
C.
The mean lies to the left of the median for a symmetric distribution.
D.
A distribution skewed to the right is said to be negatively skewed.
E.
A distribution skewed to the left is said to be positively skewed.
Answers
Answer:
The correct answer would be The mean lies to the left od the median for a positively skewed distribution
Step-by-step explanation:
Answer: The mean lies to the left odd the median for a positively skewed distribution
Jin is planning to drive from City X to City Y. The scale drawing below shows the
distance between the two cities with a scale of 1/4 inch = 14 miles.
Answers
Answer:
84 miles
Step-by-step explanation:
Distance between the two cities on the drawing = 1½ in.
Scale of drawing = ¼ inches is to 14 miles
Actual distance between the two cities using proportion:
(14*1½)/¼
Actual distance = 84 miles
HELP ME PLS, the function-
Answers
What is 2/3 of 9?
2
3
6
7
Answers
Answer: 6
Step-by-step explanation:
2/3 of 9 is basically 2/3 times 9
Answer:
6, because this and that is this and that bam boom bap, just trust me bro
. The figure below shows a circular
driveway. What is the area of the
driveway?
Answers
Answer:
C
Step-by-step explanation:
A= πr squared
D=r*2
r=24
π=3.14
A= π(24 * 24) = 576
A= π576
A=10808.64
A=10808.6
Help Plis ...............
Answers
Answer:
it is positive 3/4
Step-by-step explanation:
it is the opposite of -3/4
Answer:
it would be a positive 3/4
The average temperature for four days was 22°. What must the temperature be on the fifth day in order to make 23° the temperature for the five days?
Answers
Answer:
27°C
Step-by-step explanation:
Average temperature on 4 days
[tex] = \frac{total \: temperatures \: for \: 4 \: days}{4} [/tex]
Total temperatures for 4 days
= 4(22)
= 88
If the average temperature throughout 5 days is 23°,
total temperature for 5 days
= 5(23)
= 115
Temperature on the 5th day
= total temperatures for 5 days -total temperature for 4 days
= 115 -88
= 27°C
What is the value of y=8−3x when x=5?
When x=5, y=
Answers
Answer:
-7 will be the answer.
Step-by-step explanation:
By Putting the value of x, we get:
y=8-3x
y=8-3(5)
y=8-15
y= -7
find the value of x
help please !
Answers
Answer:
56°
Triangles are supposed to equal 180° when all the degrees inside are added, and when you add 44 and 80 it equals 124
Now you subtract 124 from 180 and then you get 56
So the answer would be 56° :)
A machine is shut down for repairs if a random sample of 100 items selected from the daily output of the machine reveals at least 15% defectives. (Assume that the daily output is a large number of items.) Suppose that a random sample of 20 items is selected from the machine. If the machine produces 5% defectives, find the probability that the sample will contain at least three defectives, by using the following methods.
a. The normal approximation to the binomial
b. The exact binomial tables
Answers
my brain can't process this lol
Find the surface area.
Answers
Answer:
do you want to me to find it for all or just 1
Answer:
88 [tex]m^{2}[/tex]
Step-by-step explanation:
The surface are is the total area of all the faces
Opposite faces have the same area
Label each side either l, h or w
SA of a cuboid = 2lw + 2lh + 2hw
(2 x 4 x 6) + (2 x 4 x 2) + (2 x 6 x 2) = 8
pls help =pdndjn mkZbn v
Answers
Answer:
Step-by-step explanation:
Past: The birds flew away quickly
Present: The geese honk at the passerby
Future: The ducklings will hatch soon
Answer:
[Past] The birds flew away quickly.
[Present] The geese honk at passersby.
[Future] The ducklings will hatch soon.
_______________________________
I can't see the options on the second image.
Given m|n, find the value of x.
t
156°
х.
Answers
Answer:
i think the answer would be 156° .
hope it helps you ^.^
Help me please I’m not smart -
Answers
In the formulae below, make x the subject:
1. a) P = 2mx
Answers
Answer:
x = P/2m
Step-by-step explanation:
x is the subject of the formula, and we can express it as: x = P / (2m)
How make x the subjectTo make x the subject in the formula P = 2mx, we can rearrange the equation to isolate x on one side.
Starting with the equation:
P = 2mx
To solve for x, divide both sides of the equation by 2m:
P / (2m) = (2mx) / (2m)
This simplifies to:
P / (2m) = x
Therefore, x is the subject of the formula, and we can express it as:
x = P / (2m)
Learn more about equation at https://brainly.com/question/29174899
#SPJ2
Oil prices are projected to increase by 125% by next August. A quart of oil currently costs $1.25. What is the projected cost of a gallon of oil next August? Round your answer to the nearest hundredth.
Answers
Answer:$2.81
Step-by-step explanation:
1.25 is 100% of the price
125% + 100% = 225%
x = price by august
x = 225% (1.25)
225% = 2.25
2.25(1.25) = 2.8125 ≈ $2.81
Another way to see it:
=
225(1.25) / 100 = 2.8125
Does the point (-8, 8) satisfy the inequality 16x + 15y = -8?
yes
no
Answers
Answer:
Yes
Step-by-step explanation:
16x+15y=-8
16(-8)+15(8)=-8
-8=-8
Hope that helps :)
Answer:
True
Step-by-step explanation:
The left side − 8 is equal to the right side − 8 , which means that the given statement is always true.
Brainliest for both correct answers
Answers
Answer:
Question 1: A
Question 2: D
Step-by-step explanation:
I hope it helps
In APQR, what is the mZQ? Enter your answer in the box.
Answers
Answer:
∠Q = 105°
Step-by-step explanation:
(6x + 5) + (11x - 5) + x = 180°
combine like terms:
18x = 180°
x = 10°
∠Q = 11(10) -5 = 105°
A graph of f(x)=10x^2-11x-6 is shown on the coordinate grid.
What are the zeros of f(x)?
-2/5 and 3/2
-6
-9 and 4
11/20 and -9
Answers
Answer:
-2/5 and 3/2
Step-by-step explanation:
f(x)=10x²-11x-6
0=10x²-11x-6
(5x+2)(2x-3)=0
5x+2=0, 2x-3=0
5x=-2, 2x=3
x=-2/5, x=3/2
Given the diagram below, find the value of x.
A
14
B
X
с
30
The value
of x is?
Answers
Answer:
yes 11000
Step-by-step explanation:
5. In a right triangle, the sum of the lengths of the two legs is 100 meters. What are the lengths of the three sides
of this right triangle if the triangle's area is maxed out?
Answers
Answer:
6m by 8m by 10m
Step-by-step explanation:
6²+8²= 100
36+64=100
100=100