The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
4
Answers
Answer:
x = 2√2
Step-by-step explanation:
Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.
Now, since we see that it is also a right angled triangle, it means one angle is 90°.
Let the equal angles be a.
Thus;
a + a + 90 = 180 (since sum of angles in a triangle is 180)
2a + 90 = 180
2a = 180 - 90
2a = 90
a = 90/2
a = 45°
Now, using sine rule, we can find x. Thus;
x/sin 45 = 4/sin 90
sin 90 = 1
sin 45 = 1/√2
Thus;
x = (4 × 1/√2)/1
x = 4/√2
Let's rationalize the denominator to get;
x = (4/√2) × √2/√2
x = (4√2)/2
x = 2√2
Related Questions
When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.
Time of Day When Best Ideas Occur
Time Number of Inventors
6 A.M.-12 noon 271
12 noon-6 P.M. 123
6 P.M.-12 midnight 327
12 midnight-6 A.M. 245
Required:
a. Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?
Answers
Answer:
a.
0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.
0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.
0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.
0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.
b. They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the total outcomes.
We have:
A total of 966 inventors.
Question a:
6 A.M. to 12 noon
271 out of 966, so:
[tex]p = \frac{271}{966} = 0.2805[/tex]
0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.
12 noon to 6 P.M.
123 out of 966, so:
[tex]p = \frac{123}{966} = 0.1273[/tex]
0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.
6 P.M. to 12 midnight
327 out of 966, so:
[tex]p = \frac{327}{966} = 0.3385[/tex]
0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.
12 midnight to 6 A.M.
245 out of 966. So
[tex]p = \frac{245}{966} = 0.2536[/tex]
0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?
0.2805 + 0.1273 + 0.3385 + 0.2536 = 1
They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.
Identify complementary angles in the given figure.
Answers
Answer:
<6 and <4
Step-by-step explanation:
Complemetary angles are angles that their measure add up to 90 degrees
the angles meet this requirment in this image are angle <6 and angle <4
Evan invested $800 in an account that pays 3.25% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Evan would
have in the account 12 years after his initial investment. Round to the nearest tenth
(if necessary).
Answers
Answer:
Evans would have $852.8
Step-by-step explanation:
Given
[tex]PV = \$800[/tex]
[tex]r = 3.25\%[/tex]
[tex]t = 2[/tex]
[tex]n = 1[/tex] --- annually'
Required
The future value
This is calculated using:
[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]
So, we have:
[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]
[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]
[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]
[tex]FV = 800 * (1 .0325)^2[/tex]
[tex]FV = 852.845[/tex]
[tex]FV = 852.8[/tex]
FV =
You have decided after graduating from an institution beyond high school, you want to live on your own. You have entered a career with a net income of $4785 per month. You search the local area finding an amazing deal at Succex Apartment Homes in Grapevine, Texas. Floor plan C fits within your budget.
The apartment is empty when you move in, so you will have to decorate making some adjustments on your financial budget to afford a place to stay. A floor plan will be provided to you.
What is the area of the Masters Bedroom? *
16.51 square meters
19.11 square meters
14.04 square meters
29.4 square meters
Answers
Answer:
16.51 square meters.
Step-by-step explanation:
The area of the bedroom can be determine by the formula:
Area = Length * Width
Length of the room is 4.3 meters while width of the master bedroom is 2.4 meters. The length of the closet is 0.6 meters and width is 1.5 meters. The area can be determined by:
2.4 - 1.5 = 0.9 meters
4.3 - 0.6 = 3.7 meters
Area = 3.7 * 0.9
= 3.3 meters.
Conversion from meters to square meters = 3.3^2
Area = 16.51 square meters.
Write and graph an inequality to represent each situation.
The stock is worth at least $3.5
Answers
Answer:
Step-by-step explanation:
Let stock worth be x.
The inequality will be x ≥ 3.5
The graph will be a number line with numbers 1, 2, 3 , 4 , 5 , 6 . . .
Then darken a small circle at 3.5 and darken the line
moving towards 4, 5 , 6 . . . and finally end with an arrow mark. showing it goes to ∞
This year, a small business had a total revenue of
$
62
,
100.
If this is
35
%
more than their total revenue from the previous year, what was the total revenue the previous year?
Answers
Answer:
21,735
Step-by-step explanation:
i need help with this one plz! (marking BRAINLIST) :)
Answers
Answer: (a) = 110 degrees, (b) = 8
If I understand the picture correctly, (a) wants you to find the angle K. It first shows us that both J to K, and L to K are equal in length of 11, thus there is no deviation in angle 35 degrees with L (so they both equal each other). Therefore, the angle K will equal 180 degrees subtracted by the sum of J and L, which is 110 degrees.
For (b), it appears that all the angles have the same singular mark at the edges, so all sides will equal 8.
I hope this helped!
A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.
Age Group
Hours of Sleep 39 or younger 40 or older
Fewer than 6 38 36
6 to 6.9 61 58
7 to 7.9 76 74
8 or more 65 92
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?
Answers
Answer:
Sleep hours per night is independent.
Step-by-step explanation:
Given the data:
Hours of Sleep 39 or younger 40 or older
> 6 _____38 36
6 to 6.9 _ 61 58
7 to 7.9 __76 74
8 or more 65 92
The Chisquare statistic is to be used to perform the analysis :
The hypothesis :
H0: Sleep hours per night is independent
H1: Sleep hours per night is not independent
χ² = (observed - Expected)² / Expected
To save computation time. We could use a Chisquare calculator to perform the analysis :
The test statistic = 4.0061
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (4-1)*(2-1) = 3*1 = 3
The Pvalue = 0.261
Since, Pvalue > α ; We fail to reject the H0 ;and conclude that sleep hours per night is independent.
______________total ___%
> 6 _____38 36__ 74 __ 14.8
6 to 6.9 _ 61 58 __ 119 __23.8
7 to 7.9 __76 74___150__30
8 or more 65 92___157__31.4
_______240 _260__500_100
Identify horizontal or vertical compression stretch of the function g(x) = 6x
Answers
Answer:
dhjfydhftb7cuvdihcdjxuihy
Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.
$650, 5%, 1 year
Help
Answers
Answer:
32.5
Step-by-step explanation:
I=Prt
I= 650*0.05*1
I=32.5
01 1 point If a customer spends more than $20, he receives a 10% discount on his total bill: What does a customer whose bill is $80 /pay?
Answers
Answer:
try 40%
Step-by-step explanation:
help fast The graphs below have the same shape. What is the equation of the red
graph?
no links plz
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]B)\text{ } G(x)=x^3-5[/tex]
»»————- ★ ————-««
Here’s why:
According to the question provided, functions 'f' and 'g' are the same shape. The parent function 'f' is shifted 5 units down to create function 'g'.⸻⸻⸻⸻
[tex]\boxed{g(x)=x^3-5}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Choose all of the symbols that make the following sentence true.
4 ^0 ___ 5 ^-1
=
<
≥
≤
≠
>
Answers
Answer:
≠ and >
Step-by-step explanation:
_________________
What is the nearest quarter hour to 12.09
Answers
Answer:
I think 12:00
Step-by-step explanation:
please thank my answer
Answer:
I think 12:15
there only 6 minutes to 12:15. But at 12:00 there are 9 minutes
A car that is normally $4200 is on sale for 80% of its original cost.
what is the sale price of the car?
Answers
Answer:
$3360
Step-by-step explanation:
4200(.80) = 3360
anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car
i need help with this one plz! (marking BRAINLIST) :)
Answers
Answer:
Sinx = c/b
cosx = a/b
tanx = c/a
Step-by-step explanation:
B is hypotenuse, a is adjacent, c is opposite of angle x.
Sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent
Can someone please help me with this
Answers
Answer:
y = 4x
y = -1/3 × x + 6
y = x + 1
y = 1
y = 5x
Step-by-step explanation:
the slope of a line is the factor of x in the equation representing the ratio of y/x. it stands for the number of units y changes, when x changes by another number of units.
like the factor 4 tells us that when x changes by 1, then y changes by 4.
a line parallel to another line means their slopes are identical (otherwise they could not be parallel).
the slope of a perpendicular line (cutting the other line in a 90 degree angle) is simply reversing y and x in the slope ratio. so, a slope of 4 (4/1) would simply turn into 1/4.
now the 5 tasks are easy, right ?
A y=4x-1, B y=4x + c
and because B passes through the origin = (0,0),
c is 0 (0=4×0 + c = c)
B y = 4x
A y=-3x+1, B y=-1/3 × x + c
and B passes through (12,2), 2 = -1/3 × 12 + c = -4 + c,
c = 2 + 4 = 6
B y = -1/3 × x + 6
A y = ax + c for (5,6) and (7,8), B is identical
6 = a×5 + c => c = 6 - a×5
8 = a×7 + c => 8 = a×7 + 6 - a×5 = a×2 + 6
=> a×2 = 8-6 = 2
=> a = 1, c = 6 - 1×5 = 1
=> A and B y = x + 1
A is vertical. B is perpendicular to it. perpendicular to vertical is horizontal. so, B is a flat line. which means y is a constant value (the same value for whatever value of x you want to use). so it goes flat in parallel to the x-axis through what value of y ? the point (4,1) tells us that y=1
and that is the equation for B
A 15x -3y = -6 => 3y = 15x + 6 => y = 5x + 2
B is parallel, so y = 5x + c
and B passes through (4,20), 20 = 5 × 4 + c = 20 + c,
c = 20 - 20 = 0
B y = 5x
You want to deposit $1000 in a savings account for 3 years. One bank
adds a $100 bonus to your principal and offers a 2% simple annual
interest rate. Another bank does not add a bonus, but offers 6% simple
interest per year. Which bank should you choose? Explain.
Answers
Answer:
2nd bank
Step-by-step explanation:
bank one:10*2=(20*3=60)
$1000+$100+$60=$1160
total after 3 years = $1160
bank two:$10*6=(60*3=180)
$1000+$180=$1180
total after 3 years = $1180
Hector has 10 cups of flour which equation shows how to determine the number of 2/5 of a cup servings there are in the 10 cups of flour?
Answers
Answer:
10 divided by two-fifths = 25.
In a triangle ABC, let G denote its centroid and let M,N be points in the interiors of the segments AB,AC, respectively, such that M,G,N are collinear. If r denotes the ratio of the area of triangle AMN to the area of ABC then find r.
Answers
Answer: hello options related to your question is missing attached below is the missing option
answer :
4/9 ≤ r < 1/2 ----- ( c )
Step-by-step explanation:
Given that G denotes the centroid of triangle ABC and points M, N are points found in the interiors of segments AB,AC
also Given that r denotes ratio of triangles AMN to triangle ABC
attached below is a detailed solution
Heeeeeeeeeeelppppppppppppppppppp
Answers
A)
So please brainliest my answer I would really appreciate it and best of wishes!!
Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?
Answers
Step-by-step explanation:
[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3
(⅛ + ¾ +1)n = 48.75
15/8 n = 48.75
1.875 n = 48.75
n = 48.75/1.875
n = 26
so, the cost of :
the brush = ⅛×26 = $ 3.25
the sketchbook = ¾×26 = $ 19.5
the pain set = $ 26
What is the equation of a circle with radius 4 and center (0,8)?
Answers
The equation of circle with the center at (h,k) is:
[tex] \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }[/tex]
r stands for radius. Therefore r^2 = diameter or 2×radius.
The question has already given the information we need, which are:
radius = 4the center at (0,8)Since the center is (h,k) - therefore the center is at h = 0 and k = 8 making it (h,k) = (0,8).
Substitute the values in the equation:
[tex] \large{ {(x - 0)}^{2} + {(y - 8)}^{2} = {4}^{2} }[/tex]
Simplify to the simplest form
[tex] \large \boxed{ {x}^{2} + {(y - 8)}^{2} = 16} \: \: \: \: \huge{ \green{\checkmark}}[/tex]
Answer
The equation of a circle is x^2+(y-8)^2 = 16If JK is formed by J(-7,-8) & K(1,4), determine if L(-9,5), lies on the perpendicular bisector.
Part A: What elements do you you need to know to confirm that Point L is on the perpendicular bisector of JK?
Part B: Find the elements you described in Part A , explain your work.
Part C: Verify if Point L is on the perpendicular bisector of JK. Justify your conclusion.
Answers
Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
Bisector Theorem: When a point has been on the perpendicular bisector of a segment, the perpendicular bisector is equivalent towards the segment endpoints. They understand that conversation also valid in addition to the Theorem including its perpendicular bisector. So the distance b/w L and J, L, and k must be found. Examine it then.
For point b:
Calculating the distance among two point:
[tex]d_0 = \sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}[/tex]
Calculating the distance among J and L
[tex]d_1 = \sqrt{((-9)-(-7))^2 + (5)-(-8))^2}[/tex]
[tex]=\sqrt{(-2)^2+(13)^2}\\\\ = \sqrt{173}[/tex]
Calculating the distance among K and L
[tex]d_2 = \sqrt{((-9)-(1))^2 + (5)-(4))^2}[/tex]
[tex]=\sqrt{(10)^2+(1)^2}\\ = \sqrt{101}[/tex]
For point c:
As these two distances are not equal, L doesn't really lie on the JK bisector.
PLZ HELP ASAP
The white triangle drawn on the road sign in the picture has a height of 8 and a base of 5 which formula would be correct to find the area of this triangle
1) A= 1/2 (8) (5)
2) A=2(8)+2(5)
3) A=1/2(8+8)(5+5)
4) A=2(8)(8)+2(5)(5)
Answers
Answer:
[tex]\text{1) }\frac{1}{2}(8)(5)[/tex]
Step-by-step explanation:
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex]. Since we're given a base of 5 and a height of 8, the area is given by [tex]\boxed{\text{1) }\frac{1}{2}(8)(5)}[/tex].
A table cost $ 495.00 There is a 9% tax. What is the final price?
Answers
Answer:
i also need help with these one please help
Step-by-step explanation:
Answer:
$539.55
Step-by-step explanation:
Is 0.01011011101111011111 rational or irrational?
Answers
Answer:
It is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful....What is the solution to this system of equations?
Answers
Answer:
the equation has no solution
si se vendieron 8 refrescos y cada uno tiene un costo de $9.50 ¿cuánto dinero colectó
con esa venta?
Answers
find the value of variable x
Answers
Answer:
[tex]x=33[/tex]
Step-by-step explanation:
Since all three angles marked form one side of a line, they must add up to 180 degrees. Therefore, we have the following equation:
[tex]90+(x+1)+(3x-43)=180,\\x+1+3x-43=90,\\4x-42=90,\\4x=132,\\x=\boxed{33}[/tex]
Answer:
x=33
Step-by-step explanation:
The three angles form a straight line, which is 180 degrees
90+ x+1 + 3x-43 = 180
Combine like terms
4x+48 = 180
Subtract 48 from each side
4x+48-48 = 180-48
4x = 132
Divide by 4
4x/4 = 132/4
x=33