The triangle below is equilateral. Find the length of side x in simplest radical
form with a rational denominator.
Answers
Answer:
[tex]\frac{4\sqrt{3} }3}[/tex]
Step-by-step explanation:
Since it is an equilaterla triangle, we can see the side opposite to that of side length 4 is 60 degrees. Since the other angle is a right angle (90 degrees), we can find that the other side is 30 degrees (the degrees add up to 180). We can also see that this is a 30-60-90. We can see that the side x, through the identity (you can find 30-60-90 identity online), we see that the side x is [tex]\frac{4}{\sqrt{3}}[/tex]. However, it is also asking us to simplify this, so we multiply the top and bottom by [tex]\sqrt{3}[/tex] and get [tex]\frac{4}{\sqrt{3} } = \frac{4\sqrt{3} }{3}[/tex]
Related Questions
What is the range of tanx?
1. all real numbers
2. -1 ≤ y ≤ 1
3. y > 0
Answers
all real numbers except the 90 and 270 because of cosx
y=(x^4)-(6^3)+(50x^2)+122x=65
find the zeros
Answers
pretty sure this is a joke question about south park my teacher put on my test but i dont watch south park
the question is
TRUE or FALSE
if you ever come across a physican named dr. doctor RUN!
Answers
Answer: true you should run
Determine if the sequence is geometric . If it is , find the common ratio , the explicit formula and the recursive formula .
1. -40 , 20 , -100 , 500
2. 4 , 20 , 100 , 500
3. 4 , 24 , 144, 864
5. 3 , -12 , 48 , -192
Answers
Step-by-step explanation:
if it is a geometric sequence, then
sn = sn-1 × r
with r being the common ratio.
1.
s2 = s1 × r
20 = -40 × r
r = 20/-40 = -1/2
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
-100 = 20 × -1/2 = -10
this is wrong, so, it is not geometric.
2.
s2 = s1 × r
20 = 4 × r
r = 20/4 = 5
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
100 = 20 × 5 = 100
s4 = s3 × r
500 = 100 × 5 = 500
this is all correct, so, it is geometric.
sn = sn-1 × 5
sn = s1 × 5^(n-1) = 4 × 5^(n-1)
3.
s2 = s1 × r
24 = 4 × r
r = 24/4 = 6
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
144 = 24 × 6 = 144
s4 = s3 × r
864 = 144 × 6 = 864
this is all correct, so, it is geometric.
sn = sn-1 × 6
sn = s1 × 6^(n-1) = 4 × 6^(n-1)
5.
s2 = s1 × r
-12 = 3 × r
r = -12/3 = -4
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
48 = -12 × -4 = 48
s4 = s3 × r
-192 = 48 × -4 = -192
this is all correct, so, it is geometric.
sn = sn-1 × -4
sn = s1 × (-4)^(n-1) = 3 × (-4)^(n-1)
n is m% of what?
It DEFINITELY a variable
Answers
Determine the y-intercept of the following equation.
(-2 - 1)(2+3) = y
Answers
Answer:
(0,-15)
Step-by-step explanation:
i think.. trust someone else!! I'm not 100% sure...
HELP PLZ PLZ ITS DUE IN 30 MINUTES
Answers
Answer:
wouldn't that be...24x²?
A man earns $9.99 for each of the first 36 hours he works in one week and $14.99 in overtime pay for each
additional hour he works in the same week. How much money will he make if he works 46 hours in one week?
Answers
Answer:
459.54
Step-by-step explanation:
46(9.99)
=459.54
Answer:
$159.89
Step-by-step explanation:
36 hours + 10 hours = 46
14.99 * 10 = 149.9
(36 hours) $9.99 + (overtime pay) $149.9 = (Total money) $159.89
$9.99 + $149.9 = $159.89
$159.89
Write an equation in slope-intercept form of the line that passes through (−1, 4) and (0, 2)
Answers
[tex]\text{Given that,}\\\\(x_1,y_1) = (-1,4), ~~ (x_2,y_2) =(0,2)\\\\\\\text{Slope,}~ m =\dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{2-4}{0-(-1)} = \dfrac{-2}{0+1} = -2\\\\\text{The equation with given points,}\\\\y-y_1 =m(x-x_1)\\\\\implies y -4 = -2(x+1)\\\\\implies y = -2(x+1)+4\\\\\implies y = -2x -2 +4\\\\\implies y = -2x +2\\\\\text{This is the slope-intercept form(y =mx +b)}[/tex]
JACKIE BROUGHT 3/4 OF A GALLON OF ICED TEA TO THE PARTY. BILL BROUGHT 7/8 OF A GALLON OF ICED TEA TO THE SAME PARTY. HOW MUCH ICED TEA DID JACKIE AND BILL BRING TO THE PARTY?
Answers
Answer:
your welcome... hope this helps
Step-by-step explanation:
What are all the fractions that are between 1/2 and 1.
Answers
Answer:
2/4, 3/5,3/4, 2/3,13/25, 27/50 11/20, 14/25, 29/50,31/50, 63/100,16/25,33/50,17/25,7/10,18/25,37/50,19/25,77/100,39/50,4/541/50, 83/100, 21/25 , 17/20, 43/50 , 87/100,22/25,9/10, 91/100, 23/25, 93/100, 47/50, 19/20 , 24/25 97/100, 49/50,99/100(note that I did not state all the fractions between 1/2 and 1)
Step-by-step explanation:
Firstly one half(1/2) represents 0.50 as a decimal and 1 would be 1.00
This is like saying finding Fractions that give you percentages between 50% and 100%
for example:
you could simplify 52/100 and get 31/50
31/50 as a decimal would be 0.52 and 0.52 falls between(0.50 and 1.00) 1/2 and 1
example 2: 89/100= 0.9 (same as0.90) and [90/100] is same as 9/10 = 0.9
0.90 or 0.9 (zero point nine) is not the same as 0.09(zero point zero nine
If you are using a casio calculator, you can simplify the fraction by putting in your numerator then pressing |a b/c| button then enter the denominator, then the calculator should simplify the fraction, if the fraction remains the same, this means that it cant be further simplified.if your calculator has
| a b/c| then you can also use it.
or use an online calculator or simplify if you wish
To find the decimal of that fraction you can simply divide the numerator by the denominator, Example; 82/100 is same as 0.82 and 41/50 is same as 0.82.
2(4x - 1) < 4(3x+1), where x ∈ {set of all negative Integers}
Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
Given inequation:
[tex]\sf 2(4x-1)<4(3x+1), x\in \{Set\ of\ negative\ integers\}[/tex]
[tex]\sf\longmapsto 8x-2<12x+4[/tex]
[tex]\sf\longmapsto 8x-2-4<12x+4-4[/tex]
[tex]\sf\longmapsto 8x-6<12x[/tex]
[tex]\sf\longmapsto 8x-6-8x<12x-8x[/tex]
[tex]\sf\longmapsto -6<4x[/tex]
[tex]\sf\longmapsto 4x>-6[/tex]
[tex]\sf\longmapsto \dfrac{4x}{4}>\dfrac{-6}{4}[/tex]
[tex]\sf\longmapsto x >-1\dfrac{1}{2}[/tex]
Therefore:
[tex]\sf\longmapsto\boxed{ x=\{-1\}}\ \ Ans.[/tex]
hehehejejwjjejejjejejwkwkwkekekejjeue
Answers
Answer: The last answer is correct.
Step-by-step explanation:
f (x) = x^2 g (x) = (x-9)^2 +3 we can think of g as a translated (shifted) verson of f. complrte the description of the transformation
Answers
Step-by-step explanation:
Given:
f(x) = x² and g(x) = (x - 9)² + 3If g is the translation of f then it is:
g(x) = f(x - 9) + 3This is a shift right 9 units and up 3 units
Answer:
Yes
Step-by-step explanation:
f(x)=x²
y=x²Shift nine units right
y={x-9)²Shift 3 units up
g(x)=(x-9)²+3$22.66 is 2% of what number
Answers
Answer:
1,133
Step-by-step explanation:
2%=0.02
$22.66÷0.02=$1,133
You invested $5,000 in a 10 year CD at the age of 12. The account pays 2.5% interest compounded continuously. How much money will you have after 10 years? (Round to the nearest cent.)
Answers
Answer:
Do PRT: 5009.31
Step-by-step explanation:
Princable: 5000
Rate: 2.5
Time: 10
Answer:
After a discount of 25%, the sale price of a game system is $149.25. what is the original price?
Answers
Answer:111.94
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
25% = 25/100 = 25 ÷ 100 = 0.25.
100% = 100/100 = 100 ÷ 100 = 1.
New value =
149.25 - Percentage decrease =
149.25 - (25% × 149.25) =
149.25 - 25% × 149.25 =
(1 - 25%) × 149.25 =
(100% - 25%) × 149.25 =
75% × 149.25 =
75 ÷ 100 × 149.25 =
75 × 149.25 ÷ 100 =
11,193.75 ÷ 100 =
111.9375 ≈
111.94
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?
-Whats the First mechanic: $ -----per hour
-Whats the Second mechanic: $ ---- per hour
Answers
Two mechanics worked on a car, The first mechanic worked for 20 hours and the second mechanic worked for 5 hours together they charged a total of $1150.
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
* Their rate is dollars per hour ($/hr)
mechanic #1 worked for 20 hours (hr × $/hr = $)
20x = money earned by mech#1
and mechanic #2 worked for 5 hours
5y = money earned by mech#2
together they charged a total of $1150. So the amount of money earned by both mechanics.
20x + 5y = 1150
the sum of the two rates was $95 per hour.
x + y = 95
which means
x = 95 - y
plug (95 - y) in for "x" in the other equation to get everything in terms of one variable.
20(95 - y) + 5y = 1150
solve for y
1900 - 20y + 5y = 1150
1900 - 15y = 1150
-15y = 1150 - 1900
-15y = -750
y = -750/-15
y = 50 $/hr
Now use this to solve for x
x + y = 95
x + 50 = 95
x = 95 - 50
x = 45 $/hr
mech#1 charged 45$/hr
mech #2 charged 50$/hr
How can multistep linear equations be written to represent different
scenarios?
Answers
Answer:
Linear equations use one or more variables where one variable is dependent on the other. Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit
The following system of linear equations is solved by graphing them on the coordinate plane.
y=3x−2y=−35x−1
Which ordered pair is the best approximation of the solution to the system?
(0,−1)
(−1,0)
(−1,−1)
(1,1)
Math lol
Answers
Answer:
(0, -1)
Step-by-step explanation:
Maybe you're graphing ...
y = 3x -2y = -3/5x -1These lines meet in the 4th quadrant. The closest point among the answer choices is on the negative y-axis: (0, -1).
Hanna has 16 pencils. She gets 3 new
pencils from Mrs. Lewis. She divides
the pencils equally between her 2
sisters. How many pencils does each
sister get?
Answers
Answer:
9.5
Step-by-step explanation:
If Hanna starts off with 16, and Mrs. Lewis GIVES(add) her 3 more, then she has 19 because 16+3=19. Then we divide by 2 because there are 2 sisters. so 19/2 = 9.5
Hello! I hope this helped you. If this is wrong please let me know. Thank you.
Anna categorized her spending for this month into four categories: Rent, Food, Fun, and Other.
If Anna spent a total of $2900 this month, how much did she spend on Rent?
Answers
Answer:
.26 * 2900= 754 dollars
Step-by-step explanation:
I'm not sure if it's right.
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
○ A. Zero
○ B. Two
○ C. Infinity many
○ D. One
Answers
Explanation: the solution of two lines on a graph is where they intersect.
Find the length x. Please help
Answers
Step-by-step explanation:
# easy learning
good luck and god Blees you
anyone willing to help??
Answers
For the expression:
(9x^2 + 4y^2 -12xy) / (4y^2 - 9x^2)
Find the domain
Answers
Answer:
Interval Notation (-∞, ∞)
Set-Builder Notation: {x|x ∈ R} (all real numbers = R)
Step-by-step explanation:
I plugged this into a graphing calculator and was able to find the domains by looking at where the lines stopped (they didn't stop) and wrote the f(x) based off of it
In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8. . A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.Is 20 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?
Answers
Answer:
Yes, 35 feet is enough
The angle of elevation is 4.1º
Which statement is true about point Y?
Point Y is the center of the circle that passes through points D, F, and N.
Point Y is the center of the circle that passes through points M, N, and E.
Point Y is the center of the circle that passes through points L, M, and N.
Point Y is the center of the circle that passes through points D, E, and F.
Answers
Answer:
D, E and F
Step-by-step explanation:
Beause y is a point. It is a prime example physics.
Simplify. (5b2−3b+2)+(2b−4)
A.5b2+5b+6
B.5b2−5b−6
C.5b2−b−2
D.6b4−2
Answers
Answer:
5b2 - b -2
Step-by-step explanation:
The answer is (c)
5b^2-b-2
A group of students organized a car wash to raise money for a local charity. The students charged $9.99 for each car they watched.In 3.5 hours they washed 14 cars.at that rate how much money could they earn in 8 hours?
Answers
Answer:
First you would divide 12 cars by 3 hours to see how many cars get washed per hour
Then you know that 4 cars get washed in one hour so you multiply it by $5.00 because you want to see how much money they earn in one hour
After you know they earn $20.00 per hour you multiply that by 8 because you want to see how much money they earn in eight hours
So your final answer is $160 for washing cars in 8 hours