Please help!
If we write [tex]\sqrt{2} + \frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}}[/tex] in the form [tex]\frac{a \sqrt{2} + b \sqrt{3}}{c}[/tex], such that [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are positive integers and [tex]c[/tex] is as small as possible, then what is [tex]a+b+c[/tex]?
Answer:
[tex]a+b+c=9+8+6=23[/tex]
Step-by-step explanation:
Let’s first simplify our expression. We have:
[tex]\displaystyle {\sqrt2+\frac{1}{\sqrt2}+\sqrt3+\frac{1}{\sqrt{3}}[/tex]
For the second term, multiply both the numerator and denominator by √2. This yields:
[tex]\displaystyle \frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex]
Similarly, for the fourth term, multiply both the numerator and denominator by √3. This yields:
[tex]\displaystyle\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
Hence, our expression is now:
[tex]\displaystyle =\sqrt{2}+\frac{\sqrt{2}}{2}+\sqrt{3}+\frac{\sqrt{3}}{3}[/tex]
Let’s combine them. First, we will need common denominators.
Our denominators are 2 and 3. So, our common denominator will be its LCM.
The LCM of 2 and 3 is 6.
Hence, let’s make each term’s denominator 6.
For the first term, we can multiply both layers by 6. Hence:
[tex]\displaystyle \sqrt{2}=\frac{6\sqrt{2}}{6}[/tex]
For the second term, we can multiply both layers by 3. Hence:
[tex]\displaystyle \frac{\sqrt{2}}{2}=\frac{3\sqrt{2}}{6}[/tex]
For the third term, we can multiply both layers by 6. Hence:
[tex]\displaystyle \sqrt{3}=\frac{6\sqrt{3}}{6}[/tex]
And for the last term, we can multiply both layers by 2. Hence:
[tex]\displaystyle \frac{\sqrt{3}}{3}=\frac{2\sqrt{3}}{6}[/tex]
So, our expression is:
[tex]\displaystyle =\frac{6\sqrt{2}}{6}+\frac{3\sqrt{2}}{6}+\frac{6\sqrt{3}}{6}+\frac{2\sqrt{3}}{6}[/tex]
Add:
[tex]\displaystyle =\frac{6\sqrt{2}+3\sqrt{2}+6\sqrt{3}+2\sqrt{3}}{6}[/tex]
Combine like terms:
[tex]\displaystyle=\frac{9\sqrt{2}+8\sqrt{3}}{6}[/tex]
This cannot be simplified. So, c is as small as possible.
Hence: a=9, b=8, and c=6.
Therefore:
[tex]a+b+c=9+8+6=23[/tex]
3x^2y^2/6xy
please answer asap
Answer:
-3xy • (xy - 2)
Step-by-step explanation:
if ur supposed to be simplyfying it that should be the answer i think
Answer: 3xy⋅(xy−2) Your Welcome:)
:
PLEASE HELP IM TIMED
Jessica and Jonathan need to figure out how much to charge for their lemonade. First, they need to know how much they spent on ingredients! As seen in the table, they bought 6 containers of lemon juice, 2 packages of sugar, and 2 bottles of water.
What is the total amount of money they spent?
1) $12.90
2) $16.34
3) $18.75
4) $20.16
Answer:
20.16
Step-by-step explanation:
add
Answer:
20.16
Step-by-step explanation:
Got it on Freckle
Write an expression
Your cellphone costs $0.50 for the first minute and $0.35 for
each additional minute.
Answer:
0.50+0.35x
Step-by-step explanation:
Answer:
0.5+0.35m
Step-by-step explanation:
As an estimation we are told 5 miles is 8 km.
Convert 30 miles to km.
Answer:
48km
5miles = 8km
×6 = ×6
30miles= 48km
I need help with this prob
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 18 fl oz per . How fast was the pipe leaking in gallons per ?
Answer:
0.140625 gallons per
Step-by-step explanation:
By doing a quick search we discover that there are 1 fl oz is equal to 0.0078125 gallons. Therefore, in order to find out how fast the pipe was leaking in gallons, we simply multiply the rate of fl oz by the number of gallons for every fl oz like so...
18 fl oz * 0.0078125 gallons = 0.140625 gallons
draw a rough sketch of a closed curve that is not a polygon
Answer:
I have inserted a photo.
Hope this helps :D
What is 53 percent of 49?
2.597
25.97
259.7
2,597
Answer:
25.97
Step-by-step explanation:
.53 x 49 = 25.97
school and eat breakfast, and a 60% chance that she will be late for school or eat breakfast. What
is the probability that Elaine will eat breakfast
HURRY PLEASE HELP ME!!!This graph shows a bicyclist moving at a constant rate. Write and equation for bicycle rider A.
Answer:
y= 30x
tep-by-step explanation:
At a grand-opening sale, 20% of the first 500 customers won a prize. How many of the first 500 customers won a prize? A50 B100 C200 D1,000
Answer:The Answer is ________ Please Make sure You Put it In and Trust Have a wonderful day/Night:)
Step-by-step explanation:
Answer:
100.
Step-by-step explanation:
500/10=50 =10%
50 x 2 = 100 = 20%
I hope this helps :D
NEED HELP ASAP THANKS
Answer:
D. 7 1/2
Step-by-step explanation:
-3 divided by (-2/5) = 7 1/2
HELP WILL GIVE BRAINLIEST
Answer:
A. 2000 square inches
B. 53.1 square inches
Given: O ∈ AB , ON is ∠ bisector of ∠AOC, OF is ∠ bisector of ∠COB, m∠FOB=70°. Find: m∠AON
Answer:
AOC = 20 degrees
Step-by-step explanation:
We know that FOB is 70 degrees, and COF is 90 degrees. So just add 70+90 and get 160 degrees. Then you subtract that from AOB which is 20 degrees.
Pleasee need help!!Calculate the value of x in the diagram.
A. 40°
B. 50°
C. 80°
D. 90°
Answer:
d
Step-by-step explanation:
Answer:
D. 90
Step-by-step explanation:
So you're given 130 degrees. that 130 angle and the angle inside the triangle next to it, are supplementary which means they add up to 180. So you have a 40 degree and a 50 degree angle + x. together they must add up to 180
40+50+x=180
90+x=180
x=90
Log3(2)+log3(8)
Pls help asap
Answer:
[tex]log_{3}[/tex] 16
Step-by-step explanation:
Using the rule of logarithms
logx + logy = log(xy), then
[tex]log_{3}[/tex]2 + [tex]log_{3}[/tex]8
= [tex]log_{3}[/tex](2 × 8)
= [tex]log_{3}[/tex] 16
What are all them pls i am stuck
Answer:
6. is proportional, 7. is not proportional, 8. is not proportional
Step-by-step explanation:
15 POINTS WILL GIVE BRAINLIEST
Find the range of the following piecewise function.
f(x){x^2+2 if -5≤x<3}
f(x){x-4 if 3≤x<7}
[27,3)
(-22,3]
(27,3]
[-22,3)
Answer:
[27,3) i think
Step-by-step explanation:
Two trapezoids below are similar what is the length of RS?
9514 1404 393
Answer:
11.5 m
Step-by-step explanation:
The fact that the figures are similar means the side lengths are proportional:
RS/QT = BC/AD
RS/(7 m) = (2.3 m)/(1.4 m)
RS = (7 m)(2.3/1.4) . . . . . . multiply by 7 m
RS = 11.5 m
Find the slope of the following graph 1) 0 2) No slope 3) 1
Answer:
it is 0
Step-by-step explanation:
hope it helps <3
Using the slope concept, it is found that this graph has a slope of 0.
Given two points (x,y) on a linear graph, the slope is given by the change in y divided by the change in x, that is:
[tex]m = \frac{\Delta_y}{\Delta_x}[/tex]
In this question, two of the points are: (1, 1.5) and (2, 1.5). Then, the slope is:
[tex]m = \frac{\Delta_y}{\Delta_x} = \frac{1.5 - 1.5}{2 - 1} = \frac{0}{1} = 0[/tex]
This graph has a slope of 0.
A similar problem is given at https://brainly.com/question/5029023
The following table shows the salary of 7 people in an office last year.
Name Income
Andy £13500
Bevan £27500
Cheryl £13750
Deva £79000
Elliott £19250
Frankie £27500
Grace £15000
a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service.
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?
Answer:
a. Mean = £27928.57
b. Mean without Deva's income = £19416.67
Step-by-step explanation:
The mean is calculated by dividing the sum of values by number of values. Given 7 values will be used to calculate mean.
So,
Number of values = n = 7
Now,
[tex]Mean = \frac{Sum}{No.\ of\ values}\\=\frac{13500+27500+13750+79000+19250+27500+15000}{7}\\=\frac{195500}{7}\\=27928.5714..[/tex]
Rounding off to two decimal places
Mean income = £27928.57
Now we have to calculate mean without Deva's income so the number of values will be 6 and the sum will be:
[tex]Sum = 195500-79000 = 116500[/tex]
The mean without Deva's income is:
[tex]Mean = \frac{116500}{6} = 19416.6666..[/tex]
Rounding off to 2 DP
Mean = £19416.67
Hence,
a. Mean = £27928.57
b. Mean without Deva's income = £19416.67
I need help with the equation inserted in the picture.
Answer:
x = 4
-4x+21 => 5
Step-by-step explanation:
The given triangle in the picture is isosceles triangle which means that two sides of the triangle are equal.
So,
[tex]Side\ 1: -4x+21\\Side\ 2: -4x+21\\Side\ 3: 6\\Perimeter = 16[/tex]
Now
Putting all the values in equation for perimeter
[tex]Side\ 1+Side\ 2+Side\ 3 = 16\\-4x+21 -4x+21 + 6 =16\\-8x +48 = 16\\-8x = 16-48\\-8x = -32\\\frac{-8x}{-8} = \frac{-32}{-8}\\x = 4[/tex]
Putting x = 4 in side 1
[tex]=-4(4)+21\\= -16+21\\=5[/tex]
Hence,
x = 4
-4x+21 => 5
Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Mariana and Russell both went bowling last weekend, but not together. Mariana went during
open bowling time, paying $10 for shoe rental and $1 per hour. Russell went on family night,
when each hour was $2 and shoe rental was $3. As it turned out, they played for the same
number of hours and spent the same amount. How much did each one spend? How many
hours did each one bowl?
Mariana and Russell each spent $
and bowled for
hours.
Answer:
16
m=10 per hour=1
Step-by-step explanation:
share £80 in the ratio 1:3:4
Answer:
£10, £30, £40
Step-by-step explanation:
Divide the share by the sum of the numbers in the ratio.
1 + 3 + 4 = 8
80 / 8 = 10
Multiply each number in the ratio by 10 to find the value of each share.
1 × 10 = 10
3 × 10 = 30
4 × 10 = 40
Answer:
Step-by-step explanation:
total ratio=1+3+4
=8
first part
1/8x 80euros=10euros
second part
3/8 x 80euros=3x10euros
=30euros
third part
4/8x80euros=4x 10 euros
=40euros
Plz help I’m desperate
Answer:
Step-by-step explanation:
f(-2)=5
Since Pemdas is used, taking care of that x is squared before multiplying -3 to make sure you don't mess up the signs.
Enjoy your day love <3
Given f(x) = -2x³ + x² - 2 find f(1) -3 -1 1 3
Answer:
-3
Step-by-step explanation:
Substitute -1 into the expression for every place of x, and evaluate it.
i am in need of help
Answer:
(in the image)
Step-by-step explanation:
for the slope one - both triangle a and b have a slope of 5/3 (b's goes from 15/9 to 5/3 because of simplifying)
for the second one - 5/3=15/9 because the sides of both triangles correspond
My Answer to that:
5 - 3= 15 - 9 (Statement)- 5/3 = slope (Reason)
Definition of slope (Statement) - triangle A is similar to triangle B (Reason)
- sorry if wrong but that is the answer I would put
graph y = 4x-9 please
Step-by-step explanation:
Just take two random points, always remember ,take x=0 and find his correspondent y
in this case y=4*0-9=-9
first point (0,-9)
second one:
take any x you want, I took 2 randomly, and y will be
y=4*2-9=8-9=-1
second point is (2,-1)
find these points on graph and connect them with a ruler ! And that is the line you are searching for!
We want to graph the line y = 4*x - 9.
The graph can be seen at the end of the answer.
To graph a given linear function, we need to find two points that belong to the function, and then connect them with a line.
To find the points we just evaluate the function in two different values of x, so let's do that.
For x = 0 we have:
y = 4*0 - 9 = -9
Then we have the point (0, -9)
For x = 1 we have:
y = 4*1 - 9 = 4 - 9 = -5
Then we have the point (1, -5)
Now we just can graph these two points on a coordinate axis, and connect them with a line.
The graph is shown below
If you want to learn more, you can read:
https://brainly.com/question/18196858
In a flash of sheer brilliance, Stefan invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Stefan wants to travel back in time, x, and how much electricity (in megawatts) his time machine needs, y .
Answer:
[tex] y = x [/tex].
Step-by-step explanation:
Equation to represent the proportional relationship between years (x) and megawatts (y) is represented as [tex] y = kx [/tex].
Where k = constant of proportionality, which is y/x.
To find k, we can use the coordinates of any point on the line. Let's use (4, 4).
k = y/x = ⁴/4 = 1
Substitute k = 1 into [tex] y = kx [/tex].
✅Equation representing the relationship would be:
[tex] y = (1)x [/tex].
[tex] y = x [/tex].
