Answer:
See Explanation
Step-by-step explanation:
Let us assume that [tex] \sqrt 3 - \sqrt 5[/tex] is a rational number.
So, it can be expressed in the form of [tex] \frac{p}{q} [/tex] where p and q are integers.
[tex]\therefore \sqrt 3 - \sqrt 5=\frac{p}{q}[/tex]
[tex]\therefore \sqrt 3 =\frac{p}{q}+ \sqrt 5[/tex]
[tex]\therefore \sqrt 3 =\frac{p+q\sqrt 5}{q}[/tex]
Squaring both sides:
[tex] (\sqrt 3) ^2 =\bigg(\frac{p+q\sqrt 5}{q}\bigg ) ^2 [/tex]
[tex]\therefore 3 =\frac{p^2 +5q^2 +2\sqrt 5 pq}{q^2 } [/tex]
[tex]\therefore 3q^2 ={p^2 +5q^2 +2\sqrt 5 pq}[/tex]
[tex]\therefore 0 = p^2 +5q^2 -3q^2 +2\sqrt 5 pq [/tex]
[tex]\therefore - 2\sqrt 5 pq=p^2 +2q^2 [/tex]
[tex]\therefore \sqrt 5 = \bigg (\frac{p^2 +2q^2}{-2pq} \bigg) [/tex]
[tex]\therefore \sqrt 5 = - \bigg(\frac{p^2 +2q^2}{2pq} \bigg) [/tex]
Since, p and q are integers so [tex] - \bigg(\frac{p^2 +2q^2}{2pq} \bigg) [/tex] is rational.
[tex]\therefore \sqrt 5 [/tex] is also rational.
But it contradicts the fact that [tex]\sqrt 5 [/tex] is irrational.
Hence, our assumption that [tex] \sqrt 3 - \sqrt 5[/tex] is rational is wrong.
[tex] \therefore \sqrt 3 - \sqrt 5[/tex] is irrational.
please please help!!, please show help if possible :D
Brad swims 4 laps every 6min how long does it take him to swim 14 laps?
Answer:
21 minutes
Step-by-step explanation:
4 goes into 14 three times which is 18 minutes. We need 2 more laps four for 6 can be 2 for 3.
A quadratic function is shown on the graph below.
Which statement BEST describes its domain and range?
PLEASE HELP ME! THANK YOU!
The domain is the input value which is the x values
Because the graph continues off the page in a U shape the domain is any real number.
The bottom of the U is at x = 3 and y = 2 so the range is any number greater than or equal to 2
The answer is the first choice.
Please help me! I'm stuck and I don't know what to do!!! By the way, please don't insert a link, as I cannot reach them.
Answer:
study more so you can understand
Your parents take you to dinner at your favorite restaurant for your birthday. The cost of the
meal is $75. The restaurant adds a 10% tax to the meal. What is the total cost of the meal
including tax?
$
Answer:
$82.5
Step-by-step explanation:
75x 0.1 = 7.5
75 + 7.5 =
$82.5
A right triangle has legs that measure 8 feet and 6 feet. What is the length of the hypotenuse?
A. 2 feet
B. 5 feet
C. 10 feet
D. 14 feet
Help ASAP!
Answer:
C) 10 feet
Step-by-step explanation:
h² = 8² + 6² = 64 + 36 = 100
h = √100 = 10
Some one help ASAP!!
Jeffrey multiplies one side of the equation 34+116=150 by
a number m. What does he need to do to balance the
equation?
Answer:
multiply the 150 on the other side by 'm' also
(34+116)m = 150m
Step-by-step explanation:
equations must maintain balance
HELP HELP HELP HELP JUST TWO SMALL THINGS
put down whatever pls give me actual answers
Answer:
for what question i dont see the quetsion
Step-by-step explanation:
translate the phrase into a variable expression. use the letter m to name the variable. if necessary, use the asterisk for multiplication and the slash for division. the total number of minutes billed on the phone bill split between 3 phones
Answer:
m/3
Step-by-step explanation:
fghbzsvbftgzgbtefnysffafbydfs
help please !!!!.......
Answer:
x=60°,120°
Step-by-step explanation:
4sinx=3cosecx
4sinx-3cosecx=0
4sinx-3/sinx=0
4sin²x-3=0
sin²x=3/4
sinx=√(3/4)
sinx=√3/2=sin60°,sin(180-60)
Answer:
sin (180-60)is the correct answer Hope it helps you have a great day keep smiling be happy stay safe
The perimeter of a rectangle is 20 cm. The length of the rectangle is 3 cm less than 2 1/4 times the width. Find the dimensions of the rectangle
Answer:
the dimension of the rectangle is 4 cm and 6 cm respectively
Step-by-step explanation:
The computation of the dimension of the rectangle is shown below:
Given that
The perimeter of the rectangle is 20 cm
The width be x
So, the length would be 2 1 ÷ 4 x - 3 i.e. 9 ÷ 4x - 3
Now as we know that
Perimeter of the rectangle = 2 (length + width)
20 = 2 (9 ÷ 4x - 3 + x)
20 = 9 ÷ 2x - 6 + 2x
20 = 4.5x - 6 + 2x
26 = 6.5x
x = 4 cm
Now the length would be
= 9 × 4 ÷ 4 - 3
= 6 cm
Hence, the dimension of the rectangle is 4 cm and 6 cm respectively
A boy weighs 27 kilograms. Hoy much does he Weigh in pounds?
Answer:
59.5248
Step-by-step explanation:
heeeeeeeeeeeeeeeelp solve the following Q
Answer:
[tex]\huge\boxed{\sf \frac{y-5}{y-3} }[/tex]
Step-by-step explanation:
Solving it by mid-term break method:
[tex]\displaystyle =\frac{y^2-3y-40}{y^2-11y+24} \\\\= \frac{y^2 -8y+5y-40}{y^2-3y-8y+24} \\\\= \frac{y(y-8)+5(y-8)}{y(y-3)-8(y-3)} \\\\Take \ (y-8) \ and \ (y-3)\ common\\\\= \frac{(y-8)(y-5)}{(y-8)(y-3)} \\\\= \frac{y-5}{y-3} \\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer:
[tex]\frac{y+5}{y-3} \textrm{ where } y \ne 8[/tex]
Step-by-step explanation:
We'll first factorize the quadratic equations by finding their zero-points:
[tex]y^2 - 3y - 40 = 0\\\Delta = (-3)^2 - 4\cdot 1 \cdot -40 = 9 + 160 = 169\\\sqrt{\Delta} = 13\\y = \frac{3 \pm 13}{2}\\y_1 = 8\\y_2 = -5\\y^2 - 3y - 40 = (y - 8)(y + 5)\\~\\y^2 - 11y + 24 = 0\\\Delta = (-11)^2 - 4\cdot 1\cdot 24 = 121 - 96 = 25\\\sqrt{\Delta}} = 5\\y = \frac{11 \pm 5}{2}\\y_1 = 8\\y_2 = 3\\y^2 - 11y + 24 = (y - 8)(y - 3)[/tex]
Now we can use this to simplify the whole division:
[tex]\frac{y^2-3y-40}{y^2-11y+24} = \frac{(y-8)(y+5)}{(y-8)(y-3)} = \frac{y+5}{y-3} \textrm{ where } y \ne 8[/tex]
Help I need this quick
A triangle has angle measurements of 41°, 41°, and 98°. What kind of triangle is it?
Answer:
isosceles triangle?????????????????.................
Isosceles apparently lol.
Triangle G F E is cut by line segment H J. Line segment H J goes from side G E to F E. The length of G F is 4 x minus 4, the length of H J is x + 3, and the length of J E is x minus 1.
If H is the midpoint of GE and J is the midpoint of FE, determine the following lengths.
HJ =
JE =
Answer:
HJ = 8 JE = 4
Step-by-step explanation:
it is given that H is the midpoint of GE and J is the midpoint of FE. According to the midpoint theorem the line segment connecting the midpoint of two sides is parallel to the three side and its length is half of the third side. since JH is connecting the midpoints.
HJ= 1/2 (GF)
x + 3 = 1/2 (4x - 4)
x + 3 = 2x - 2
x = 5
^ Thus meaning the value of x is 5.
Now you just fill into your equations:
HJ = x + 3 = (5) + 3 = 8
JE = x - 1 = (5) - 1 = 4
Therefore, HJ = 8; JE = 4.
Answer:
HJ = 8
JE = 4
Step-by-step explanation:
Your welcome.
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 378 milliliters of the drug, how many milliliters of compound B are needed?
Answer:
216 milliliters
Step-by-step explanation:
Since, there are 3 milliliters of compound A used for every 4 milliliters of compound B.
Therefore,
A : B = 3 : 4
Let the common multiplier of the given ratios be x.
So, A = 3x & B = 4x
Since, chemist wants to make 378 milliliters of the drug.
Therefore, total volume of drug = 378 milliliters.
3x + 4x = 378
7x = 378
x = 378/7
x = 54
4x = 4*54 = 216
Thus, 216 milliliters of compound B are needed.
Solve the following:
⅜x - 16 = 16
Answer:
x = 256/3
Step-by-step explanation:
3/8x - 16 = 16
Add 16 to both sides
3/8x = 32
Multiply 8 by both sides
3x = 256
Divide 3 by both sides
x = 256/3 or 85.3333333
please answer this for me?
Answer:
abkjjnjnnnnjxnjxbksbx
Step-by-step explanation:
Lol idont know sorry
Can someone help (this is 12 year old math)
Answer:
Then why are you even doing that?
Step-by-step explanation:
The volume of a right rectangular prism can be found by using the product 6(4)(18). Which expression could also be used to determine the volume of this prism?
A. 6 + 4 + 18
B. 2(6 + 4 + 18)
C. 32(18)
D. 4(6)(18)
Answer:
c
Step-by-step explanation:
Answer:
guys its D
Step-by-step explanation:
A truck is painting traffic lines along a highway the truck paints 8 miles of lines in 3 hours at the rate how many miles can a truck paint in 12 hours.
Answer:
The truck can paint 32 miles in 12 hours.
Find the length of the third side. If necessary, round to the nearest tenth. 11 11
Answer:
If we are talking about a triangle with two sides being of equal length: 11, then you can use Pythagorean Theorem to solve.
Step-by-step explanation:
Imagine the sides labeled as a, b, and c. a and b are both 11. We have to find the value of c. we can do this by writing a^2+b^2=c^2. so 11^2+11^2=c^2. All that is left to do is find the square root of c^2 and you are left with your answer.
Kathleen, a professional golfer, had an average score last season
of 80 points. This season, her average score has been 72 points.
What is the percent of decrease in Kathleen's average score?
(|currentavg-initialaverage|/initialavg)*100 gives percent difference so:
(|72-80|)/(80)*100
gives a 10 percent difference (decrease)
A bottle holds exactly 2/3 pint of liquid. How many 2/3-pint bottles can be filled from a 24-pint container
Answer:
36 number of 2/3-pint bottles can be filled from a 24-pint container
Step-by-step explanation:
Volume of the container is 24 pint
Volume of the bottle is 2/3 pint
Number of 2/3 pint bottles that can be filled from 24 pint container is
[tex]\frac{24}{\frac{2}{3} } \\= 24 * \frac{3}{2} \\= 12 * 3\\= 36[/tex]
36 number of 2/3-pint bottles can be filled from a 24-pint container
if 14 men can cultivate 42acres of land in 18weeks, how many weeks will 21 men working at the same rate take to cultivate 56 acres of land
Answer:
16 weeks
Step-by-step explanation:
What is the percentage change from 5 to 8?
Answer:
60%
Step-by-step explanation:
8-5=3
3/5=0.6 and 0.6 = 60%
so 3 is 60% or 5
so 5+3 is a 60% increase
(WIll mark as brainliest) Which one of these graphs is a function and why and why not?
b/2+1=5
solve this equation
Answer:
b=8
Step-by-step explanation:
b/2+1=5
b/2=5-1
b/2=4
b=4×2
b=8