Answer:
[tex]\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
[tex]\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
Step-by-step explanation:
[tex]\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}[/tex]
Method 1
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{a} =a[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}[/tex]
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:[/tex]
[tex]\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}[/tex]
Simplify the denominator:
[tex]\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4[/tex]
Therefore:
[tex]\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}[/tex]
Method 2
[tex]\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:[/tex]
[tex]\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}[/tex]
Simplify the denominator using the radical rule [tex]\sqrt{a} \sqrt{b} =\sqrt{ab}[/tex]:
[tex]\implies (\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})=\sqrt{(3-\sqrt{5})(3+\sqrt{5})[/tex]
[tex]\implies\sqrt{(3-\sqrt{5})(3+\sqrt{5})}=\sqrt{9-5}=\sqrt{4}=2[/tex]
Therefore:
[tex]\implies \dfrac{5\sqrt{3+\sqrt{5}}}{2}[/tex]
[tex]\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}[/tex]
To rationalise:-
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } [/tex]
There is a formula in math if there is root in denominator
for example
[tex] \frac{1}{ \sqrt{a - b} } [/tex]
we can say rationalize by multiplying √(a-b) in numerator and denominator both
[tex] \frac{1}{ \sqrt{a - b} } \times \frac{ \sqrt{a - b} }{ \sqrt{a - b} } \\ \frac{ \sqrt{a - b} }{a - b} [/tex]
In here
[tex] \frac{5}{ \sqrt{3 - \sqrt{5} } } \times \frac{ \sqrt{3 - \sqrt{5} } }{ \sqrt{3 - { \sqrt{5} } } } \\ \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } [/tex]
but still here is root to remove this we have to multiply
3 + √5 in numerator and denominator.
[tex] \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5} ) }{ {3}^{2} - { (\sqrt{5} )}^{2} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5}) }{9 - 5} \\ \frac{5( \sqrt{3 - \sqrt{5} } )(3 + \sqrt{5}) }{4} [/tex]
What is the third quartile of this data set?
14, 18, 20, 21, 25, 32, 38, 42, 48
A. 42
B. 36
C. 40
D. 38
Answer:
40 so C would be your answer.
The third quartile of the data set is 38.
What is Quartile?Quartiles are statistical measures that divide a dataset into four equal parts, each representing 25% of the data. They are used to analyze the distribution and spread of data.
There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3).
To find the third quartile of a data set, we need to arrange the data in ascending order and then locate the value that divides the upper 25% of the data from the lower 75%.
Arranging the data set in ascending order:
14, 18, 20, 21, 25, 32, 38, 42, 48
The data set has 9 values, so the third quartile will be the value at the
(9 0.75)th position
= 6.75th position.
Since we can't have a fractional position, we round up to the nearest whole number, which is 7.
The value at the 7th position is 38. Therefore, the third quartile of the data set is 38.
Learn more about Quartile here:
https://brainly.com/question/29809572
#SPJ7
Some of Mr. Edward's students want to buy him a gift. If each of
them pays $2, they will be short of $4 for the gift. If each of them
pays $3, there will be an extra $3. How much does the gift cost?
Answer:
It depends on how many students there are in Mr. Edwards class
Step-by-step explanation:
(3y+2)(y–1) simplify??
Answer:
[tex]\boxed{\sf{3y^2-y-2}}[/tex]Step-by-step explanation:
Given:
Isolate the term of y from one side of the equation.
(3y+2)(y-1)
Use the foil method.
[tex]\underline{\text{FOIL METHOD:}}[/tex]
[tex]\Longrightarrow: \sf{\left(A+B\right)\left(C+D\right)=AC+AD+BC+BD}[/tex]
(3y+2)(y-1)=3yy+3y(-1)+2y+2(-1)
Solve.
[tex]\sf{3yy=3y^2}\\\\\\\sf{3y(-1)=-3y}\\\\\\\sf{2(-1)=-2}[/tex]
[tex]\sf{3y^2-3y+2y-2}[/tex]
Add or subtract the numbers from left to right.
Solutions:
[tex]\sf{-3y+2y=-y}[/tex]
[tex]\Longrightarrow: \boxed{\sf{3y^2-y-2}}[/tex]
Therefore, the correct answer is 3y²-y-2.I hope this helps. Let me know if you have any questions.
Answer:
3y^2-y-2
Step-by-step explanation:
(3y+2)(y–1)
Use the FOIL method
First 3y * y = 3y^2
outer 3y * -1 = -3y
inner 2 * y = 2y
last 2 * -1 = -2
Add them together
3y^2 -3y +2y -2
Combine like term
3y^2-y-2
PLS HALP!
Bisect line segment AB.
Steps.
1. Center your compass at A so that it measures more than half way to B. Draw arcs above and below segment AB.
2. Using the same compass measurement as step 1, center your compass at B. Draw two arcs above and below segment AB so that they intersect the arcs from step 1. Name these intersection points C and D.
3. Draw line CD.
4. Name the intersection of line segment AB and line segment CD, point M.
5. CD is a segment bisector of segment AB.
Answer:
Shown in the photo
Step-by-step explanation:
I just followed the steps. If you need more help let me know :)
AB is tangent to circle O at A. Find the length of radius r to the nearest tenth. A to B is 11. B to O is 8.
Please answer ASAP will mark as brainlist
Answer: 3.6
Step-by-step explanation:
Below are the marks obtained by 7 students out of 40 questions on a maths test.
11, 27, 10, 27, 14, 33, 11
Find the mean absolute deviation.
(If the answer is a decimal, round it to the nearest tenth.)
Answer: according to my calculator, the answer is 8.5714285714286 i hope this is correct lol,
Step-by-step explanation: Hope this helps ^_^
each morning, danai buys breakfast on her why to work. In the past thirty days, she bought a bagel on 6 days, a banana on 12 days, a doughnut on 3 days, and an orange on 9 days. If she bought one item per day, what is the probability that she bought either a banana or an orange? Show or explain your work and write you answer in the space provided.
Answer:
0.7 or 70%Step-by-step explanation:
Total number of days
6 + 12 + 3 + 9 = 30The number of days she bought a banana or orange
12 + 9 = 21The probability of buying a banana or an orange is
P(b or o) = 21/30 = 0.7 = 70%Answer:
[tex]\sf \dfrac{7}{10}=0.7=70\%[/tex]
Step-by-step explanation:
Given information:
Bagel bought on 6 daysBanana bought on 12 daysDoughnut bough on 3 daysOrange bought on 9 daysTotal number of days = 30
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Probability of buying a banana:
[tex]\implies \sf P(Banana)=\dfrac{12}{30}[/tex]
Probability of buying an orange:
[tex]\implies \sf P(Orange)=\dfrac{9}{30}[/tex]
Therefore,
[tex]\implies \sf P(Banana) \: or \: P(Orange)=\sf \dfrac{12}{30}+\dfrac{9}{30}=\dfrac{21}{30}=\dfrac{7}{10}[/tex]
So the probability of buying either a banana or an orange is:
[tex]\sf \dfrac{7}{10}=0.7=70\%[/tex]
A 5 metre long ladder is placed against a wall. It reaches
4.3 metres up the wall. What is the angle between the
ladder and the ground?
IS
5m long ladder placed against 4.3m up the wall.
to find:the angle between the ladder and the ground.
solution:Based on the given conditions, formulate:
sinx=4.3÷5
Evaluate the equation/expression:
x= 1.03527 or 2.10632
x= 1.03527°
or x= 2.10632°
Please help. Will mark brainlyest!!
Answer:
D
Step-by-step explanation:
It goes 2 down. The ' mark shows that it is the new one
A softball has a volume of about 29 cubic inches. Find the radius of the softball. Round your answer to the nearest tenth
Frank wants to find the area enclosed by the figure at the right. The figure has semicircular on each side of a 40-meter by 40 meter square. Find area enclosed by the figure. 3. 14
dibujar esta parabola y= 3x^2
What is the sum of the diagonals in a rectangle whose area is 25v3 and whose width is 5?
Answer:
Sum of diagonals = 20 units
Step-by-step explanation:
[tex]A(rectangle)=25\sqrt 3\: units^2\\w(rectangle) =5\: units[/tex]
To find: Sum of diagonals
[tex]A(rectangle)=l(rectangle)\times w(rectangle) [/tex]
[tex]\implies l(rectangle)=\frac{A(rectangle)}{w(rectangle)}[/tex]
[tex]\implies l(rectangle)=\frac{25\sqrt 3}{5}[/tex]
[tex]\implies l(rectangle)={5\sqrt 3}\: units[/tex]
Let the diagonals of the rectangle be [tex]d_1\:\&\:d_2\: units[/tex]
Diagonals of a rectangle are equal in measure.
[tex]\implies d_1=d_2=\sqrt{l(rectangle)^2+w(rectangle)^2}[/tex]
(By Pythagoras Theorem)
[tex]\implies d_1=d_2=\sqrt{(5\sqrt 3)^2+(5)^2}[/tex]
[tex]\implies d_1=d_2=\sqrt{75+25}[/tex]
[tex]\implies d_1=d_2=\sqrt{100}[/tex]
[tex]\implies d_1=d_2=10\: units[/tex]
[tex]Sum \:of \:diagonals = d_1+d_2[/tex]
[tex]\implies Sum \:of \:diagonals = 10+10[/tex]
[tex]\implies Sum \:of \:diagonals = 20\: units[/tex]
Math extra credit can somebody help?
The TV chef didn't know the first thing about cooking. He was just hired for his wavy blonde hair and charming British accent. So last Tuesday, while the gullible audience thought the chef was mixing up a world-renowned hollandaise sauce, he was actually just mixing a 5 ounce sauce containing 50% tangy mustard with another sauce containing 75% tangy mustard to get a sauce containing 70% tangy mustard. How many ounces of the 75% tangy mustard sauce must the chef have used?
The number or amount of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .
Number of ouncesFirst step
Since 5 ounce sauce containing 50% tangy
Hence:
5 oz×.50 tangy
=2.50 oz-tangy
Second step
(5+x)×0.7=3.5+0.7x
Third step
2.50+0.75x=3.5+0.7x
Collect like term
0.75x-0.7x=3.5-2.50
0.05x=1
Divide both side by 0.05
x=1/0.05
x=20 ounces
Therefore the number of ounces of the 75% tangy mustard sauce must the chef have used is: 20 ounces .
Learn more about number of ounces here:https://brainly.com/question/10618309
help plsssssssssssssss
Explanation:
The arc markings for each angle show that we have two pairs of congruent angles (angle O = angle Q, angle M = angle R). This takes care of the two "A"s in "ASA". The tickmarks show us that the sides MO and RQ are the same length, so this takes care of the "S" of "ASA". Note the congruent sides are between the angles mentioned. The order is important.
Solve each equation.
a.8x=2/3
b.1 1/2=2x
c.5x=2/7
d.1/4x=5
e.1/5=2/3x
Twice a number is 500 more than six times the number. What is the number?
Answer:
-125
Step-by-step explanation:
Twice a number is x*2
x*2 = 500 + x*6
=> x = -125
please help me with the question
Answer:
The answer is B.
Step-by-step explanation:
4x-7 = 2x+9
2x = 16
x = 8
And then we put x into the equations.
y = 32 - 7
y = 25
We then check it with the other equation just to make sure we are correct.
y = 16 +9
y = 25
Therefore, the answer is (8,25).
Determine if the situation represents a proportional relationship. Explain your reasoning.
Aaron Rodgers can throw a football 44 yards in 2 seconds. Patrick Mahomes can throw
a football 84 yards in 3 seconds. Show your work.
Answer:
Step-by-step explanation:
44/2 is 22
84/3 is 28
Patrick Mahomes can throw more yards/sec
Round your answers to 2 decimal places
use 3. 14 for
Answer:
3
Step-by-step explanation:
0.1 rounds to 0 and 0.04 also rounds to zero. Therefore, the answer is 3.
Jim picks a five digit odd number. The second digit is less than 5. The fourth digit is a cube number. The first digit is a prime number. How many different numbers could he pick?
Answer:
3,000 numbers.
Step-by-step explanation:
First digit: 2, 3, 5, or 7 (primes)
Second digit: 0, 1, 2, 3, or 4 (less than 5)
Third digit: 0-9
Fourth digit: 0, 1, or 8 (cubic numbers)
Fifth digit: 1, 3, 5, 7, or 9 (odd numbers)
So we have 4 * 5 * 10 * 3 * 5 = 3,000 possible numbers.
I need help asap pls
Answer:
Circumference = 25.14 cm
Area = 50.28 cm²
Step-by-step explanation:
∴ Circumference = 2πr
⇒C = (2) (22/7) (4)
⇒C = 25.14 cm
∴ Area = πr²
⇒A = (22/7) (4)²
⇒A = 50.28 cm²
Hope that helps...
Factorise 4x^2-y^2 please help
Answer:
(2x + y)(2x - y)
Step-by-step explanation:
1. Simplify the square 4x²:
(2x)² - y²
2. Apple the difference of two squares formula x² - y² = (x + y)(x - y):
(2x + y)(2x - y)
hope this helps!
Identify the relationship between the graphs of
these two equations.
2y = 6x + 5
6y=-2x + 1
Click on the correct answer.
parallel
perpendicular
neither
You are trying to help Rhonda understand the concept of a 5% slack in the line. You explain that having a 5% slack means that the length is 5% longer than it would be if it were completely straight. You compare ️ABC to Figure DEF, where curve DE is 5% longer than line segment AB.
Enter curve DE, given the curve is 5% longer than line segment АВ.
The length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC. The measure of the curve DE is 10.5 units
Pythagoras theoremThe theorem states that the length of the hypotenuse AB is equal to the sum of the square of other two sides AC and BC.
According to the theorem;
AB^2 = AC^2 + BC^2
AB^2 = 6^2 + 8^2
AB^2 = 36 + 64
AB = 10
If the curve DE is 5% longer than line segment АВ, the measure of curve DE is given as;
DE = 1.05 * 10
DE = 10.5
Hence the measure of the curve DE is 10.5 units
Learn more on Pythagorean theorem here: https://brainly.com/question/343682
#SPJ1
Record: 0/2 Score: 0 Penalty: 1 off
Complete: 79
Emily Trelow
Transforming Formulas
The formula to calculate the gravitational force between two objects is F₁ = GM₁M₂,
where M₁ and M₂ are the masses of the objects, G is the gravitational constant and
r is the distance between the objects. Solve for M₁ in terms of F, G, M₂ and r.
Answer: M₁ =
Submit Answer
Newton's Law of Gravitation:
Statement: According to this law, when two mass bodies are separated at finite distance then there must be an attractive force experience by them which is directly proportional to the product of their masses and inversely proportional to the square of their separation.
Consider two mass bodies m1 & m2 be kept at distance d. Then the force of attraction F is given as
[tex]Fam_{1}.m_{2}[/tex]
[tex]Fa1/d^2[/tex]
Now, from above equations, we have
[tex]Fa\frac{m_{1}m_{2}}{d^2}[/tex]
or, [tex]F=G\frac{m_{1}m_{2}}{d^2}[/tex]
Here [tex]G=6.67*10^{-11}Mm^2kg^{-2}[/tex] is the universal gravitational constant.
What is the following product? startroot 30 endroot times startroot 10 endroot
Answer:
Hello there! 10 square of 3
I WILL GIVE BRAINLIEST!!!!!
Answer:
See below
Step-by-step explanation:
Inscribed angles encompass twice as many degrees of arc as their angle measure
soo 2* { 6x-5 + x+17 } = 360
shows x = 24 then ROP = x+17 = 41 degrees
Find the value of x.
17
X-4
Answer:
x = 12.5
Step-by-step explanation:
17 = 2(x - 4)
17 = 2x - 8
17 + 8 = 2x - 8 + 8
25 = 2x
12.5 = x