5/root of 7 - 2 is rationalized by multiplying the numerator and denominator by what?
Answers
The considered fraction is ationalized by multiplying the numerator and denominator by the expression as given by: Option A: √7 + 2
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
(we used the identity [tex](b-c)(b+c) = b^2 - c^2[/tex])
We actually rationalize just for the use of that later denominator or numerator(if they seem to be helpful).
Remember that
[tex]\dfrac{b-c}{b-c} = 1[/tex]
thus, multiplying it with the fraction doesn't change its value, and just change the way how it looks. We assume that b-c is not 0
For this case, the given fraction is:
[tex]\dfrac{5}{\sqrt{7} - 2}[/tex]
Thus, here we will multiply the denominator with [tex]\sqrt{7} + 2[/tex] so that we can use the identity [tex](b-c)(b+c) = b^2 - c^2[/tex].
Thus, we get:
[tex]\dfrac{5}{\sqrt{7} - 2} \times \dfrac{\sqrt{7} + 2}{\sqrt{7} + 2} = \dfrac{5(\sqrt{7} + 2)}{(\sqrt{7})^2 - 2^2} = \dfrac{5(\sqrt{7} + 2)}{3}[/tex]
See, the denominator now looks a bit better. We try to make it look smooth and simplified because division is more complex than multiplication, so its better to have square root term in numerator than in denominator.
Thus, the considered fraction is ationalized by multiplying the numerator and denominator by the expression as given by: Option A: √7 + 2
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Related Questions
A shipping crate is shaped like a rectangular
prism. It is 5 feet long by 3 feet wide by 3 feet
high. What is the volume of the crate?
Answers
The volume of the rectangular prism having the dimension 3 feet wide, 5 feet long, and 3 feet tall is 45 cubic feet.
What is a rectangular prism?A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.
A crate is shaped like a rectangular prism. The crate is 3 feet wide, 5 feet long, and 3 feet tall.
The volume of the rectangular prism will be given as
Volume = length × width × height
Then put the values, we have
Volume = 3 × 5 x 3
Volume = 45
The volume of the rectangular prism having the dimension 3 feet wide, 5 feet long, and 3 feet tall is 45 cubic feet.
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Volume
LBH5(3)(3)5(3)²5(9)45ft³20 POINTS!!! ILL MARK BRAINLIEST! The hypotenuse of the triangle is 32, what is the radius of Circle B? Is the radius the same all around? If, both circles have the same ratio of equal radii all around, does that make them similar, what do we think about the similarity of all circles?
circle A is 1st image
circle b is 2nd image with question on it
Answers
Answer:
the radius is 4, it is the same all around, they are similar, all circles are similar
Step-by-step explanation:
you can use Pythagoras's theorem to find the radius. √33 ^2 = 32. the other lengths must be equal because they are radii. therefore they are √16 which is 4.
Junk food is known for having a lot of "empty calories." Which statement BEST explains the meaning of that term?
A.
Empty calories do not have many nutrients.
B.
Empty calories are made entirely from sugar.
C.
Empty calories need exercise to burn them off.
D. Empty calories are excluded from daily calorie counts.
Answers
Answer:
A
Step-by-step explanation:
Answer:
A. Empty calories do not have many nutrients.
Step-by-step explanation:
Suppose that scores on an exam are normally distributed with mean 80 and standard deviation 5, and that scores are not rounded. What is the probability that a student scores higher than 85 on the exam
Answers
Answer:
3
Step-by-step explanation:
cus it's two 80s and 2 5 so 5 minus 2 is 3
What range of weights measured on an analytical balance with a precision of 0.2mg,will round to 2.0g.What is te relative percent precision of these weights
Answers
The range of weights measured on an analytical balance with a precision of 0.2mg,will round to 2.0g is 0.1900 g to 0.2100 g.
What is analytical balance?The analytical balance is the device which is used to measure the mass or weight of the object with high level of precision.
Even using the analytical balance equipment, you do not get the accurate weight. For the measurement of the 0.2 g the precision level is ±0.1 mg.
For the positive number, the value will be 0.2100 gFor the negative number, the value will be 0.1900 g.The range of weights measured on an analytical balance with a precision of 0.2mg,will round to 2.0g is 0.1900 g to 0.2100 g.
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HELP ME PLEASE!!!!!!!!
Answers
Answer:
I think th answer is either 1753 or 17
what is 5x - 3y + 2z, x =3, y = one third , z = 5 what does this equal
Answers
Answer:
asnwer 24
Step-by-step explanation:
x = 3
y = 1/3
z = 5
------------------------------
5( 3 ) - 3(1/3) + 2(5)
15 - 1 + 10 = 24
Rewrite the expression 2(3 - 4k) as a difference. Show your work.
Answers
Answer:
Step-by-step explanation:
Use Distributive Property: a*(b -c) = a*b - a*c
2(3 -4k) = 2*3 - 2*4k
= 6 - 8k
please help mee i beg
Answers
Step-by-step explanation:
8.5 × -3 = a
-25.5 = a
b - 7 = -11
b = -4
c -(-3) = 15
c = 12
d - 4 = 32
d = 36
if you still have any doubts feel free to ask
Which equation is true when the value of X is -12?
A. 1/2x +22= 20
b 15 - (1/2)x=21
c 11- 2x= 17
d 3x- 19= -17
Answers
Answer: B is right
Step-by-step explanation: Check the file for steps
Which relation is a function?
Answers
Answer:
the third (bottom left) option
Step-by-step explanation:
for every valid value of x there must be exactly one value of y.
the first option is valid only for positive x, but then for every valid x there are always 2 possible y values (a positive and a negative one).
the second option is defined for only one value of x (3), but this x has infinitely many y values.
the fourth option is a circle defined for -r <= x <= r (r being the radius). in this defined interval almost every x has 2 assigned y values (only x = -r and x = r have one y value).
x is an acute angle. Find the value of x in degrees. sin (x)= 0.8
Answers
60 Degrees
[tex]\bold{EXPLANATIONS:}[/tex]
the capacity of cylindrical water tank is 539 litres. if its height is 1.4 metres then find the radius of the base.
Answers
Answer:
350m
Step-by-step explanation:
• Capacity= volume/1000
• but we know that the volume of the cylinder is
[tex]\pi {r}^{2}h[/tex]
so substitute it I'm the volume space
• The substitute for
[tex]\pi \: as \: \frac{22}{7} \: and \: h \: as \: 1.4 \: and \: also \: capacity \: as \: 539[/tex]
• 539 = ((22/7)× r²× 1.4)/1000
• when you simplify you get r as 350m
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Does anyone know how to do this? I need to finish. My IXL before tomorrow I really need help!
Answers
Answer:
1. 72 to 56
2. 90 to 70
Step-by-step explanation:
To fill in the blanks you need to find similar ratios,
For the first one, the ratio is 72 and ___,
because 72 is in the 9's column, find out what times 9 equals 72,
9 × ? = 72
Simply divide to find the answer,
72 ÷ 9 = ?
= 8
Now that you know that 9 is being multiplied by 8, multiply 8 and 7 together,
8 × 7
= 56
Hence the answer is 56 for the first blank,
For the second one, the ratio is 90 and ___,
because 90 is in the 9's column, find out what times 9 equals 90,
9 × ? = 90
Once again simply divide to find the answer,
90 ÷ 9 = ?
= 10
Now that you know that 9 is being multiplied by 10, multiply 10 and 7 together,
7 × 10
= 70
Hence the answer is 70 for the second blank,
please just answer my question on this image
Answers
Answer:
It's the first one because 5 x 3 = 15 and 10 x 3 = 30 and 15 x 3 = 45 and so on..
Step-by-step explanation:
Answer:
The first one answer, because pattern X is 3 times the corresponding term in pattern Y.
5 x 3= 15
10 x 3=30
15 x 3= 45
20 x 3=60
Identify the vertex of the function, F(x) =3(x-1)2 + 5.
Answers
Answer:
f
(
x
)
=
3
(
x
−
1
)
2
+
5
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
3
h
=
1
k
=
5
Find the vertex
(
h
,
k
)
.
(
1
,
5
)
image of graph
please help! what is the arc RU? thank you so much!
Answers
Answer: 92° or 1.6057 radians
Step-by-step explanation:
the 4 angles created by the intersecting lines SU and RT have to equal 360°
<v = 88° because of vertical angles so
88° • 2 = 176°
360° - 176° = 184°
184°/ 2 = 92°
92°+92°+88°+88° = 360°
then, that makes 92° the central angle of arc RU and the central angle degrees is always equal to the arc it subtends
hope this helps :)
The function f(t) is given by the graph. What is the domain of f(t)?
Answers
Check the picture below.
Answer:
-4 ≤ t ≤ 4
Step-by-step explanation:
Help plssss:) I need a complete answer
Answers
(2 , 1)
[tex]\bold{EXPLANATIONS:}[/tex]
Answer:
b is the correct answer
have a good day and I hope this helps :D
if you need more detailed answer just tell me
What is 3/4 divided by 7/10
Answers
Answer:
1.07
Step-by-step explanation:
What set of numbers are shaded on the
hundred chart?
A only the factors of ten
B only the multiples of 10
C only the factors of 20
D only the multiples of 20
Answers
Answer:
D - 20, 40, 60, 80, 100 are all multiples of 20
Step-by-step explanation:
Factors of 10 - 10, 5, 2, 1
Multiples of 10 - D and 10, 30, 50, 70, 90
Factors of 20 - 20, 10, 5, 4, 2, 1
:)
5.0.75% of 80 is what number?
A. 0.6
B.0060
C.60
D.6000
Answers
Answer:
Um im sure the answer is C btw
Step-by-step explanation:
correct me if im wrong
on her first day of work, mia sold one straw hat. on day two, she sold three straw hats. on day three, she sold five straw hats, on each succeeding day, she sold two more straw hats than she had sold on the previous day. how many straw hats in total had mia sold after working 40 days?
Answers
If Mia sold 2 more hats on each suceeding day, after working 40 days it is expected Mia had sold a total of 1523 hats.
How many hats will Mia sell everyday?Day: Hats
1 = 12=33 = 54=75= 96=117= 138= 159=1710=1911= 2112=2313= 25among othersYou can notice the number of hats she will sell follow a pattern as there are only sequential odd numbers.
How many hats will Mia sell in total?By following the sequence let's add the hats she will sell everyday:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 + 73 + 75 + 79 = 1523Learn more about sums in: https://brainly.com/question/13013054
What is the slope of the line that contains these points?
xxx 555 666 777 888
yyy -5−5minus, 5 -6−6minus, 6 -7−7minus, 7 -8−8minus, 8
Answers
Answer:i tink its D) - 4/3
Step-by-step explanation:
im bad at mat, so im sorry if im wron
Answer:a
Step-by-step explanation:
a
Paul is going to buy a collectible vintage painting from a local art gallery. the painting is priced at $600 in the gallery. the gallery owner does accept credit cards but prefers cash. in fact, he offers to give paul a 5% discount if he can pay in cash. paul doesn't have any cash but can get a cash advance on his credit card. his credit card has an apr of 16% on credit purchases and a 32% apr on cash advances. assuming paul wants to pay the painting off over 12 months, which of the following is true? a. paul will pay a total of $696, over 12 months, if he purchases the painting with his credit card. b. paul will pay a total of $653.28, over 12 months, if he purchases the painting with his credit card. c. paul will pay a total of $782.40, over 12 months, if he purchases the painting with a cash advance for discounted purchase price. d. paul will pay a total of $708.96, over 12 months, if he purchases the painting with a cash advance for discounted purchase price.
Answers
When Paul will pay the amount over 12 months, if he purchases the painting with cash advance the discounted purchase price will be $782.40. Then the correct option is C.
What is APR?APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.
Paul is going to buy a collectible vintage painting from a local art gallery.
The painting is priced at $600 in the gallery.
The gallery owner does accept credit cards but prefers cash.
In fact, he offers to give paul a 5% discount if he can pay in cash.
Paul doesn't have any cash but can get a cash advance on his credit card.
His credit card has an apr of 16% on credit purchases and a 32% apr on cash advances.
When Paul will pay the amount over 12 months, if he purchases the painting with cash advance the discounted purchase price will be
[tex]\rm A = 0.95 \times 600 (1+\dfrac{0.32}{12})^{12}\\\\A = 782.40[/tex]
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Rearrange 4x+2y to make Y the subject.
Answers
y= -2x
Explanation:
4x+2y=0
2y= -4x
y= -2x
Dara and Jo share £420 in the ratio 2:5.
Calculate how much Dara and Jo receive each.
Answers
Answer:
Dara receives £120 and Jo receives £300
Step-by-step explanation:
D:J
2:5
5+2=7
£420÷7= £60
1 on the ratio= £60
Dara:
£60 × 2= £120
Jo:
£60× 5= £300
The letters in the word MATHEMATICIAN were put in a box. What is the chance of getting letter A?
Answers
Answer:
3/13
Step-by-step explanation:
There are a total of 13 letters in the word and 3 of them are A’s so 3/13 is the probability of getting an A.
The probability of getting the letter A is given by P ( A ) = 3/13
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability of getting the letter A be P ( A )
Now , the word is given as S = { "MATHEMATICIAN " }
The number of letters in the word S = 13 letters
The number of letter A in the word = 3 A's
So , probability of getting the letter A , P ( A ) = number of letter A in the word / number of letters in the word S
On simplifying , we get
The probability of getting the letter A , P ( A ) = 3/13
Hence , the probability is 3/13
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Please help. I'll mark you brainliest if right. I really need help
Answers
Explanation:
cosΘ + 1 = 0
cosΘ = -1
Using the unit circle to help, we must determine what value of theta (in radians) makes cosine -1.
On the unit circle, there is only place where cosine is -1, and that is at π.
Since it asks to find all solutions, we use the “+ 2kπ” to account for them. (Let me know if you need an explanation of why this works/what this means.)
What is the call out fee
Answers
Answer:
A set amount charged for a repairman to come to one's house, or to a broken-down vehicle, which is added to the cost of the actual repair.