Answers
Answer:
[tex]c =\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Required
Shorten
We have:
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}[/tex]
Rationalize
[tex]c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}[/tex]
Expand
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}[/tex]
[tex]c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}[/tex]
Take positive square roots
[tex]c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}[/tex]
Take LCM
[tex]c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}[/tex]
Collect like terms
[tex]c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}[/tex]
[tex]c =\frac{8}{3}[/tex]
Related Questions
If △CFE≅△PTR, complete each of the following statements:
CE¯¯¯¯¯¯¯¯ ≅
TR¯¯¯¯¯¯¯ ≅
∠P ≅∠
∠F ≅∠
△FEC ≅△
△RPT ≅△
Answers
Based on the definition of congruent triangles, the statements will be completed as follows:
CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECFRecall the following about Congruent Triangles:
The three angles of one triangle is congruent to the three corresponding angles in another triangle if both triangles are congruent triangles.The three sides of one triangle is congruent to the three corresponding sides in another triangle if both triangles are congruent triangles.Given that △CFE≅△PTR, thus:
CE corresponds to PR, therefore CE ≅ PRFE corresponds to TR, therefore FE ≅ TRCF corresponds to PT, therefore CF ≅ PT∠P corresponds to ∠C, therefore ∠P ≅ ∠C∠T corresponds to ∠F, therefore ∠T ≅ ∠F∠R corresponds to ∠E, therefore ∠R ≅ ∠EThus, based on the definition of congruent triangles, the statements will be completed as follows:
CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECFLearn more about congruent triangles on:]
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The container hold 1/2 gallon of water. It is 3/4 full. How many gallons of water are in the container?
Answers
Based on the capacity of the container and the capacity currently being used, the amount of water in the container is 3/8 gallons.
The container is capable of holding 1/2 gallons of water.
If it is holding 3/4 of that 1/2 gallons, the amount of water it would be holding is:
= Capacity of container x Percentage full
= 1/2 x 3/4
= 3/8 gallons of water
In conclusion, the container is currently holding 3/8 gallons of water.
Find out more about this at https://brainly.com/question/11459708.
isha's art club has $250. They sell 6 paintings for $16 each. They buy 9 sketchbooks that cost $13 each. Aisha says they now have about $280. Is Aisha’s estimate reasonable? Aisha’s estimate is not reasonable. They earned about $120 and spent about $120 so they should have the same amount of money as they started with. Aisha’s estimate is not reasonable. They earned about $100 and spent about $120 so they should have about $20 less than they started with. Aisha’s estimate is reasonable. They earned about $100 and spent about $130 so they should have about $30 more than they started with. Aisha’s answer is reasonable. They earned about $60 and spent about $90 so they should have about $30 less than they started with.
Answers
Answer:
Step-by-step explanation:
Aisha’s estimate is not reasonable.
They earned about $100 and spent about $120 so they should have about $20 less than they started with.
Help me I need this urgent
Answers
Answer:
b(-1)= -6
b(0)= -4
b(4)= 4
Step-by-step explanation:
2(-1) - 4
-2-4=-6
2(0) - 4
0 - 4 = -4
2(4) - 4
8 - 4 = 4
Answer:
-6, -4, 4
Step-by-step explanation:
Which is true? A 0.9919 > 0.999 B 1.4359 < 1.446 C 2.6953 = 2.75 D 4. 9395 > 5.0
Answers
Option B. is true.
A isn't true because 0.9919 is lesser than 0.999.C is false because 2.6953 is lesser than 2.75. They are not equal.D is also false because 4.9395 is not greater than 5.0.Answer:
B. 1.4359 < 1.446
Hope you could get an idea from here.
Doubt clarification - use comment section.
PLEASE HELP ME WITH THIS ASAP !!
Answers
Answer:
132cm^2
Step-by-step explanation:
SA of square based pyramid:
SA = 2bs + b^2
b = base
s = slant height
-> 2(6)(8) + 6^2
-> 96 + 36
= 132cm^2
Answer:
132
Step-by-step explanation:
[tex]tsa = {a}^{2} + 2al[/tex]
[tex]tsa = {6}^{2} + 2(6)(8)[/tex]
[tex]tsa = 36 + 96[/tex]
[tex] = 132[/tex]
In the figure below, AABC is similar to A EFG. What is the length of EG? Enter only the number.
A
5
N
3
12
16
F
G
B
The solution is
Answers
Answer:
EG = 20
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{EG}{AC}[/tex] = [tex]\frac{EF}{AB}[/tex] , substitute values
[tex]\frac{EG}{5}[/tex] = [tex]\frac{12}{3}[/tex] = 4 ( multiply both sides by 5 )
EG = 5 × 4 = 20
A line segment has endpoints (-1, -1) and (-1, 2).
Which vertex would form a triangle that is connected to the endpoints of the line segment?
А.
(-1, 6)
B
(-1, -2)
С
(-1,0)
D
(2,-1)
Answers
Answer:
D. (2, - 1)Step-by-step explanation:
Both the given points have x- coordinate of -1.
The first three of the answer options have same -1 as the x-coordinate, this means all three points are on the same line.
It is therefore impossible to have those as vertices of a triangle.
Correct option is D
HURRY PLS!
Evaluate if a= 4 and b=7
28÷ b+7
A. 14
B. 11
Answers
Step-by-step explanation:
Hi, I think correct variant is B
(28÷7)+7=4+7=11
I need help plz it’s due tonight !!!!!!!
Answers
Answer:
hmm it's like ut I do know and my answer
A hiker maintains an average speed of 3 3/4 km/h. How many kilometers will the hiker walk in 5 hours
Answers
Answer:
3 3/4 km = 1 hr
_______. ____
x 5
5 (3 3/4) = 18.75 km
Answer:
Explanation:
18.75 km
What is (-2) (3 4/7)
Answers
Answer:
option 1
Step-by-step explanation:
(-2) (25/7)
-50/7 = -7 1/7
Answer:
Option A is correct.
Step-by-step explanation:
(-2) (3 4/7)
=> (-2) x (3 4/7)
=> -2 x 25/7
=> -50/7
=> -7 1/7
Therefore, Option A is correct.
a box 4cm by 6cm by 8cm is painted on all six faces and then cut into cubes with the 2 cm sides. how many oof these cubes have only one side painted?
Answers
Answer:
hola saludos desde kansas city
area of a triangle b-2s^2+3t^2 h-4s^2-3t^2
Answers
Answer:
1 flmpysc - ax + x - y - 2
this could help
A pine tree measured 40 1 / 2 feet tall. Over the next 7 1 / 2 years, it grew to a height of 57 feet. During the 7 1/2 years, what was the average yearly growth rate of the height of the tree?
Answers
The average yearly growth rate of the height of the tree is 2 1/3 feet
Given:
original height of the pine tree = 40 1/2 feet
Height in next 7 1/2 years = 57 feet
Change in height = Height in next 7 1/2 years - original height of the pine tree
= 57 height - 40 1/2 feet
= 17 1/2 feet
Average growth rate yearly = Change in height / number of years
= 17 1/2 feet ÷ 7 1/2 years
= 35/2 ÷ 15/2
= 35/2 × 2/15
= (35 × 2) / (2 × 15)
= 70/30
= 2 10/30
= 2 1/3 feet
Therefore, the average yearly growth rate of the height of the tree is 2 1/3 feet
Learn more about fraction:
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EC
What is the Arabic numeral for this Roman numeral?
VII
07
09
08
STUR
Answers
Answer:
07
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
V = 5
I = 1
V + I + I = 5 + 1 + 1 = 7
Hope that helps
What expressions is equivalent to -19.2 - (-3.8)
Answers
Answer:
-19.2
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
Factor the expression:
16x^2+25
A) (4x-5i)(4x-5i)
B)(4x-5i)(4x+5i)
C) (4x-5)(4x+5i)
D (4x+5)(4x-5)
Answers
Answer:
B) (4x-5i)(4x+5i)
Step-by-step explanation:
The expression can be treated as the difference of squares, and factored accordingly. That factoring is ...
a² -b² = (a -b)(a +b)
__
Here, we have ...
a² -b² = 16x² -(-25)
a² = 16x² ⇒ a = 4x
b² = -25 ⇒ b = √-25 = 5i
Then the factoring is ...
(a -b)(a +b) = (4x -5i)(4x +5i)
Answer:
Answer:
B) (4x-5i)(4x+5i)
Step-by-step explanation:
The expression can be treated as the difference of squares, and factored accordingly. That factoring is ...
a² -b² = (a -b)(a +b)
__
Here, we have ...
a² -b² = 16x² -(-25)
a² = 16x² ⇒ a = 4x
b² = -25 ⇒ b = √-25 = 5i
Then the factoring is ...
(a -b)(a +b) = (4x -5i)(4x +5i)
Step-by-step explanation:
Mr. Bailey announced the grade distribution for
his science fair projects. Of the 36 students in the
class, 12 earned A's, 18 earned B's, and 6 earned
C's. If Mr. Bailey were to randomly select one of
his students to talk about their project, what is the
probability that the student chosen had earned an
A on their science fair project?
Answers
Answer:
12/36
Step-by-step explanation:
Cuz 12 earned A's so it's 12/, then there are 36 choices so it would be 12/36.
Help help help math math
Answers
Answer:
I think its vertical opposite angle
The quotient of 2 numbers, p and q
A: pq
B: p+q
C: p/q
D: p - q
Answers
Answer:
b
Step-by-step explanation:
pls pls pls mark me as brainliest
Answer:
C: p/q
Step-by-step explanation:
Quotient is the result of dividing two numbers so C would be the best answer
Hope this helps! :D
Identify the function as a power function, a polynomial function, or neither.
[tex]fx=\frac{x^2}{x^2-1}[/tex]
Answers
Answer:
I think this is neither. As you can see the value of x reaches infinity and negative infinity, the value gets infinetly closer to 1.
1/3x+80=1/2x+120 what’s the answer??
Answers
Answer:
−240
1/3x+80=1/2x+120
please help meeeeeee
Answers
Answer: That would be distributive
Step-by-step explanation:
Work out the area of the shaded shape. Need answer ASAP
Answers
Answer:
Step-by-step explanation:
A = 3(6) + 2(5 + 3 + 2) = 38 m²
Which equation is an example of the identity property of addition?
O A. 6.5 = 1
O B. 6+0= 6
O C. 6+(-6)=0
O D. 6.1= 6
HELPPP! ILL GIVE BRAINNLIST
Answers
Answer:
B.
Step-by-step explanation:
Adding 0 to 6 gives the same value (6).
Zero is called the Identity element of Addition,
22) A corporate charter specifies that the company may issue up to 20 million shares of stock. The company sells 12 million shares to investors and later buys back 3 million shares. The current number of shares of treasury stock after these transactions have been accounted for is:
Answers
Answer:
11 million
Step-by-step explanation:
20 -12 +3 = 11
There will be 11 million shares of stock in the treasury.
The probability of randomly meeting someone with a phone number that ends in 3 is
Answers
Answer:
0,1,2,3,4,5,6,7,8,9
Step-by-step explanation:
: probability of meeting someone with a phone number that ends with 3 .....
= 3/total amount of no ×100
3÷10= 0.3
: 0.3×100= 30% probability.
Assuming a phone number is 10 digits long and the last digit can be any of the 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) with equal probability, the probability of randomly meeting someone with a phone number that ends in 3 is 1/10, or 0.1.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
If the phone number is 10 digits long, there are 10 possible digits that could be at the end. Since only one of those digits is a 3,
the probability of randomly selecting a phone number that ends in 3 is:
1/10 = 0.1 or 10%
Learn more about probability here:
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Line k passes through the point (6, -7) and has a slope m= -1/2.
Which is the equation of a line that is perpendicular to line k and passes through the
point (-4, 9)?
Answers
Answer:
y = 2x + 17
Step-by-step explanation:
lmk if you want an explanation
If a square has an area of 49 ft', what is the length of one of its sides? The perimeter?
Answers
Answer: 12.25 ( each side )
Step-by-step explanation
Divide 49 by 4, which is 12.25
