Answers
If a = 6 - [tex]\sqrt{35} [/tex], find the value of a² + [tex] \frac{1}{a²} [/tex]
Solution:-a = 6 - [tex]\sqrt{35} [/tex] (Given)
Now, first of all we have to find the value of [tex] \frac{1}{a} [/tex].
So, [tex] \frac{1}{a} [/tex] = [tex] \frac{1}{6 \: - \: \sqrt{35}} [/tex]
[tex] \frac{1}{a} [/tex] = [tex] \frac{6 \: + \sqrt{35}}{(6 \: - \: \sqrt{35})(6 \: + \: \sqrt{35})} [/tex]
[tex] \frac{1}{a} [/tex] = [tex] \frac{6 \: + \sqrt{35}}{(6)² \: - \: (\sqrt{35})²} [/tex]
[tex] \frac{1}{a} [/tex] = [tex] \frac{6 \: + \sqrt{35}}{36 \: - \: 35} [/tex] [tex] (\because \sqrt{35} \: × \: \sqrt{35} \: = \: 35) [/tex]
[tex] \frac{1}{a} [/tex] = [tex] \frac{6 \: + \: \sqrt{35}}{1} [/tex]
[tex] \frac{1}{a} [/tex] = 6 + [tex]\sqrt{35} [/tex]
Now, we have to find the value of a² + [tex] \frac{1}{a²} [/tex]
So, a² + [tex] \frac{1}{a²} [/tex] = [tex] (a \: + \frac{1}{a})² [/tex] - 2.a.[tex] \frac{1}{a} [/tex]
a² + [tex] \frac{1}{a²} [/tex] = [tex] (6 \: - \sqrt{35} \: + \: 6 \: + \sqrt{35})² [/tex] - 2
a² + [tex] \frac{1}{a²} [/tex] = (12)² - 2
a² + [tex] \frac{1}{a²} [/tex] = 144 - 2
a² + [tex] \frac{1}{a²} [/tex] = 142
The value of a² + [tex] \frac{1}{a²} [/tex] is 142. [Answer]
Related Questions
7b-2/5 = 6b-7/5
Solve for b.
Answers
Answer:
b = -1
Step-by-step explanation:
here's your solution
=> 7b - 2/5 = 6b - 7/5
=> 7b - 6b = -7/5 + 2/5
=> b = (-7+2)/5
=> b = -5/5
= b = -1
hope it helps
Answer:
b = -1
Step-by-step explanation: I put all the like terms together by moving 6b and -2/5, which then changed their signs to negative and positive, respectively.
7b-2/5 = 6b-7/5
7b-6b = 2/5-7/5
b = -1
I hope this helps. :)
What function does the graph represent
Answers
Help please
Mathematics
Answers
Answer:
21.5sqft
Step-by-step explanation:
The area of the square is 10ft*10ft = 100sqft
The area of the circle is 5ft*5ft*pi = 25pi sqft
We're supposed to use 3.14 for pi, so the circle is around 25*3.14 sqft = 78.5sq ft
The area left over is 100sqft - 78.5sqft = 21.5sqft
Answer:
21.5 sq. feet
Step-by-step explanation:
Find area of squareFind area of circleSubtract area of circle from square to get area of remaining clothI need help with these questions.
Please show workings.
Question 1:
A trader made a profit of 20% on a radio which he sold for N144 .Calculate the cost price of the radio .
Question 2:
A motor dealer sold a car at a loss of 20% by selling it at N10,000 . Find the cost price.
Note :
Cost price formula :
[tex]C.P = S.P-P \\ or S.P+L[/tex]
Selling Price Formula :
[tex]S.P = C.P + P \\ or C.P - Loss[/tex]
Profit Percentage ( P% ) formula :
[tex] P \% = P/C.P × 100 \\ l \% = l/C.P × 100[/tex]
Answers
Answer:
Question 1
Given
SP = 144P = 20%CP = xUse formula and solve for x:
SP = CP + P144 = x + (20% of x)144 = x + 0.2x144 = 1.2xx = 144/1.2x = 120Cost price is N 120
Question 2
Given
SP = 1000P = -20% (negative because of loss)CP = xUse formula and solve for x:
SP = CP + P10000 = x - (20% of x)10000 = x - 0.2x10000 = 0.8xx = 10000/0.8x = 12500Cost is N 12500
Peter says, "If you subtract 18 from my number and multiply the difference by - 3, the
result is -36." What is Peter's number?
Peter's number is
Answers
Answer:
its 30
Step-by-step explanation:
(x-18)x-3=-36
(36-18)
12x-3
=-36
Answer:
-90
Step-by-step explanation:
-90-18×-3=-36
so that's the answer to the problem or it should be
5 cm
3 cm
9 cm
Area =
Answers
Explanation:
9x5x3
15•9 = 135
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME
Answers
Answer:
lol xdxdxd how you not know fraction? this is basic math this is why you failed lolol
Step-by-step explanation:
Factorise 3c^2-c
Please help me quick
Answers
Answer:
c(3c - 1)
Step-by-step explanation:
3c² - c
Common factor = c
Factored:
c(3c - 1)
Please help it's for trig
Answers
Answer:
-4
Step-by-step explanation:
Given the expression
h(x) = -x^2 +4x
h(-2) = (-2)^2 + 4(-2)
h(-2) = 4 + (-8)
h(-2) = 4 - 8
h(2) = -4
Hence the value of the function when x = -2 is -4
Find (12.34) x (0.7). Explain how you got it
Answers
all i did was multiply. but lmk if it’s right
A regular octagon has a perimeter represented by the expression: p= 48y - 40. Write an expression to represent the length of one side of the octagon
Answers
Answer:
6y-5
Step-by-step explanation:
(48y- 40)/8 because an octagon has 8 equal sides.
-hope this helps:)
Mr. Pete just got a great deal at Lowe’s on tiles for his new patio. He wants to
tile his patio in the shape that is rectangular. His patio measures 108 inches by
144 inches. Find the fewest square tiles he can use without cutting any of them.
Answers
Answer:
The fewest square tiles he can use without cutting any of them = 12 square tiles
Step-by-step explanation:
The given dimensions of Mr. Pete's rectangular patio = 108 inches by 144 inches
The area of the patio = 108 in. × 144 in. = 15,552 in.²
We note that when square tiles are used the must fit both the length and the with of the rectangular patio
Therefore, we have;
The dimensions of the square tiles that the fewest number of tiles is the highest common factor, HCF, of 108 inches and 144
The HCF of 108 and 144 are found from by the prime factors as follows;
108 = 2² × 3³ = 2² × 3² × 3
144 = 2⁴ × 3² = 2² × 3² × 4
From which we have;
The HCF of 108 and 144 = 2² × 3² = 36
Therefore, the size of the sides of the square tiles that will give the fewest number of tiles is 36 inches
The number of the 36 inches square tiles that fit into the length of the rectangular patio = 144 inches/(36 inches/tile) = 4 tiles
The number of the 36 inches square tiles that fit into the breadth of the rectangular patio = 108 inches/(36 inches/tile) = 3 tiles
The total number of tiles he will use = (4 × 3) tiles = 12 tiles = The fewest square tiles he can use without cutting any of them.
Dad is getting food ready for my birthday party! Including me, there will be 18 people at the party. Dad is baking cookies for us! He can bake 24 cookies per batch.
How many batches should I tell Dad to make so we can each have 4 cookies?
Answers
He should bake 4 batches.
Explanation:
There are 19 kids so if they get 4 each there would all eat a total of 76 cookies.
76 divided by 24 isn’t an even quotient so you round it to 4.
A gemstone is cut in the shape of a triangular pyramid. The area of the base of the pyramid is 42 square millimeters. The height of the pyramid is 4 millimeters. What is the volume of the gemstone? (Recall the formula V = one-third B h.)
Answers
Answer:
the volume of the gemstone is 56 millimeters^3
Step-by-step explanation:
The computation of the volume of the gemstone is shown below:
As we know that
The volume of the triangular pyramid is
= (1 ÷ 3) × (base area) × h
Now put the given values to the above formula
= 1 ÷ 3 × 42 × 4
= 56 millimeters^3
Hence, the volume of the gemstone is 56 millimeters^3
The above formula should be used and the same should be considered
Use each student's quiz score to answer the questions.
Annika's quíz scores
60%, 75%, 78%, 80%, 85%, 85%, 90%
Josiah's quíz scores
62%, 85%, 68%, 79%,83%, 90%,92%
Annika has a mean that is
mean,
Josiah's median is______
Annika's median
The range is
Who has the lowest interquartile range?
Answers
Answer:
Annika has a mean that is 79%
Mr. Brown purchased 5.75 pounds of chicken that cost $2.40 per pound.
What is the total the Mr. Brown paid?
Answers
Answer:
8.15 is the answer
Step-by-step explanation:
It takes Bobby 12 hours longer to build a robot than it takes Alex. Together, they can build the Robot in 8 hours. How long does it take Bobby to build the robot by himself?
Answers
Answer:
24 hours
Step-by-step explanation:
The computation of the number of hours taken by Bobby to build the robot by himself is shown below:
Given that
Bobby could take 12 hours
Together they could build in 8 hours
So based on the above information
the number of hours taken by Bobby to build the robot by himself is
Let us assume the above line be x
So,
[tex]\frac{1}{8}-\frac{1}{12} = \frac{1}{x} \\\\\frac{6 - 4}{48} = \frac{1}{x} \\\\\frac{2}{48} = \frac{1}{x} \\\\x = \frac{48}{2}[/tex]
x = 24 hours
A hot chocolate recipe calls for three teaspoons of cocoa for every cup of milk. How many teaspoons of cocoa are needed for a batch that uses three cups of milk?
Answers
Answer:
9 teaspoons are needed
Step-by-step explanation:
multiply 3 teaspoons by 3 cups to find the answer.
the answer is 9 teaspoons.
9 teaspoons are needed for a batch that uses three cups of milk.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that hot chocolate recipe calls for three teaspoons of cocoa for every cup of milk.
We need to find multiply 3 teaspoons by 3 cups to find the answer.
Therefore, we will use unitary method;
3 teaspoons x 3 cups = 9
Hence the answer is 9 teaspoons.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ2
what is the slope of the line?
Answers
Answer:
2/3
Step-by-step explanation:
rise/run
2 up, 3 right
Answer:
[tex]m=\frac{2}{3}[/tex]
Step-by-step explanation:
PLEASE HELP,,, TIMED!!
Consider f (x) = StartFraction negative 14 x Superscript 4 Baseline + 2 x + 18 Over x Superscript 4 Baseline minus 3 x squared EndFraction Which statement represents the correct interpretation of Limit of f (x) as x approaches plus-or-minus infinity
Answers
Answer:
I know that is not a!
Step-by-step explanation:
I just submitted it and I got it wrong unfortunately it does not tell me the correct answer but at least it brings your options down to only 3! I am really sorry I do hope this helps a little!
Answer:
It is D
Step-by-step explanation:
Got it correct!
What is the area of this shape?
Answers
Answer:
12mm (triangle)
165mm (whole shape)
Step-by-step explanation:
The triangle is 6 x 4 = 24 ÷ 2= 12
(divide by 2 because its a teiangle)
2nd shape is 10 x 8 = 80
3rd shape is 6 x 12 = 72
72 + 80 + 12 = 165mm
Find g(x), where g(x) is the translation 2 units right of f(x)=x2. Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Answers
Answer:
g(x) =( x² - 2 )
Step-by-step explanation:
We have the orignal function, and that is x².
to shift 2 units to the right, we add two the value of the x² in parebtheses, and it shifts 2 units to the right in the graph.
plz help me with this one
[tex]y = - 3 \\ y = 3x + 12[/tex]
Answers
Answer:
-3=3x+12
Step-by-step explanation:
The first term of a geometric sequence is 5 and the common ratio is 2. What is the 4th term of the sequence?
Answers
Answer:
80Step-by-step explanation:
[tex]a_n=a_1\cdot r^{n-1}\\\\a_1=5\\r=2\\n=4\\\\a_4=5\cdot2^4=5\cdot16=80[/tex]
Lenny has 7/8 cup of milk. He used 5/8 cup to make a cake and 2/8 cup to make cupcakes. How much milk did he have left after making both?
Answers
Expand LaTeX: (4a - 3b^3)^2.
Answers
(4a-3b^3)^2
(4a-3b^3)(4a-3b^3)
16a-12ab^3-12ab^3+9b^3
16a+9b3
Divide 9 by 3 then subtract two double the result
Answers
Answer:
2
Step-by-step explanation:
9 ÷ 3 - 2 × 2
3 - 2 × 2
1 × 2
2
What is the approximate volume of the cone?
Use 3.14 for π.
A 1206 cm³
B 2170 cm³
C 3260 cm³
D 6510 cm³
Answers
condense this logarithm to a single logarithm
6log 5u
Answers
Answer:
log_5(u^6)
Step-by-step explanation:
According to log rules, log_a(b^n) = nlog_a(b), reversing this we get that log_5(u^6) is what you are looking for.
what is x ?
3/2x -1=5
Answers
Answer:
4
Step-by-step explanation:
3/2x -1 = 5
then
3/2x = 5+1
then
3/2x = 6
then
x = 6 / (3/2)
then
x = 6 *2/3
then
x = 4