Answer:
x+(1/x) = 10 and x²+ (1/x²) = 98Step-by-step explanation:
Given that :
x = 5-2√6
1/x = 1/(5-2√6)
The denominator = 5-2√6
The Rationalising factor of 5-2√6 = 5+2√6
On Rationalising the denominator then
⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]
⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]
⇛ 1/x = (5+2√6)/[5²-(2√6)²]
Since (a+b)(a-b) = a²-b²
Where ,
a = 5 and b = 2√6⇛1/x = (5+2√6)/(25-24)
⇛ 1/x = (5+2√6)/1
⇛ 1/x = 5+2√6
Now,
x +(1/x)
⇛ 5-2√6+5+2√6
⇛ 5+5
⇛ 10
Therefore, x+(1/x) = 10.
On squaring both sides then
⇛ [x+(1/x)]² = 10²
⇛ x²+2(x)(1/x)+(1/x)² =100
⇛ x²+2+(1/x)² = 100
⇛ x²+(1/x²) = 100-2
⇛ x²+(1/x²) = 98
Therefore, x²+(1/x²) = 98.
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Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....
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Combined, there are Asians, Africans, Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by . The difference between the number of Europeans and Americans is . If the number of Africans is doubled, their population exceeds the number of Europeans and Americans by . Determine the number of Asians, Africans, Europeans, and Americans in this village
There are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.
To determine the number of Asians, Africans, Europeans, and Americans in the village, the following calculation must be performed:
A.S + A.F + E.U + A.M = 177 A.S = A.F + E.U + 69 E.U - A.M = 13 E.U = A.M + 13 2A.F = E.U + A.M + 29 A.F + E.U + 69 + A.F + E.U + A.M = 177 A.F + A.M + 13 + 69 + A.F + A.M + 13 + A.M = 177 2A.F + 3A.M = 177 - 13 - 13 - 69 E.U + A.M + 29 + 3A.M = 82 A.M + 13 + A.M + 29 + 3A.M = 82 5A.M = 82 - 13 - 29 A.M = 40/5 A.M = 8 E.U = 8 + 13 = 21 A.F = (21 + 29) / 2 = 25 A.S = 177 - 25 - 21 - 8 = 123
Therefore, there are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.
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License plates in the great state of Utah consist of 2 letters and 4 digits. Both digits and letters can repeat and the order in which the digits and letters matter. Thus, AA1111 and A1A111 are different plates. How many possible plates are there?
Answer:
Step-by-step explanation:
The correct option is 3. Step-by-step explanation: It is given that License plates in the great state of Utah consist of 2 letters
A theater group made appearances in two cities. The hotel charge before tax in the second city was $ 1500 higher than in the first. The tax in the first city was
3%, and the tax in the second city was 9.5%. The total hotel tax paid for the two cities was $580. How much was the hotel charge in each city before tax?
First city:
si
Х
5
?
Second city: 0
I’m
9514 1404 393
Answer:
first city: $3500second city: $5000Step-by-step explanation:
Let x and y represent the hotel charges in the two cities. The relations we are given are ...
x - y = -1500 . . . . . . second city hotel charge was 1500 more
0.03x +0.095y = 580 . . . . . total tax paid was 580
Using the first equation, we can write an expression for x:
x = y -1500
Substituting that into the second equation gives ...
0.03(y -1500) +0.095y = 580
0.125y = 625 . . . . . . . add 45 to both sides and simplify
y = 5000 . . . . . . . . . . multiply by 8
x = 5000 -1500 = 3500
The hotel charges were ...
First city: $3500
Second city: $5000
What is slope I need help finding the slope please help me
The slope is 3 this is intergers solution the right side is positive and left side is negative
PLEASE HELP WITH THIS ONE QUESTION
Answer:
X = 0 or X = -2
Step-by-step explanation:
2x^4 + 16x = 0
x^4 + 8x = 0
x(x+2) (4+x^2_2x) = 0
x + 2 = 0
or
4+x^2_2x=0
How much money must be deposited at the end of each year if the objective is to accumulate $250,000 after 10 years? Assume interestis eamed at the rate of 10 percent compounded annually. How much interest will be eamed?
Answer:
Step-by-step explanation:
sasđdádd
Sandy threw a ball 86 inches. She
picked it up and threw it another 12
inches. Then she threw it another 10
inches. How many feet in total, did
Sandy throw the ball?
Due tomorrow
i need some help here plzzzzzzzzzz
NO LINKS!!!!!!
Answer:
I'm pretty sure it's A,B, and D.
Step-by-step explanation:
How many groups of 3/4are in 11/4
Answer:
12
Step-by-step explanation:
there are 12 3/4 on 11/4
There are 2 pigs, 3 chickens, 4 cows and 5 ducks on a farm. If the farmer wants 3 animals
for a play but only needs one two-legged animal, how many ways can he choose the three animals?
Answer:
6 ways
Step-by-step explanation:
1: 2 pigs, 1 chicken
2: 2 pigs, 1 duck
3: 1 pig, 1 cow, 1 chicken
4: 1 pig, 1 cow, 1 duck
5: 2 cows, 1 chicken
6: 2 cows, 1 duck
The farmer can choose the animal in 6 ways as per different combinations.
Solution to the above problem
The different combinations can be written as follows:
nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time
Since we want 3 animals we can make different pairs as listed below
1: 2 pigs, 1 chicken
2: 2 pigs, 1 duck
3: 1 pig, 1 cow, 1 chicken
4: 1 pig, 1 cow, 1 duck
5: 2 cows, 1 chicken
6: 2 cows, 1 duck
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Kendrick bought a laundry hamper online. It cost $9 plus 10% shipping and handling. What was the total cost?
Work Shown:
10% of $9 = 0.10*9 = 0.90
The shipping cost is $0.90, or 90 cents.
This means the total cost goes from $9 to $9.90
Screenshot proidedpls answer quick
Answer: The price of the torch is 2 and 2/2.5 is 80% or 8/10th of the total price.
Step-by-step explanation:
x is the price of the battery
x + 1.50 is the price of the torch
x + (x + 1.50) is 2.50
x + (x + 1.50) = 2.50
2x = 2.50 - 1.50
2x = 1
x = 1/2
x = 0.50
The price of the torch is 2 and 2/2.5 is 80% or 8/10th of the total price.
Two sides of a triangle measure 27 inches and 32 inches. Which could represent the length of the third side?
Answer:
Step-by-step explanation:
The third side could have dimension x
32 - 27 < x < 32 + 27
5 < x < 59
There are a few special triangles
Equilateral triangle could have legs
27, 32, 27
or
32, 27, 32
A right triangle could have the third side
√(27² + 32²) = √1753 which is about 41.87
or
√(32² - 27²) = √295 which is about 17.18
Notice all these fit within the original limits specified.
Answer:
The third side is greater than 5 but less than 59.
Step-by-step explanation:
Remember: Given any two sides of a triangle, the length of the third side is greater than the difference but less than the sum of the length of the two given sides.
So 27 and 32 The given two sides
32 - 27 = 5 Greater than the difference (greater than 5)
32 + 27 = 59 Less than the sum (less than 59)
Complete the table using the equation y = 8x + 9.
Answer:
×=9-y
Step-by-step explanation:
you can do it believe in your self
please assist me
NO LINKS!!
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today, I hope you are having a nice day!
We can solve this in two steps, Comprehension and Solving. I'll go ahead and start with Comprehension.
If you have any questions feel free to ask away!!
Comprehension
We know according to the laws of geometry that all angles in a triangle add up to 180 degrees.
We also know that in an isosceles angle, the base angles are equation to each other.
Now that we know what we need to know, we can setup an equation.
[tex]2x-6+(2x)=180[/tex]
We can do this because first of all, we know that 2x-6 is one of the angles and as per the base angles of an isosceles triangle we know that both base angles are x, therefore we can add 2x to get 180 degrees.
I'll start solving now.
Solving
We can solve this by using the equation we made above and solving it with algebra.
[tex]2x-6+2x=180\\4x-6=180\\4x=186\\x=46.5[/tex]
We know that x is equal to 46.5 degrees. We can check that by inputting it into the equation.
[tex]2(46.5)-6+2(46.5)=180?\\4(46.5)=186?\\46.5=46.5[/tex]
We've proven that our answer is correct by double checking,
Therefore the answer is 46.5!
Cheers!
if a chocolate cake is divided into six equal slices and each slice has 280 calories
Answer:
Whats the question?
Step-by-step explanation:
Answer:
1,680
Step-by-step explanation
6 slices each 280 calories, 280 x 6 = 1,680
Which of the following best describes the equation below?
y^2=x
A.
both a relation and function
B.
function only
C.
neither a relation nor a function
D.
relation only
Answer:
I believe it's a relation
Answewant to be allies?
Step-by-step explanation: lol
Please Help! I will give you a lot of points! (It's really the guess & check I'm having trouble with. Is there an easier way to find the standard divisor (d)?)
Four people pool their money to buy 60 shares of stock. The amount that each person contributes is shown in the following table. Use Adam's method with d=108 to apportion the shares of stock.
----Only pay attention to number 12 in the picture
Answer:
See below
Step-by-step explanation:
The given modifier solves this without further update.
See attached table
Evaluate the expression for the given variable values.
3∣m+2n∣2−(mn)2 if m=3 and n=−5
how do you find a missing fraction of a pie chart? (:
Answer:
Pasend pic
Step-by-step explanation:
Para I answer ko75% of the amount is 4.5 cm
Answer:
6
Step-by-step explanation:
can someone pls help me … I really need help
Answer:
It's the last one!
Step-by-step explanation:
Which of the following correctly describes the graph?
Answer:
C is correct
Step-by-step explanation:
The x and y axes are linear, the plot is linear. The constant rate of change is assured with those conditions.
convert this fraction to a decimal 1/200
Answer:
0.005
Step-by-step explanation:
Three times the difference “2x minus 1” is the opposite of 9 times x. Solve for x.
Answer:
x = 1/5 - first box
Step-by-step explanation:
Let's interpret this by using what I call the "isolated-x method."
First, we can simplify whatever's being affected in the parentheses.
#1: 3 times (2x) is equal to 6x
#2: 3 times (- 1 | equal to -1) results in -3, or + -3
So now we're working with 6x - 3 = -9x.
Now, we'll add a positive 9x to the -9x, since it can be hugely helpful to have one side result in 0.
Now we're working with 15x (6x + our new 9x) - 3 = 0
Since we have "whole like terms" we can now easily add 3 to each side.
Now we're working with 15x = 3 (0 + our new 3)
We can finish by dividing each side by 3.
15x = 3 now turns into 5x = 1.
To get from 5 to 1 you can multiply 5 by its "multiplicative inverse," also known as 1/5.
Therefore, x = 1/5
Hopefully this helped a bunch! Tell me if you need any further assistance...
( :
find the inverse for the function f(x)= 14-3x/8-2x
Answer:
y = 8x/93
Step-by-step explanation:
To get the find the inverse function, swap x and y and solve the equation for x.
In a garden 30% of the plants are carrots. If 63 plants are not carrots, how many of the plants are carrots.
Must show each step.
Answer: 27 see my work
Step-by-step explanation:
1. We know that 30% are carrots, meaning that 70% are not carrots (30% + 70% = 100%)
2. Since 70% and 63 of the plants are not carrots, we know that 63 = 70%
3. We need to find 30% of the plants (all of the carrots) so let’s divide 63 by 7
63 = 70%
*divide both by 7*
9 = 10%
4. We know that 9 plants is equivalent to 10% of the plants, so let’s multiply by 3 to get the number of carrots
9 = 10%
*multiply by 3*
27 = 30%
There are 27 carrots
given the sequence tn defined recursively below, find t4.
Answer:
[tex]t_4 = 20[/tex]
Step-by-step explanation:
The base case in the recursive function are:
[tex]t_1 = 1[/tex]
[tex]t_2 = 2[/tex]
The recursive case is equal to:
[tex]t_n = 2t_{n-1} + 3t_{n-2}[/tex]
So replace [tex]t_n[/tex] for [tex]t_4[/tex]:
[tex]t_4 = 2t_{3} + 3t_{2}[/tex]
In the new expression [tex]t_2[/tex] is a base case so you don't have to worry for that part, but [tex]t_3[/tex] is still the recursive case so evaluate again in [tex]t_n[/tex]
[tex]t_3 = 2t_{2} + 3t_{1}[/tex]
[tex]t_2[/tex] and [tex]t_1\\[/tex] are define as base cases so you replace for it's numbers:
[tex]t_3 = 2(2) + 3(1) = 7[/tex]
Now return to [tex]t_4[/tex] and replace for the new values:
[tex]t_4 = 2(7) + 3(2) = 14 + 6 = 20[/tex]
So the final answer is 20
simplify the expression 5 (6 + 7 and) using the distributive property
Answer:
65
Step-by-step explanation:
5(6 + 7)
Distribute 5 to 6 and 7.
(5x6)+(5x7)
Multiply.
30+35
Add.
65
Hope this helps :)
Translate triangle ABC using the vector ( 6, - 2).
Answer:
Move each vertex 6 to the right, and 2 to the bottom, rest of the triangle will come automatically. It should look similar to the one I drew.
After translation vertices of triangle ABC are (0, 3), (7, 3) and (6, -2).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
The given vector is (6, -2).
From the given triangle vertices are (-6, 1), (1, 1) and (0, -4)
From the given vector, it shows 6 units right shift and 2 unit down shift.
Here, vertices of image are
(-6, 1)→(-6+6, 1-(-2))→(0, 3)
(1, 1)→(1+6, 1-(-2))→(7, 3)
(0, -4)→(0+6, -4-(-2))→(6, -2)
Hence, after translation vertices of triangle ABC are (0, 3), (7, 3) and (6, -2).
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