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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Similar questions;
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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Six less than the product of 8 and a number equals 2
Answer:
unknown number = 1
Step-by-step explanation:
Let the unknown number be x.
(8×x)-6=2
8x-6=2
8x=2+6
=8
x=8÷8
=1
Hence, unknown number = 1.
Determine which consecutive integers do not have a real zero of f(x) = x3 + 9x2 + 8x – 5 between them.
The difference between the two is 4,5
Rewrite as equivalent rational expressions with denominator (c- 9) (c+9)(c + 6):
Answer:
Step-by-step explanation:
as (c + 9)(c - 9) = c² - 81
and (c - 9)(c + 6) = c² - 3c - 54
8(c + 6) = 8c + 48
(c² - 81)(c + 6) (c - 9)(c + 9)(c + 6)
10c(c + 9) = 10c² + 90c
(c² - 3c - 54)(c + 9) (c - 9)(c + 9)(c + 6)
The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. 8 / (c² - 81)
2. 10c / (c² - 3c - 54)
Now,
Solve the expressions for the denominator (c- 9) (c+9)(c + 6) as;
1. 8 / (c² - 81) = 8 / (c² - 9²)
= 8 / (c + 9) (c - 9)
Thus, 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c² - (9- 6)c - 54)
= 10c / (c² - 9c + 6c - 54)
= 10c / [c(c-9) + 6(c - 9)]
= 10c / (c + 6) (c - 9)
Thus, 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
Therefore, The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;
1. 8 / (c² - 81) = 8 / (c + 9) (c - 9)
2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)
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20. True or False
When you multiply or divide
by a negative number, you
flip the sign
Answer:
That is true
You must flip the sign when you are multiplying or dividing by a negative number
(PHOTO) Please help me need this done by tomorrow thank you.
Answer:
2x+78=5x+15
78-15=5x-2x
3x=63
x=21
The number 40.8 is what percent of 68?
A circle has diameter 11 cm
Pythagoras theorem
Please answer will mark BRAINELIST:)
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y = 2 1/2 x + 5
Step-by-step explanation:
We were recently going over this. Slope formula: y2 - y1 / x2 - x1. In our case the slope is 2 1/2, and the y-intercept is 5.
Tell me if I'm wrong :)
-2-(3(x+6)-9-(7-x)-3x
Answer:
- 24 - 5x
Step-by-step explanation:
1) Remove Parentheses
-2 - 3x - 6 - 9 - 7 + x - 3x
2) Collect like terms
( -2 - 6 - 9 - 7) + (-3x+x-3x)
3) Simplify
3/4 x 2 5/8 ÷ 2 + 10/12
The product factor is 4,200.If one of the factor is 60 what is the other factor?Explain
Answer: The other factor is 70
Explanation: 4,200 divided by 60 is 70.
Graph the image of this figure after a dilation with a scale factor of 12centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer:
1.(-4,2)
2.(2,4)
3.(-2,8)
Answer:
(1,2) (0,4) (-4,2)
Step-by-step explanation:
took the quiz and got it right.
Tell whether the pairing is a function.
2.
Input
3
6
9
12
Output
1
2
N
1
Is it a function?
Answer:
I believe that it is function
Which choice is equivalent to the product below?
V14.18
A. A
B. 28
C. 4/28
D. 16.17
SUBMIT
Answer: Choice A. [tex]4\sqrt{7}[/tex]
===================================================
Work Shown:
[tex]\sqrt{14}*\sqrt{8}\\\\\sqrt{(14)*(8)}\\\\\sqrt{(7*2)*(2*4)}\\\\\sqrt{7*(2*2)*4}\\\\\sqrt{7*4*4}\\\\\sqrt{4*4*7}\\\\\sqrt{4}*\sqrt{4}*\sqrt{7}\\\\2*2*\sqrt{7}\\\\4\sqrt{7}\\\\[/tex]
20 feel from the ground i need a ladder placed 15 feet from the house what is the length
Answer:
helooo
Step-by-p explanation:
Given f(x) and g(x) are inverse functions. If f(-2)=1 then g(1)=-2
True
False
True.
The y-axis of the f(x) must equal to the x-axis of g(x)
The x-axis of the f(x) must equal to the y-axis of g(x)
string is 38 cm longer than his desk. Length of his reading book is 26 cm, what is the length of his string?
Answer:
has in lenght of 2 or 5
Step-by-step explanation:
odyssey ware
ig i d k
The figure below shows the graph of function f with domain [-1,1] and range [0,1].
The domain are the possible input while the range are the possible output
of a function.
(a) The domain = [-√2, √2], the range = [0, 2](b) The domain = [-1, 1], the range = [0, 1](c) The domain = [-1, 1], the range = [0, -1](d) The domain = [0, 2], the range = [0, 1](e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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PLEASE LOOK AT THE PHOTO !Number 32 please help me and thank you
❤️❤️❤️
Answer: 4 1/4 hours
Explanation: 2.5 + 1.75 = 4.25
4.25 = 4 1/4
Rewrite 2/11 and 1/7 so that they have a common denominator
Answer:its 22 and 7...........................
Step-by-step explanation:
PLEASE SHOW YOUR WORK!!!
Solve for y: 3^3 + 14 y- (25y - 13) = y + 7y - 9y
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3^3+14*y-(25*y-13)-(y+7*y-9*y)=0
Equation at the end of step 1
((3³ + 14y) - (25y - 13)) - -y = 0
Pull out like factors :
40 - 10y = -10 • (y - 4)
Equation at the end of step3:
-10 • (y - 4) = 0
STEP4:
Equations which are never true:
Solve : -10 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4
[tex]y = 4[/tex]Please Help! it's simple!
Answer:
28.27
circumference of finding a circle divided by two.
[tex](2\pi \:r {}^{2} ) \div 2[/tex]
(2×3.14×9)/2
56.55/2
28.27
Which inequality represents this sentence?
A number is no less than 48.
n < 48
n > 48
n < 48
n>48
The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.
Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.
It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.
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Answer: The correct answer is n≥48
Step-by-step explanation: Give me the brainiest
SOmeone help me i'm stuck on thia question
Answer:
17
Step-by-step explanation:
Ben left town a at 22:25 and arrived at Stone b at 2:40 the next morning how long did is Journey take
Answer: The journey took 4 hours and 15 minutes.
PLEASE HELP!!
What is the equation that represents the sequence shown below?
7/2, 7/4, 7/8, 7/16, ….
Answer:
7/2(1/2)^(n-1)
Step-by-step explanation:
multiplied by 1/2 each time, and first one is 7/2, so 7/2(1/2)^(n-1)
If GH is an altitude, what would mZGHF have to be?
Answer:
Using this formula, we can derive the formula to calculate the height (altitude) of a triangle: Altitude = (2 × Area)/base.
Step-by-step explanation:
Which equations and/or functions represent the graphed line? Select three options.
i included the graph and choices in the attachment (;
Answer:
1,3,4
Step-by-step explanation:
hope this helped
Select the statements which could describe the graph of a nonproportional relationship.
Answer:
what it says iiiiiiii888i888iiiii
Given:In quadrilateral WXYZ , and bisect each other at point A.
Prove: Quadrilateral WXYZ is a parallelogram.
Statement
Reason
1. and bisect each other. given
2. WA = YA
XA = ZA
definition of bisection
3. m∠YAZ = m∠XAW
Vertical Angles Theorem
4.
SAS criterion for congruence
5. ∠ YWX ≅ ∠WYZ
Corresponding angles of congruent triangles are congruent.
6. ||
converse of Alternate Interior Angles Theorem
7. m∠XAY = m∠ZAW
Vertical Angles Theorem
8. ∆XAY ≅ ∆ZAW
SAS criterion for congruence
9. ∠XZW ≅ ∠ZXY
Corresponding angles of congruent triangles are congruent.
10. ||
converse of Alternate Interior Angles Theorem
11. Quadrilateral WXYZ is a
parallelogram.
definition of parallelogram
Answer:
Given:In quadrilateral WXYZ , and bisect each other at point A.
Prove: Quadrilateral WXYZ is a parallelogram.
Statement
Reason
1. and bisect each other. given
2. WA = YA
XA = ZA
definition of bisection
3. m∠YAZ = m∠XAW
Vertical Angles Theorem
4.
SAS criterion for congruence
5. ∠ YWX ≅ ∠WYZ
Corresponding angles of congruent triangles are congruent.
6. ||
converse of Alternate Interior Angles Theorem
7. m∠XAY = m∠ZAW
Vertical Angles Theorem
8. ∆XAY ≅ ∆ZAW
SAS criterion for congruence
9. ∠XZW ≅ ∠ZXY
Corresponding angles of congruent triangles are congruent.
10. ||
converse of Alternate Interior Angles Theorem
11. Quadrilateral WXYZ is a
parallelogram.
definition of parallelogramTriangles can be similar or congruent. Similar triangles will have congruent angles but sides of different lengths. Congruent triangles will have completely matching angles and sides. Their interior angles and sides will be congruent. Testing to see if triangles are congruent involves three postulates, abbreviated SAS, ASA, and SSS.