Answers
[tex]\\ \rm\Rrightarrow \left(x+\dfrac{1}{x}\right)^2[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x}\right)^2\dots(1)[/tex]
.Find x²[tex]\\ \rm\Rrightarrow \left(\dfrac{1}{\sqrt{2}+\sqrt{5}}\right)^2[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{2+2\sqrt{10}+5}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{2\sqrt{10}+7}[/tex]
Now put in eq(1)
[tex]\\ \rm\Rrightarrow \left(\dfrac{\dfrac{1}{2\sqrt{10}+7}+1}{\dfrac{1}{2\sqrt{10}+7}}\right)^2[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{1+2\sqrt{10}+7}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{2\sqrt{10}+8}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{(2\sqrt{10}+8)\cancel{(2\sqrt{10}+7)}}{\cancel{2\sqrt{10}+7}}\right)^2[/tex]
[tex]\\ \rm\Rrightarrow (2\sqrt{10}+8)^2[/tex]
[tex]\\ \rm\Rrightarrow 40+32\sqrt{10}+64[/tex]
[tex]\\ \rm\Rrightarrow 32\sqrt{10}+94[/tex]
More simplification (If required)
[tex]\\ \rm\Rrightarrow 2^52^{\frac{1}{2}}\sqrt{5}+94[/tex]
[tex]\\ \rm\Rrightarrow 2^{5+\frac{1}{2}}\sqrt{5}+94[/tex]
[tex]\\ \rm\Rrightarrow 2^{\frac{11}{2}}\sqrt{5}+94[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{2^{11}}\sqrt{5}+94[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{2048(5)}+94[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{10240}+94[/tex]
Most accurate
[tex]\\ \rm\Rrightarrow 101.19+94[/tex]
[tex]\\ \rm\Rrightarrow 195.19[/tex]
Related Questions
I NEED HELP! ASAP, THIS IS SO HARD AND MY BRAIN HURTS, IF U HELP ME WITH OTHER QUESTIONS LIKE THIS ILL GIVE U 50+ POINTS
Answers
Answer:
24.3
Step-by-step explanation:
We need to follow the order of operations PEMDAS:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Carry out the operation in the parentheses first:
3³ + 14.7 ÷ 7 - (1.2 × 4)
⇒ 3³ + 14.7 ÷ 7 - 4.8
Now the exponent:
⇒ 3³ + 14.7 ÷ 7 - 4.8
⇒ (3 × 3 × 3) + 14.7 ÷ 7 - 4.8
⇒ 27 + 14.7 ÷ 7 - 4.8
Now, the division (there is no multiplication):
⇒ 27 + 14.7 ÷ 7 - 4.8
⇒ 27 + 2.1 - 4.8
Finally, carry out the addition and subtraction (from left to right)
⇒ 27 + 2.1 - 4.8
⇒ 29.1 - 4.8
⇒ 24.3
2x+4 (2x+7)= 3(2x+4)
solve x
Answers
[tex]2x + 4(2 x + 7) = 3(2x + 4)[/tex]
to find:solve the ( x ).
solution:[tex]2x + 4(2x + 7) = 3(2x + 4)[/tex]
[tex]2x + 8x + 28 = 6x + 12[/tex]
[tex]10x + 28 = 6x + 12[/tex]
[tex]4x + 28 = 12[/tex]
[tex]4x = - 16[/tex]
[tex]x = - 4[/tex]
2x+4(2x+7)= 3(2x+4)
2x+8x+28=6x + 12
10x+28=6x + 12
4x+28=12
4x= -16
x=-4
HELP ASAP. Worth 10 points
Judy studied for 7/12 of an hour, and her sister studied for 2/3 of an hour. About how much time did they spend studying altogether?
They studied for half an hour.
They studied for an hour.
They studied for a little less than an hour.
They studied for a little more than an hour.
Answers
Answer:
They studied for a little more than an hour?
Step-by-step explanation:
7/12 of 60 Mins is 35 mins and 2/3 is 40 mins 40+35=75 mins
which is a little more than an hour, 15 mins more to be precise.
Find the measure of
Answers
Step-by-step explanation:
angles a,f,g form a triangle
sum of angles in ∆ = 33 + 112+ a = 180
145 + a = 180
a = 35°
The radius of a circle with area A is approximately $\sqrt{\frac{A}{3}}$ . The area of a circular mouse pad is 48 square inches. Estimate its radius to the nearest tenth
Answers
The radius of the circular mouse pad is 3.91 inches if the area of a circular mouse pad is 48 square inches.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
The area of the circular mouse pad = 48 square inches
The area of the circle:
[tex]\rm A = \pi r^2[/tex]
[tex]\rm 48 = \pi (r)^2[/tex]
Take π = 3.14
r = 3.909 inches ≈ 3.91 inches
Thus, the radius of the circular mouse pad is 3.91 inches if the area of a circular mouse pad is 48 square inches.
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Zahara asked the students in her class their gymnastic scores and recorded the scores in the table shown below:
Gymnastic Scores
Score Number of Students
0 1
1 1
2 2
3 6
4 4
5 3
6 2
Based on the table, what is the mean gymnastic score?
Answers
Answer:
It would be 3.5
Step-by-step explanation:
1+1+2+6+4+3+2
so the mean is 3.5
30 POINTS!!!!! HELP QUICK
Find the area of the shaded region.
Use 3.14 for pi.
Answers
The area of the shaded region is 994.74 square in if the area of the circle is 1384.74 square in and the area of the triangle is 390 square in.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
As we know, the area of the circle is given by:
A = πr²
r = 21 in
A = 3.14(21)² = 1384.74 square in
Area of the triangle:
a = (39)(20)/2 = 390 square in
The area of the shaded region = 1384.74 - 390 = 994.74 square in
Thus, the area of the shaded region is 994.74 square in if the area of the circle is 1384.74 square in and the area of the triangle is 390 square in.
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Patrick is designing a large stained glass window for the library. If the area of the window is 36 feet, how long is each side
Answers
write the ratio in the simplest form 40kg : 480g
Answers
Answer: 1kg : 12g
Step-by-step explanation: Ratio in the simplest form is to divide both numbers by the greatest factor.
40 divided by 40 is 1
480 divided by 40 is 12
The answer is 1 kg : 12g
The temperature was 6° C.
By how much has it fallen if it is now -5° C?
Answers
Answer:
11 °C
Step-by-step explanation:
Initial temperature = 6 °CFinal temperature = - 5°CChange in temperature= 6 - (-5)
= 6 + 5
= 11 °C
Hope it helps you in your learning process.
Answer:
The temperature has fallen by 11° C.
Step-by-step explanation:
6° C - (-5° C) = 11° C.
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answers
Answer:
(4, 0) and (-2, 0)(1, -9)(0, -8)Step-by-step explanation:
Finding the x-intercepts :
y-value of the x-intercept is 00 = (x - 4)(x + 2)x - 4 = 0 ⇒ x = 4x + 2 = 0 ⇒ x = -2The x-intercepts are : (4, 0) and (-2, 0)Finding the vertex :
Expanding the function ff(x) = (x - 4)(x + 2)f(x) = x² - 4x + 2x - 8f(x) = x² - 2x - 8Vertex = (h, k)h = -b/2a = -(-2)/2(1) = 1k = (1)² - 2(1) - 8k = 1 - 2 - 8 = -9The vertex is : (1, -9)Finding the y-intercept :
Substitute x = 0 in the functionf(0) = 0² - 2(0) - 8f(0) = -8The y-intercept is : (0, -8)In order to find x-intercept, the f(x) or y will be 0
=================
(x-4)(x + 2) = 0
(x-4) = 0, (x + 2) = 0
x = 4, x = -2
x intercepts: (4, 0) and (-2, 0)
2) What is the ordered pair of the vertex?In order to find vertex use the formula: x = -b/2a
y = (x-4)(x + 2)
y = x² -4x + 2x -8
y = x² - 2x -8
Now find x-coordinate of vertex:
x = -(-2)/2(1)
x = 2/2
x = 1
y coordinates: (1-4)(1 + 2) = -9
Ordered pair of vertex: (1, -9)
3) What is the y intercepts of the graph?In order to find y intercept, insert x = 0
y = (0-4)(0 + 2)
y = -8
y intercept: (0, -8)
Help me please asap!!! NOTE : PLEASE LOOK AT THE 3 PICTURES & I NEED A EXPLANATION
Answers
Step-by-step explanation:
3/5 - 1/3 = 4 /15
5/6 - 2/3 = 5/6 - 4/6 = 1/6
7/9 - 2/3 = 7/9 - 6/9 = 1/9
5/8 - 1/6 = (15 - 4) /24 = 11/24
(All the above ones I have taken common factor and subtracted them)
5 x 9/10 = 45/10 = 9/2 (simplified)
2/7 x 3 = 6/7
3 x 2/15 = 6/15
4x 2/6 = 8/6 = 4/3 (simplified form)
Hope this helps!!!
i don’t understand how to find x to solve.
Answers
Answer:
X + 3
Step-by-step explanation:
There is no definite working. The first container is what I call the base because everything is a little above the first container, X. They are basically asking you what is the total of the four jars bigger than X. In other words how many steps more to climb before the top floor while you are on the first step. So then you add the other numbers like 0.5 etc which will give you X +3. Hope it helps.
The diameter of a circle is 12 centimeters. What is the circle's area?
Answers
BEST ANSWER :
CIRCLE
solve for area
A = 113.1 cm^2
d diameter = 12 cm.
Answer:
Area of circle = π r^2
Step-by-step explanation:
Diameter = 12
Radius = 12/2
= 6
Area = π x 6^2
= π x 36
= 113.04
therefore the area of the circle is 113.04
find the volume pleaseeeee
Answers
Volume = length * width * height
= 10 * 3 * 6
= 180 cubic inches
Answer Number 2 pleaseeee
Answers
Answer:
Yes
Step-by-step explanation:
What is the length of ZA? ZA = 3cm ZA = 4cm ZA = 5cm ZA = 6cm
Answers
Answer:
please what is the correct question
Answer: its the last one
Step-by-step explanation:
A die is being rolled. Find the probability of rolling less than a 3.
Answers
Answer: 2/6
Step-by-step explanation:
Probability is nothing but the
number of favourable outcomes / number of total outcomes
Emma enjoys flying kites. her red kite has a maximum altitude of 117.46 meters, and her black kite has a maximum altitude of 362.26 feet. one foot is the same as 0.3048 meters. which kite has a higher maximum altitude, and how many feet higher is it? a. the black kite has a maximum altitude 74.62 feet higher than the red kite. b. the black kite has a maximum altitude 33.66 feet higher than the red kite. c. the red kite has a maximum altitude 23.11 feet higher than the black kite. d. the red kite has a maximum altitude 7.04 feet higher than the black kite.
Answers
The red kite has a maximum altitude 23.11 feet higher than the black kite.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
1 feet = 0.3048 meters, hence:
117.46 m = 117.46 m * 1 ft per 0.3048 meter = 385.37 feet
Difference in height = 385.37 feet - 362.26 feet = 23.11 feet
The red kite has a maximum altitude 23.11 feet higher than the black kite.
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• A. All real numbers
• B. All real numbers except 2
• C. All real numbers except -6
• D. All real numbers except -6 and 2
Answers
Answer:
Option C
Step-by-step explanation:
you cancel the whole parentheses.
So you know, x+6 can't equal to 0.
that's why there is a choice that is all real numbers but not -6.
Answer:
A. All real numbers
Step-by-step explanation:
Given
(x - 2)(x + 6)/7(x + 6) = (x - 2)/7On cross multiplying,
(x - 2)(x + 6)(7) = (x - 2)(x + 6)(7)LHS = RHSThis means on applying any value for x, both sides will be equalHence, the correct option is AWhich of the following fall between 12 and 13?
Answers
4) In each of the following figures, find the value of the angles a,b,c,x,y,and z
Answers
Step-by-step explanation:
due to the principle of identical angles in parallel lines when intercepted by an inclined line,
y = 49°
the angles above an intersected line are the same as below that intersected line (just mirrored left-right).
and at the bottom, the angles an insecticide line has with one line must be the same as with another line that is parallel to the first line.
so, both indicated angles are the same as the original angle on the top : 49°
Does the infinite geometric series diverge or
converge? Explain.
5 + 20 + 80 + 320 +
Answers
Answer:
Diverge
Step-by-step explanation:
Infinite geometric series: In infinite geometeric series, if the common ratio 'r' is in between the interval -1 < r < 1, then it converges. If the common ratio 'r' is is not in the interval -1 < r < 1, then it diverges.5 + 20 + 80 + 320 + .....
[tex]\sf Common \ ratio = \dfrac{second \ term}{first \ term}\\[/tex]
[tex]\sf r = \dfrac{20}{5}\\\\ r = 4[/tex]
r = 4 is not in the interval -1 < r < 1. So this infinite geometric series diverges.Image attached:- Solve if you can!
Answers
This is a set of rules for order of expressions that is taught to a large number of students at the advance arithmetic and early algebra phases of their schooling. For the expression given in the question it directs:
6/2(1 + 2) = 6/2(3) —Do what is in the parentheses first.
= 6/2(3) — No change because next come handling exponents, of which there are none.
= 3(3) —Do multiplications and divisions in order from left to right.
= 9. —Repeating previous step since there is one division and one multiplication.
There are problems with this set of rules because they were designed for advanced arithmetic and early algebra. They do not handle more advanced expressions. For advanced arithmetic, typically all operations are expressed explicitly, so that 6/2(1 + 2) would not be given, but instead 6/2 × (1 + 2). We will see in the next convention how this distinction can be important, and standard PEMDAS/BODMAS do not distinguish the two expressions
A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M
Answers
Answer:
hope it's helpfull...... ;)
ANSWER FAST, WILL MARK!!!
Answers
Answer:
(2, 3)
Step-by-step explanation:
The solution of two equations on a graph is where they intersect. In this case (2, 3) is the answer.
Answer:
(x,y) = (2,3) so C?
Step-by-step explanation:
=> y = x/2+2
=> y = x + 1
from that info, you can tell y = y, meaning x/2 + 2 = x+1
solving:
=> x/2 + 2 = x + 1
=> 1/2x +2 = x + 1
=> -x -x
=> - 1/2x + 2 = 1
=> -2 -2
=> -1/2x = -1
=> * 2/-1 * 2/-1
=> x = 2
solve using substitution now:
(let's plug it in to the easiest y = statement)
=> y = x+1
=> y = 2 +1
=> y = 3
(2,3) is your answer
1/5 x 1/5 x 1/5 x 1/5
Answers
The two expressions below have the same value when rounded to the nearest hundredth. log subscript 5 baseline b. log subscript 9 baseline 48 what is the approximate value of log b to the nearest hundredth? 0.93 1.23 9.16 65.53
Answers
The value of log b to the nearest hundredth is 1.23. The correct option is the second option - 1.23
Evaluating logarithmFrom the question, we are to determine the value of log b to the nearest hundredth
From the given information
[tex]log_{5}b = log_{9}48[/tex]
But,
[tex]log_{9}48 =1.76186[/tex]
∴ [tex]log_{5}b =1.76186[/tex]
By one of the laws of logarithm
∴ [tex]b =5^{1.76186}[/tex]
b = 17.0407
Then,
log b = log(17.0407)
= 1.2315
∴ log b ≅ 1.23
Hence, the value of log b to the nearest hundredth is 1.23. The correct option is the second option - 1.23
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Answer:
The answer is 1.23
Step-by-step explanation:
Trust me I took the edge quiz 2022
Select the correct answer from each drop-down menu. The table below represents the function f, and the following graph represents the function g. x -6 -5 -4 -3 -2 -1 0 1 f(x) 8 -2 -8 -10 -8 -2 8 22 Complete the following statements. The functions f and g have . The y-intercept of f is the y-intercept of g. Over the interval [-6, -3], the average rate of change of f is the average rate of change of g.
Answers
Answer:
Complete the following statements.
The functions f and g have the same axis of symmetry.
The y-intercept of f is greater than the y-intercept of g.
Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.
Answer:
First blank: The same axis of symmetry
Second blank: Greater than
Third blank: Less than
Step-by-step explanation:
PLATO
Please mark Brainliest <( ¨ )
Find the maximum value on (0, infinity) for f(x)=7x-2xlnx
Answers
f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).
How to obtain the maximum value of a function?To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
f(x) = max{0,x} then f(x)=0 if x<0 and f(x)=x if x≥0.
f(x)=7x-2xlnx
When x tends to -∞, f is the constant function zero, therefore limit n tends to infinity f(x) = 0.
When x tends to ∞, f(x)=x and x grows indefinitely. Thus limit n tends to infinity f(x) = infinity.
f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x) = x and if x<0, f'(0)=0 (the derivative of the constant zero).
In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,
f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).
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