Answer:
The expression can be simplified into [tex]2\,\sqrt{5} +2\sqrt{2}[/tex]
with no square roots in the denominator
Step-by-step explanation:
We are considering the expression [tex]\frac{6}{\sqrt{5}-\sqrt{2} }[/tex] which I believe is what you wanted to type in your question.
The idea behind simplification of the expression, is normally associated with the rationalization of the denominator by eliminating irrational numbers from it. This means to get rid of any "irrational" number expression (like in this example, the square root of non-perfect square numbers ([tex]\sqrt{5}\,\,\,and \,\,\sqrt{2}[/tex]).
We proceed by writing this quotient in an equivalent form by multiplying its numerator and its denominator by what is called the "conjugate" of the denominator. In our case, multiply by " [tex](\sqrt{5} +\sqrt{2})[/tex] ", because such product will allow the denominator to become a rational number:
[tex]\frac{6}{\sqrt{5}-\sqrt{2} }\,*\,\frac{(\sqrt{5}+\sqrt{2} )}{(\sqrt{5}+\sqrt{2}) } =\frac{6\,(\sqrt{5}\,+\,\sqrt{2} )}{\sqrt{5}^2-\sqrt{2}^2 }=\frac{6\,(\sqrt{5}\,+\,\sqrt{2} )}{3}=2\,\sqrt{5} +2\sqrt{2}[/tex]
where we find all square roots eliminated from the denominator
Box 1: Dimensions: x by 3x by x3 Area of base = x(3x) = 3x2 Box 2: Dimensions: x by 4x – 1 by x3 Area of base = x(4x – 1) = 4x2 – x Complete the statements about the number of terms in the polynomial representing the volume of each box. Box 1's volume will be a Box 2's volume will be a . Explain your reasoning.
Answer:
Box 1's volume will be a monomial
Box 2's volume will be a binomial
Explain your reasoning:
Box 1’s volume is modeled by a monomial times a monomial, so it will be a monomial. Box 2’s volume is modeled by a monomial times a binomial, so it will be a binomial.
Step-by-step explanation:
Feel free to copy and paste! Hope this helps! Have a great day!
BTW...If you have any questions for school...any grade level, any subject...just comment or ask. I will be sure to answer as soon as I can!! <3
The volume of a box is the amount of space it can occupy.
Box 1's volume will be a monomialBox 2's volume will be a binomialThe given parameters are:
Dimensions of box 1: x by 3x by x^3
Dimensions of box 2: x by 4x - 1 by x^3
The volume of the box is calculated by multiplying the dimensions.
So, we have:
Box 1
[tex]V_1 = x \times 3x \times x^3[/tex]
[tex]V_1 = 3x^5[/tex]
Box 2
[tex]V_2 = x \times (4x - 1) \times x^3[/tex]
[tex]V_2 = (4x - 1) \times x^4[/tex]
Open brackets
[tex]V_2 = 4x^5 - x^4[/tex]
After calculating the volumes, we have:
[tex]V_1 = 3x^5[/tex] ---- box 1
[tex]V_2 = 4x^5 - x^4[/tex] ---- box 2
Hence,
The volume of box 1 is monomial, because it has 1 termThe volume of box 2 is binomial, because it has 2 termsRead more about volumes at:
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Which expression is equivalent to (x^14 y^1/6)^1/2
A.x^1/2y^4
B. X^1/8y8
C.x^1/4y^8
D.x^1/4y^4
Please help its timed
Answer:
x^1/8 y^8
Step-by-step explanation:
To obtain the answer to the question given above, let us simplify the expression (x^1/4 y^16)^1/2.
This is illustrated below:
(x^1/4 y^16)^1/2
(x^1/4)^1/2 • (y^16)^1/2
x^1/4×1/2 • y^16×1/2
x^1/8 y^8
Therefore, x^1/8 y^8 is equivalent to (x^1/4 y^16)^1/2.
someone please help me !!
Answer:
3<x<52
Step-by-step explanation:
0<2x-6<52
6<2x<52
3<x<52
Answer:
3 x 9
Step-by-step explanation:
3<x<9 . Just did this. Acellus is lame but better than normal school. Good luck with the rest im only on lesson 84
write the sum using sigma notation 3^2+4^2+5^2+...+10^2
[tex]\sum\limits_{i=3}^{10}\big i^2[/tex]
or:
[tex]\sum\limits_{i=1}^{8}\left(2+i\right)^2[/tex]
or:
x₁=3, x₂=4, x₃=5, .... x₈=10
[tex]\sum\limits_{i=1}^{8}\big x_i^2[/tex]
The sigma notation of 3^2+4^2+5^2+...+10^2 is: [tex]\sum\limits^{10}_{n = 3} n^2[/tex]
How to express the sum as a sigma notation?The sum is given as;
3^2+4^2+5^2+...+10^2
The above means that the sum of the squares of integers from 3 to 10
Using the above statement, the sigma notation is:
[tex]\sum\limits^{10}_{n = 3} n^2[/tex]
Where n represents the current integer
Read more about sigma notation at:
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Please help marking brainliest QUICK
Answer:
50 lbs.
Step-by-step explanation:
Answer:
45.65
Step-by-step explanation:
Can someone please answer this question?
Answer:
you answer would be A. I hope this helps
Step-by-step explanation:
Does (3, –8) make the equation y = –x + –5 true?
Answer:
true
Step-by-step explanation:
y = –x + –5
Substitute the point into the equation
-8 = -3 + -5
-8 = -8
This is true so the point is a solution to the equation
(-4ab - 5a + 3) - (-7ab + 9)
________________________________
Hey!!!
solution,
(-4ab - 5a +3)-(-7ab+9)
=-4ab -5a+3 + 7ab - 9
= -4ab+7ab-5a+3-9
= 3ab-5a-6
Hope it helps...
Good luck on your assignment
______________________________
Find the sum. Write your answer in simplest form. 2 1/2+ 5 5/8
Answer:
8 1/8
Step-by-step explanation:
2 4/8 plus 5 5/8
4/8 because it equals to 1/2
Answer:
8 1/8
Step-by-step explanation:
2 1/2+ 5 5/8
2 4/8 + 5 5/8
7 9/8
8 1/8
What is the surface area of a cylinder with base redius 2 and height 9
Answer:
[tex]138.23units^2[/tex]
Step-by-step explanation:
[tex]A=2\pi rh+2\pi r^2=2*\pi *2*9+2*\pi *2^2=138.23008\\138.23units^2[/tex]
Answer:
44pi
Step-by-step explanation:
Look at the attachment
What value is a discontinuity of x squared plus 2 x plus 3, all over x squared minus x minus 12?
x = −1
x = −2
x = −3
x = −4
Answer:
x=-2
hope this helped
I NEED HELP REALLY BAD PLEASE ANSWER THIS QUESTION AS SOON AS POSSIBLE!!!! Which of the following expressions represents the distance between 3/4 and 2
A. 3/4 - 2
B. 2-(-3/4)
C. None Of the above
this is on khan academy and I really need help
A: 3/4 - 2.
Hope this helped!
Answer:
its A
Step-by-step explanation:
HURRY PLSSS
A builder uses parallelogram-shaped stones as decoration around a building’s windows. The stones come in many different sizes. Each stone has a base length of x inches and a height of (4x − 2) inches. Write a polynomial to describe the area of a stone. Then find the area of a stone that has a length of 8 inches.
ANSWER CHOICES
4x ^2 − 2x; Area = 240 in^2
4x ^2 − 2; Area = 240 in^2
4x ^2 − 2; Area = 254 in^2
4x ^2 − 2x; Area = 30 in.
Answer:
C)
Step-by-step explanation:
the answer is c because you multiply 4 and 2 and get 8 and multiply 8 by 8 and get 64 then you use 4 again and multiply 64 by 4 so you get 256 and round that 254
Answer:
Step-by-step explanation:
Which set of angles could NOT form a triangle? A. three acute angles B. One right angle, two acute angles C. One right angle, one acute angle, one obtuse angle D. One obtuse angle, two acute angles
Answer:
C. One right angle, one acute angle, one obtuse angle
Step-by-step explanation:
A triangle is a closed geometrical figure. It is an enclosed figure with three sides and three angles. The sum of the angles of a triangle is 180°. A triangle can be formed with three acute angles. A triangle can be formed with one right angle and the other two being acute angles. A triangle can be formed with one obtuse angle and the other two being acute angles. A triangle cannot be formed with one right angle, one acute angle, one obtuse angle.
(02.07 LC)
Which relationship is always correct for the angles x, y, and z of triangle ABC?
A
x
C
Ox+ z = y
Oy + z = x
O x + y + z = 180 degrees
Ox + y + z = 90 degrees
Answer:
Ox+y+z=180
Step-by-step explanation:
The relationship which is always rue for the three angles x, y and z of triangle ABC is x + y + z = 180°.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We know that a triangle has three angles.
Let x, y and z be the three angles of the given triangle.
We know that, the interior angles of a triangle sum up to 180°.
The given three angles are x, y and z.
So, x + y + z = 180°
Hence the correct relationship that describes all the three angles of the triangle is that x + y + z = 180°.
To learn more about Triangles, click on the link given :
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ANSWERR ASAPP!!! I GIVE BRAINLIESTT!!
just tell me if I'm correct
Answer:
Yes you are correct for x AND y
Step-by-step explanation:
Yes, your answer is correct.
Hannah invests £350 in an account that pays 3.5% compound interest per annum. Work out how much money Hannah will have in her account in 12 years.
Please answer !!???????????!!! PLEASE 15 points!!!!!!!!!!!
Answer:
Question 9: slope= 4
Question 10: 10x+5y = -25
Step-by-step explanation:
For question 9, since it is a linear function, you can think of it as y=mx+b. "m" is the slope value. In your instance, m=4 so the slope is 4. For question 10, you need to reorder it into y=mx+b by moving the -25 to the left side and moving the 5y to the right side. After you do this, you should get 10x+25=-5y. Then divide both sides by -5 to get -2x-5=y. Since m is a negative value, the function has a negative slope. Since the "b" value is the y-intercept and this case it's -5, the y-intercept of the equation is -5.
If a book is 33 hour and 45 min long , how many days would it take you to read it if you read 3 hours a day ?
Answer:
11
Step-by-step explanation:
33.45 ÷ 3 = 11.15 but round it
(im not 100% sure but I hope this helps)
Tammy needs to make a total of 60 deliveries this week. sao far she has completed 42 of them. what percentage of her total deliveries has Tammy completed?
Answer:
70%
Step-by-step explanation:
42/60= 0.7 = 7/10 = 70%
Identify the independent and dependent quantities in each problem solution then write a function to represent a problem situation :
Nathan is riding the scooter at a rate of 6 miles per hour
Answer:
independent: riding the scooter
dependent: miles ridden
function: y=6x
Step-by-step explanation:
Answer:
independent: riding the scooter
dependent: miles ridden
function: y=6x
Step-by-step explanation:
Need help with a question
Answer: -4 meters
Step-by-step explanation:
8 - 4 = 4; If it started at 4 meters depth and then went down to 8 meters depth, then it submerged 4 meters.
Answer:
-4
Explanation:
To find the change in depth simply subtract how many meters it was below the surface by how many meters it was at the starting point.
8 - 4
-4
Therefore, the change in depth was -4 meters.
What is 14% of 8.5? Round to the nearest hundredth (if necessary).
Answer:
1.19
Step-by-step explanation:
Hope this helps :) I try to just get straight to the point so sorry for no work
The above table shows the number of widgets, gizmos, and blibbets purchased by a company for three months and the total amount spent for all items each month. Let x1, x2, x3 represent the cost for each widget, gizmo, and blibbet. Complete the linear system:
Answer:
Step-by-step explanation:
Cost of widget is 22.53, gizmo is 31.67, and blibbet is 8.65.
What is Cramer's rule?Cramer's rule is a form of formula for finding the solution of linear equations system of with as many equations as unknown.
Given that,
[tex]\left\{\begin{matrix}11x_1& 16x_2 & 25x_3 & =971\\15x_1& 22x_2& 8x_3 & =1104 \\ 9x_1& 12x_2& 17x_3& =730 \\\end{matrix}\right.[/tex]
solution by Cramer's rule
[tex]A = \begin{vmatrix} 971& 16& 25\\1104 & 22& 8\\ 730& 12& 17\\\end{vmatrix}[/tex]
[tex]A = -320[/tex]
[tex]A_1={\begin{vmatrix} 971& 16& 25\\ 1104& 22& 8\\ 730& 12& 17\\\end{vmatrix}[/tex]
[tex]A_1 = 7210[/tex]
[tex]A_2=\begin{vmatrix}11 & 971 &25 \\ 15& 1104 & 8 \\ 9& 730& 17\\\end{vmatrix}[/tex]
[tex]A_2=-10135[/tex]
[tex]A_3=\begin{vmatrix} 11& 16& 971\\ 15& 22& 1104\\ 9& 12& 730\\\end{vmatrix}[/tex]
[tex]A_3=-2770[/tex]
[tex]x_1=A_1/A\\ x_2=A_2/A\\ x_3=A_3/A\\[/tex]
[tex]x_1=\frac{-7210}{-320} \\ x_2=\frac{-10135}{-320} \\ x_3=\frac{-2770}{-320} \\[/tex]
[tex]x_1=\frac{721}{32} \\ x_2=\frac{2027}{64} \\ x_3=\frac{277}{32} \\[/tex]
[tex]x_1=22.53 \\ x_2=\ 31.67 \\ x_3=8.65\\[/tex]
Hence cost of widget is 22.53, gizmo is 31.67, and blibbet is 8.65.
Learn more about Cramer's rule
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Can someone help me ???????
Answer:
Step-by-step explanation:
15/3= 5
Orrrr
15/-3=-5
ABC and ACD are both right-angled triangles.
D
a)
Explain why the length of AC
is 13 cm.
5 cm
C
5 cm
b)
Calculate the length of AD.
Give your answer correct
to 1 decimal place.
B
A
12 cm
Answer:
In the picture attached, the question is shown.
a) Applying Pythagorean theorem to triangle ABC, and solving for AC:
CB² + BA² = AC²
5² + 12² = AC²
√169 = AC
13 cm = AC
b) Applying Pythagorean theorem to triangle ACD, and solving for AD:
CD² + AC² = AD²
5² + 13² = AD²
√194 = AD
13.9 cm = AD
Explain what the mean absolute deviation is in general. Explain what the MAD means in the context of Robin and Evelyn’s data.
Answer: The MAD describes the average distance from a data point to the mean. It measures variability. For this data, it shows that Evelyn’s scores varied slightly more than Robin’s.
Step-by-step explanation: Add 8+1+5+0+12 and divide it by 5 and get 5.2
Answer:
Mean absolute deviation is the average distance between the mean of o set of numbers. The MADs for Robin and Evelyn's data show that Evelyn's scores or slightly more varied than Robin's.
Step-by-step explanation:
One angle is 60 degrees, the other
is 60 degrees, What is my missing
angle? What is
my
first and
last name?
hi this is my first answer
a straight angle has 180°,
here your given angle is 60+60=120°
so your missing angle is 180-120=60°
Step-by-step explanation:
The missing angle is 60° (180 - 60 - 60=60)
Its name: equilateral triangle
If f(x) = (x^2-36)/(x+6) is continuous at x = -6, find f(-6) a)-12 b)12 c)6 d)-6
Answer:
A
Step-by-step explanation:
[tex]f(x)=\dfrac{x^2-36}{x+6}= \\\\\\\dfrac{(x-6)(x+6)}{x+6}= \\\\\\(x-6) \\\\\\f(-6)=((-6)-6)=-12[/tex]
Therefore, the correct answer is choice A. Hope this helps!
Answer:
=-12
Step-by-step explanation:
f(x) = (x^2-36)/(x+6)
Factor the numerator. The numerator is the difference of squares
(a^2 -b^2) = (a-b)(a+b)
f(x) = (x-6)(x+6)/(x+6)
Cancel the like terms
f(x) = x-6
f(-6) = -6-6
= -12
Please help me with this answer im not that good in math
Answer:
B. A = 96 cm2
Step-by-step explanation: