The solution to the division of the given surd is: [tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
Division of Surds.The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.
Given that:
[tex]\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}[/tex]
i.e.
[tex]\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }[/tex]
Using the fraction rule:
[tex]\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}[/tex]
[tex]\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }[/tex]
By simplification, we have:
[tex]\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }[/tex]
[tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
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On a coordinate plane, triangle R S T has points (0, 4), (0, negative 2), and (3, negative 2).
△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).
The distance between the x-coordinates of R and T is
.
The distance between the y-coordinates of R and T is
.
R' is
from T, so the coordinates of R' are
.
The values gotten for the coordinate plane are;
The distance between the x-coordinate of R and T is 3.The distance between the y-coordinate of R and T is 6.R' is (-1, 2) from T, so the coordinates of R' are (2, 0).Why the above values?The Reason for the obtained value is that since thee rule for the dilation of ΔRST is:
The vertices of the given triangle are R(0, 4), S(0, -2), T(3, -2)Then, the distance that exist between the x-coordinate of R and T will be:
3 - 0
= 3
Then the distance between the y-coordinate of R and T will be:
4 - (-2)
= 6
Note that the location of the point R' is said to be relative to point T and as such:
The location of point R'
= (-1 + 3, 2 - 2)
= R'(2, 0)
Hence R' is (-1, 2) from T, and the coordinates of R' is (2, 0)
Therefore, The values gotten for the coordinate plane are;
The distance between the x-coordinate of R and T is 3.The distance between the y-coordinate of R and T is 6.R' is (-1, 2) from T, so the coordinates of R' are (2, 0).Learn more about coordinate plane from
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Answer:
C.) ✔ 3
D.) ✔ 6
B.) ✔ 1 unit left, 2 units up
D.) ✔ (2, 0)
Step-by-step explanation: i hope this helps :)
In triangle TUV Y is the centroid if YW=9 find TY
Applying the centroid theorem, the length of TY is calculated as: 18 units.
What is the Centroid Theorem?According to the centroid theorem, given a triangle like TUV with Y as the centroid, the theorem states that:
TY = 2/3(TW)
YW = 9 units
TW = TY + 9
Plug the values into the equation
TY = 2/3(TY + 9)
3(TY) = 2(TY + 9)
3(TY) = 2(TY) + 18
3(TY) - 2(TY) = 18
TY = 18
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What’s the answer to this?
Answer:
See attached image.
250 shirts at $50/shirt is the equilibrium.
Step-by-step explanation:
Consider triangle EFG. F 8 10 CA 55.8 OB. 82.8 OC 94.8 OD. 41.4 12 E What is the approximate measure of angle G? G Consider triangle EFG . F 8 10 CA 55.8 OB . 82.8 OC 94.8 OD . 41.4 12 E What is the approximate measure of angle G ? G
Using the law of cosines, it is found that the approximate measure of angle G is of 41.4º.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.In this problem, we want to find angle G, hence c = 8, then:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
[tex]8^2 = 10^2 + 12^2 - 2(10)(12)\cos{G}[/tex]
[tex]240\cos{G} = 180[/tex]
[tex]\cos{G} = \frac{3}{4}[/tex]
[tex]G = \arccos{\left(\frac{3}{4}\right)}[/tex]
G = 41.4º.
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Answer: DE NADA
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
what is the following product?
√10 10
A)10
B) 10/10
C) 10√10
D) 100
Answer: C
Step-by-step explanation:
[tex]\sqrt10 10=10\sqrt{10}[/tex]
Solve the linear system.
x + y = -3
y = 2x
Answer:
x = -1
y = -2
Step-by-step explanation:
You can use the method of substitution to solve this equation. Since you know that y= 2x, you can substitute that value into x + y = -3:
x + (2x) = -3
Combine like terms:
3x = -3
x = -3/3
x = -1
Now that you know the value of x, you can substitute it into any of the two equations (I'll be choosing y = 2x)
y = 2x
y = 2 (-1)
y = -2
So your solution is x = -1, y = -2
Point form: (-1, -2)
A telegraph pole stands on a line joining two points P and Q on the ground.
The telegraph pole is 9 m tall. The angle of depression of the top of the pole to point P
is 4°. The angle of depression of the top of the pole to point Q is 7º. What is the
horizontal distance between P and Q.
Step-by-step explanation:
let's call the top of the pole T, and the ground point of the pole G.
so, the situation gives us 2 right-angled triangles:
PTG and QTB.
from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.
the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).
the inner angle at PTG = 90 - 4 = 86°
the inner angle at QTG = 90 - 7 = 83°
and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :
angle P = 180 - 90 - 86 = 4°
angle Q = 180 - 90 - 83 = 7°
yes, they are the same as the angles of depression (must be the same).
so, we know from both triangles 1 side and all 3 angles.
with the law of sine we can get every missing side.
particularly we need the second legs (sides in the ground) to get the distance between both points.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides always opposite of their related angles.
TG/sin(4) = PG/sin(86)
PG = 9×sin(86)/sin(4) = 128.7059963... m
TG/sin(7) = QG/sin(83)
QG = 9×sin(83)/sin(7) = 73.29911785... m
the distance between P and Q can have now 2 solutions :
if P and Q are on different sides of the pole, then
PQ = 128.7059963... + 73.29911785... = 202.0051142... m
but if they are on the same side of the pole, then their distance is
PQ = 128.7059963... - 73.29911785... = 55.40687846... m
due to the phrasing of the first sentence I suspect the first solution to be right.
but just in case, I gave you also the second possible solution.
How many outfits can be made with 40 shirts and 15 pairs of pants
Answer:
600
Step-by-step explanation:
So I'm assuming an outfit is considered one shirt, and one pair of pants... But anyways, this can be expressed in a graph. So for each shirt, there are going to be 15 possible pants you can chose. And this goes for each shirt. So in other words you're simply adding up 15, 40 amount of times. Or 15 * 40, which is 600. I attached an image that illustrates this graph. You can also think of it in terms of choosing one of 15 pants and then for each pant, there are 40 possible shirts to choose from. This is essentially adding up 40, 15 times, or in other words 40 * 15, which is going to get you the same result. But in my diagram I used it in terms of choosing a shirt first.
Answer:
600
Step-by-step explanation:
Pair 1 of pants goes with 40 shirts
Pair 2 of pants goes with 40 shirts
Pair 3 of pants goes with 40 shirts
Pair 4 of pants goes with 40 shirts
Pair 5 of pants goes with 40 shirts
Pair 6 of pants goes with 40 shirts
Pair 7 of pants goes with 40 shirts
Pair 8 of pants goes with 40 shirts
Pair 9 of pants goes with 40 shirts
Pair 10 of pants goes with 40 shirts
Pair 11 of pants goes with 40 shirts
Pair 12 of pants goes with 40 shirts
Pair 13 of pants goes with 40 shirts
Pair 14 of pants goes with 40 shirts
Pair 15 of pants goes with 40 shirts
Add up everything (not including the 1,2,3,4,5,...14,15 pairs of pants because each pair of pants goes with 40 different shirts so u just add up all the 40's) and you would get 600 outfits.
Another simple way of doing this would just be multiplying 40x15
How tall is the tower?
Answer:
93.6 ftStep-by-step explanation:
[tex]\bf \cfrac{AB}{BC} = \tan(60) [/tex]
[tex] \bf \cfrac{x}{50} = \sqrt{50} [/tex][tex]\bf x = 50 \sqrt{3} [/tex]Length of tower:-
[tex]\bf x + 7[/tex][tex]\bf 50 \sqrt{3} + 7[/tex][tex]\bf 93.6025[/tex][tex] \bf = 93.6[/tex]Therefore, the tower is 93.6ft tall.
-------------------------------------------
How dose the graph of g(x)=x+5 compare with the graph of the parent function f(x)=x?
The graph of f(x) is shifted up by 5 units to get g(x)
How to compare the functions?The functions are given as:
g(x) = x + 5
f(x) = x
Substitute f(x) = x in g(x) = x + 5
So, we have:
g(x) = f(x) + 5
The above means that the graph of f(x) is shifted up by 5 units to get g(x)
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ABCD is an isosceles trepezoid with midsegment top enclose M N end enclose. m angle B A D equals 65 degree
The answers are as follows:
What is isosceles trapezoid?A trapezoid with its two nonparallel sides equal.
Given:
<BAD =65
As, MN is mid segment
So,
BC= 2CM
BC = 16
Now, ABCD is isosceles trapezoid
BC= AD
So, AD= 16
and, Using mid- point theorem
MN= 1/2 AB
MN = 1/2* 22
MN= x = 11
Also, co- interior angle sum is 180 in trapezium
<BAD + <BCD = 180
<BCD + 65 =180
<BCD = 115
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If x=7y and x = 4y = 24, then X=?
Can someone help me with this please?
Answer: 14.79
Step-by-step explanation:
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]
Rewrite x² - 10x = 4 so that the left side is a perfect square trinomial.
x² - 10x -4 = 0
x² - 10x + 25 = 4
x² − 10x + 25 = 29
x². - 10x + 10 = 14
Answer:
C
Step-by-step explanation:
x²-10x+(-10×0.5)²=4+(-10×0.5)²
x²-10x+25=29
5 calculators cost £31.25
3 pens cost £2.91
Work out the cost of 30 calculators and 30 pens.
Answer:
£216.60
Step-by-step explanation:
If 5 calculators cost £31.25, then each calculator costs £6.25
If 3 pens cost £2.91, then each pen cost £0.97
30(6.25) + 30(0.97) = £216.60
Please explain the logics and steps to solve this problem below thank you TT
5, 10, 15, ..., 100
If each term in the sequence above is 5 more than the previous term, how many times does the digit zero appear in the sequence?
(A) 9 (B) 10 (C) 11 (D) 50 (E) 51
---
the answer is number C) 11
however the answer I've chosen was 50
Since there are 10 values that have the zero digits, hence the zero digits appear 10 times in the sequence
Sequence and seriesSeries are defined as sum of sequences. Given the following sequence
5, 10, 15, ..., 100
The common difference is 5 and the number that have digits zero in the sequence are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100
Since there are 10 values that have the zero digits, hence the zero digits appear 10 times in the sequence
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? Question
Segment FG is on a number line with point F at 1.2. Point H lies on FGat 3.15. Point H is the length of FGfrom point G. What
are the location of G and the length of FG?
Type the correct answer in each box. Use numerals instead of words.
The location of G is?
The length of FG is?
A number line is a line that shows the locations of all directed numbers. The answers required to the question are:
i. The location of G is 2.18.
ii. The length of FG is 0.98.
A number system is a system that can be used to locate the position of directed numbers on a number line. A number line has two ends: positive and negative ends. This starts from negative infinity to positive infinity. Thus all numbers can be located on a number line.
Directed numbers are numbers that have either a positive sign or a negative sign. Thus all numbers are directed numbers.
From the given question, let the distance between FG and GH be represented by x (since Point H is the length of FG from point G).
Thus,
Point FH = 3.15 - 1.20
= 1.95
x = [tex]\frac{FH}{2}[/tex]
= [tex]\frac{1.95}{2}[/tex]
x = 0.975
So that,
Location of point G = 1.200 + 0.975
= 2.175
Therefore, the location of G is 2.175 (2.18). And the length of FG is 0.975 (0.98).
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Answer:
Location of G: 6.4
Length of FG: 5.2
Step-by-step explanation:
correct on Edementum/Plato
Determine the equation, in vertex form, of a parabola that has been:
(a) reflected in the x-axis and horizontally shifted right 4 units.
(b) vertically compressed by a factor of 1/4 and vertically translated 5 units down
(c) vertically stretched by a factor of 4, translated 3 units left and 2 units up
Answer:
[tex]a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).[/tex]
Good luck!
Two friends bring lemonade to your cookout. one brings 2.7 liters and the other brings 3.54 liters. how much lemonade do they bring
The total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.
The methods we use to add or subtract decimals are as follows:
Vertically align the decimal points. Any necessary zeros should be entered.Treat the integers as whole numbers when adding or subtracting them.Align the decimal point with the numbers being added or subtracted so that it sits vertically above the sum or difference.In the question, we are informed that two friends bring lemonade to the cookout. The first brings 2.7 liters and the second brings 3.54 liters.
We are asked to find the total lemonade brought by them to the cookout.
To find the total lemonade, we add both the decimal quantities following the steps discussed.
2.7
+ 3. 54
Step 1: Adding zeroes:
2.70
+ 3. 54
Step 2: Treating them as numbers and adding:
2.70
+ 3. 54
________
624
Step 3: Aligning decimal points:
2.70
+ 3. 54
________
6.24
Thus, the total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.
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Need help with this geometry question
Answer:
Complementary: Angle SRP and Angle PRQ
Supplementary: Angle SRO and Angle SRQ
Step-by-step explanation:
Complementary: 90 degrees
Angle SRP and Angle PRQ
Supplementary: 180 degrees
Angle SRO and Angle SRQ
30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answer:
A. 2640
Step-by-step explanation:
44 feet per second 30 miles per hour is 2640 feet per minute
which number can each term of the equation be multiplied by to eliminate the fraction before solving -3/4m-1/2=2+1/4m
Answer:
4
Step-by-step explanation:
LCM of 2 and 4 (denominators of fraction)
= 4
pls help 10 points for whoever helps
Answer:
see image
Step-by-step explanation:
Putting the data on the line plot is not too bad. Just put an x above the number on the numberline. If a number in the data set repeats, just stack those x's up over the numberline. It seems like the hardest part is labelling the number line. Each tick mark can be 1/8. On the image I wrote all the fractions in eighths at the bottom, then to label the numberline I used the simplified fractions. For example I started with 1 3/8 because it was the smallest number in the data set. Next is 1 4/8, but simplified that is 1 1/2. So 1 1/2 is how we label the numberline.
There were 12 pieces of data, but really only six numbers because some were repeated.
Stack x's above the numberline. Done! You have a line plot. See image.
Answer:
1. 1/⅜
2. 1/⅜
3 is 2/¼
4 is 2/¼
5 is 2/¼
6 is 2/⅞
7 is 2/⅞
8 is 2/⅞
9 is 3/⅛
10 is 3/⅛
11 is 3/⅛
Step-by-step explanation:
Mixed number to Improper Fraction
1.9/4
2.13/4
3.23/8
4.25/8
5.23/8
6.25/8
7. 5/2
8.9/4
9. 23/8
10. 5/2
11. 11/8
12. 25/8
then you make it into the same denominator
1. 18/8
2. 26/8
3. 23/8
4. 25/8
5. 23/8
6. 25/8
7. 20/8
8. 18/8
9. 23/8
10. 20/8
11. 11/8
12. 25/8
then what ever numerator is smallest you put at front and it goes onto the biggest one
e.g ASCENDING ORDER
However you'll need to put it back into the normal mixed number, so all you have to do is revert let's say 25/8 into 3/⅛, and put it onto the graph
1. 1/⅜
1. 1/⅜2. 1/⅜
. 1/⅜3 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞
. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞7 is 2/⅞
8 is 2/⅞
9 is 3/⅛
9 is 3/⅛10 is 3/⅛
11 is 3/⅛
and number 12 which is the biggest and the last one the you should put(on the end of graph) is
3/¼
I did rush this so I hope this is the correct answers
Jon, Dave, and Kevin collected rocks at the beach. Each boy collected 25 rocks. How many rocks did the boys collect in all?
By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.
How many rocks did the boys collect in all?
We know that there are 3 boys, and each boy collected 25 rocks.
If we take the product between the number of boys and the number of rocks that each boy collected, we get:
R = 3*25 rocks = 75 rocks.
We conclude that the boys collected 75 rocks in total.
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an experimental design that permits simultaneous statistical conclusions about two or more factors is a
Factorial design is the correct choice for the answer as an experimental design that permits statistical conclusions about two or more factors is a factorial design.
A factorial experiment is a type of research methodology that allows the study of main and interaction effects between two or more independent variables and on one or more outcome variables.
This is called a mixed factor experiment. For example, a researcher may choose to treat mobile phone use as a factor within a subject by testing the same participant with and without mobile phone use (the order of these two conditions). Balance).
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Which of these lines are skew to line EF?
The skew lines are CG, DH, AD, BC.
What is skew lines?Two or more lines which have no intersections but are not parallel.
Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.
As, by the definition
The lines skew to EF is CG, DH, AD, BC
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If f(x) = -x-2 and g (x) =x^2, what is (g^0f)(-6)?
Answer: 16
Step-by-step explanation:
[tex](g \circ f)(-6)=g(f(-6))\\\\f(-6)=-(-6)-2=4\\\\\implies g(f(-6))=g(4)=4^2 = \boxed{16}[/tex]
The value of the function estimation; (g°f)(-6) is; 64.
What is the value of the function estimation?It follows from the task content that; the fumcti given are; f(x) = -x-2 and g (x) =x².
Hence, the function (g°f) (x) can be evaluated as; (-x-2)² = x² +4x +4.
Ultimately, when x = 6; (g°f)(-6) = 6² +4(6) +4 = 64.
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HELPPPPP!!
Sarai loves music and decides to paint a music staff on her bedroom wall. She knows that it is important to make the lines parallel, or the end result will not look correct. She pencils in the image below, but before she uses paint, she wants to make sure the lines are parallel. Remembering what she has learned in Geometry class, she uses a piece of tape to make a transversal and decides to measure some angles.
Using Sarai’s measurements, Line 1 must be parallel to Line 3 according to which postulate or theorem?
Can you also please explain how you got the answer? thank you <3
Using Sarai's measurements, Line 3 must be parallel to Line 5 by option (A) Converse of Alternate Exterior Angles Theorem.
What is the Alternate Exterior Angles theorem?The alternate Exterior Angles theorem states, "If two lines are parallel and they are intersected by the same straight line then the alternative exterior angles formed by the figure are equal to each other."
The converse of this theorem states that "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."
Here in Sarai's measurement, we can conclude that Line 3 and Line 5 are intersected by one straight line, and the formed alternate exterior angles both are 65, which shows they are equal to each other.
Hence by Converse of the Alternate Exterior Theorem, we can say that both lines are parallel to each other.
So, Line 3 must be parallel to Line 5 according to the Converse of Alternate Exterior Angles Theorem.
Hence Option (A) is correct.
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Find the value of x and y (2^x+y 2^x-y) =(16,1) in order pair
Answer:
i don't know sorry :(
Step-by-step explanation:
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y.
x=2, y=5
The equation that relates x and y is y = 2.5x.
How to solve variation?
The values of x and y vary directly. Therefore,
y α x
where
x and y are the variable.Hence,
y = kx
where
k = constant of proportionality.Therefore,
x = 2
y = 5
5 = 2k
k = 5 / 2
k = 2.5
Hence, the equation that relates x and y are as follows;
y = 2.5x
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