Rationalizing the denominator of the expression, it is found that the simplified expression is given by:
[tex]\frac{\sqrt{6}(12x + 20x^2) + 3\sqrt{x} + 5\sqrt{x^3}}{x(96x - x)}[/tex]
What is the expression that we have to simplify?It is given by:
[tex]\frac{3 + 5\sqrt{x^2}}{4\sqrt{6x^2} - \sqrt{x}}[/tex]
We rationalize the denominator, using the subtraction of perfect squares, hence:
[tex]\frac{3 + 5\sqrt{x^2}}{4\sqrt{6x^2} - \sqrt{x}} \times \frac{4\sqrt{6x^2} + \sqrt{x}}{4\sqrt{6x^2} + \sqrt{x}}[/tex]
Then, solving the expression:
[tex]\frac{(3 + 5\sqrt{x^2})(4\sqrt{6x^2} + \sqrt{x})}{16(6x^2) - x}[/tex]
[tex]\frac{12\sqrt{6x^2} + 3\sqrt{x} + 20x^2\sqrt{6} + 5\sqrt{x^3}}{96x^2 - x}[/tex]
[tex]\frac{\sqrt{6}(12x + 20x^2) + 3\sqrt{x} + 5\sqrt{x^3}}{x(96x - x)}[/tex]
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is this the RIGHT answer
Answer:
Yes
Step-by-step explanation:
The horizontal line on a graph is the x axis and the "C" appears to be on the horizontal line therefore the answer would be x-axis
reasons its not the other answer choices
Y axis is the vertical line
Origin is where the two axis cross
Quadrant 1 may appear where C is however the C is pointing to the X axis
How do you find the rule of a cartesian plane line using the table of values with the coordinates on it?
The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that.
What is a coordinate system?A coordinate system is a system in geometry that uses one or more integers, or coordinates, to determine the position of points or other geometric components in a unique way.
The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that. In a graph of distance versus time, for example, the independent variable is likely to be time, and the horizontal axis is likely to be named something that suggests that--"t," for example, or perhaps "days".
It is fairly convenient to use "x" to name a general independent variable. The corresponding dependent variable in a two-variable relation is conventionally called "y". The horizontal axis in x-y graphs is usually labelled "x" and is called the "x-axis."
This convention is sufficiently well-used that we often call the horizontal number line of the graph the "x-axis" even if it is labelled something else.
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Which could be a first step in solving the equation
1/4 x + 1/2 = 3/4x
in an efficient way? Select two answers.
A.
multiply by 4 on both sides
B.
multiply by 2x on both sides
C.
subtract 1/4x from both sides
D.
add 1/2 from both sides
A first step in solving the equation 1/4 x + 1/2 = 3/4x will be answer A multipllied by 4 on both sides.
What is an equation?
The equation is actually a relationship between the numbers and the variables.The given equation is 1/4 x + 1/2 = 3/4x
Now the solution of the equation will be:-
1/4 x + 1/2 = 3/4x
By multiplying with 4 the equation will become:-
x+2=3x
3x-x=2
2x=2
x=1
Hence the solution of the given equation will be x=1
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Answer:A
Step-by-step explanation:
Multiplying each by 1/4.We have;4x1/4 + 4x1/2 = 4x3/44/4 + 4/2 = 12/41 + 2 = 33=3This is the most effective way.
Look at this set of 5 numbers: 21471 By how much would the mode decrease if the number 1 were added to the set?
Answer:
ZeroStep-by-step explanation:
The mode is the number of most repeated data in the set.
Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).
If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.
There is no change in mode, so the mode decrease is zero.
Answer:
The mode would not decrease
Step-by-step explanation:
Given set of numbers: 2, 1, 4, 7, 1
The mode is most frequently occurring data value.
Therefore, 1 is the mode of the given data set as there are two of this data value.
If we add 1 to the data set, the set becomes: 2, 1, 4, 7, 1, 1
Therefore, 1 is still the mode since there are now three of this data value.
In conclusion, the mode would stay the same.
is 14/4 rational or irrational
Answer:
Rational
Step-by-step explanation:
All fractions are rational numbers but it is not necessary that all rational numbers are fractions.
Have a nice day! :)
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth if necessary. (Square units)
Answer:
389.1 units² (nearest tenth)
Step-by-step explanation:
Regular polygon: all side lengths are equal, all interior angles are equal.
Apothem: a line drawn from the center of any polygon to the midpoint of one of the sides
Radius: a line drawn from the center of the polygon to a vertex.
Therefore, we have been given the apothem of this regular dodecagon.
Formulae[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]
where:
n = number of sidesl = length of one sidea = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)[tex]\textsf{Length of apothem (a)}=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
l = length of one siden = number of sidesSolutionFirst, calculate the length of one side of the regular dodecagon by substituting a = 11 and n = 12 into the apothem formula:
[tex]\implies 11=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]
[tex]\implies l=11 \cdot 2 \tan\left(\frac{180^{\circ}}{12}\right)[/tex]
[tex]\implies l=44-22\sqrt{3}[/tex]
Now substitute n = 12, the found value of l, and a = 11 into the area formula:
[tex]\implies \textsf{Area}=\dfrac{12(44-22\sqrt{3})(11)}{2}[/tex]
[tex]\implies \textsf{Area}=389.0622274...[/tex]
[tex]\implies \textsf{Area}=389.1\: \sf units^2 \: (nearest\:tenth)[/tex]
Answer:
389.1 square units
Step-by-step explanation:
Area of the Dodecagon (12-sided polygon)
Area Formula
Area (A) = number of sides (n) x length of side (l) x apothem (a) x 1/2Finding the length (l)
Apothem Formula
a = l / 2tan(180/n)°11 = l / 2 tan15°l = 11 × 2tan(45 - 30)°l = 22 x (2 - √3)l = 44 - 22√3 unitsFinding Area
A = 12 × (44 - 22√3) x 11 x 1/2A = 66 x (44 - 22√3)A = 389.1 square units (approx.)theres 1 circle split into 4 parts 1/4 in each and another circle with 8 parts and 1/8 in each m/4=6/8
Answer:
m = 3
Step-by-step explanation:
see image.
6/8 = 3/4
Use the picture in the problem or use algebra to find m. See image.
An article sells for $415. 80. You wish to discount it by 20%. At what price will you offer it after the discount?
Answer:
$332.64
Step-by-step explanation:
Since we are applying a discount to a price tag, we will be decreasing the amount of that price tag.
In this case, we will be taking 20% off of $415.80. This means that our new price tag will be 80% of what it originally was. To find the answer, we must first change 80% into a decimal.
80% -> [tex]\frac{80}{100}[/tex] -> 0.980
Next, we multiple $415.80 by 0.80 as shown below:
[tex]415.80(0.80)[/tex]
Our answer will be:
$332.64
can someone help me with this problem please? Thank you!
Answer:
50
Step-by-step explanation:
since the Pythagorean theorem is
[tex]c=[/tex] √[tex]a^2+b^2[/tex]
b is the bottom line (48)
a is the right line (14)
c is the top line (c)
plug that in
[tex]c =[/tex] √[tex]14^2 + 48^2[/tex]
then do the exponets
[tex]14^2[/tex] = 14 * 14 = 196
[tex]48^2[/tex] = 48 * 48 = 2304
then add them together
196 + 2304 = 2500
[tex]c =[/tex] √2500
the sqrt of 2500 is 50 (50 * 50 = 2500)
c = 50
your answer is 50
hope this helps:)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate the value of c using Pythagoras theorem ~
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = {14}^{2} + {48}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = \sqrt{196 + 2304} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = \sqrt{2500} [/tex]
[tex]\qquad \sf \dashrightarrow \: c = 50 \: units[/tex]
A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 5.5. what are the dimensions of such a cylinder which has maximum volume?
Check the picture below.
so hmm if we look at the cone straight from the front and check a cross-section of it, it'd look like the cross-section of the right-hand-side of the picture.
Now, with the cylinder having radius "r" and height "h", those two triangles we see in greenish color are similar, thus we can use proportions to correlate "h" and "r", so let's do that.
[tex]\cfrac{2.5-h}{r}~~ = ~~\cfrac{h}{5.5-r}\implies 13.75-5.5h-2.5r+rh=rh \\\\\\ 13.75-2.5r=5.5h\implies \boxed{\cfrac{13.75-2.5r}{5.5}=h}[/tex]
now, let's plug that in the volume of the cylinder's equation
[tex]V(r)=\pi r^2\cdot \cfrac{13.75-2.5r}{5.5}\implies V(r)=\cfrac{\pi }{5.5}(13.75r^2-2.5r^3) \\\\\\ \cfrac{dV}{dr}=\cfrac{\pi r(27.5-7.5r)}{5.5}\hspace{5em}0~~ < ~~r ~~ < ~~ 2.5[/tex]
now, our "r" variable can't be 0 or 2.5, as the cylinder tiptoes up and down, because if that ever happens, our cylinder's volume goes poof.
[tex]0=\cfrac{\pi r(27.5-7.5r)}{5.5}\implies 0=27.5-7.5r\implies 7.5r=27.5 \\\\\\ r=\cfrac{27.5}{7.5}\implies r=\cfrac{11}{3}[/tex]
the way I do region testing for the 1st derivative, is I usually grab the critical point and subtract hmm say 0.0000001 from it and put it in a variable in my calculator, then I add 0.0000001 to it and put it in another variable, then I use that variable in the 1st derivative calculation. Anyhow, doing so and running a 1st derivative test, we'd see that the region to the left of 11/3 is positive whilst the region to the right is negative, as you can see in the picture at the bottom, yielding a maximum extremum, r = 0 is another critical point but as we noticed the constraints is out of bounds, so not in consideration.
so V(r) is at a maximum when r = 11/3
[tex]\blacksquare~~ r=\cfrac{11}{3} ~~\blacksquare \hspace{5em} \cfrac{13.75-2.5\left( \frac{11}{3} \right)}{5.5}=h~\hfill \implies ~\hfill \blacksquare~~ \cfrac{5}{6}=h ~~\blacksquare[/tex]
You are given a vector in the xy plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. Determine the direction of a vector
You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;
How to know the direction of a vector?We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^
Where A is the magnitude of the resultant
x is the value of the x-component
y is the value of the y-component
We are given;
Magnitude of vector = 84 units
Y-component of the vector = -67 units
Thus,
[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]
From A above, let us take the positive value of the x-component and as such our original vector will be;
A = 56.68i^ - 66j^
The direction of the vector V is;
[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]
Since it points entirely to the negative x-axis, then the angle is;
180 - (-27.15) = 207.15°
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Cole ate 2/3 of the cookies in the cookie jar. Jim ate 1/4 of the cookies
left. If the cookie jar started with two-dozen cookies, how many cookies
are still in the jar?
Answer:
6
Step-by-step explanation:
first, we start with 2 dozen = 2 * 12 = 24 cookies
next, cole eats 2/3 of the cookies
2/3 of the cookies = 2/3 * 24 = 16
we are then left with
original # - # of cookies cole ate = 24 - 16 = 8
next, jim eats 1/4 of the cookies left
cookies left = 8
1/4 of cookies left = 1/4 * 8 = 2
cookies left - cookies jim eats = cookies still in jar = 8 - 2 = 6
Solve the inequality. Graph the solution. Describe the graph in the area provided. Be sure to indicate where there is an open or closed circle and what direction the number line is shaded in.
To solve this problem, we can to simply plot using a graphing tool and the region under the area would be given. We would see there's no solution for this compound inequality
Graphing of InequalityThe given inequalities in this question are
x + 4 > 0.0132 ≤ - 4xWhen we plot this, we would see that no solution exists for this compound inequality problem.
Kindly check the attach image for more details.
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PLEASE HELP :))
Select the correct answer from each drop-down menu consider the given triangles
The length of side PR in PQR is____ and the measure of J in JKL is___
The measure of the side PR in PQR is 8.07 units and the measure of angle J in JKL is 35.30 degree.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
Applying cos law in the triangle PQR:
[tex]\rm PR = \sqrt{5^2+9^2-2(5)(9)cos63}[/tex]
PR = 8.07 units
Applying sin law in the triangle, JKL:
[tex]\rm Angle \ J = sin^{-1}[sin 52 \ (\dfrac{11}{15})][/tex]
Angle J = 35.30 degree
Thus, the measure of the side PR in PQR is 8.07 units and the measure of angle J in JKL is 35.30 degree.
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Answer: POR NADA
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
To convert
Convert 0.75 liter to milliliters.
Enter your answer in the box.
mL
Answer:
750 mL
Step-by-step explanation:
Unit Conversion Rate
1 Liter (L) = 1000 Milliliters (mL)Solving
1 x 0.75 L = 1000 x 0.75 mL0.75 L = 750 mLAnswer:
750
Step-by-step explanation:
.75 x 1000 = 750
multiply volume value by 1000
hope this helps!
please need help asap i will mark branliets
Choose the graph that correctly represents the equation 3x + 9y = −18. btw one of the graphs is the anwser
Answer:
Step-by-step explanation:
jfift
A textbook has 428 pages numbered in order starting with 1. You flip a random page in the book in a way that is equally likely to stop at any of the pages. (Type your answers as fractions).
What is the probability that you turn to page 45?
Answer:
1/428
Step-by-step explanation:
There are 428 pages,
Each page likely to be turned onto as equally as every other page,
and there is one possible correct page.
Select the correct answer.
A piece of gold has a mass of 14.12 grams and a volume of 4 cubic centimeters.
What is the density of the gold?
A. 3.53 g/cm^3
B. 0.28 g/cm^3
C. 1.77 g/cm^3
D. 0.57 g/cm^3
The density of the gold substance is 3.53 g/cm^3
What is the density of a substance?The density of a substance is the degree of compactness of a substance and it can be determined by the ratio of the mass of the substance to volume.
Mathematically, the density can be computed as:
[tex]\mathbf{Density = \dfrac{mass}{volume}}[/tex]
[tex]\mathbf{Density = \dfrac{14.12 \ g}{4 \ cm^3}}[/tex]
Density = 3.53 g/cm^3
Therefore, we can conclude from the above calculation that the density of the gold with a mass of 14.12 grams and a volume of 4 cubic centimeters is 3.53 g/cm^3.
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Answer:
A 3.53 g/cm^3 if it not a it still 3.53g/cm^3
Step-by-step explanation:
find x if the ekvation is
x-3x+7x/2-1=9
Step-by-step explanation:
i got confused whether it is 7/2 or /2-1
A seesaw has a plank of 4.5 m long which is supported by a pivot at its center and moves in a vertical plane above the pivot. If the height of the pivot pillar above the ground is 1 m, through what maximum angle can the seesaw beam move?
Since the pivot pillar is 1 m above the ground, maximum angle can the seesaw beam move is 26.39°
The maximum angle can be gotten using trigonometric ratios answer the question,
What are trigonometric ratios?Trigonometric ratios are the ratios of the sides of a triangle.
What are angles?Angles are a measure of rotation or bearing.
Given that the seesaw plank is 4.5 m long and the pivot pillar is 1 m above the ground, when the seesaw is at maximum angle, it forms a right angled triangle with the ground.
It also forms a smaller similar triangle with the same maximum angle Ф which is gotten from the trigonometric ratio
sinФ = h/L where
h = height of pivot pillar above ground = 1 m and L = length of midpoint of plank = 4.5m/2 = 2.25 mMaximum angle seesaw beam can moveSo, Ф = sin⁻¹(h/L)
= sin⁻¹(1 m/2.25 m)
= sin⁻¹(1/2.25)
= sin⁻¹(0.4444)
= 26.39°
So, maximum angle can the seesaw beam move is 26.39°
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Kim projects an image using a ratio
of image measurements to projection
measurements of 2:9. A car in the
image has a width of 0.2 meter. Find
the width of the car in the projection.
x represents the
y represents the
Equation:
The width
projection is
the car in the
meter.
Answer:
= 0,16m
Step-by-step explanation:
we are given the ratio there the 2 is for the image 9 is for the car so we say 9 divide by 11 multiply by 0,2
are all natural numbers also an integer? (yes/no) [math 2+]
The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
Area of three rectangles
3LB3(8)(6)24(6)144units²Area of two triangles
1/2(6)(4)3(4)12units²Total
144+12156units²Write an expression for each phrase. 1. Robert mows 10 more yards than twice the number Jim mows.
Answer:
2x + 10 = x
Step-by-step explanation:
Let Jim mows x yards -> Robert mows = 2x + 10 yardsAccording to the given condition:2x + 10 = x (This is the required expression)2x - x = -10x = -10Let him mows x
Twice x=2x10more =2x+10Robert mows
2x+10 yardsA watermelon has a mass of 6.45 kilograms. What is the mass of the watermelon in grams
6540 g
Calculations ↓Convert kilograms (kg) into grams (g) by multiplying the amount of kilograms (kg) by 1000 :
[tex]\boxed{\rm{6.45\:kg\:\:\:\:\:\:\:}}[/tex] times 1,000 --> [tex]\boxed{\rm{6540\:g\:\:\:\:}}[/tex]
So the mass of the watermelon is :[tex]\Large\text{6540\:g}[/tex]
[tex]\small\text{hope\:helpful~}[/tex]
The second and fourth terms of a sequence are 64 and 100. If the sequence is arithmetic, write an equation for
the nth term.
If d is the common difference between consecutive terms, then
[tex]a_4 = a_3 + d = a_2 + 2d[/tex]
We have [tex]a_2 = 64[/tex] and [tex]a_4 = 100[/tex], so
[tex]a_4 - a_2 = 100 - 64 = 36 = 2d \implies d = 18[/tex]
Then the 1st term in the sequence is
[tex]a_2 = a_1 + d \implies 64 = a_1 + 18 \implies a_1 = 46[/tex]
and the n-th term would be
[tex]a_n = a_1 + (n-1) d \implies a_n = 46 + 18 (n-1) \implies \boxed{a_n = 18n + 28}[/tex]
Find 1 + 3 + 5 + … + 389.
Answer:
The rule is +2
This is the 194th term
Step-by-step explanation:
This is an arithmetic sequence because 2 is added every time.
2x + 1 = 389
2x = 388
x = 194
194* 2 + 1 = 389
mark brainliest please!
Answer:
398 i think
Step-by-step explanation:
simplify- 4c^2-36/8c^2-24c/12c+36/2c^2-6c
pls help :)
[tex]\displaystyle \dfrac{\dfrac{4c^2-36}{8c^2-24c}}{\dfrac{12c+36}{2c^2 -6c}}\\\\\\=\left(\dfrac{4c^2 -36}{8c^2 -24c}\right) \cdot \left(\dfrac{2c^2 -6c}{12c+36}\right)\\\\\\=\left[\dfrac{4(c^2 -9)}{8(c^2-3)}\right]\cdot\left[\dfrac{2(c^2-3)}{12(c+3)}\right]\\\\\\=\dfrac{8(c^2-3^2)}{8 \cdot 12(c+3)}\\\\\\=\dfrac{(c+3)(c-3)}{12(c+3)}\\\\\\=\dfrac{c-3}{12}[/tex]
[tex]\text{Hence the answer is d.}[/tex]
Answer:
d
Step-by-step explanation:
separate the 2 divisions and simplify each , that is
[tex]\frac{4c^2-36}{8c^2-24c}[/tex] ← factor numerator/ denominator
= [tex]\frac{4(c^2-9)}{8c(c-3)}[/tex] ← factor difference of squares on numerator
= [tex]\frac{4(c-3)(c+3)}{8c(c-3)}[/tex] ← cancel (c - 3) and 4/8 on numerator/ denominator
= [tex]\frac{c+3}{2c}[/tex]
---------------------------------------------------
[tex]\frac{12c+36}{2c^2-6c}[/tex] ← factor numerator/ denominator
= [tex]\frac{12(c+3)}{2c(c-3)}[/tex] ← cancel 12 and 2 on numerator/ denominator
= [tex]\frac{6(c+3)}{c(c-3)}[/tex]
----------------------------------------------------------
to divide the top fraction by the lower fraction
leave top fraction, change division to multiplication, turn lower fraction upside down.
[tex]\frac{c+3}{2c}[/tex] × [tex]\frac{c(c-3)}{6(c+3)}[/tex] ← cancel (c + 3) and c on numerator/ denominator
= [tex]\frac{c-3}{2(6)}[/tex]
= [tex]\frac{c-3}{12}[/tex] → d
Part A: Explain why x = 6 makes 4x − 5 ≤ 19 true but not 4x − 5 < 19. (5 points)
Part B: What value from the set {4, 5, 6, 7, 8} makes the equation 4x + 3 = 23 true? Show your work. (5 points)
This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality 4x − 5 < 19 since 6 is excluded
Inequality expressionInequalities are equation not separated by an equal sign
Given the inequality expression
4x − 5 ≤ 19
4x ≤ 19 + 5
4x ≤ 24
x≤ 6
This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality 4x − 5 < 19 since 6 is excluded
Given the equation
4x + 3 = 23
4x = 23 - 3
4x =20
x = 5
Hence 5 is the solution from the given set
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Someone please tell me if this is right or not!!
Answer:
close countess
Step-by-step explanation:
remember that the sign has to be postive so just change all the signs , then, you'll have a leading coefficient of +1, in front of the [tex]x^{2}[/tex], the 5 is in front of the 2nd term, they were just trying to trick you with that. the last answer is good :)