Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{\frac{1}{x} }{(\frac{1}{x})^2+1 }[/tex]
= [tex]\frac{\frac{1}{x} }{\frac{1}{x^2}+1 }[/tex]
Multiply numerator/ denominator by x² to clear the fractions
= [tex]\frac{\frac{1}{x}(x^2) }{(\frac{1}{x^2}+1)x^2 }[/tex]
= [tex]\frac{x}{1+x^2}[/tex]
= [tex]\frac{x}{x^2+1}[/tex]
Randy is building a fence at the side of his warehouse. He has 120 m of fencing and plans to use the
side of the warehouse as one side of the rectangular fenced area. What are the dimensions of the
maximum area Randy can enclose?
please please answer this quick.
Answer: 60 meters
Explanation:
"It will probably help to have a diagram to look at:
Since we're told that the fenced area is to be a rectangle, draw a rectangle.
Since one side is to be the barn, choose a side of the rectangle to be a the barn. (It doesn't matter which side you choose.)
Label the two sides of the rectangle that are connected to the barn as "x". (Since this is a rectangle these opposite sides should be the same.)
The hardest part is the side opposite the barn. We know that we have 120 meters of fence to use. It hope it makes sense that to get the maximum area we should use all the fencing. So the lengths of the three "non-barn" sides will be 120. So how do we express the length of the side opposite the barn? Well if we know what "x" was it would be easy. For example if x = 35 then the side opposite the barn would be 120 - 35 - 35 = 50. We now use this same logic even though we don't know what "x" is yet. The side opposite the barn will be
120 - x - x
which simplifies to:
120 - 2x
We can now find a solution. The area of any rectangle is length times width (or base times height). So for our rectangle the area will be: A = x (120 - 2x)
This is a quadratic equation so I am going to rewrite it in ax^2+bx+c: A=-2x^2 + 120x
We should recognize that the graph of a quadratic equation will be a parabola. And since the squared term is x^2 this parabola will open upward or downward. And since the "a" is negative (-2 to be specific), this parabola will open downward. If we picture a downward-opening parabola in our minds we should be able to understand that the vertex of the parabola will be the highest point of the graph. So the x-coordinate of the vertex will give the the maximum value for A, the area.
So we just need to figure out the x-coordinate of the vertex. This can be done by completing the square or by just knowing that the x-coordinate of the vertex would be '-b/2 + a.'
Our "b" is 120 and our "a" is -2 so the x-coordinate of the will be: -(120/2*(-2)) = 30
This is the x that gives us the maximum area. (If you're curious as to exactly what number this maximum area is, just substitute 30 for x into A=-2x^2+120x)
So we can label the two sides of "x" as 30's. And since the side opposite the barn is 120 - 2x, it will be 120 - 2(30) = 120 - 60 = 60 meters."
-jsmallt9
please help ! Find all the missing angel measures in angel 1,4,7,10,13 the picture is attached above please help !! It’s for geometry (:
Answer: ∠1 = 52°, ∠4 = 40°, ∠7 = 100°, ∠10 = 49°, ∠13 = 65°
Step-by-step explanation:
There are three formulas you need to find the angles. Each formula is based on where the vertex lies.
On the circle: Measure of the angle = (1/2) the arc (Images 1-3)
∠4 = (1/2)°80 ∠10 = (1/2)(18° + 80°) ∠13 = (1/2)130°
= 40° = (1/2)98° = 65°
= 49°
Inside the circle: (1/2) Sum of the Big arc and Little Arc (Image 4)
∠7 = (1/2) (130° + 70°)
= (1/2)200°
= 100°
Outside the circle: (1/2) Difference of Big arc and Little Arc (Image 5)
∠1 = (1/2)[(62° + 130°) - (70° + 18°)]
= (1/2) (192° - 88°)
= (1/2)104°
= 52°
I can only add 5 attachments. If you want to see image 6 (which contains the measures for all of the angles), you will need to ask the question again. Sorry!
4x
10x
h = 4x
h = 10x
Step-by-step explanation:
the answer would be 40 4x 10x h = 4x
may i know the answer for this please
Answer:
14, 16
Step-by-step explanation:
The prime factorization of 224 is 2⁵ × 7. To make it a perfect square, we need the bases to have an even exponent, therefore we divide it by 2 × 7 = 14 to get 16.
Please answer this in two minutes now
Answer:
the slope is zero so,it dont have mx value in equn it just have c value.
Please answer this question now in two minutes
Answer:
(5, -3)
Step-by-step explanation:
(-16+x)/2 = -5.5 => x=5
(4+y)/2 = 0.5 => y=-3
Heather draws a polygon with x number of sides. The sum of the interior angles of her polygon is 60 times the number of sides. How many sides does Heathers polygon have?
Answer: hexacontagon
has 60 sides and interior angles is 10440 degrees.
Step-by-step explanation:
I kinda think its wrong but hope this helps, if its wrong, im sorry
Answer:
Heather's polygon has 3 sides.
Step-by-step explanation:
S = 60x Try plugging in number for x that will work
I found that when x = 3, the equation was true
S = 60x Substitute
S = 60(3) Multiply
S = 180 If the sum of the interior angles is 180, the only shape that can be made is a triangle, which has 3 sides.
A preimage (2,-3) is translated to (3,2). What type of transformation has occured?
Answer:
Reflection.
Step-by-step explanation:
The reflection of the point (x,y) across the x-axis is the point (x,-y).
The reflection of the point (x,y) across the line y = x is the point (y, x).
Given the preimage (2,-3).
Step 1: Reflect (2,-3) accross the x-axis, to obtain: (2,3) Step 2: Reflect (2,3) accross the the line y = x to obtain: (3,2)Therefore, the type of transformation that has occured is Reflection.
Please help!!me don’t understand
Answer:
x=45
Step-by-step explanation:
the sum of straight angle=180
2x+45+x=180
3x=180-45
3x=135
x=135/3=45
Answer:
45 degree
Step-by-step explanation:
Since it is an straight line it means all of the added angles together equal 180
2x+45+x=180
3x+45=180
3x=135
x=135/3
x=45
You are given two offers for a monthly wage. Option A is to be paid one cent on the first day of the month, with your wages doubling each day (2 cents on day 2, 4 cents on day 3, 8 cents on day 4, etc.) for the rest of this 30 day month. Option B is to be paid $1 on the first day of the month, with your wages increasing $100 each day ($101 on day 2, $201 on day 3, $301 on day 4, etc.). Which option will give you more money by the end of the month? Make sure to support your answer.
Answer:
Option B.
Step-by-step explanation:
If you begin with one dollar a day there will get you more by the end of the month because on day 2 your on 201 already which is more than you get in that month with one cent.
The first option (A) will give you more money than option (B).
What are the geometrical progression series and arithmetic progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
Given that
Case A). Doubling each day
1 + 2+ 4 + 8 + 16 .... it is form a GP series with common ratio (r) 4/2 = 2
Number of terms (n)
Sum = 30( [tex]2^{30}[/tex] - 1)/(2 - 1) = $2147483464.
Case B). Adding $100 each day
1 + (101 + 201 + 301 ....) it is form a ap series with common difference d = 201 - 101 = 100.
Number of terms = 29
Sum = 1 + 29/2 + [ 2 (101) + 28(100)] = $43530
Hence it is clear that case (A) will give you more money.
For more information about the geometrical progression
brainly.com/question/4853032
#SPJ5
Mention
rational numbers which are
less than 5
Answer:
Here are some rational numbers less than 5:
4, 4.2, -3, 0, 1/10, -5/16
A rational number is a number than can be written as a fraction of integers.
Answer:
rational numbers below 5 are 4,3,2,1,-1,-2,-3,-4 e.t.c
this is the question click it
Answer:
C.
Step-by-step explanation:
5/8 = 20/32
20/32 ÷ 2 = 10/16
10/16 ÷ 2 = 5/8
Answer:
C
Step-by-step explanation:
You can see that both of the numbers are being multiplied by 4/4 which gives you a proportional relationship unlike the other answers there.
9a
+ 6b
Help please
Answer:
3(3a+2b)
Step-by-step explanation:
9a+6b
3 times 3a=9a
3 times 2b=6b
Answer:
3(3a+2b)
Step-by-step explanation:
9a+6b
3²•a+(2.3)b
3(3²•a/3 +2•3b/3)
3(3²-¹ •a +2b)
3(3a+2b)
Cylinder a has a radius 2 cm and contains water to a height of 10cm cylinder b has a radius 5cm and is empty. Some of the water is poured from cylinder a to b the height is now the same
Answer:
h = 1.38 cm
Step-by-step explanation:
The question is at what value is the height of both cylinders the same:
The area of the circular base on each cylinder is:
[tex]Area=\pi r^2\\A=4\pi \ cm^2\\B=25\pi \ cm^2[/tex]
The initial volume in cylinder A is:
[tex]V=4\pi *10\\V=40\pi\ cm^3[/tex]
We have that Va + Vb = 40π. The height of water in each cylinder as a function of volume is:
[tex]h_A=\frac{V_a}{4\pi}\\h_B=\frac{V_b}{25\pi}[/tex]
If both heights are the same:
[tex]\frac{V_a}{4\pi}=\frac{V_b}{25\pi}\\V_b=\frac{25}{4}V_a \\V_a+V_b=40\pi\\V_a+\frac{25}{4}V_a=40\pi\\V_a=5.5172\pi\ cm^3[/tex]
The height 'h' is:
[tex]h=\frac{5.5172\pi}{4\pi}\\ h=1.38\ cm[/tex]
The perimeter of the rectangle is 34cm. The perimeter of triangle is 30 cm find the value of n
Answer:
It Should Be 12cm
What is the simplified form of x plus 2 over x squared minus 3x minus 10⋅ x minus 3 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5
Answer:
x+2
Step-by-step explanation:
write the problem out and then understand
Pls help ima mark BRAINLIST
Answer:
G.
Step-by-step explanation:
Since the y-int is (0, 4), you know you have to have an equation that has a +4 in it. When you calculate for the slope, you should get 4/3, and so the only equation that has those 2 is G.
PLEASE HELP, AND PLAESE EXPLAIN!!!
Answer:
D. 22.5 sq. un.
Step-by-step explanation:
W divides BU so that there is a ratio of 1;2 meaning that there are 3 parts.
That means that 3 parts is BUV; we know that one of those parts is 4.5 sq. un. so 4.5*3=13.5 sq. un. - Also 4.5*2=9 to get WUV
V is the midpoint of the line BS so that means that BUV and UVS are equal
we know that BUV is 13.5 so we multiply that by 2 to get the whole triangle
=27
The last step is to get rid of BVW which we know is 4.5
27-4.5=22.5
witch number is not a perfect square 1 25 30 36
Answer:
30
Step-by-step explanation:
It's just not a perfect square.
Answer:
30
Step-by-step explanation:
Perfect squares are numbers that can be expressed by another numbers times itself. The only number that is not a perfect square in this list is 30.
(-3 2/3)^2 (thast 3 and 2 thirds btw)
Hey there! :)
Answer:
[tex]\frac{121}{9}[/tex]
Step-by-step explanation:
We can solve this by first converting -3 2/3 to an improper fraction:
[tex]-3\frac{2}{3} = \frac{-11}{3}[/tex]
Square the fraction:
[tex](\frac{-11}{3})^{2} = (\frac{-11}{3}) * (\frac{-11}{3}) = \frac{121}{9}[/tex]
please help! find the value of each shape
Answer:
see below
Step-by-step explanation:
red triangle= 36/2= 18
orange circle= 45- 18= 27
blue square= 53- 27= 26
Step-by-step explanation:
red= 18
yellow= 27
blue= 26
Find M<1 A) 84 B) 90 C) 44 D) 168
Answer:
m∠1 = 90°
Step-by-step explanation:
Since the line is tangent to the circle, it creates a perpendicular bisector with the diameter. That means that the m∠1 has to be 90°
Find The surface area of the pyramid
Answer:
85 ft^2
Step-by-step explanation:
Let us calculate the area of the triangles and the base.
For the triangles, we can use the area formula and get 5 • 3 which is 15. Since there are 4, we multiply it by 4 and get 60.
For the base, we have 5 • 5, which is 25. Adding it together, we get 85.
If you are stuck on how to find surface area, all you have to do is find the area of each side and add.
I hoped this helped!
Please help me I’m desperate
Answer:
The firstStep-by-step explanation:
[tex]\frac29x+3>4\frac59\\{}\quad-3\quad-3\\\\\frac29x\ >\ 1\frac59\\\div\frac29\quad \, \div\frac29\\\\x>1\frac59\div\frac29\\\\x>\frac{14}9\times\frac92\\\\x>\frac{7}1\times\frac11\\\\x>7[/tex]
That means every x wich is greater than 7
Segment AX and Segment EX are secant segments that intersect at point X. What is the length of ED? a. 1 b. 3 c. 6 d. 9
Answer:
B. 3
Step-by-step explanation:
We can use secant theorem.
AX × BX = EX × DX
AX = 7 + 2 = 9
9 × 2 = (3 + x) × 3
18 = 9 + 3x
18 - 9 = 3x
9 = 3x
x = 9/3 = 3
The length of ED is 3 units.
Answer: B. 3 units
Good luck!
What is the value of x in the equation 3x – 1/9 = 18, when y = 27?
Answer:
Here you go mate!
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
3x - 1/9y = 18
Put y as 27 and evaluate.
3x - 27/9 = 18
3x - 3 = 18
Add 3 on both sides.
3x = 21
Divide 3 on both sides.
x = 7
simplify (3+ radical sign 2)(3- radical sign 2)
Answer:
using identity (a+b)(a-b) = a^2 -b^2
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JL=25 and JM=5, find KM.
HELP ME PLEASE!!!!!!
Answer:
KM = 15
Step-by-step explanation:
From the diagram, ΔJKL and ΔJKM are similar to each other because they share the same angle J and they are both right angle triangle. Therefore they are similar by AA property.
Since JL=25 and JM=5, JM = JL + JM= 25 + 5 = 30
Since ΔJKL and ΔJKM are similar to each other, therefore:
[tex]\frac{JK}{JL}=\frac{JM}{JK}\\ Substituting:\\\frac{JK}{30}=\frac{5}{JK}\\JK^2=150\\JK=\sqrt{150}\\ \\From\ hypotenuse:\\JK^2=JM^2+KM^2\\Substituting:\\(\sqrt{150} )^2=5^2+KM^2\\150=25+KM^2\\KM^2=150-25=125\\KM=\sqrt{125}\\ KM=15[/tex]
Which property can be used to solve the equation? StartFraction d Over 10 EndFraction = 12 addition property of equality subtraction property of equality multiplication property of equality division property of equality
Answer:
multiplication property of equalityStep-by-step explanation:
Given the equation d/10 = 12. To get the value of d, the follwoing steps can be used to solve for the value of d;
Multiply both sides by 10
d/10 * 10 = 12*10
d = 120
It can be seen from the calculation above that multiplication operation was used to get the solution to the equation. It can therefore be concluded that the multiplication property of equality was used to solve the equation.
What is 220% of 400? A. 88 B. 880 C. 8,800 D. 88,000
Answer:
The correct answer is B. 880
Step-by-step explanation:
220%=2.2
2.2(400)=880
Answer:
B. 880
Step-by-step explanation:
220% × 400
= 220/100 × 400
= 88000/100
= 880