The dimensions to maximize the area must be:
length = (√3)/2width = (√3)/2How to get the dimensions of the rectangle?The rectangle with the largest area that can be inscribed on a circle of radius 3, will be a rectangle whose diagonal is equal to the diameter of the circle, so we have:
√(x + y) = 6 units.
Where x and y are the dimensions of the rectangle. We also must have that:
x < 6 unitsy < 6 units.Now, because we have limits, the largest area (which is the product of x and y) happens when x and y have the same value x = y, then we have:
√(x + x) = 6 units.
√(2x) = 6 units.
x = (√3)/2 = y
So the rectangle is actually a square of side length = (√3)/2
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HELP The recursive rule for a sequence is shown An=An-1 +4 a1=14 write the explicit rule in simplified form for the sequence An=
Answer:
aₙ = 4n + 10Step-by-step explanation:
Given is the AP with
The first term of 14The common difference of 4Explicit rule for the sequence is
[tex]a_n=a_1+(n-1)d=14+(n-1)(4)=14+4n-4=4n+10[/tex]Answer:
[tex]\sf a_n=4n+10[/tex]
Step-by-step explanation:
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
Given recursive rule:
[tex]\begin{cases} \sf a_n=a_{n-1}+4\\ \sf a_1=14\end{cases}[/tex]
Therefore, the next two values in the sequence are:
[tex]\begin{aligned} \implies \sf a_2 & = \sf a_{2-1}+4\\& = \sf a_1+4\\& = \sf 14+4\\& = \sf 18\end{aligned}[/tex]
[tex]\begin{aligned} \implies \sf a_3 & =\sf a_{3-1}+4\\& = \sf a_2+4\\& = \sf 18+4\\& = \sf 22\end{aligned}[/tex]
Explicit formula
[tex]\sf a_n=a+(n-1)d[/tex]
where:
[tex]\sf a_n[/tex] is the nth terma is the first termn is the number of the termd is the common difference between termsGiven:
[tex]\sf a = a_1=14[/tex][tex]\sf d = 22-18=4[/tex]Substituting the given values into the formula:
[tex]\sf \implies a_n=14+(n-1)4[/tex]
[tex]\sf \implies a_n=14+4n-4[/tex]
[tex]\sf \implies a_n=4n+10[/tex]
Therefore, the explicit rule in simplified form for the sequence is:
[tex]\sf a_n=4n+10[/tex]
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I WILL GIVE BRAINLYEST AND 60 POINTS. Please help me ASAP.
Rectangle PQRS is plotted on a coordinate plane. The coordinates of P are (– 1, 4) and the
coordinates of Q are (– 1, – 4). Each unit on the coordinate plane represents 1 centimeter, and
the area of Rectangle PQRS is 64 square centimeters. Find the coordinates of Points R and S
given these conditions:.aPoints R and S are to the left of Points P and Q.bPoints R and S are to the right of Points P and Q
Answer:
This may or may not help be it might get you close.
Can someone pls help me with this.
Joe and Charmaine walk around a track.Joe walks each lap in 12 minutes. Charmaine walks each lap in 8 minutes.The two of them begin at the starting line at the same time. They walk until they meet again.
How much time does it take for them to meet again at the starting line?
How many laps does Joe complete
How many laps does Charmaine complete?
Answer:
[A] It will take 24 minutes for Joe and Charmaine to meet again at the starting line.
[B] Joe will complete 2 laps
[C] Charmaine will complete 3 laps.
Step-by-step explanation:
Factor two numbers 12 and 8:
12 = 2×2×3
8 = 2×2×2
Find LCM of 12 and 8:
Lcm of 12 and 8 - 2×2×3×2 = 24
Therefore,
[A] How much time does it take for them to meet again at the starting line?
It will take 24 minutes for Joe and Charmaine to meet again at the starting line.
[B] How many laps does Joe complete
Joe will complete 2 laps
[C] How many laps does Charmaine complete?
Charmaine will complete 3 laps.
~lenvy~
A rectangle made of square tiles measures 10 tiles long and 8 tiles wide.
What is the width of a similar rectangle whose length is 15 tiles?
Answer:
12 tiles
Step-by-step explanation:
Let,
The rectangle with dimensions "10 tiles and 8 tiles" be known as "s".The rectangle with dimension "15 tiles" be known as "l"Since the length of the larger rectangle is similar to the smaller rectangle, we can compare the dimensions of both rectangles by forming a ratio.
[tex]\text{(L of "s")}:\text{(B of "s")}= \text{(L of "l")}: \text{(B of "l")}[/tex]
Let,
⇒ Length of "s" be L₁⇒ Breadth of "s" be B₁⇒ Length of "l" be L₂⇒ Breadth of "l" be B₂[tex]\implies \text{L}_{1} }:\text{B}_{1} = \text{L}_{2} : \text{B}_{2}[/tex]
We are already given:
Length of "s" = L₁ = 10 tilesBreadth of "s" = B₁ = 8 tilesLength of "L" = L₂ = 15 tiles[tex]\implies 10:8 = 15 : \text{B}_{2}[/tex]
To simplify the ratio, multiply the extremes together and take them on one side. Then, multiply the middles together and take them on the other side.
[tex]\implies 10 (\text{B}_{2}) = 15(8)[/tex]
Divide 10 both sides to obtain the width of the larger rectangle.
[tex]\implies \dfrac{10 (\text{B}_{2}) }{10} = \dfrac{15(8)}{10}[/tex]
Simplify the equation as necessary.
[tex]\implies \text{B}_{2} = 12[/tex]
Thus, the width of the larger rectangle is 12 tiles.
I need this done right now please i need help
Step-by-step explanation:
AB = x + 5 ...................
can you please help me solve this logarithm function
Answer:
I think the solution is x=84 if this is correct can u mark me brainliest
Answer:
[tex]\boxed{\sf{x=84}}[/tex]Step-by-step explanation:
This problem can be solved by using the logarithm function.
Isolate the term of x from one side of the equation.
First, you divide by -6 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{-6\log _3(x-3)}{-6}=\dfrac{-24}{-6}}[/tex]
Solve.
Divide the numbers from left to right.
-24/-6=4
Rewrite the problem down.
[tex]\Longrightarrow: \sf{\log _3(x-3)=4}[/tex]
x-3=81
Add by 3 from both sides.
[tex]\Longrightarrow:\sf{x-3+3=81+3}[/tex]
Solve.
Add the numbers from left to right.
81+3=84
[tex]\Longrightarrow: \boxed{\sf{x=84}}[/tex]
Therefore, the solution is x=84, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
A water storage tank is in the shape of a cone with the pointed end down. If the radius is 21 feet and the depth of the tank is 14 feet, find the volume of the tank in cubic feet. Use 22/7 for π.
The volume of the water storage tank is the amount of space in it
The volume of the water storage tank is 6468 cubic feet
How to determine the volume?The given parameters are:
Radius (r) = 21 feet
Height (h) = 14 feet
The shape of the water storage tank is a cone.
And the volume of a cone is:
V = 1/3πr^2h
So, we have:
V = 1/3 * 22/7 * 21^2 * 14
This gives
V = 6468
Hence, the volume of the water storage tank is 6468 cubic feet
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The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'
Answer:
a) {5, 6}
b) {2, 3, 4, 5, 6, 7, 8, 9}
c) {0, 1, 7, 8, 9}
d) {0, 1, 2, 3, 4}
Step-by-step explanation:
The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.
__
A∩B{2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}
__
A ∪ B{2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}
__
A'U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}
__
B'U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}
True or False: limx➡️0^+ e^-5/x =0
well, we can take a peek at this from the standpoint of moving from the right towards 0, but never getting there.
[tex]e^{-\frac{5}{x}}\implies \cfrac{1}{e^{\frac{5}{x}}}\qquad \qquad \stackrel{x = 1}{\cfrac{1}{e^{\frac{5}{1}}}}\implies \cfrac{1}{e^5}\qquad \qquad \stackrel{x=0.000001}{\cfrac{1}{e^{\frac{5}{0.000001}}}}\implies \cfrac{1}{e^{500000}}[/tex]
as "x" is moving towards 0, the denominator is becoming larger and ever larger, whilst the numerator is remaining the same, thus the fraction is become ever smaller, going towards = 0.
A cube has a volume of (0.75xy)3 cubic centimeters.
What is the volume of the cube expressed as a fraction?
Answer:
[tex]\frac{27}{64} x^{3} y^{3} cm^{3}[/tex]
Step-by-step explanation:
0.75 means 75/100 which is equal to 3/4.
Cube of 3/4 is [tex]\frac{3^{3} }{4^{3} }[/tex]= 27/64
x cube means x will be multiplied with itself thrice, which is [tex]x^{3}[/tex]and following the same logic, y cube means y will be multiplied with itself three times which is [tex]y^{3}[/tex]. The unit [tex]cm^{3}[/tex]at the last is very important, because, without it, the value does not show that this value is used to represent a volume so we write the units after writing the value.
Joseph wants to line his garden with a fence that cost $2.25 per foot. The length of the garden is 6 yards and the width is 2.5 yards. what is the total cost?
Answer:
$38.25
Step-by-step explanation:
Perimeter of a rectangle = 2W + 2L
(where W is the width and L is the length)
Given:
width = 2.5 ydlength = 6 yd⇒ perimeter = (2 x 2.5) + (2 x 6)
= 5 + 12
= 17 yd
Given:
cost of fence = $2.25 per foot⇒ total cost = 17 x 2.25
= $38.25
Perimeter:-
2(L+B)2(6+2.5)2(8.5)17ydToatl cost::
17(2.25)34+4.2538.25$The ratio of two numbers is 4 to 3. The sum of the numbers is 49. What are the two numbers?
Answer:
28/21
Step-by-step explanation:
28/21 is the equivalent to 4/3.
We know this is the fraction we are looking for because 28 + 21 = 49
Hope that helps!
Compound Shapes
Find the area of each figure, round your answer to one decimal place if necessary
12 ya
30
1)
3)
2)
3
12 yd
18
12 ya
3
20 yd
24
Area
Area
Area
4)
5)
6)
17 cm
4 cm
7.5 m
8 orn
12 cm
10 m
5 m
Area:
Area:
Area:
9)
7)
8)
35 m
3.5 m
20 in
TO in
18 in
21 m
21 in
18 in
20 in
3.5 m
21 m
Area:
Area:
Area:
Applying the formula for areas of rectangle, triangle, & circle, area of each figure is:
1. 27
2. 537.9
3. 384
4. 168.5
5. 96.3
6. 73.1
7. 357.1
8. 1,029
9. 744
What is the Area of a Circle?Area of a circle = πr², where r is its radius.
What is the Area of a Rectangle?Area of a rectangle = length × width
What is the Area of a Triangle?Where b is the height and b is the base length, area of triangle = 1/2bh.
What is the Area of a Square?Area = s², where s is the side length.
1. Area of the figure = area of square + area of rectangle = s² + length × width
Area of the figure = 3² + 6 × 3 = 27 ft²
2. Area of the figure = area of circle + area of rectangle = πr² + length × width
Area of the figure = π(7²) + 24 × 16 = 537.9 ft²
3. Area of the figure = area of smaller rectangle + area of bigger rectangle
Area = 12 × 12 + 20 × 12 = 384 yd²
4. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(8²) + 1/2(8)(17) = 168.5 cm²
5. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh
Area of the figure = (10)(7.5) + 1/2(7.5)(5) = 96.3 m²
6. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(4²) + 1/2(8)(12) = 73.1 cm²
7. Area of the figure = area of 1/2circle + area of rectangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(10²) + (20)(10) = 357.1 in.²
8. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh
Area of the figure = (35)(21) + 1/2(28)(21) = 1,029 m²
9. Area of the figure = area of square + area of rectangle = s² + length × width
Area of the figure = 18² + 21 × 20 = 744 in.²
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if the area of a circle is 36 x 3.14 inches squared find its diameter
Answer:
36
Step-by-step explanation:
36 x 3.14 = 113.04
Since to find a diameter from the area, you need to divide by 3.14
113.04 divided by 3.14 = 36
But since its already there you can just figure out that 36 is the diameter and you don't have to do any calculating
Porter drove due east 20 miles on Interstate 23, then due south 23 miles on Interstate 77. To the nearest hundredth of a mile, how far was he from his starting point?
A. 30.48 mi
B. 26 mi
C. 11.36 mi
D. 43 mi
Answer: D. 30.48 miles
Step-by-step explanation:
You basically use Pythagorean Theorem!
a2 + b2 = c2
Square root 20^2 +23^2
=√20^2 + 23^2
=20 x 2 + 23 x 2
= 929
And round it=
30.48 miles.
You want to buy a new computer that costs $2250. You check your savings-account balance and realize that to buy the computer, you will need $125 more than what you have in your savings account (s). How much money do you have in your savings account?
Answer:
$2,125
Step-by-step explanation:
Subtract: 2250-125=2125
Hope this helps! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
1)
Which of these are equations of lines that are parallel to the x-axis?
Select all that apply.
A. y=-3
3
4
B. y =5.3
5
C. X=
6
x 6
D. X=-7
k
E. y = 20
F. X = 8.2
Please Help - Find the Volume
I know the answer is 1982.0 ft³. However, I don't know how to get to that answer. I keep getting 2112ft³.
Answer:
1982.0 ft³
Step-by-step explanation:
The composite figure can be decomposed into a cube and a square pyramid. The volume is the sum of the volumes of these.
__
pyramidThe square base of the pyramid is 12 ft on each side, so the diagonal of the base is 12√2 feet. (The diagonal of a square is √2 times the side length.) Then the distance from a corner to the center of the base is half that, or 6√2 feet.
That distance and the height of the pyramid form a right triangle whose hypotenuse is the given 10 ft measure of the length of the edge of a face of the pyramid. Then the height can be found using the Pythagorean theorem:
h² +(6√2)² = 10²
h² = 100 -72 = 28
h = 2√7 ≈ 5.291503 . . . ft
The volume of the pyramid is ...
V = 1/3Bh = 1/3s²h
V = 1/3(12 ft)²(5.2910503 ft) ≈ 253.992 ft³
__
cubeThe volume of a cube is given by ...
V = s³
V = (12 ft)³ = 1728 ft³
__
total volumeThe total volume of the figure is the sum of the pyramid volume and the cube volume:
total volume = 253.992 ft³ +1728 ft³ = 1981.992 ft³
The volume of the figure is about 1982.0 ft³.
_____
Additional comment
Your figure for the volume seems to assume the height of the pyramid is 8 feet. That length is the slant height of one face of the pyramid. It would be the hypotenuse of a right triangle whose other legs are 6 ft and the height of the pyramid. Then we would have ...
h² +6² = 8²
h² = 64 -36 = 28 . . . . as above
The pyramid height is the perpendicular distance from the plane of the base to the peak. It is measured through the middle of the volume, not along one face.
If x = 2 and y = 3, then 4x
Answer: 8
Step-by-step explanation: Substituting x for 2 since we know the value, 4(2) is 8.
Answer: 8
Step-by-step explanation:4*2=8
What is the y-intercept of the quadratic function
f(x) = (x – 6)(x – 2)?
(0,–6)
(0,12)
(–8,0)
(2,0)
Answer:
(0,12)
Step-by-step explanation:
B.(0,12)
Ved drew the shape below by combining exactly 3 triangles of the same size and shape
The area of each triangle is (1/3) of the area of the whole shape.
What is an area?Area is the amount of space occupied by a two dimensional shape or object.
Ved drew the shape below by combining exactly 3 triangles of the same size and shape.
Hence:
Combined area = sum of each area = 3 * area of each triangle
The area of each triangle is (1/3) of the area of the whole shape.
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On their vacation, the Lupines stay at a hotel that
has a rectangular swamp for a swimming pool. The
swamp has a perimeter of 124 feet. The length is
10 feet less than 5 times its width. What are the
length and width of the swamp?
Step-by-step explanation:
Given :-
Let width be x and length be 5x - 10 according to the questionTo find:-
Measurement of length and widthSolution :-
Formula for perimeter of rectangular swamp = 2(L+W)
Putting the known values ,124 ft. = 2( 5x -10 + x )
124 ft. = 2(6x - 10)
124 ft. = 12x - 20
124+20 = 12x
144/12 = x
12 = x
putting the values of x
Length = 5x-10
5×12 - 10 = 50 feetwidth = X
12 feet
perimeter =2L+2W or 2(L+W)
124= 2(5W-10+W)
perimeter =2( 6W-10)
124 = 12W-20
124+20=(12W+20-20
144=12W
144÷12=12W÷12
12=W
The two figures are similar. Write the similarity statement. Justify your answer using factor and showing all work. Describe (in general since it isn't on a graph) the transformations from ABC to the new figure. Please don't troll this is for a unit test!!!!
First Triangle
A to B: 40
B to C: 60
C to A: 50
Second Triangle
X to Y: 31.25
Y to Z: 25
Z to X: 37.5
Answer:
B to C;60
Step-by-step explanation:
Z to X;37.5 CORRECT ME IF IM WRONG #Carryonstudents
Define then compare and contrast diverges and converges.
Answer:
Convergence is defined as the movement of two forces together while divergence implies the movement of two forces apart. In the world of economics, finance, and trading, divergence and convergence describe the directional relationship between two trends, prices, or indicators.
Placing a down payment on a home is a common practice among homebuyers and, in many cases, is required by the lender for eligibility reasons. As the Payans’ real estate agent suggested in part C, it’s also important to help keep the mortgage payment low and within the homebuyer’s monthly budget to avoid the risk of default. Write two to three sentences summarizing what might happen if the Payans were to default on their monthly mortgage payments.
Answer:
If the Payans were to default, their credit score could be lowered. The Payans could also lose their house. With both of those things on their record, it would make it harder for the Payans to qualify for another loan.
Hope this helps!
find in grammes 1/5 of 2 kg + 60 g
Answer:
460
Step-by-step explanation:
1/5 of 2kg is .4 kg
.4kg converted to grams is 400 grams
400g + 60g= 460
THE ANSWER IS 460
if right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (S).
Answer:
tan(S) = 12/5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you the tangent ratio is ...
Tan = Opposite/Adjacent
In the given triangle, the side opposite angle S is RT, which has length 12. The side adjacent to angle S is ST, which has length 5. Then the tangent of angle S is ...
tan(S) = RT/ST
tan(S) = 12/5
_____
Additional comment
The rest of the trig functions in this triangle are ...
sin(S) = 12/13
cos(S) = 5/13
tan(R) = 5/12
sin(R) = 5/13
cos(R) = 12/13
Answer:
tan(S) = [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Hi there!
We are given ΔRST, where ST=5, RT=12, and RS=13
We want to find the tangent of angle S (the notation tan(S) means "tangent of angle S")
In trigonometry, tangent refers to the ratio of the opposite side/adjacent side.
The opposite side is the side that is opposite to the angle that we are referencing (in this case, angle S); in this case, that side is RT, which is 12
The adjacent side is the leg that is adjacent to the opposite side; in this case, that side is ST, which we were given as 5
Therefore, tan(S) will be [tex]\frac{RT}{ST}[/tex], or [tex]\frac{12}{5}[/tex].
Hope this helps!
probably very easy but i do need some help asap
my calculations are not giving me the answer i'm supposed to receive which is
9y^3(3-y)
Answer:
[tex]\sf 9y^3(3-y)[/tex]
Step by step explanation:
[tex]\sf 27y^3-9y^4[/tex]
Factor out common term 9 :
[tex]\sf \implies 9(3y^3-y^4)[/tex]
Apply exponent rule [tex]\sf a^{bc}=a^{b+c}=a^ba^c[/tex] :
[tex]\sf \implies 9(3y^3-y^{1+3})[/tex]
[tex]\sf \implies 9(3y^3-y^1y^3)[/tex]
Factor out common term [tex]\sf y^3[/tex]:
[tex]\sf \implies 9y^3(3-y^1)[/tex]
Apply exponent rule [tex]\sf a^1=a[/tex] :
[tex]\sf \implies 9y^3(3-y)[/tex]
A research study compares three treatments with n=5 in each treatment. If the Ex values for the three treatments are 5, 10, and 15, then the between treatments' degrees of freedom would be equal to_
a) 12
b) 3
c) 2
d) 14
The between treatments' degrees of freedom would be equal to 10
What is degrees of freedom?Degrees of freedom is a combination of how much data you have and how many parameters you need to estimate.
Given the data in the question;
A research study comparing three treatments with n = 5 in each treatment produce;
that is: n₁ = 5, n₂ = 5, n₃ = 5
T₁ = 5, T₂ = 10, T₃ = 15,
SS₁ = 6, SS₂ = 9, SS₃ = 9
∑x² = 94
First, we obtain the grand total;
G = T₁ + T₂ + T₃ = 5 + 10 + 15 = 30
N = n₁ + n₂ + n₃ = 5 + 5 + 5 = 15
Total SS = ∑x² - ( G²/N )
we substitute
Total SS = 94 - ( (30)²/ 15 )
Total SS = 94 - ( 900 / 15 )
Total SS = 94 - 60
Total SS = 34
To get the SSbetween or Between SS;
Between SS = ∑( T²/n ) - ( G²/N )
Between SS = ∑( (5)²/5 + (10)²/5 + (15)²/5 ) - ( (30)²/ 15 )
Between SS = ∑( 25/5 + 100/5 + 225/5 ) - ( 900 / 15 )
Between SS = ∑( 5 + 20 + 45 ) - 60
Between SS = 70 - 60
Between SS = 10
Hence the between treatments' degrees of freedom would be equal to 10.
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Select all of the triangles below which are translations of triangle X.
All the triangles below which are translations of triangle X are,
⇒ A, B, D, E, F
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Since, A translation of a triangle is moving it up down or side to-side on the axis, not changing the shape flipping it or the orientation.
Hence, By all the graphs;
All the triangles below which are translations of triangle X are,
⇒ A, B, D, E, F
Thus, All the triangles below which are translations of triangle X are,
⇒ A, B, D, E, F
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Answer:
A, F
Step-by-step explanation:
The only two images that are just translations of triangle X are A and F.
Triangles A and F are obtained by moving triangle X some combination of up, down, left, and right. That is just a translation.
All other triangles shown involve something else in addition to a translation such as a reflection, rotation, or dilation.
Answer: A, F