A rectangle with proportions close to the Golden Ratio of approximately 1:1.618 is believed to be aesthetically pleasing.
What is the golden rectangle?A rectangle with sides that are in the golden ratio, or roughly 1:1.618, is referred to as a golden rectangle. This ratio has been employed in art, architecture, and design for ages since it is seen to be aesthetically beautiful.
To build a golden rectangle, start with a square and then add a smaller square to one of its sides to form a rectangle. The smaller rectangle is then used to repeat this procedure until you obtain a rectangle whose sides are in the golden ratio.
The layout of credit cards is one instance of a situation in real life that makes use of a golden rectangle. Golden rectangles are a popular shape for credit cards because of their attractive proportions and visual balance. A golden rectangle may also be used in credit card designs to help the card stand out from other cards and be simpler to recognize. The dimensions of several paintings, sculptures, and structures are more instances of how golden rectangles are used in the design.
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1. A cake recipe requires 4 cups of flour to make 12 cupcakes. Using the same cake recipe, what is the amount of flour needed for 1 cupcake?
Answer:
1/3rd a cup
Step-by-step explanation:
make me brainly
What is the volume of the rectangular prism?
y
=
x
−
1
and
y
=
−
5
x
−
13
?
Answer:
x = -3
y = 2
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(-3,2)
Equation Form:
x = -3, y = 2
Pls answer quick;-; 20 points!
The top and bottom lines are parallel. What is the value of x?
A. 105
B. 45
C. 100
D. 65
Answer:65
Step-by-step explanation:
Hi
It’s 65 bc 35+80= 115. And triangles are 180° so 115-180= 65.
Hope it helped
Answer:
65
Step-by-step explanation:
The value of 35 degrees can be translated from the opposite diagonal. Adding the 80 degrees and 35 degrees equals 115 degrees. Finally find the remainder 180-115= 65
A waitress earned a 18% tip.What decimal is equivalent to 18%
0.18
Step-by-step explanation:Percentages and decimals are closely related. As a matter of fact, we don't need to use any actual math to solve this question because there is a shortcut.
Answer by Dividing
One way to solve the question is by dividing. Percentages are numbers that represent a portion of 100. So, to find the decimal form we can divide the percentage by 100.
18/100 = 0.18Shortcut
While dividing by 100 can work, there is an easier way to find the decimal form. Dividing by 100 will always be equivalent to moving the decimal point 2 digits to the left.
This means that 18.0 becomes 0.18 when using this shortcut.Which function in vertex form is equivalent to f(x) = x2 x 1? f(x) = (x one-quarter) squared three-quarters f(x) = (x one-quarter) squared five-quarters f(x) = (x one-half) squared three-quarters f(x) = (x one-half) squared five-quarters
The function in vertex form is equivalent to [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].
What are quadratic equations?A quadratic equation is an equation of degree 2 in other words.Quadratic equations have the form ax² + bx + c = 0 and are second-degree algebraic expressions.
The standard quadratic function with vertex (h, k) is ;
[tex]\rm y = a(x - h)^2 + k[/tex]
The general quadratic equation is found as;
[tex]\rm y = ax^2 + bx + c[/tex]
The value of h is given as;
[tex]\rm h = \frac{-b}{2a}[/tex]
For the given equation in the problem;
[tex]\rm y = x^2 + x + 1[/tex]
The value of the k is found by;
[tex]\rm y =( \frac{-1}{2}) ^2 - \frac{1}{2} + 1 \\\\ y= \frac{1}{4} - \frac{1}{2}+ 1 \\\\ y= \frac{1}{4}- \frac{2}{4}+ \frac{4}{4}\\\\ y= \frac{3}{4}[/tex]
So the vertex is at [tex]\frac{-2}{4}[/tex] and [tex]\frac{1}{4}[/tex] then the vertex form is:
[tex]y = (x +\frac{2}{4} )^2 + \frac{3}{4}[/tex]
Hence the functions in vertex form are equivalent [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].
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Answer: OPTION 3
Step-by-step explanation:
Which value of b will cause the quadratic equation x2 bx 5 = 0 to have two real number solutions?
Any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.
Given quadratic equation is:
[tex]x^{2} +bx+5=0[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.
To have two real number solutions the discriminant of a quadratic equation should be greater than or equal to zero.
[tex]D\geq 0[/tex]
[tex]b^{2} -4(1)(5)\geq 0[/tex]
[tex]b^{2}-20 \geq 0[/tex]
[tex]b^{2} -(2\sqrt{5}) ^{2}\geq 0[/tex]
[tex](b+2\sqrt{5} )(b-2\sqrt{5} )\geq 0[/tex]
b∈[tex](-\infty,-2\sqrt{5}][/tex]∪[tex][2\sqrt{5},\infty)[/tex]
Hence, any value in the interval (-∞,-2√5] ∪[2√5,∞) will cause the quadratic equation x2+bx+5 = 0 to have two real number solutions.
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Use the box method to distribute and simplify (5x+2)(3x+3)
Answer:
3(5x^2+7x+2)
Step-by-step explanation:
(5x+2)(3x+3)
I use the foil method, but if you need to use a different method you can look online at how it is done, but this should give you the correct answer.
First
Outside
Inside
Last
First you multiply 5x and 3x together (the first values in each bracket), which gives you 15x squared (15x^2)
Then you multiply the 5x and 3 (the values on the "outside" of the equation --> first and last) which gives you 15x
Then you multiply the "inside" values (the ones in the middle of all the terms), which is 2 and 3x, and gives you 6x
Last you multiply the 2 values that are last in each bracket, 2 and 3, which gives you 6
So then you put then in order of the exponent
15x^2+15x+6x+6
Then you collect like terms (which means terms that have the same number of the variable) and you're left with the answer
15x^2+21x+6
Then most likely you need to further simplify and you can common factor a number out (take the highest number that evenly mutiplies into each term and divide it out of each), so that you have,
3(5x^2+7x+2)
Can you help me solve this two questions please??? :(
whats the answer to 98÷24
Why is V10 equal to 5
need this question now I think it's only a good answer
For ellipses:
-First, let's use completing the square method to determine values of a(semi-major axis), b(semi-minor axis), and the coordinates of the center of the ellipse.
[tex]\mathsf{x^2+4y^2-10x-24y+45=0}[/tex][tex]\mathsf{x^2-10x+4y^2-24y=-45}[/tex][tex]\mathsf{(x^2-10x)+4(y^2-6y)=-45}[/tex][tex]\mathsf{(x^2-10x+25)+4(y^2-6y+9)=-45+25+4(9)}[/tex][tex]\mathsf{(x-5)^2+4(y-3)^2=16}[/tex][tex]\mathsf{\dfrac{(x-5)^2}{16}+\dfrac{(y-3)^2}{4}=1}[/tex][tex]\mathsf{\dfrac{(x-5)^2}{(4)^2}+\dfrac{(y-3)^2}{(2)^2}=1}[/tex]-The center of the ellipse is at C(5, 3), semi-major axis, a = 4, and semi-minor axis, b = 2.
-Since the major axis of the ellipse is horizontal, the distance between the center of the ellipse and the co-vertices of the ellipse is ±b.
[tex]\mathsf{CoV_1=(5,3+b)}[/tex][tex]\mathsf{CoV_2=(5,3-b)}[/tex]-The coordinates of the co-vertices of the ellipse are:
[tex]\mathsf{CoV_1=(5,3+2)} \longrightarrow \mathsf{CoV_1=(5,5)}[/tex][tex]\mathsf{CoV_2=(5,3-2)} \longrightarrow \mathsf{CoV_2=(5,1)}[/tex]For the parabola:
-We have the following data:
The parabola is opening to the left and axis symmetry along the major axis of the ellipse (axis of symmetry: y = 3):
[tex]\mathsf{(y-k)^2=-4a(x-h)}[/tex]The focus of the parabola is the center of the ellipses.
F = (5, 3)-The parabola is passing through the co-vertices of the ellipse:
-The parabola is passing through poînts (5, 5) and (5, 1)
-From the first data, we know that the value of k is equal to 3 because the axis of symmetry of the parabola is y = 3.
[tex]\mathsf{(y-3)^2=-4a(x-h)}[/tex]-From the second data, we know that the x-coordinate of the vertex is at h = 5 + a. (Note: the distance of the focus of the parabola and the vertex of the parabola is equal to ±a, since the parabola is opening the the left we use -a)
[tex]\mathsf{F=(5,3)}[/tex]
[tex]\mathsf{F=(h-a,k)}[/tex][tex]\mathsf{5=h-a}[/tex][tex]\mathsf{h=5+a}[/tex][tex]\mathsf{V=(h,k)}[/tex][tex]\mathsf{V=(5+a,3)}[/tex]-Substitute the coordinates of the vertex of the parabola
[tex]\mathsf{(y-3)^2=-4a[x-(5+a)]}[/tex][tex]\mathsf{(y-3)^2=-4a(x-5-a)}[/tex][tex]\mathsf{(y-3)^2=-4ax+20a+4a^2}[/tex]-From the third data, we know that if the poînts lies on the parabola, the coordinates of the poînts must satisfy the equation of the parabola.
Using the point (5, 5), x = 5, y = 5:
[tex]\mathsf{(y-3)^2=-4ax+20a+4a^2}[/tex][tex]\mathsf{(5-3)^2=-4a(5)+20a+4a^2}[/tex][tex]\mathsf{4=-20a+20a+4a^2}[/tex][tex]\mathsf{4a^2=4}[/tex][tex]\mathsf{a^2=1}[/tex][tex]\mathsf{a=1}[/tex]-Another way to solve for the value of a is using the formula for the length of the latus rectum (LR = 4a). Since the length of the latus rectum is equal to the minor axis of the ellipse, we can easily solve for the value of a.
[tex]\mathsf{LR=4a}[/tex][tex]\mathsf{4=4a}[/tex][tex]\mathsf{a=1}[/tex]-Substitute the value of a in the equation:
[tex]\mathsf{(y-3)^2=-4a[x-(5+a)]}[/tex][tex]\mathsf{(y-3)^2-4(1)[x-(5+1)]}[/tex][tex]\mathsf{(y-3)^2=-4(x-6)}[/tex][tex]{\boxed {\red{{\mathsf{(y-3)^2=-4(x-6)}}}}}[/tex](ノ‥)ノ
Solve for x: 5-(x + 5) >-2(x + 4)
x>-8
x<-8
x>-18
x<-18
write the equation from each line, Plus helpp
Answer:
the slope u find by looking for where the line hits an exact + and the y-int is where the line touches the y-axis
GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(a) broke even,
(b) lost 4 cents,
(c) gained 4 cents,
(d) lost 10 cents,
(e) gained 10 cents
two pipes= $1.20
solution:Selling price of the first pipe = $1.20
Profit = 20%
Let’s try to find the cost price of the first pipe
CP = Selling price - Profit
CP = 1.20 - 20% of CP
CP = 1.20 - 0.20CP
CP + 0.20CP = 1.20
1.20CP = 1.20
CP = 1.20/1.20
CP = $ 1
Selling price of the Second pipe = $1.20
Loss = 20%
Let’s try to find the cost price of the second pipe
CP = Selling price + Loss
CP = 1.20 + 20% of CP
CP = 1.20 + 0.20CP
CP - 0.20CP = 1.20
0.80CP = 1.20
CP = 1.20/0.80
CP = $1.50
Therefore, total cost price of the two pipes
= $1.00 + $1.50
= $2.50
And total selling price of the two pipes
= $1.20 + $1.20
= $2.40
Loss = $2.50 – $2.40 = $0.10
Therefore, Mr. Jones loss 10 cents.
answer= option d.
Hamilton path or Circuit? explain answer
Answer:
Hamilton
Hamilton
Hamilton
Circuit
Circuit
The radius of a circle is 2.6 ft. Find the circumference
to
the
nearest
tenth
to the nearest tenth.
Answer:
16.3 ft
Explanation:
circumference of circle = 2πr ( r is the radius )
Here radius = 2.6 ft
Circumference:
2 * π * 2.65.2 π16.3 ftDigram :
[tex] \setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 2.6ft\ cm}\end{picture}[/tex]
[tex] \\ \\ [/tex]
Given :
radius of circle = 2.6 ft[tex] \\ \\ [/tex]
To find :
Circumference = ?[tex] \\ \\ [/tex]
Solution :-
We know :
[tex] \boxed{ \rm Circumference_{(\sf circle)} = 2\pi \: radius}[/tex]
[tex] \\ [/tex]
So:-
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2\pi \: radius \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2 \times \dfrac{22}{7} \times 2.6\\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} = 2 \times \dfrac{22}{7} \times \dfrac{26}{10} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{44}{7} \times \dfrac{26}{10} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{1144}{7 \times 10} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf Circumference_{(\sf circle)} =\dfrac{1144}{70} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\bf Circumference_{(\bf circle)} =16.34~ft\{approx\} \\ [/tex]
A confidence interval is constructed to estimate the value of.
A closed cylinder has how many faces ?
Answer:
3 faces
A cylinder has 3 faces - 2 circle ones and a rectangle (if you take the top and bottom off a tin can then cut the cylinder part on the seam and flatten it out you would get a rectangle). It has 2 edges and no vertices (no corners).
Step-by-step explanation:
[tex] \huge\fbox\blue{ANSWER} [/tex]
A cylinder has 3 faces - 2 circle ones and a rectangle
Look at this table:
х
ONN
у
10
20
7
4
12
16
Is this relation a function?
Answer:
I think the answer is No
Step-by-step explanation:
It is not a function because there cannot be two points on the same x value. Hope I remembered this correctly.
I need help finding this answer, check the screenshot for all the info
Cooper asked his classmates, "How many days do you floss your teeth in a
typical week?" The table shows Cooper's data.
How many observations did he record?
A. 24
B. 7
C. 27
D. 21
Answer:
D
Step-by-step explanation:
Each box represents one observation.The data table is 7 boxes by 3 boxes. 7 * 3 is 21, so the answer is D.
Hope this helps :)
Have a nice day!
FOR EDMENTUM/PLATO pls help and if u got the rest pls share:)
Part D
What is the probability that client D, the 39-year-old you’re considering for a 20-year policy, lives to be 59 years old? Client D is an Asian female, but there is no specific life table for Asian females; look in table 3, which is a general table for females.
12pt
Characters used: 0 / 15000
Part E
What is the probability the client E, the 68-year-old you’re considering for a 10-year policy, lives to be 78 years old? Remember that client E is a non-Hispanic black male.
12pt
Characters used: 0 / 15000
Part F
What is the probability that client F, the 53-year-old you’re considering for a 20-year policy, lives to be 73 years old? Remember that client F is a Hispanic female.
The probability that client D will be able to live to be 59 years old is 0.4.
How to calculate probability?Youe information is incomplete. Therefore, an overview of probability will be given.
Let's assume that there is an entire population of 50 people and the number of those that lives to 59 years is 20.
Therefore, the probability that can be deduced of those that live to 59 years will be:
= 20/50 × 100
= 2/5 × 100.
= 40%
= 0.4
In conclusion, the probability is 0.4.
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A circular piece of fabric has a radius of 1. 2 ft. The fabric sells for $5. 40 per ft². What is the total cost of the circular piece of fabric? use 3. 14 for pi. $6. 48 $20. 35 $24. 42 $40. 69.
Answer:
$24.42
Step-by-step explanation:
3.14*r^2= area
3.14*1.2^2=4.52
5.40*4.52=24.42
Answer:
Step-by-step explanation:
Remark
First find the area of the circular piece of fabric. Then deal with cost per square foot.
Area of the fabric
Area = pi * r^2
Area = 3.14 * 1.2^2
Area = 3.14 * 1.44
Area = 4.5216 square feet
Cost
1 square foot costs 5.40 dollars
4.5216 square feet costs x Cross multiply
x = 5.40 * 4.5216
Answerx = 24.42 dollars for the fabric bought.
A triangle is dilated by a scale factor of n = one-third. which statement is true regarding the dilation? it is a reduction because n > 1. it is a reduction because 0 < n < 1. it is an enlargement because n > 1. it is an enlargement because 0 > n > 1.
The second statement is true. It is a reduction because 0 < n < 1.
What is dilation?
Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
Given: A triangle is dilated by a scale factor of n = 1/3. As n is less than 1 but greater than 0.
A dilation is a rigid transformation that forms an image that is the same shape as of the original figure but with a different size. A dilation transforms a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never changes.
A dilation that forms a larger image is known as enlargement. A dilation that forms a smaller image is known as reduction.
• If n is greater than 1, then the image is an enlargement.
• If n is between 0 and 1, then the image is a reduction.
• If n is 1, the figure and then the image is exactly the same.
Hence the second statement is true. It is a reduction because 0 < n < 1.
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A tunnel with a parabolic arch is 12 m wide. If the height of the arch 4 m
from the left edge is 6 m, can a truck that is 5 m tall and 3.5 m wide pass
through the tunnel? Justify your decision.
Check the picture below.
Pls pls pls help ill give you whatever :(
Answer:
I'm not positive but it should be 16/625
Step-by-step explanation:
if it is brainlist would be nice
45/8 ÷ 11/9 in simplest form
Answer:
high chance tat it is 405/88. mixed farction = 4 53/88
Step-by-step explanation:
What is the surface area of the prism?
Length: 15mm
Width: 3mm
Height: 4mm
Answer:
234mm
Step-by-step explanation: