Mathematics Middle School

Determine the unknown side length of the golden rectangle with the given side length.

s = ____ t=9
a.
5.56
c.
4.94
b.
4.85
d.
5.26


Please select the best answer from the choices provided

Answers

Answer 1
Answer: option a. 5.46

Explanation:

The side lengths of the golden rectangle are in the proportion:

          1
--------------------
golden number

The golden numbrer is:

  1 + √5
-----------
     2

So, the ratio is:

       1
--------------
   1 + √5
   ---------
       2

And, using the properties of the division of fractions, that is equivalent to:

      2
-------------
 1 + √5

Since you have the given side t = 9, you can set the proportion, to find the unknown lenght, s:

    2               s
--------- =   ---------
1 + √5           t


    2               s
--------- =   ---------
1 + √5           9

And you can solve for s:

s = 9 * 2 / (1 + √5) ≈ 18 / (1 + 2.236) = 18 / (3.236) ≈ 5.56.

Which is the option a. 5.56

Answer 2
Final answer:

To determine the unknown side length of a golden rectangle, set up a proportion and solve a quadratic equation.

Explanation:

The golden rectangle is a rectangle in which the ratio of the longer side to the shorter side is equal to the golden ratio, approximately 1.618. To determine the unknown side length, we can set up a proportion using the given side length and the golden ratio:

s / t = (s + t) / s

Substituting the given values, we have:

s / 9 = (s + 9) / s

Cross multiplying and simplifying, we get:

s^2 = 9(s + 9)

By solving this quadratic equation, we find that the unknown side length is approximately 4.94. Therefore, the correct answer is c. 4.94.

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Related Questions

Fred makes 2.50 less per hour than Barney. Barney makes 15.75 per hour. How much does Fred make per hour?

1) $14.75

2) $15.00

3) $13.25

4) $12.75

Answers

The answer is C) $13.25
The answer is C 15.75-2.50

Melissa’s father is 194 cm tall. He is 79 cm taller than Melissa. How tall is Melissa?

Answers

Melissa is 115cm talk
I think Melissa is 115cm, because i think u have to subtract 194 to 79 than u get ur answer

Let E be the point of intersection of the diagonals of a parallelogram. The lengths of the line segments from E to two of the parallelogram’s vertices are 3 meters and 4 meters. What are the lengths of the segments from E to the other two vertices of the parallelogram? Justify your answer.

Answers

The length is going to be 3m and 4m.
The diagonals of a parallelogram has the following property:

They bisect each other. Which means each diagonal divides the other diagonal in two equal halves.

So, the point of intersection of two diagonals is the midpoint of both diagonals. If the distance from that point of intersection E, to the vertices of parallelogram is 3 meters and 4 meters, the distance from E to opposite vertices will also be the same i.e. 3 meters and 4 meters respectively, because the diagonals bisect each other.

a gardener can plant 17 seeds in 25 minutes at that rate how long will it take him to plants 51 seeds

Answers

51 / 17 = 3
3 * 25 = 75

Answer: It will take the gardener 75 minutes to plant 51 seeds.

Hope this helps!

If the gardener plants 51 seeds, then the time taken will be 75 minutes.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

A gardener can plant 17 seeds in 25 minutes at that rate.

We know that the ratio of time and number of seed plantations will remain the same.

Let T be the time and S be the number of seed plantations.

T / S = 25 / 17

If the gardener plants 51 seeds, then the time taken will be

T / 51 = 25 / 17

T = 1275 / 17

T = 75 minutes

If the gardener plants 51 seeds, then the time taken will be 75 minutes.

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Of the following sets, which numbers in {0, 1, 2, 3, 4} make the inequality 7x + 3 < 17 true?

{0}

{0, 1}

{0, 1, 2}

{2, 3, 4}

Answers



the set that makes the inequality true is{0, 1,}

Hello,

The correct answer is B) {0, 1}

Hope this helps!!!! Happy Holidays!!!! (:

sombody please help me fast

Answers

A because you subtract 15from 20 and it =5 or 1/4
The answer is 5, hope it helps.

a box of crackers has a volume of 48 cubic inches. what is the volume of a similar box that is smaller by a scale factor of 2/3

Answers

For this case what you need to know is that the original volume of the cookie box is:
 V = (w) * (l) * (h)
 Where,
 w: width
 l: long
 h: height.
 We have then:
 V = (w) * (l) * (h) = 48 in ^ 3
 The volume of a similar box is:
 V = (w * (2/3)) * (l * (2/3)) * (h * (2/3))
 We rewrite:
 V = ((w) * (l) * (h)) * ((2/3) * (2/3) * (2/3))
 V = (w) * (l) * (h) * ((2/3) ^ 3)
 V = 48 * ((2/3) ^ 3)
 V = 14.22222222 in ^ 3
 Answer:
 the volume of a similar box that is smaller by a scale factor of 2/3 is:
 V = 14.22222222 in ^ 3

What’s the ordered pairs of
y = 10x + 18? The image is down below.

Answers

Okay 2
Really
4
During
32
Square
67
First, if ordered pairs are in the form of (x,y) then the first one means plug in x with 0. If you do that, you get y= -10(0)+18. Simplify to get y=18. So, for the first one, it is (0,18). For the next one, you plug in 1 for x. So, y=-10(1)+18. Simplify to get y=-10+18. Simplify again to get y=8. So the second one is (1,8). For the last one you have only the y value, so plug in 78 for y. So, 78=-10x+18. We want to isolate x, so subtract 18 from both sides. You get 60=-10x. Now divide by -10 to get -6=x. So, the last ordered pair is (-6,78)

Solve the linear system of equations using addition. Graph the equations to verify your solution. -4x=y+3

Answers

In standard form the answer would be y=-4x-3

Answer:

Step-by-step explanation:

given equation,

-4 x = y + 3

y = -4 x -3........................(1)

comparing equation 1 with

 y = m x + c

m = -4 and  c = -3

now using this we can easily plot the graph where c is the y-intercept and m is the slope of line .

so, the plot is shown in the graph attached below.

Help me with surface area plssss

Answers

Answer:  The surface area of the given cylinder is:  " 747. 32  in² " .

______________________________________________________
Explanation:
______________________________________________________
The formula for the "Surface Area, "S. A." , of a cylinder : 

" S.A. = 2 [tex] \pi [/tex] r² + 2[tex] * \pi [/tex] * r * h " ;

in which:   [tex] \pi [/tex] = 3.14 (we shall use this approximation) ; 

                           S.A. = surface area (in "square units" ;
                                                            in our case, "square inches" ; 
                                                                 or; " in² " ) ;
                                r = radius = 7 in. 

                                h = height = 10 in. 
__________________________________________________
   Let us plug in our "known" — and/or "given" — values ; into the formula & solve for the "S.A." (surface area of this "cylinder") :
__________________________________________________

 →  S.A. = 2 [tex] \pi [/tex] r² + 2 * [tex] \pi [/tex] * r * h ; 


→  S.A.  =  2 (3.14) * (7 in.)²   +    2 * (3.14) * (7 in) * (10 in)  ; 

→  S.A.  = [ 2 * (3.14) * (7²)  * (in²) ] +  ( 2 * 3.14 * 70 *  in²) ;

              = ( 2 * 3.14 * 49 * in² ) + (439 .6 * in²) ; 

              = (307. 72 in²) + (439 .6 in²) ; 

              =  747. 32  in² ; 
______________________________________________________________
 →  Note:  This answer is already rounded to the nearest hundredth.  Apparently, the "image attached" mentioned to round the answer "to the nearest hundredth"; however, this part of the "image attached" appears to have been "cut off" .
______________________________________________________

→ This answer is already rounded to the nearest hundredth.
______________________________________________________
Answer:  The surface area of the given cylinder is:  " 747. 32  in² " .
______________________________________________________

How many triangles can be made if two sides are 4 inches and the angle between them is 90°? (5 points) 1 2 More than 2 None

Answers

How many triangles can be made if two sides are 4 inches and the angle between them is 90°?

1
2
More than 2
None

Answer is: 1

Answer:

The answer is 1. This is because when the lengths of two sides and the angle between them is given, only one unique triangle can be formed.



3. Scatter plots are used to look for a pattern of association, or trend, between
A. one set of values
B. two sets of values
C. three sets of values
D. four sets of values
correct answer get Brainiest

Answers

i would say b because its 2 or more points on a graph otherwise its just a point

(64+28+76)÷6 show how you can calculate the number of 3/4 cup servings

Answers


[tex](64 + 28 + 76) \div 6 = 24.66666666666666666[/tex]

Rewrite 0.434343... as a fraction

Answers

Final answer:

The repeating decimal 0.434343... can be rewritten as a fraction by defining the decimal as a variable, manipulating the equation, and finally isolating the variable to find that the fraction form of 0.434343... is 43/99.

Explanation:

To rewrite the repeating decimal 0.434343... as a fraction, we first define the repeating decimal as a variable, let's call it x = 0.434343.... Then, to isolate the repeating section, we multiply x by 100, given the two-digit repeat, which gives us 100x = 43.434343.... By subtracting the original equation from this new one, we get: 99x = 43, because 100x - x = 43.434343... - 0.434343... simplifies to 99x = 43. Dividing both sides by 99 gives us x = 43/99, which is the fraction form of the repeating decimal.

To rewrite the repeating decimal 0.434343... as a fraction, we first denote it as x. Next, we can subtract the non-repeating part from the repeating part to get a new number, y. Then, we can express x and y as fractions and solve for the repeating fraction part.

in the decimals chart, the memory cue for dividing by a whole number is "up." what does that mean?

Answers

Rounding up is a rule that is used, no matter what the value is. We round numbers up to get a better estimate for our answers. The memory cue for dividing by a whole number "up" just means that you will be bringing the decimal up.

Answer:

It means that you have to put the decimal point in the quotient exactly above the decimal point in the dividend.

Step-by-step explanation:

In the picture attached, the decimals chart is shown. There you can see where you have to put the decimal point in the quotient when you are dividing a decimal number by a whole number.

I need the right answer please

Answers

The right answer is not among those offered. The domain is
.. {-9, -6, 4, 7}

___
The 4th selection {4, 7} is the best of those offered, but it is not correct.

How deep is a well that takes eight cranks on the six- inch diameter windlass to raise the bucket?

Answers

In order to answer this, you would need to find the circumference of the windlass. This would represent the distance of one rotation. When you know the distance of one rotation, you would then multiply it by eight for all eight Kranks. This is knowing each crank is a complete turn. Here is the formula C= pi times the diameter. So, 3.14 x 7 is 18.84 inches for 1 crank. 18.84 inches times 8 equals 150.72 inches. This is an approximation because pi is an approximation.

please awnser i fraction form 4 3/4 times 3 3/5 times 15

Answers

Simplify the following:
(4 + 3/4) (3 + 3/5)×15

Put 3 + 3/5 over the common denominator 5. 3 + 3/5 = (5×3)/5 + 3/5:
(4 + 3/4) (5×3)/5 + 3/5 15

5×3 = 15:
(4 + 3/4) (15/5 + 3/5)×15

15/5 + 3/5 = (15 + 3)/5:
(4 + 3/4) (15 + 3)/5×15

15 + 3 = 18:
(4 + 3/4)×18/5×15

Put 4 + 3/4 over the common denominator 4. 4 + 3/4 = (4×4)/4 + 3/4:
(18×15)/5 (4×4)/4 + 3/4

4×4 = 16:
((16/4 + 3/4)×18×15)/5

16/4 + 3/4 = (16 + 3)/4:
(18×15)/5 (16 + 3)/4

16 + 3 = 19:
19/4×18/5×15

19/4×18/5×15 = (19×18×15)/(4×5):
(19×18×15)/(4×5)

15/5 = (5×3)/5 = 3:
(19×18×3)/4
The gcd of 18 and 4 is 2, so (19×18×3)/4 = (19 (2×9) 3)/(2×2) = 2/2×(19×9×3)/2 = (19×9×3)/2:
(19×9×3)/2

19×9 = 171:

(171×3)/2

171×3 = 513:

Answer: 513/2

The result of 4 3/4 times 3 3/5 times 15 is 513/2.

To multiply the fractions 4 3/4, 3 3/5, and 15, we first need to convert the mixed numbers to improper fractions.

4 3/4 can be written as (4 * 4 + 3)/4 = 19/4

3 3/5 can be written as (3 * 5 + 3)/5 = 18/5

Now we multiply the fractions:

(19/4) * (18/5) * 15 = (19 * 18 * 15)/(4 * 5) = 5130/20

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 10:

5130/20 = (5130 ÷ 10)/(20 ÷ 10) = 513/2

Therefore, the result of the multiplication in fraction form is 513/2.

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Juan will put fencing around the outside of the enclosure. How much fencing does he need for the enclosure?

Answers

If Juan intends to put fencing around the enclosure, that means that we are looking at the perimeter of the image (the outside). We can count the amount of lines between the dots to determine how much fencing he will need. After counting the perimeter of this figure, we see that the total is 22. We do not know what the units are, so for now we can just say that he will need 22 units of fencing to fully enclose this shape.

simplify 2y+(4+5y) expression

Answers

2y+(4+5y)
2y+4+5y
7y+4

Answer: 11y

Step-by-step explanation:

2y+(4+5y)  

2y+4+5y

7y+4

= 11y

Hey guys! Could someone help me with this problem? I got the wrong answer! The answer is B, but I don’t know how to get it! Could you work it out and explain?! Thank you so much! God Bless!

Answers

When it says 'which has a greater rate of change' it is referring to 'what has a greater slope.' So, let's calculate each thing's slope:

Table:
I'm going to pick the easiest values to work with, so I'll pick the points (0, -2) and (1, -9/5) - I simplified the mixed fraction. So, here we go, the slope formula is:
[tex] m =\frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{- \frac{9}{5} - (-2)}{1-0} = \frac{- \frac{9}{5} - ( -\frac{10}{5} )}{1-0}[/tex]
[tex] m = \frac{ \frac{1}{5} }{1} = \frac{1}{5} [/tex]

So, the table's slope is -1/5.

Graph
We can, again, pick two points. I'll pick the two given: (5, 0) and (0, -3).  Let's start off with the same formula:
[tex] m =\frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{-3-0}{0-5} = \frac{3}{5} [/tex]

The graph's slope is 3/5.

Now, we just have to decide which is bigger: -1/5 or 3/5. So, clearly:
3/5 > -1/5. 

The 3/5 slope was the graph, hence it has the greater rate of change (that's why it's B). If anything doesn't make sense, feel free to DM me or ask!

A remodeling project calls for sanding a chair with a disk sander. The sanding disk used on the sander has a radius of 4.5 inches. Find the area of the disk. Use 3.14 for pi.

Answers

The answer is 28.26 in sq.

Need help with number 13 please, thanks.

Answers

The answer is I) 103. So the temperature started at 101, then went up to 103. Going up is not negative. F and G are out of the picture, because they are negative. It is not H because the temp. is 103, not 101. It changed. I is your answer.
~Deceptiøn
I is the right answer.

At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School.

A.
Left-handed: 424
Right-handed: 483
B.
Left-handed: 28
Right-handed: 378
C.
Left-handed: 48
Right-handed: 504
D.
Left-handed: 56
Right-handed: 560
E.
Left-handed: 30
Right-handed: 315

Answers

Answer:

The anwers Is C and E.


A relationship between two quantities is proportional if the ratio between those quantities is always equivalent.

Hint #22 / 4

Let's look at the ratio between right- and left-handed students at East Middle School.

6

0

9

right

5

8

left

=

1

0

.

5

right per left

58left

609right

​  =10.5 right per left

At East Middle School, there are

1

0

.

5

10.5 right-handed students for every left-handed student.

Hint #33 / 4

Now we can compare the other combinations of values for left-handed and right-handed students. Which ratios are equivalent to the ratio at East Middle School?

So the anwers is C AND E


Answer:

C and E cuz why not

Step-by-step explanation:

jordan has a marble collection. 4/12 of the marbles are red. 2/4 are green. what fraction of her total marbles are red and green

Answers

2/4(3/3) = 6/12

6/12 + 4/12 = 10/12

10/12 or 5/6 is your answer

Hope this helps

simplify and show work 5 1/3+(-3 9/18)

Answers

What we must do in this case is to subtract both numbers step by step. We have then:
 Step 1:
 5 1/3 - 3 9/18
 Step 2:
 (5-3) + (1/3 - 9/18)
 Step 3:
 (5-3) + (0.3 - 0.5)
 Step 4:
 (2) + (-0.2)
 Step 5:
 1.8
 Answer:
 1.8
 Equivalently:
 1 4/5

Add the two expressions.

−6.3x+4 and 1.5x−6

Enter your answer, in simplified form, in the box.

please help fast 30 points!

Answers

(-6.3x + 4) + (1.5x - 6)

-6.3x + 1.5x = -4.8x
4 + (-6) = -2

-4.8x - 2 is your answer


the correct answer is -4.8x - 2

What is the approximate volume of the cone?

Use 3.14 for π .


A. 1206 cm³

B. 2170 cm³

C. 3260 cm³

D. 6510 cm³

Answers

The formula is A 1,206. 
 
The approximate volume of the cone is 1206(A)

A hollow crystal ball is made of glass that is 3 centimeters thick. The ball has a radius to the outside surface of 8 centimeters. What is the approximate volume of glass used to make the ball? Use 3.14 for pi.

Answers

Answer:

The approximate volume of glass is equal to [tex]1,620.24\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the sphere ( crystal ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

the approximate volume of glass is equal to

[tex]V=\frac{4}{3}\pi (rb^{3}-ra^{3})[/tex]

[tex]rb=8\ cm[/tex]

[tex]ra=(8-3)=5\ cm[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(8^{3}-5^{3})=1,620.24\ cm^{3}[/tex]

What is the value of the x in this figure?

Answers

I believe its 45 because a right angle equals 90 degrees and if you multiply 45 and 2, it'll give you a right angle(90 degrees)
x=45°
180÷2=90
90÷2
=45
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