prove that every positive integer can be written as a finite sum of distinct integral powers of the golden ratio.

[tex]\displaystyle\\Answer: \frac{400}{93}\approx4.3[/tex]

Step-by-step explanation:

[tex]\displaystyle\\4:0.93=\\\\\frac{4}{0.93 }=\\\\\frac{4}{\frac{93}{100} } \\\\\frac{4*100}{93} \\\\\frac{400}{93} \approx\\\\4.3[/tex]

Answer:

-1

Step-by-step explanation:

Tn = a+(n-1)d (general formula)

Tn = 8-n (given formula)

T9 =8-9

T9=-1

Answer:

C. 73.5lbs

Step-by-step explanation:

Nate's total sales is  83,666.67.

The first step is to determine the commission on sales of $75,000

Commission : 0.025 x $75,000 = $1,875

The second step is to determine the amount of commissions earned on sales above $75,000: $2135 - $1,875 = $260

The next step is to determine the amount earned above $75,000

Amount of sales above $75,000 : $260 / 0.03 = $8,666.67

Total sales for the week :  $8,666.67 + $75,000 = 83,666.67

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Answer:

Step-by-step explanation:

{(0, 2), (1, –1), (2, 3), (3, –2)}

Answer:basically, x never reats with a different y

(x,y)

A is a fn of x since x never repeats

B is a fn of x since x never repeats

C is a fn of x since x never repeats

D is not since we have (1,2) and (1,-2) so this is the answer

Step-by-step explanation:

Answer: 1:8

Step-by-step explanation:

13 tables

104 chairs

Ratio: 13:104

divide both sides by 13

13:104 = 1:8

The degree of the polynomial formed is 6.

The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.

For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

Now the given functions are:

[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x

Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).

(g°h)(x) is equal to g[h(x)]

=g[2x+5]

=3(2x+5)²-1

=3(4x²+20x+25)-1

=12x²+60x+74

Now we find (f ° g° h)(x)

(f ° g° h)(x)=f[g(2x+5)]

f[g(2x+5)]=f(12x²+60x+74)

f(12x²+60x+74)=(12x²+60x+74)³

Now we have to simplify the expression:

(12x²+60x+74)³

=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]

The largest degree of the variable x in the polynomial is 6.

hence the degree of [f o go h](x) is 6.

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The area of a persian rug in a metre square is given by 10.03 m2. It is calculated by using the concept of area and conversion of units of a quantity.

What is the conversion of units?

Conversion of units is the transformation between various units of measurement for the same quantity, simply the conversion of units deals with converting a quantity into different units without changing its magnitude.

Calculation of the area of the persian rug with given width and length

Given:

Length = 12 feet

Width = 9 feet

The basic step involved in solving this problem is to convert the length and width given in feet into metre

We know that 1 feet = 0.3048 m

Length = 12 × 0.3048

           = 3.657 m

Width = 9 × 0.3048

         = 2.743 m

Area of rug = length × width

=  3.657 × 2.743

= 10.03 m2

Hence, the required area of the persian rug is 10.03 m2.

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Answer:

5

Step-by-step explanation:

Answer:

y = (-1/6)x - 4

Step-by-step explanation:

Line equations are usually expressed in the following format:

y = mx + c

Where m is the gradient (slope), and c is the y-intercept.

We can fill in the value of m right away as we are given it in the question:

y = (-1/6)x + c

And we are given the point (-6,-3), so we can fill in the values for x and y, in order to find the value of c:

-3 = (-1/6)(-6) + c

Rearrange and simplify this:

-3 = 1 + c

c = -4

Finally, substitute the value of c back into the original equation to get the final equation of the line:

y = (-1/6)x - 4

The solution to the expansion of each polynomial is;

1. (x + 9)(x² - 9x + 81) = x³ + 729

2. (y² - 7)(y⁴ - 7y² + 49) = y⁶ − 14y⁴ + 98y² - 343

3. (x² - 5)(x⁴ + 5x² + 25) = x⁶ - 125

4. (8x - 9y)(64x² + 72xy + 81y²) = 512x³ - 729y³

5. (10m - 11) (100m² + 110m + 121) = ​1000m³ - 1331

1) We want to expand the polynomial;

(x + 9)(x² - 9x + 81)

= x³ + 729

2) We want to expand the polynomial;

(y² - 7)(y⁴ - 7y² + 49)

Multiplying out gives;

y⁶ −7y⁴ + 49y² −7y⁴ + 49y² - 343

Combining like terms gives;

y⁶ − 14y⁴ + 98y² - 343

3) We want to expand the polynomial;

(x² - 5)(x⁴ + 5x² + 25)

Multiplying out gives;

x⁶ - 125

4) We want to expand the polynomial;

(8x - 9y)(64x² + 72xy + 81y²)

Multiplying out gives;

512x³ - 729y³

5) We want to expand the polynomial;

(10m - 11)(100m² + 110m + 121)

Multiplying out gives;

1000m³ - 1331

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Answer: she could buy 10 cookies.

Step-by-step explanation:

In order to figure out how many cookies she can buy just do 20÷2.

The quotient of 7/8 divided by 2/5 will be C. 35/16.

The quotient simply means that we have to divide.

Therefore, the quotient of 7/8 divided by 2/5 will be:

= 7/8 ÷ 2/5

= 7/8 × 5/2

= 35/16

In conclusion, the correct option is C

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I think using properties can help you mentally find answers to problems because if you know what property you are going to use, then you can know what you are doing, thus it's helping you mentally find answers.

Answer:

Step-by-step explanation:

Answer:

0.153 or 15.3%

Step-by-step explanation:

Subtract save percentage last season from save percentage this season:

0.738 - 0.585 = 0.153

Convert the decimal answer to a percent

0.153 x 100% = 15.3%

The statement that a function is decreasing on an interval if the output values decrease as the input values decrease is FALSE.

A decreasing function refers to a function where the value of the output moves in a different direction from the value of the input.

For instance, in a decreasing function, the value of the output would decrease when the value of the input increases.

In conclusion, it is false that a function is decreasing if the output and the input are both decreasing.

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The slope of the line that passes through the points (-9, 0) and (−17,4) is -2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

The formula to calculate slope is -

m = x2 - x1 / y2 - y1

(-9, 0) and (−17,4)

m = -17 + 9 / 4 - 0

m = -8/4

m = -2

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Answer: −8n+3+n+11

Add the terms

−7n+3+11

Solution

−7n+14

Step-by-step explanation: hope this helps

Answer:

Step-by-step explanation:

(x+4) = -6

x + 4 + 6 = -6 + 6

x = 10

Answer:

g(-6) = -6

g(0) = 5

g(7) = 8

h(-6) = 10

h(0) = -1

h(7) = -4

Step-by-step explanation:

g(x) = (1/3) f(x)

g(-6) = (1/3)(-18) = -6

g(0) = (1/3)(15) = 5

g(7) = (1/3) (24) = 8

h(x) = -g (x) + 4

h(-6) = -(-6) + 4 = 10

h(0) = -(5) + 4 = -1

h(7) = -(8) + 4 = -4

I hope this helps!

Answer:

0.03 is the correct answer

Step-by-step explanation:

0.02866009 = 0.03

Answer:

k = -4

Step-by-step explanation:

8 = 2k - 8 - 6k

Collect like terms

8 = -4k - 8

Add 4k to both sides (nice to have variable on left, constants on right)

8 + 4k = -8

Subtract 8 from both sides

4k = -16

Divide both sides by 4

k = -4

Thus, 36° is the smaller angle and 144° is the greater angle.

For instance, the complement angle of 130° and the angle of 50° is 180°. Complementary angles add up to 90 degrees. When the two extra angles are combined, they create a straight line and an angle. The two angles that complement one another do not necessarily need to be close to one another, it should be emphasised. As a result, two angles may be supplementary if their sum is 180 degrees. The study of various shapes is one of the main areas of mathematics.

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The third angle of 16 degrees and 102 degrees is 62 degrees.

The third angle of 119 degrees and 23 degrees is 38 degrees.

The third angle of 28 degrees and 87 degrees is 65 degrees.

The third angle of 96 degrees and 51 degrees is 33 degrees.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

In order to determine the missing angle, subtract the sum of the two given angles from 180.

180 - (16 + 102) = 62

180 - (119 + 23) = 38

180 - (28 + 87) = 65

180 - (96 + 51) = 33

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Answer:

$45

Step-by-step explanation:

100% = $75

100% - 40% = 60% (discounted price)

60% = 0.6

0.6 x 75 = 45

60% = $45 (discounted price)

Answer:

you have it right.

Domain is 3[tex]\leq[/tex]x[tex]\leq[/tex]positive infinity

Range is 5[tex]\leq[/tex]y[tex]\leq[/tex]positive infinity

Step-by-step explanation:

The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Triangle law of vectors states that for a ΔABC

The sum of vectors of two sides is equal to the third side vector.

Two vectors are said to be Parallel if one vector is scalar multiple of other.

In the given figure

In ΔABC , D is mid point of AB and E is the mid point of AC .

By using triangle law of vectors for ΔADE

AE+AD=ED......(1)

Now using triangle law of vectors addition for ΔABC

CA+AB=CB    ....(2)

(as given that E is the mid point of CA , we can write [tex]AE=\frac{1}{2} CA[/tex]

CA=2AE.....(3)

and D is mid point of AB , we can write [tex]AD=\frac{1}{2} AB[/tex]

AB=2AD......(4)

Substituting (3) & (4) in (2) we get

2AE+2AD=CB

2(AE+AD)=CB

SUBSTIUTTING VALUES OF (AE+AD) from (1) we get

2ED=CB

[tex]ED=\frac{1}{2} CB[/tex]

Hence , the line joining the midpoints of two sides of a triangle is  half of third side.

Since ED is (1/2) of CB i.e. ED is scalar multiple of CB.

Hence they are parallel.

Therefore , The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

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According to the given statement,

366 liters of natural oil is needed to make 671 L synthetic oil.

Essential oils, which are more natural, are slightly different from synthetic oils. An intentionally created chemical component is present in synthetic oils, which are used as lubricants.

Full synthetics and semi-synthetic oils are the two primary types of synthetic oils. Full synthetics originate from crude oil or byproducts in this situation. Conventional oils are produced using chemical procedures rather than distillation. The resulting synthetic oil has a higher molecular make-up and frequently exhibits more consistent characteristics. Synthetic oils are used in many cosmetic and medicinal goods, just like their more natural equivalents.

According to the given values;

The ratio of natural to synthetic oil

= 6:5

If 671 liters have to be made then,

Add 6+5=11

So, 6/11 of 671liters will be = 366 liters of natural oil

and, 5/11 of 671 liters will be = 305 liters of synthetic oil

Hence, 366 liters of natural oil is needed.

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