Solve for F in terms of K:

[tex]K=\frac{5}{9}(F+459.67)[/tex]

Answer:

10 cms.

Step-by-step explanation:

The circumcircle passes through each vertex of the hexagon so the radius is  equal to one of the  2 equal sides of an isosceles triangle with base = 10 cm and vertex = 60 degrees.

So considering this triangle  the base angles are ( 180 - 60) / 2 = 60 degrees.  So we have an equilateral triangle with each side = 10 cm.

Therefore the  radius is 10 cm. long.

The radius of the circumcircle of the regular hexagon is approximately 5.77 cm.

In a regular hexagon:

- Each side length  s = 10 cm.

- The circumcircle passes through all vertices of the hexagon, making it the circle that circumscribes the hexagon.

The radius R of the circumcircle of a regular hexagon can be related to its side length s by the formula:

[tex]\[ R = \frac{s}{\sqrt{3}} \][/tex]

Let's apply this formula:

[tex]\[ R = \frac{10}{\sqrt{3}} \][/tex]

To simplify [tex]\( \frac{10}{\sqrt{3}} \)[/tex], multiply the numerator and the denominator by [tex]\( \sqrt{3} \)[/tex]

[tex]\[ R = \frac{10 \cdot \sqrt{3}}{3} \][/tex]

Therefore, the radius of the circumcircle of the regular hexagon with a side length of 10 cm is [tex]\( \frac{10 \sqrt{3}}{3} \)[/tex] cm. This is the exact value of the radius in terms of [tex]\( \sqrt{3} \)[/tex]. If you need a numerical approximation, you can calculate it as follows:

[tex]\[ R \approx \frac{10 \times 1.732}{3} \approx \frac{17.32}{3} \approx 5.77 \text{ cm} \][/tex]

A single chicken lunch will cost $7 so option (C) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the cost of chicken = c

cost of ham = h

Given,

Sharon's Deli charged the Business Club $231 for 18 chicken lunches and 14 ham lunches.

So,

18c + 14h = 231

And,

$225.00 for 15 chicken lunches and 16 ham

So,

15c + 16h = 225

By solving both equations

h = 7.5 and c = 7

Hence, a single chicken lunch will cost $7

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ANSWER

[tex]T.S.A = 150\pi[/tex] square inches.

EXPLANATION

The total surface area of a cylinder is given by;

[tex]T.S.A = 2\pi \: r(r + h)[/tex]

The height of the cylinder is , h=10in.

The radius of the cylinder is, r=5in.

We substitute the known values into the formula to obtain;

[tex]T.S.A = 2\pi \times 5(5+ 10)[/tex]

[tex]T.S.A = 10\pi(15)[/tex]

In terms of π, the total surface area is

[tex]T.S.A = 150\pi in^2[/tex]

Answer: x=-4,3+5x; 3,-5x

step-by-step explanation: I just used ,athway. this is what is told me. i hope this helps

[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0[/tex]

[ correction added, Thanks to @stef68 ]

[tex]\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)[/tex]

To find the polynomial of degree 3 with real coefficients and specific zeros and y-intercept, we use the fact that complex zeros occur in conjugate pairs. We can express the polynomial as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant. By plugging in the y-intercept value, we can solve for the constant a.

To find the polynomial with degree 3 and real coefficients that has a y-intercept of 60 and zeros 3 and 1+3i, we can use the fact that complex zeros occur in conjugate pairs. Given that 1+3i is a zero, its conjugate 1-3i is also a zero. Therefore, the polynomial can be expressed as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant.

Since the polynomial has a y-intercept of 60, we know that f(0) = 60. Plugging in x=0, we can solve for the constant a:

f(0) = a(0-3)(0-(1+3i))(0-(1-3i)) = 60

Since the constant a is the only unknown variable, we can solve for it:

-3*(1+3i)*(1-3i) = 60/a

-3*(1-9i^2) = 60/a

12 = 60/a

a = 5

Therefore, the polynomial f(x) = 5(x-3)(x-(1+3i))(x-(1-3i)) has the desired properties.

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Answer:

The correct answer is A, 73

Step-by-step explanation:

First we have to arrange the whole numbers in ascending order. i-e from smallest to largest. Showing it as follows:

53 54 59 62 64 65 66 68 70 71 75 78 79 79 83 83 86 90 91 94                

Now we would find the median by taking the middle number. But this series consists of even numbers. There are 20 numbers. So we will take the middle two numbers and find their average like follows:

71 + 75 = 146/2  = 73

The answer is 73

Answer:

median =73

Step-by-step explanation:

Given list of data is

{94,79,83,78,70,66,68,75,53,54.79,59,83,91,64,65,71,62,86,90}.

Now we need to find about what is the median for the data listed above.

So first we need to rearrange the given data in increasing order. then we can easily find the middle number as median.

Sorted list of data is:

{53, 54, 59, 62, 64, 65, 66, 68, 70, 71, 75, 78, 79, 79, 83, 83, 86, 90, 91, 94}

there are two numbers at the middle 71 and 75

then median = (71+75)/2=146/2=73

Step-by-step explanation:

[tex]\bold{40.}\\\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right] +\left[\begin{array}{ccc}4&1\\6&0\end{array}\right] =\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&1\\11&7\end{array}\right][/tex]

[tex]\bold{41.}\\\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right][/tex]

[tex]\bold{42.}\\\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]

[tex]\bold{43.}\\\\CD=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\\\=\left[\begin{array}{ccc}4+0+1&-6-6+4&-8+3-1\\2+0+12&-3+0+16&-4+0-4\end{array}\right]\\\\=\left[\begin{array}{ccc}5&-8&-6\\14&13&-8\end{array}\right][/tex]

[tex]\bold{44.}\\\\2D+3C=2\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]+3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\\\\=\left[\begin{array}{ccc}(2)(-2)&(2)(3)&(2)(4)\\(2)(0)&(2)(-2)&(2)(1)\\(2)(3)&(2)(4)&(2)(-1)\end{array}\right]+\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]\\\\=\left[\begin{array}{ccc}-4&6&8\\0&-4&2\\6&8&-2\end{array}\right]+\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]

[tex]\large\bold{You\ can\ not\ add\ matrices\ of\ different\ dimensions!!!}[/tex]

Step-by-step explanation:

Some characteristics of the graph of a square root function are: both the domain and range consist of real numbers greater than and equal to zero, start from origin, etc.

The square root function is the function that is represented by the following:

f(x) = √x

We are asked to give some characteristics of a square root graph.

The characteristics are given below:

The domain of a square root function consists of all real numbers greater than and equal to zero.

The range of a square root function consists of all real numbers greater than and equal to zero.

The graph of the square root function starts at the origin.

The graph of a square root function is an increasing graph.

The graph of the square root function is a one-to-one function. This means each domain value and range value has only one corresponding domain and range value.

Therefore, we have given some characteristics of the graph of a square root function.

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Answer:

11 and 1/3 yards

Step-by-step explanation:

5 yards and 2 feet = 5 and 2/3 yards = 17/3 yards

(17/3 yards)(2) = 34/3 yards = 11 and 1/3 yards

The equivalent value of 5 yards 2 feet × 2 is 11 and 1/3 yards.

Given,

5 yards 2 feet × 2

Here,

Firstly convert feet to yard,

1 yard = 1/3 feet

So,

2 feet = 2/3 yard

So,

5 yards and 2 feet = 5 and 2/3 yards

= 17/3 yards

Now,

(17/3 yards)(2) = 34/3 yards

= 11 and 1/3 yards

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Step by step explanation:

You first subtract z on both sides of the equal sign

ax-bx=(z-y)

Since a and b both have a "x" you can subtract them

(a-b)x=(z-y)

then you divide "x" on both sides of the equal sign

[tex]\frac{a - b}{x} = \: \frac{z - y}{x} [/tex]

To find x in the equation ax-bx+y=z, combine like terms, subtract y from both sides, and then divide by (a-b) to get the formula x = (z-y)/(a-b).

To find the value of x in the equation ax - bx + y = z, you can follow these steps:

This step-by-step process allows you to solve for x in terms of a, b, y, and z.

Answer:

Sample size is 6, event of rolling an even number is 3/6 (or 1/2)

Step-by-step explanation: When you roll a dice it could be 1, 2, 3, 4, 5, or 6. Count those up and you'll have the sample size. Odds of rolling a 2, 4, or 6 (even number) is 3/6 or 1/2, or 50%

Hello! Based on this problem, 68 is part of a whole. To solve it, we can write and solve a proportion. Set it up like this:

68/x = 85/100

Cross multiply the sections. 68 * 100 is 6,800 and 85 * x is 85x. So you get 6,800 = 85x. Now, divide each side by 85 to isolate the x. 85x/85 cancels out. 6,800/85 is 80. We can check this answer by multiplying 80 by 85%. 80 * 85% (0.85) is 68. There's our answer. 68 is 85% of 80.

The number whose 85 percent gives 68 is 8000.

Given the parameters in the question:

Given Value = 68

Percentage = 85%

To find the number whose 85 percent gives 68, we can use the following formula:

Number = (Given Value / Percentage) × 100

First, convert 85% from percent to decimal:

85% = 85/100 = 0.85

Now, plug these values into the above formula:

Number = (Given Value / Percentage) × 100

Number = ( 68 / 0.85 ) × 100

Number = 80 × 100

Number = 8,000

Therefore, 68 is 85% of the number 8000.

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Hope this is what you need

Answer:

I am not sure of the equation but I interpreted it as x^2a^2+3xa^2+2a^2

Step-by-step explanation:

X^2a^2+3xa^2+2a^2

1. a^2 (x^2+3x+2)

2.a^2(x^2+2x+x+2)

3. a^2(x(x+2)+x+2)

4. a^2(x+2)(x+1)

ANSWER

(-2,2)

EXPLANATION

The rule for translating a point 'k' units to the right is

[tex](x,y)\to (x+k,y)[/tex]

If the point located at (-5, 2) is translated right 3 units, the coordinates of the image is obtained by adding 3 to the x-coordinate.

This implies that,

[tex]( - 5,2)\to ( - 5+3,2)[/tex]

[tex]( - 5,2)\to ( -2,2)[/tex]

Therefore the image is:

(-2,2)

Answer:

(-2, 2)

Step-by-step explanation:

We are given the following coordinates of a point:

[tex](-5, 2)[/tex]

If this point is translated to the right for 3 units, what will be the coordinates of its image?

Translation towards right side for 3 units means that 3 units are added to its x coordinate so the new point will be:

[tex] ( - 5 , 2 ) [/tex] [tex] \implies [/tex] [tex] ( - 5 + 3 , 2 ) = [/tex] (-2, 2)

ANSWER

The fifth term is 27

EXPLANATION

The explicit rule for the given sequence is

[tex]t_n= {2}^{n} - n[/tex]

To find the fifth term, we substitute n=5 to get,

[tex]t_5= {2}^{5} - 5[/tex]

[tex]t_5= 32 - 5[/tex]

Simplify:

[tex]t_5= 27[/tex]

The fifth term is 27

Answer:

(n×4)

Step-by-step explanation:

Divide the 2nd term by the first to find the ratio which is also n.

Answer:

n=5.

Step-by-step explanation:

The given geometric series is

1+ 4 +16 + 64 + 256

In the given G.P.  the number of terms is 5 and n represents the number of terms in a G.P. So, n=5.

Alternate method:

Here the first term is 1 and the common ratio is

[tex]r=\dfrac{a_2}{a_1}=\dfrac{4}{1}=4[/tex]

The nth term of a G.P. is

[tex]a_n=ar^{n-1}[/tex]

where, a is first term and r is common ratio.

Substitute a=1, an=256 and r=4 in the above formula.

[tex]256=(1)(4)^{n-1}[/tex]

[tex]4^4=4^{n-1}[/tex]

On comparing both sides we get

[tex]4=n-1[/tex]

Add 1 on both sides.

[tex]5=n[/tex]

Therefore, the value of n is 5.

Answer:

c

Step-by-step explanation:

Answer:

$3

Step-by-step explanation:

Whenever some type of expenditure is made, there are usually 2 types of costs available: the fixed cost and the variable cost. Former is the constant cost which has to be incurred in order to gain the advantage from the expense. Latter is the cost that varies with the duration of the expense. Therefore, total costs (TC) = fixed costs (FC) + variable costs (VC). VC can be expressed as: VC = price per hour (p) * number of hours (h). So the equation becomes TC = FC + p*h. In this question, FC = $43, TC = $64, h = 7 hours, and p is unknown. So plugging in the values give:

64 = 43 + 7p.

Solving the equation for p gives:

p = 21/7. This implies that p = 3.

Therefore, the hourly fee is $3!!!

Answer:

7h+43=64

$3 the hourly fee for the rototiller

Step-by-step explanation:

Answer:

lenght = 9

Step-by-step explanation: Area =L×W

Area = 63       7 . x= 63      x=63÷7        x=9               9×7=63

Answer: [tex]-2<x<3[/tex]

Step-by-step explanation:

You need to set up two cases (Positive case and negative case) and solve for "x".

- POSITIVE CASE IF: [tex]2x-1>0[/tex]

[tex]9(2x -1) + 4 < 49\\18x-9<49-4\\18x<54\\x<3[/tex]

- NEGATIVE CASE IF: [tex]2x-1<0[/tex]

[tex]-9(2x -1) + 4 < 49\\-18x+9<49-4\\-18x<36\\x>-2[/tex]

Therefore, the solution is:

[tex]-2<x<3[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

9 | 2x - 1 | + 4 < 49 ( subtract 4 from both sides )

9 | 2x - 1 | < 45 ( divide both sides by 9 )

| 2x - 1 | < 5

Inequalities of the type | x | < a always have solutions of the form

- a < x < a, thus

- 5 < 2x - 1 < 5 ( add 1 to all 3 intervals )

- 4 < 2x < 6 ( divide all 3 intervals by 2 )

- 2 < x < 3

Answer:

(31zy)/(13xz)

Step-by-step explanation:

A reciprocal is a number that you can multiply the original number by and get a product of 1. To find the reciprocal of a fraction, flip it upside down, putting the numerator in the denominator, and the denominator in the numerator:

[tex]\frac{31zy}{13xz}[/tex]

If we multiply this fraction by the other, we would end up simplifying it to 1 by cross multiplication.

Answer:

29 units

Step-by-step explanation:

The length of a segment of a number line is the difference of the coordinates of the end points:

45 -16 = 29

Answer:chicken nuggie

Step-by-step explanation:

The answere is simple.All yyou have to do is sum up the time required to upload aphoto frim a phone to a website.Then find the time it takes to upload ten photos and multiply it by 2.

Answer:

8 minutes.

Step-by-step explanation:

Time taken to upload 12 photographs from a smartphone to a computer = 3.5 minutes

Time taken to upload that 12 photographs from computer to a website = 1.25 minutes.

∵ The time taken for 12 photographs to upload from smartphone to a computer then to a  website = 3.5 + 1.25 = 4.75 minutes.

∴ The time taken for 1 photograph to upload to a website = [tex]\frac{4.75}{12}[/tex]

∴ Time taken to upload 20 photographs from a smartphone to a computer then to a website =  [tex]\frac{4.75}{12}\times 20[/tex]

                             = 7.916 ≈ 8 minutes.

It will take 8 minutes to upload 20 photographs.

Answer:

a.  (15, 15)

Step-by-step explanation:

We start with those two equations:

1) a - 1.2b = -3

2) 0.2b + 0.6a = 12

We'll begin by modifying equation #1 to isolate a:

a = -3 + 1.2b

Then we'll use this value for a in the second equation:

0.2b + 0.6 (-3 + 1.2b) = 12

0.2b - 1.8 + 0.72b = 12

0.92b = 13.8

b = 15

Then we'll place that value of b in the first equation to find a:

a - 1.2 (15) = -3

a - 18 = -3

a = 15

Answer:

(15,15) is right

Step-by-step explanation:

Answer:

The equation written in the standard form is written as

ax^4 + bx+c

where a and b are the coefficients of the second-order and first-order term, while c is the constant term.

The equation we have in this problem is

By comparing (1) with (2), we immediately see that

A = -3x^4

B = 7x

C = 2

Step-by-step explanation:

Hope this helps :)

Final answer:

The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is 2, as it is the term without any variables.

Explanation:

The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is the term that does not contain any variables. In this polynomial, the terms are classified based on their variable's degree. In this case, -3x^4 is the term with the variable raised to the fourth power, -7x is the term with the variable to the first power, and 2 is the term with no variable, which makes it the constant term. Therefore, the constant term is 2.

Answer:

9,18, and 36

Step-by-step explanation:

9*4=36 and 9*1=9

18*2=36 and 9*2=18

36*1=36 and 9*4=36

Answer:

multiples of 9: 9, 18, 27, 36, 45, 54, 63,72, 81, 90, 99, 108, etc.

factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

Answer:

The answer is x=9 and/or x = -12

Step-by-step explanation:

This is a quadratic formula meaning that you must take the a value (1) b value (3) and the c value (108) and plug it into the quadratic formula.

[tex]\frac{-3±\sqrt{9+4*1*-108} }{2}[/tex]

which simplifies to -3 add or subtract the sqrt of 441 divided by two.

To solve the equation x² + 3x - 108 = 0, we use the quadratic formula, which gives two solutions: x = 9 and x = -12.

The question asks to solve the quadratic equation x2 + 3x - 108 = 0. To solve this equation, we will use the quadratic formula, which is given by x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax2 + bx + c = 0. In our case, a = 1, b = 3, and c = -108.

Substituting these values into the quadratic formula gives us:

x = (-(3) ± √((3)2 - 4 ×(1) ×(-108))) / (2 ×(1))

x = (-3 ± √(9 + 432)) / 2

x = (-3 ± √441) / 2

x = (-3 ± 21) / 2

This results in two possible values for x:

So, the solutions to the equation x2 + 3x - 108 = 0 are x = 9 and x = -12.

Answer:76 and 84

Step-by-step explanation:

Answer:

1) 78 and 82

2)76 and 84

3)74 and 86

Step-by-step explanation:

1)

Given

mean, x= 80

standard deviation, sd= 2

given percentage of class= 68%

now as per the properties of normal distribution:

-68% of the scores will lie within one standard deviation, sd of the mean, x

i.e. between x-sd and x+sd

Putting values in above we get:

x-sd= 80-2 = 78

x+sd=80+2= 82

Hence about 68% of the class would score between 78 and 82

2)Given

mean, x= 80

standard deviation, sd= 2

given percentage of class= 95%

now as per the properties of normal distribution:

-95% of the scores will lie within 2 standard deviation, sd of the mean, x

i.e. between x-2sd and x+2sd

Putting values in above we get:

x-sd= 80-2(2) = 80-4 = 76

x+sd=80+2(2)= 80+4 = 84

Hence about 95% of the class would score between 76 and 84

3)Given

mean, x= 80

standard deviation, sd= 2

given percentage of class= 99%

now as per the properties of normal distribution:

-99% of the scores will lie within 3 standard deviation, sd of the mean, x

i.e. between x-sd and x+sd

Putting values in above we get:

x-sd= 80-3(2) = 80-6 = 74

x+sd=80+3(2)= 80+6 = 86

Hence about 99% of the class would score between 74 and 86!

Answer:

A, D, and F.

Step-by-step explanation:

A:

The remainder is 0, thereby satisfying the factor theorem.

D: Synthetic division is in the form p(x)/(x-a). Since -4 is the number, the factor must be (x--4) or (x+4)

F: Refer to D.