Jim, Dan and David share some sweets in the ratio 3:1:5. Jim gets 21 sweets. How many more sweets does David get over Dan?

 Recursive formula of an arithmetic sequence is given by the expression,

                          [tex]T_n=a+(n-1)d[/tex]

                 Where, [tex]T_n=[/tex] nth term

                              [tex]a=[/tex] First term of the sequence

                              [tex]n=[/tex] Number of term

                              [tex]d=[/tex] Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       [tex]T_n=a+(n-1)d[/tex]

       [tex]T_n=7+(n-1)5[/tex]

       [tex]T_n=5n+2[/tex]

If [tex]n=6,[/tex]

       [tex]T_n=7+(6-1)5[/tex]

       [tex]T_n=7+25[/tex]

       [tex]T_n=32[/tex]

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Answer:

perpendicular

Step-by-step explanation:

They form a 90 degree angle

Answer:

53

Step-by-step explanation:

Answer:

(540 - π60 cm²) or 350cm³(351.5)

Step-by-step explanation:

You'll have to subtract the volume of the rectangular prism with the cylinder.

We know that the prism's volume is V = s*s*h = 6*6*16 = 540 cm²

We also know the cylinder's volume: V = πr²h = π(4/2)²*15 = π*4*15 = π*60

Now the only step remaining is to subtract the volume of the prism with the cylinder: 540 - π*60 cm³

540 - π*60 cm³ is the full answer

350 is the approximate answer (rounded it down from 351.5 to 350cm³)

Answer:

6x + 33x²

Step-by-step explanation:

3x × 2 = 6x

3x × 11x = 33x²

Answer:

x=±8

Step-by-step explanation:

You add 11 on both sides

x^2=53+11

x^2 = 64 so

x=8 or x=-8

Answer:

16/63

Step-by-step explanation:

8/9 * 2/7

Multiply the numerators

8*2 = 16

Multiply the denominators

9*7 = 63

Put the numerator over the denominator

16/63

The Answer is: 16/63

You just  multiply 8/9 & 16/63

Answer:

See explanation

Step-by-step explanation:

Line A

gradient = 4

x-intercept = -1

y-intercept = 4

Line B

gradient = -3

x-intercept = -1

y-intercept = -3

y + 8x = - 72

x-intercept = -9

y-intercept = -72

Answer: (2,6)

Step-by-step explanation: you go the the left 3 from F then up 2 and you have it.

Answer:

[tex]4-i[/tex]

Step-by-step explanation:

Use the formula for the distance of a complex number from the origin on the complex plane.

[tex]\sqrt{a^2+b^2}[/tex]

[tex]a+bi[/tex]

[tex]4-i[/tex]

[tex]\sqrt{4^2-i^2}[/tex]

[tex]\sqrt{4^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}[/tex]

The complex number that has a distance of [tex]\sqrt{17}[/tex] is [tex]4-i[/tex].

By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)

Complex numbers are a generalization from real numbers, whose expression are of the form a + i b, where a and b are the components of the real and imaginary components, respectively. The magnitude of complex numbers is determined by Pythagorean theorem, this is, the distance from the origin to the location of the number on the complex plane:

[tex]r = \sqrt{a^{2}+b^{2}}[/tex]

If we know that a = 4 and b = -1, then the magnitude of the complex number is:

[tex]r = \sqrt{4^{2}+(-1)^{2}}[/tex]

[tex]r = \sqrt{17}[/tex]

By Pythagorean theorem the complex number 4 - i has a distance from the origin to its location of [tex]\sqrt{17}[/tex] units on the complex plane. (Correct choice: D)

The statement presents several typing mistakes, correct form is shown below:

Which complex number has a distance of [tex]\sqrt{17}[/tex] from the origin on the complex plane?

A. 2 + i 15

B. 17 + i

C. 20 - i 3

D. 4 - i

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( x - 12 ) ( x + 6 ) = 0

x - 12 = 0 and x + 6 = 0

x = 12 and x = -6

Answer:

[tex]x=12,\:x=-6[/tex] are your x intercepts

Step-by-step explanation:

[tex]\left(x-12\right)\left(x+6\right)=0\\\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\mathrm{Solve\:}\:x-12=0:\quad x=12\\x-12=0\\\mathrm{Add\:}12\mathrm{\:to\:both\:sides}\\x-12+12=0+12\\Simplify\\x=12\\\mathrm{Solve\:}\:x+6=0:\quad x=-6\\x+6=0\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\x+6-6=0-6\\Simplify\\x=-6\\The\:solutions\:to\:the\:quadratic\:equation\:are:\\x=12,\:x=-6[/tex]

Answer:

A

Step-by-step explanation:

[tex]f(x)=9(3)^x \\\\\\f(-3)=9(3)^{-3}= \\\\\\9\left(\dfrac{1}{3^3} \right)= \\\\\\9\left(\dfrac{1}{27} \right)= \\\\\\\dfrac{9}{27}= \\\\\\\dfrac{1}{3}[/tex]

Hope this helps!

Answer:

No it's not a function. (-2, 0) and (-2, 6) don't pass the vertical line test.

Step-by-step explanation:

Answer:

$180 + $15d

Step-by-step explanation:

Since Carol's Car Rentals offers a deal of $180 down payment  + $15 per day and AL's Auto Rentals offer a deal of $250 down payment  $5 per day. To calculate the cost of Carol's Car Rentals deal, we use the formula:

cost of Carol's Car Rentals = Down payment + cost per day.

If you are to rent at Carol's Car Rentals for d days; The cost of Carol's Car Rentals = Down payment + cost per day = $180 + $15 per day × d days

cost of Carol's Car Rentals = $180 + $15d

Answer:

[tex] \boxed{112} [/tex]

Step-by-step explanation:

[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]

Answer:

1

Step-by-step explanation:

Answer:

1,1.5,2.5

Step-by-step explanation:

f(x) = 3 - .5x

The domain is 1,3,4 so theses are the only inputs

f(1) = 3 - .5 = 2.5

f(3) = 3 - .5(3) = 3- 1.5 = 1.5

f(4) = 3 - .5(4) = 3-2 =1

The only outputs are 1,1.5,2.5

Answer:

5 ( r+8) (r-6)

Step-by-step explanation:

5r^2+10r-240

First factor out the greatest common factor

5( r^2 +2r - 48)

Now factor what is inside the parentheses

What multiplies to -48 and adds to 2

8*-6 = -48

8-6 = 2

5 ( r+8) (r-6)

Answer: x < 2

Explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.

Since 3 is being subtracted from x, we add 3

to both sides of the inequality to get x < 2.

Before we graph, write your answer in set notation.

We can write this as {x: x < 2}.

It's important to understand what this means.

This means that any number less than 2 is a solution to this inequality.

I have graphed the inequality for you below.

Start with an open dot on +2.

We use an open dot because +2 is not included as a solution.

Then draw an arrow going to the left.

Answer:

-1/2

Because, for every one square, the line goes down by 1/2.

Answer:

- 0.5

Step-by-step explanation:

To find the gradient of a line,

divide the value of decrease by the value across.

So, count across from the extreme left toll the extreme right = 13

Where you completed in the extreme right, you have to count down till you reach the other end of the line = 6.5

Now, you divide: 6.5 divided by 13 = 0.5

Since we counted down, it is negative = -0.5

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Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

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Answer:

A=12

B=54

C=18

Step-by-step explanation:

A=first

B=second

C=third

A+B+C=84

B=3C

A=C-6

C-6+3C+C=84

5C-6=84

5C=90

C=18

A=C-6

=(18)-6

=12

B=3C

=3(18)

=54

12, 54, and 18 so, what he said is true

Step-by-step explanation: he already gave this to you

Answer:

$7.50

Step-by-step explanation:

Since there is a 50% chance that the card is odd, the expected payoffs would be $15 * 50%=0.5*15=7.5. Hope this helps!

Answer: 39

Step-by-step explanation:

Its easy! The triangles CEF and CDE are equals because they have three sides respectively equal. So the angles FCE and angle m1 (DCE) are equal.

Then:

m1 = 39

Answer:

8

Step-by-step explanation:

8 times 8 = 64

The right answer is of option C.

hope it helps..

good luck on your assignment

Answer:

c

Step-by-step explanation:

Answer:

The slope is 1/3

Step-by-step explanation:

Just use the rise over run method i told you about earlier.

The right point is 3 units higher and 9 units more to the right.

3/9 = 1/3.

i hope this helped :)

Mark this question as brainliest if you think it was the best answer.

This is the right answer.

Answer:

Measure of angle DBF = 106°.

Step-by-step explanation:

Given in the question,

m∠DGE = 53°

and line segment GE is the angle bisector of ∠DGF.

Since segment GE is the angle bisector of ∠DGF that means it divides the angle DGF into two equal parts.

Therefore, m∠DGE ≅ m∠FGE

m∠DBF = m∠DGE + m∠FGE

m∠DBF = 2(m∠DGE)

             = 2(53)°

             = 106°

Therefore, measure of angle DBF = 106°.

Ay is any one down to work together on this? Not just this question but the whole unit of geometry

Answer:

7

Step-by-step explanation:

as it does that F thing where its equal to it....

Answer:

I wont answer for you, but ill guide you in the right direction

Step-by-step explanation: