The equation y = 1/4x represents a proportional relationship. What is the constant of proportionality?​

Problem 1

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Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

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Problem 2

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Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]

That equation represents the boundary of the circle, which is where the water can reach.

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Problem 3

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Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

rate of change or slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]

y = mx + b

"b" is y-intercept

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[tex]\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail h(4)[/tex]

[tex]\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 1/5(16-6)-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 10/5-8[/tex]

[tex]\\ \tt\bull\rightarrowtail 2-8[/tex]

[tex]\\ \tt\bull\rightarrowtail -6[/tex]

S = √2+√8+√18+√32+……………… n terms.

or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.

This is an A.P. in which a = √2. , d = √2.

Sn = n/2.[2.a +(n-1).d].

or, Sn = n/2.[ 2√2 +(n-1).√2].

or, Sn = (n/2).√2.[ 2 +n-1].

or, Sn = n.(n+1)/√2. Answer.

Given AP :√2,√8,√18,√32,...

First term = √2

Common difference = √8-√2

⇛ √(2×2×2)-√2

⇛ 2√2-√2

⇛√2

We know that

Sum of first n terms of an AP

⇛ Sn = (n/2)[2a+(n-1)d]

⇛ Sn = (n/2)[2√2+(n-1)(√2)]

⇛ Sn = (n/2)[2√2+√2 n -√2]

⇛ Sn = (n/2)[√2 n +√2)

⇛ Sn = (n/2)×(√2)(n+1)

⇛Sn = (n/√2)(n+1)

⇛ Sn = n(n+1)/√2

Additional comment:

nth term of an AP = a+(n-1)d

Sum of first n terms of an AP

Sn = (n/2)[2a+(n-1)d]

Sum of the first n terms = Sn =

(n/2)(a+an)

If a,b,c are the three consecutive terms in an AP then b = (a+c)/2

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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap

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Answer: 219

Step-by-step explanation:

From the power rules, the power [tex]3^{-2}[/tex] is equal to the fraction [tex](\frac{1}{3})^{-2}[/tex].

There are different power rules one of them is the negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]5^{-3}=(\frac{1}{5})^3=\frac{1}{125} \\ \\ \\ {\frac{4}{6} }^{-2}={\frac{6}{4} }^2=\frac{36}{16}[/tex]

Then, the question gives:

[tex]3^{-2}=({\frac{1}{3}})^2[/tex]

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Answer:

110

Step-by-step explanation:

Know the angle for BCD which is 130.

Subtract 180 from 130 and you get angle c for the triangle which is 50

Already knowing B and C, add them both which comes up to 70

All triangle angles equal 180 so subtract 70 for 180 and you get 110

Answer:

y+1=3(x+8)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(-6-(-8))

m=(5+1)/(-6+8)

m=6/2

m=3

y-y1=m(x-x1)

y-(-1)=3(x-(-8))

y+1=3(x+8)

Answer:

[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]

Step-by-step explanation:

The point-slope form of an equation for a line is  y = mx + b  (m is the slope; b is the y-intercept).

First, find the slope using the two given points.

[tex]m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]

At this stage, you know the slope and need to find the y-intercept.  Plug in one of the points (either one) into the equation.  Let's use (-5, 0).

[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b[/tex]

The equation for the line is [tex]y=\frac{1}{3}x+\frac{5}{3}[/tex].

You can check for errors by putting in the point you didn't use...

Check to make sure the point (4, 3) satisfies the equation.

[tex]3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}[/tex]   True!

Answer:

25%

Step-by-step explanation:

8-6=2

2/8=0.25

0.25×100=25%

Answer:

19 tennis rackets

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

180 - 148 = 32

I hope this helps!

Answer:

936

Step-by-step explanation:

Therefore you multiply 6 by 18 = 6×18= 108

1,044 - 108 = 936

So therefore the total is 936

The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.

The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing

Answer:

Y is cookies x is cupcakes

for the first birthday party: 20x + 40y = 61

For the second party 30x + 30y = 64.50

There aren't any other constraints

20x + 40y = 61

30x + 30y = 64.50

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

a-114=35 ⇒ a= 149

a+358=434⇒ a=76

416+a=523⇒ a=107

ax38=214⇒ a=5.63

The equation that has 112 as it's solution is not existing in the options.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given are four linear equations.

Check the solution of each equation.

a - 114 = 35

Adding both sides of the equation with 114,

⇒ a = 35 + 114 = 149

a + 358 = 434

Subtracting both sides of the equation with 358,

⇒ a = 434 - 358 = 76

416 + a = 523

Subtracting both sides of the equation with 416,

a = 523 - 416 = 107

a × 38 = 214

Dividing both sides of the equation with 38,

a = 214/38 = 5.63

Hence none of the equations have 112 as it's solution.

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Answer:

Part A: 8 ribbons

Part B: see below

Step-by-step explanation:

first 5 1/3 = 16/3

[tex] \frac{16}{3} \div \frac{2}{3} \\ = \frac{16}{3} \times \frac{3}{2} \\ = \frac{48}{6} = 8[/tex]

the answer is 8 dude!

answer

TRUE

HOPE IT WILL HELP YOU

Answer: -1 3/4

Step-by-step explanation

just add the fractions together :)

(between the -2 and -1 1/2)

Answer:

x=7

Step-by-step explanation:

1/2(x-6)=1/2

(1/2)(x)+(1/2)(−6)=1/2

1/2x+−3=1/2

1/2x−3=1/2

1/2x−3+3=1/2+3

1/2x=7/2

2*(1/2x)=2*(7/2)

x=7

tada!

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.  

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.  

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.  

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].  

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.  

(b) Explain why one rate of change is greater than the other.  

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.

Answer:

The numbers are 11,12,13

The smallest number is 11

Step-by-step explanation:

Let the first number be x

The next number is x+1

The third number is x+2

x+x+1+x+2 = 36

Combine like terms

3x+3 = 36

Subtract 3 from each side

3x+3-3 = 36-3

3x=33

Divide each side by 3

3x/3 = 33/3

x=11

The numbers are 11,12,13

The smallest number is 11

Answer:

27

Step-by-step explanation:

Use synthetic division:

8 | 1 -5 3

   __8_24

    1  3 | 27

Therefore, (x²-5x+3)/(x-8) = x+3 R27

Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

Answer:

Yes

Explanation:

1.3/7.8 = 0.167

3/18 = 0.167

An equivalent fraction is a fraction that is the same as another fraction with a different denominator.

I hope it helps.

Answer:It’s money so use the $ symbol. You got this

Step-by-step explanation:

[tex]6(31)+6(4)-6(15)=6(31+4-15)=6(20)=120[/tex]

ok done. Thank to me :>

Answer:

1/15

Step-by-step explanation:

2/3 x 1/10 = 2/30 or 1/15

Answer:

1/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's the third choice. Since the triangles are given as similar and they are right triangles, points A, B, and D are all on the hypotenuses of those 2 triangles and are co-linear. The slope between all points on a single line is constant.