find the slope of 4x-y=8 and solve

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

[tex]a_n=a_1+\left(n-1\right)d[/tex]

[tex]18-13=5,\:\quad \:23-18=5[/tex]

As the difference between all the adjacent terms is the same.

so

[tex]d=5[/tex]

[tex]a_1=13[/tex]

Arithmetic sequence sum formula

[tex]n\left(a_1+\frac{d\left(n-1\right)}{2}\right)[/tex]

Put the values

[tex]d=5[/tex]

[tex]a_1=13[/tex]

[tex]n=47[/tex]

[tex]=47\left(13+\frac{5\left(47-1\right)}{2}\right)[/tex]

[tex]=47\left(13+\frac{5\left(47-1\right)}{2}\right)[/tex]

[tex]=47\left(13+115\right)[/tex]

[tex]=47\cdot \:128[/tex]

[tex]=6016[/tex]

Thus, the sum of the first 47 terms of the given series = 6016

Answer

4

Step-by-step explanation:

d²=(6-6)²+(-7+3)²

d²=16

[tex]\sqrt{16}[/tex]=4

Answer:

Distance = √17

Step-by-step explanation:

We are looking for the distance between 5 + 4i and 9 + 3i.

This is as equal to saying we have two points in the plane, whose coordinates are; (5, 4) and (9, 3)

Distance between the 2 points will be;

D = √[(5 - 9)² + (4 - 3)²]

D = √(16 + 1)

D = √17

Incomplete question. The remaining part of the question reads;

Here are the places they could visit:

I calculated the cost of going to 'Big City Zoo and Space Science'.

Answer:

Big City Zoo = $3.86

Space science = $1.35

Step-by-step explanation:

For Big City Zoo:

Entrance fee: $2.5 x 25 = $62.5

Charges per mile: $6.5 x 36 = $234

Total cost of trip= $296.5

Final cost for all students to attend this field trip = $296.5 - $200 = $96.5. Meaning each student pays $3.86 (or $96.5/25 students).

For Space Science:

Entrance fee: $6.75 x 25 = $168.75

Charges per mile: $6.5 x 10 = $65

Total cost of trip= $233.75.

Final cost for all students to attend this field trip = $233.75 - $200 = $33.75. Meaning each student pays $1.35 (or $33.75/25 students).

Answer: w+b>12. W>3

Step-by-step explanation: because the teacher tell me

Answer:

one solution

Answer: The given equation 3x − 7 = 4 + 6 + 4x has one solution.J

Step-by-step explanation:

Answer:

One solution (x=17).

Step-by-step explanation:

First, we combine like terms and numbers (if we can). This leaves us with the equation 3x - 7 = 10 + 4x. Now, we add 7 to both sides. Now, we have the equation 3x = 17 + 4x. Next, we subtract 4x from both sides. This gets us -1x=17. We can simplify that to -x=17. Now, we divide both sides by -1 to make -x positive. This gets us x=-17. That means there is only one solution. I hope this helps!

Answer:

[tex]A = 16\pi[/tex]cm

Step-by-step explanation:

Area of a circle equation:

[tex]A = \pi r^2[/tex]

Plug in r = 4cm and solve:

[tex]A = 16\pi[/tex]cm

Answer:

ok so if its the radius:

50.27cm

if its the diameter:

12.57cm

Step-by-step explanation:

Answer:

18/2 =9

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system. Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality

Answer:

16 hours of total work time, 12 hours of work not including the original 4 hours

Step-by-step explanation:

25 percent is 1/4

To get to a whole, you need to do 4*4.

That is how many total hours of work time, -4 (the pre-existing 4) you get 12 of added time on top of the 4

Answer:

x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.

Step-by-step explanation:

Answer:

$10.2

Step-by-step explanation:

Use this formula:

Price of product after discount = Initial  Price * ( 1 - (discount/100) )

Answer:

100=(x−1)2(y+3)

Step-by-step explanation:

Suppose the centre of the circle was at the origin (where the x axis crosses the y axis). Then the equation would be:

r2=x2+y2

The reason for this format is that the length of the radius (which is of fixed length) can be related to x and y by Pythagoras. However, the circle centre is not at the origin. It is at

(x,y)→(1,−3)

So we can mathematically make this work by 'theoretically' moving the actual centre to a new centre located at the origin.

Thus we would have:

r2=(x−1)2+(y−(−3))2

r2=(x−1)2+(y+3)2

But the radius is 10 so we have

(10)2=(x−1)2+(y+3)2

100=(x−1)2+(y+3

Answer: B

Step-by-step explanation:

Answer:

K(x,y) →K'(-x, y-7)     (B)

Step-by-step explanation:

Answer:

y= -4x+7

Step-by-step explanation:

y-y1=m(x-x1)

y+1= -4(x-2)

y+1= -4x+8

y= -4x+7

Answer:

d

Step-by-step explanation:

because there is a closed dot at -4 you use the one with a line under it showing it is included and because there is open at 4 you use one without a line to show it is not included

Answer:

[tex]Measurement = 0.75ft[/tex]

Step-by-step explanation:

See attachment for complete question

Method 1:

Considering the width and length of the quilt

Given

[tex]Number\ of\ squares = 24[/tex]

Required

Determine the dimension of 1 square

The width of the quilt is 4.5ft and there are 6 squares in that dimension.

Each measurement is calculated as thus:

[tex]Measurement = \frac{4.5ft}{6}[/tex]

[tex]Measurement = 0.75ft[/tex]

Or

The length of the quilt is 3ft and there are 4 squares in that dimension.

Each measurement is calculated as thus:

[tex]Measurement = \frac{3ft}{4}[/tex]

[tex]Measurement = 0.75ft[/tex]

Method 2:

Calculate the area of the quilt.

[tex]Area = 4.5ft * 3ft[/tex]

[tex]Area = 13.5ft^2[/tex]

The area of 1 of the 24 squares is calculated by dividing the total area by number of squares

[tex]Area = \frac{13.5ft^2}{24}[/tex]

[tex]Area = 0.5625\ ft^2[/tex]

Represent the dimension of individual square with L

Area of a square is:

[tex]Area = L * L[/tex]

This gives:

[tex]L * L = 0.5625[/tex]

[tex]L^2 = 0.5625[/tex]

Take square root of both sides

[tex]L = \sqrt{0.5625[/tex]

[tex]L = 0.75ft[/tex]

Hence, the dimension of each square is 0.75ft

Answer:

The population at the beginning of 2016 is 55,326.

Step-by-step explanation:

Giving the following information:

Population 2010 (PV)= 42,000

Growth rate (g)= 4.7% = 0.047

Number of years (n)= 6 years

To calculate the population at the beginning of 2016, we need to use the following formula:

FV= PV*(1+g)^n

FV= 42,000*(1.047^6)

FV= 55,326

The population at the beginning of 2016 is 55,326.

Answer:

I believe the pattern is linear and for each month that goes by she earns $50

For each month that goes by, Michelle will increase her total savings by $50

The given parameters are:

Initial balance = $500

Savings = $50 monthly

This means that at the end of every month, her savings increases by $50.

This kind of pattern is a linear pattern

Read more about linear pattern at;

https://brainly.com/question/2097266

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Answer:

D. the runner can run less than 12 miles

Answer:

A) 1366.4 cm

Step-by-step explanation:

As, volume of a sphere = 4/3 x pi x r^3

Radius= Diameter /2

R = 3.6/2 = 1.8

So,volume of 1 egg = 4/3 x 3.14 x 1.8^3

= 24.43 = volume

So volume of 56 such eggs = 24.43 x 56 = 1,366.4 cm^3

Answer:

14 to 21

Step-by-step explanation:

reverse of 21 to 14 = 14 to 21

Answer:

40 times greater

Step-by-step explanation:

Given the following:

Pluto average distance from the sun Ps =  3.6 x 10^8 miles

venus average distance from the sun Vs = 9.0 x 10^6miles

Take the ratio:

Ps/Vs = 3.6 x 10^8/9.0 x 10^6

Ps/Vs = 0.4*10^{8-6}

Ps/Vs = 0.4*10²

Ps/Vs = 40

Ps = 40Vs

Hence the pluto's average distance from the sun is 40 times greater than that of venus

Answer:

0.0017 years

Step-by-step explanation:

Distance of North Star from Earth = 460 light years

A light year is the distance traveled by light in one year.

As per given statement:

Distance traveled by light in one second = 18600 miles

Distance traveled by light in one year ([tex]60 \times 60 \times 24\times 365[/tex]) = 18600 [tex]\times[/tex] 31536000 miles = 14506560000 = 14.51 [tex]\times[/tex] [tex]10^9[/tex] miles

We know that:

1 billion = [tex]10^9[/tex]

Therefore, 14.51 [tex]\times[/tex] [tex]10^9[/tex] miles = 14.51 billion miles

Also, it is given that speed of rocket = 1 billion miles per hour

Formula to represent relationship between Speed, Distance and Time is given as:

[tex]Distance = Speed \times Time[/tex]

[tex]Time = \dfrac{Distance}{Speed}[/tex]

[tex]Time =\dfrac{14.51\ billion\ miles}{1\ billion\ per\ hour}\\\Rightarrow Time = 14.51\ hours[/tex]

OR

0.0017 years

Answer:

The range is 40 and the midrange is 20.

For the given number, the range is 40 and the midrange is 20. Option C is correct.

Given that,
42, 20, 36, 51, 60, 28,

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

Here,
In the given series least number = 20
Largest number = 60
Range = 60 - 20 = 40

Midrange = 40 / 2 = 20

Thus, For the given number, the range is 40 and the midrange is 20. Option C is correct.

learn more about the range here:
https://brainly.com/question/12239390

#SPJ5

Answer:

C) choosing a blue, green or yellow marble.

Step-by-step explanation:

The Complement of choosing a red marble means choosing any other marble that isn't red.

From the question , it was said that there were a blue , green, yellow and red marble.

So the Complement of choosing a red marble will be choosing any other marble apart from the red so ,that will be choosing a blue yellow or green marble.

Answer:

c

Step-by-step explanation:

Answer:

28,000 Ft

Step-by-step explanation:

Answer: 16 is -15700  and 17 28,000

Step-by-step explanation:

Answer:

5 packs of sausages7 packs of rolls

Step-by-step explanation:

You need to find the common multiple.

5 x 7 = 35.

We know that before this there is no other common multiple becuase 7 does not multiply to a number that ends with a 0 or 5 until 35.

So, he will need to buy:

- 5 packs of sausages

- 7 packs of rolls

Answer:

7 packs of rolls

5 packs of sausages

Step-by-step explanation:

The easiest way to solve this question is to make a table with 3 columns

Rolls          5   10   15 20 25 30 35

Sausages  7    14   21 28 35 42 49

# packs    1    2    3    4   5    6  7

Looking at the table you can see that the first number that matches up is 35 so looking at that point we would need 7 packs of rolls and 5 packs of sausages.