Answer:
6.037Step-by-step explanation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\U (-1,4)\quad\implies\quad x_1=-1\,,\ \ y_1=4 \\\\B (8,5)\quad\implies\quad x_2=8\,,\ \ y_2=5\\\\\frac12d=\frac23\sqrt{(8+1)^2+(5-4)^2}=\frac23\sqrt{81+1}=\frac23\sqrt{82}\approx6.037[/tex]
Find the sum of the first 47 terms of the following series, to the nearest integer.
13, 18, 23, ...
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
plzzz helpppp!!!!!
How can you identify the solution to a system of inequalities?
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
HELP ASAP!!!
write the equation of the line that passes through
(2,-1) and has a slope of -4,
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
The population of a town is increasing at a constant rate of 4.7% each year. At the beginning of 2010 the population was 42,000. Find the size of the population at the beginning of 2016. Give your answer to 3 sf.
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.
HI SOMEONE PLS HELP ME
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
Sausages come in packets of 7. Bread rolls come in packets of 5. Dan wants to buy enough packs of sausages and rolls so that there are an equal number of sausages and rolls. What is the minimum number of sausages and rolls he needs to buy?
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.
What is the image point of (6,-4)(6,−4) after a translation left 4 units and down 5 units?
Answer:
(2,-9)
Step-by-step explanation:
6-4 = 2
-4-5 =9
so The answer is (2,-9)
What is the distance between (6,-3) and (6,-7)
Answer
4
Step-by-step explanation:
d²=(6-6)²+(-7+3)²
d²=16
[tex]\sqrt{16}[/tex]=4
need of help please!!!
Michelle wants to start saving for a new car. She has $500 already saved and she plans to save an additional $50 per month.
What kind of pattern do we see in this scenario? She plans to save $50 each month. For each month that goes by.
Michelle will increase her total savings by $ ____
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
How to describe the pattern?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
#SPJ6
Point K lies at (-3,4). Point K is reflected over the y-axis and then translated 7 units down to produce K’. Which rule could have been used to produce K’ from K?
Answer: B
Step-by-step explanation:
Answer:
K(x,y) →K'(-x, y-7) (B)
Step-by-step explanation:
The blue turtle lays eggs that are
approximately spherical with an average
diameter of 3.6 centimeters. Each turtle
lays an average of 56 eggs at one time.
Find the total volume of these eggs, to
the nearest tenth cubic centimeter.
I’ll give brainliest if it right!
HELPPPPPPPPPPPPPPP
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
Pluto has an average distance from the sun of 3.6 x 10^8 miles venus has an average distance from the sun of 9.0 x 10^6. How many times greater is pluto's average distance from the sun than venus?
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
1 Find the area of the circle below: 4 cm
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:
Please answer A.S.A.P.!!!!
Malcolm is trying a very low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
50 50; Malcolm needs to consume less than 20 grams of carbohydrates or more than 50 grams of carbohydrates.
B) x > 20 and x 30 and x 60; Malcolm needs to consume less than 30 grams of carbohydrates or more than 60 grams of carbohydrates.
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:
Gayle made a
baby quilt using 24 equal squares. What
are the dimensions of 1 square? Describe
two different ways to find the answer.
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
21 boys and 14 girls. What is the ratio of girls to boys in Ms. Hawthorne's class?
Answer:
14 to 21
Step-by-step explanation:
reverse of 21 to 14 = 14 to 21
Michael has finished 25% of an art project that has taken him a total of 4 hours so far. If he continues to work at the same rate, how many hours will it take for him to complete the entire project?
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
How many solutions does the equation 3x − 7 = 4 + 6 + 4x have?
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!
The number of miles, x, that a cross country athlete can run
is represented by the inequality
X + 3 < 15
What conclusion can be made about the number of miles?
Select one:
A. The runner can run more than 12 miles
B. The runner can run 12 miles
C. The runner can run 15 miles
D. The runner can run less than 12 miles
Answer:
D. the runner can run less than 12 miles
Which of the following systems of inequalities has point D as a solution?
Answer:
The answer is A
Step-by-step explanation:
How do you find the equation of the circle given center at (1,-3), and radius 10?
Answer:
note: all the twos are to the power100=(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
t/2 = 9? i need help
Answer:
18/2 =9
Step-by-step explanation:
A farmer has 12 acres of land. He plans to plant w acres of wheat and b acres of barley on his land. If he plans to plant wheat in no more than 3 acres of land, which system of inequalities represents the possible values for b and w ?
Answer: w+b>12. W>3
Step-by-step explanation: because the teacher tell me
PLS HELP ASAP THIS IS EASY
Look at the trapezoid shown below. Which transformation carries the trapezoid onto itself ?
A) a reflection across the line y = 0
B) a rotation of 180 ° about the point (- 1, 0)
C) a rotation of 180 ° about the origin
D) a reflection across the line x = - 1
Answer: D
Step-by-step explanation: a reflection across the line x=-1
answer quickly !!! Pls
Answer:
(6 × 5) + (6 × 3) = 6 × (5 + 3)
Step-by-step explanation:
Since both 5 and 3 are being multiplied by 6, the total would be 6 multiplied by the sum of 5 and 3.
A garden table and a bench cost $804 combined. The garden table costs $54 more than the bench. What is the cost of the bench?
Answer:
its 750
Step-by-step explanation:
because its 804 combined and 804-54=750 and 750+54=804
750 I agree with the other person
Light travels at a rate of approximately 186,000 miles per second. The North Star is approximately 460 light-years away from Earth. (A light-year is the distance light travels in one year.) How many yearswould it take a rockettraveling at 1 billion miles per hour to reach the North Star?
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
Mr. Richards a teacher at crosstown Elementary school, plans to take 25 students on a school trip. Here are some more facts about the trip: Only one bus is needed for the field trip, the bus company charges $6.50 per mile. The school will pay $300 for the trip, teachers go free, and each student pays the same amount. You will find the cost of this field trip. What is the final cost for all students to attend this field trip?
Incomplete question. The remaining part of the question reads;
Here are the places they could visit:
Big City Zoo> 36 miles from Crosstown; Entrance Fee: $2.5Prison Museum> 30 miles from Crosstown; Entrance Fee: $6.75Space Science> 10 miles from Crossword; Entrance Fee: $11.25I 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).
James is making a math final for his students. He already has 22 questions, and can make 12 more for every hour. Which is an equation that represents how many questions (q) he has for every hour (h)?
a.q(h) = 12h
b.q(h) = 22h + 12
c. q(h) = 12h + 22
d.q(h) = 12h-22
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.Which best describes the complement of choosing a red marble?
choosing a green or blue marble
choosing any marble
choosing a blue, green, or yellow marble
choosing a yellow marble
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: