Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3
Answers
A(-2,-4) B(8,1)
let
M-------> the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3
we know that
A--------------M----------------------B
2 3
distance AM is equal to (2/5) AB
distance MB is equal to (3/5) AB
so
step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
Mx=-2+(2/5)*10-----> Mx=2
step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2
the coordinates of point M is (2,-2)
see the attached figure
Related Questions
the slope of line one is negative 1/2 and line one is parallel to line two. what is the slope of line two?
Answers
What is an rational number between 9.5 and 9.7 and include decimal approximation to the nearest hundredth
Answers
Stan borrows $5,500 at a rate of 12% interest per year. What is the amount due at the end of 5 years if the interest is compounded continuously? In your final answer, include your calculations. PLEASE EXPLAIN.
Answers
Final answer:
To calculate the amount due at the end of 5 years with continuous compound interest, use the formula A = P*e^(rt), where A is the amount due, P is the principal, e is Euler's number, r is the interest rate, and t is the time. In this case, the amount due is approximately $10,021.66.
Explanation:
To calculate the amount due at the end of 5 years with continuous compound interest, we can use the formula A = P*e^(rt), where A is the amount due, P is the principal (initial amount borrowed), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, the principal is $5,500, the interest rate is 12% or 0.12, and the time is 5 years.
So, A = $5,500 * e^(0.12 * 5) = $5,500 * e^0.6 ≈ $5,500 * 1.82212 ≈ $10,021.66.
Therefore, the amount due at the end of 5 years with continuous compound interest is approximately $10,021.66.
Choose the equivalent percent for 4/5
40%,64%,80%,20 or none of these
Answers
Answer:
80%
Step-by-step explanation:
To convert a fraction to percent, we need to multiply the fraction with 100.
Multiply 100 and [tex]\frac{4}{5}[/tex], we get,
[tex]\frac{4}{5} (100)[/tex] = 4 × 20
= 80%
Hence, the correct option is (C) 80%.
What’s the correct answer?
Answers
Answer: 6 m
This statement:
"Jared has run two-thirds of an 18-kilometer race" can be written as an equation:
[tex]18km.\frac{2}{3}=12km[/tex]
This means two-thirds of 18 km is equivalent to 12 km
If we substract this value to the total, we have the values of the kilometers left to run:
[tex]18km-12km=6km[/tex]
Therefore the correct option is D
The length of the minute hand is 150% of the length of the hour hand.
In one hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest tenth.
Answers
[tex]s=r\cdot\theta[/tex]
where [tex]\theta[/tex] is the central angle in radians
In one hour, the hour hand makes 1/12 of a revolution (2π radians), so travels ...
[tex]s_{h}=(30\,mm) \times \frac{1}{12}\cdot 2\pi=5\pi\,mm[/tex]
In one hour, the minute hand makes 1 full revolution, so travels
[tex]s_{m}=(1.5 \cdot 30\,mm) \times 2\pi = 90\pi\,mm[/tex]
The difference in distance traveled is ...
[tex]s_{m}-s_{h}=(90\pi-5\pi)\,mm=85\pi\,mm \approx 267.0\,mm[/tex]
In an hour, the minute hand, which is 1.5 units long, travels a full revolution or approximately 9.4 units, while the hour hand, 1 unit long, covers one-twelfth, or about 0.5 units. Therefore, the minute hand travels approximately 7.9 units more than the hour hand.
Explanation:This question can be solved by first examining the distance each hand travels. In an hour, the minute hand completes a full revolution around the clock face, moving a distance equal to the clock's circumference. If we call the length of the minute hand 1.5 units, then its distance traveled is 2π(1.5).
In contrast, the hour hand moves onto the next hour, covering on-twelfth of the clock's face, or 2π(1/12) using a length of 1 unit for the hour hand. Substract the second measure from the first to find the difference. Thus, the minute hand travels about 7.9 units farther than the hour hand.
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Javier’s fuel tank holds 12 3⁄4 gallons of gasoline when completely full. He had some gas in the tank and added 10.3 gallons of gasoline to fill it completely.
How many gallons of gasoline were in the tank before Javier added some?
Answers
The number of gallons of gasoline in the tank before Javier added some is 2 3/4 gallons.
1. Subtract 10.3 gallons (the amount he added) from 12 3/4 gallons (the total capacity of the tank).
2. Calculate 12 3/4 - 10.3 to find the remaining amount of gasoline in the tank.
To subtract mixed numbers, we first convert them into improper fractions:
[tex]\[ 12 \frac{3}{4} - 10 \frac{3}{10} \][/tex]
[tex]\[ = \frac{(12 \times 4) + 3}{4} - \frac{(10 \times 10) + 3}{10} \][/tex]
[tex]\[ = \frac{48 + 3}{4} - \frac{100 + 3}{10} \][/tex]
[tex]\[ = \frac{51}{4} - \frac{103}{10} \][/tex]
To subtract fractions, we need a common denominator. Here, the least common denominator (LCD) is 20.
[tex]\[ = \frac{51 \times 5}{4 \times 5} - \frac{103 \times 2}{10 \times 2} \][/tex]
[tex]\[ = \frac{255}{20} - \frac{206}{20} \][/tex]
[tex]\[ = \frac{255 - 206}{20} \][/tex]
[tex]\[ = \frac{49}{20} \][/tex]
Now, we convert the improper fraction back to a mixed number:
[tex]\[ = 2 \frac{9}{20} \][/tex]
Therefore, Javier had 2 9/20 gallons of gasoline in the tank before adding more.
Javier had 2.45 gallons of gasoline in his tank before he added 10.3 gallons to fill it to its full capacity of 12.75 gallons.
To find how many gallons of gasoline were in Javier's tank before he added some, we need to subtract the amount he added from the total capacity of the tank. Javier's fuel tank can hold 12 3/4 gallons when full, which is equal to 12.75 gallons. He added 10.3 gallons to fill it up. Therefore, the amount of gas in the tank before he added more can be calculated as follows:
Amount of gasoline initially in the tank = Total capacity - Amount added
Amount of gasoline initially in the tank = 12.75 gallons - 10.3 gallons
Amount of gasoline initially in the tank = 2.45 gallons
Thus, Javier had 2.45 gallons of gasoline in the tank before he added the 10.3 gallons.
What plus what plus what equal 823
Answers
Hope that helped!
[30 Points] Can you guys help me with this, please? Thank you in advance.
Answers
Part (a):
We are given that:
Total number of files = 250 files
% of photos = 12%
This means that:
number of photos = percentage of photos * total number of files
number of photos = 12% * 250
number of photos = 0.12 * 250
Part (b):
We need to get the number of photos. This means that we will simply compute the result of the equation we obtained from part (a) as follows:
number of photos = 0.12 * 250
number of photos = 30 photos
Question (2):
Part (a):
We know that:
Total amount spent should be less than $80
Amount spent on food = $68.25
Price per each carton of juice = $3
Assuming that number of juice cartons is x, therefore:
amount spent on juice = $3x
Putting the above into inequality, we can find that:
total amount spent > amount spent on food + amount spent on juice
80 > 68.25 + 3x
80 - 68.25 > 68.25 + 3x - 68.25
11.75 > 3x
Part (b):
Now, we want to get the number of cartons, this means that we will solve the inequality in part (a) for x as follows:
11.75 > 3x
11.75 / 3 > 3x / 3
3.9 > x
Now, we can not buy 0.9 carton of juice. This means that we need to approximate the result.
We have:
x < 3.9
The nearest whole number that satisfies this inequality is 3.
This means that Quan can buy a maximum of 3 cartons of juice to satisfy his budget inequality
Question (3):
Part (a):
We can represent the hexagonal using trapeziums and rectngles which are considered simpler polygons.
The division as well as the dimensions are shown in the attached image.
Part (b):
To get the area of the hexagonal, we will get the area of the overall rectangle and remove from it the area of the two dotted triangles.
This can be done as follows:
area of rectangle = length * width = 11 * 24 = 264 in²
area of top right triangle = 0.5 * base * height = 0.5 * 4 * 5 = 10 in²
area of bottom left triangle = 0.5 * base * height = 0.5 * 10 * 4 = 20 in²
Now, we have:
area of hexagonal = 264 - 10 - 20
area of hexagonal = 234 in²
Another solution to get the area:
We can get the area by getting the area of each of the simpler polygons and add them.
This can be done as follows:
area of left trapezium = [tex] \frac{7+11}{2} * 10 = 90 [/tex] in²
area of middle rectangle = 10 * 11 = 110 in²
area of right trapezium = [tex] \frac{6+11}{2} * 4 = 34[/tex] in²
Therefore:
area of hexagonal = 90 + 110 + 34 = 234 in²
Hope this helps :)
What is the value of a in the question a/35 +20= 18
Answers
Steps:
1)35( a/35+20)= 18*35
2)35(a/35)+35(20)=18*35
3)35/35a+ 35(20)=18*35
4)35a/35+35(20)=18*35
5)35a/35*700=18*35
6)a+700=18*35
7)a+700=630
8)Subtract 70 both sides
9)Which gives you -70
Hope it helps :))
What is the decimal equivalent of the fraction?
5/33
A) 0.15⎯⎯⎯⎯
B) 0.15
C) 0.1⎯⎯5
D) 0.15⎯⎯
Answers
The decimal equivalent of the fraction 5/33 is option A. o.15....
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
The given fraction is 5/33.
We have to find the decimal corresponding to the given fraction.
For that divide 5 by 33.
5 is not divisible by 33.
So add 0 and it become 50.
50 = (33 × 1) + 17
And the quotient is 0.1 with remainder 17.
Now 17 is not divisible by 33.
Add 0 and it becomes 170.
170 = (33 × 5) + 5
Quotient becomes 0.15 with remainder 5.
Again the remainder is 5 and add 0 and becomes 50.
It continues.
So the quotient is 0.1515....
Hence the decimal form is 0.(15) repeating.
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How many sucrose molecules are in 3.0 moles of sucrose
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triangle shown to the right is 120 sq units. find the base and height
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120 = 1/2 * base * height
Multiply by 2 on both sides. This will cancel out the 1/2 on the right side of the equation and isolate our variables, the base and height. You get:
240 = base * height
There wasn't enough information given on the triangle (at least in your description) for the most accurate answer so your answer just becomes any pair of factors at equal to 240.
1, 240
2, 120,
3, 60
4, 80
6, 40
8, 30
10, 24
12, 20
16, 15
Those are all the possibilities not including fractional factors (ex: 1/4 and 960).
I really need help with these problems
Answers
[tex]x^2+14x+48=x^2+6x+8x+48=x(x+6)+8(x+6)=\boxed{(x+6)(x+8)}[/tex]
11.
[tex]\dfrac{t^2-4t-32}{t-8}=\dfrac{t^2-8t+4t-32}{t-8}=\dfrac{t(t-8)+4(t-8)}{t-8}\\\\=\dfrac{(t-8)(t+4)}{t-8}=t+4\\\\Answer:\boxed{t+4;\ t\neq8}[/tex]
What is the answer for 6
Answers
Formula for SA of a pyramid is: lw+l(√w/2)^2+h^2+w√l/2^2+h^2
We're given all pieces of information, b(l)=9 w=9 h=16
You should be able to plug those values into the equation yourself.
im not sure how to do this please help
Answers
the answer is 1.292
Raul walks 3/8 of a mile to school Laurie walks two thirds of a mile to school how much longer is Lori's walk then Raul's walk
Answers
First you have to make the denominators the same
2/3 = 16/24
3/8 = 9/24
Now you subtract them
16/24 - 9/24 = 7/24
The answer is 7/24
Hope this helps!
Suppose and exponential function is to fit to a set of data. Which of the following residual plots indicates that this function was an appropriate fit for the data?
Answers
The appropriate fit for an exponential data is given by D.
This is because it shows the perfect exponential fit for the residuals.
the larger of two numbers is eight more than the smaller number. their sum is twenty-two. find the number
Answers
20/36= x/1200
in this situation, what does x equal?
Answers
Cross multiply.
36 × x and 20 × 1,200
36x = 24,000
x = 666.67
x equals 667, or 666.67.
if a triangular prism has dimensions of 11,14 and 8 what is the volume
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the probability of a chance event is close to 0. which statement about the event is true/ (A) the event is likely to occur (B) the event has the same chance of occuring or not occuring (C) the event is unlikely to occur (D) the event is definately not going to occur
Answers
Now, if the probability of a chance event is close to 0, then the event is unlikely to occur.
The Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long. About how many times longer is Mariner Valley than the Grand Canyon?
Answers
Mariner Valley = 212 km
Number of times longer = 212 ÷ 29 = 7.31 times (Nearest hundredth)
Answer: 7.31 times
Answer:
7.31 times.
Step-by-step explanation:
We have been given that Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long.
To find the number of times Mariner Valley is longer than the Grand Canyon, we will divide 212 by 29.
[tex]\frac{212}{29}=7.3103448\approx 7.31[/tex]
Therefore, the Mariner Valley is 7.31 times longer than the Grand Canyon.
80 men and 60 women are enrolled in calculus. There are 40 business majors, 30 biology majors, 15 computer science majors, and 5 mathematics majors. No person has double major. If a single calculus student is chosen, find the following probabilities
Answers
[tex]80 + 60 + 40 + 30 + 15 + 5 = 230[/tex]
Calculus = 80 + 60 = 140
Probability :
[tex] \dfrac{140}{230} = \dfrac{14}{23} [/tex]
Answer : 14/23 or in decimal form, 0.61.
Hope this helps. - M
The probability of selecting a male calculus student is approximately 57.14%, a female calculus student is approximately 42.86%, a business major calculus student is approximately 28.57%, a biology major calculus student is approximately 21.43%, a computer science major calculus student is approximately 10.71%, and a mathematics major calculus student is approximately 3.57%.
To find the probabilities, we will use the formula:
Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability of selecting a male calculus student:
There are 80 male students in calculus, so the probability of choosing a male student is:
Probability (Male) = 80 / (80 + 60) = 80 / 140 ≈ 0.5714 or 57.14%
Probability of selecting a female calculus student:
There are 60 female students in calculus, so the probability of choosing a female student is:
Probability (Female) = 60 / (80 + 60) = 60 / 140 ≈ 0.4286 or 42.86%
Probability of selecting a business major calculus student:
There are 40 business majors in calculus, so the probability of choosing a business major student is:
Probability (Business Major) = 40 / 140 ≈ 0.2857 or 28.57%
Probability of selecting a biology major calculus student:
There are 30 biology majors in calculus, so the probability of choosing a biology major student is:
Probability (Biology Major) = 30 / 140 ≈ 0.2143 or 21.43%
Probability of selecting a computer science major calculus student:
There are 15 computer science majors in calculus, so the probability of choosing a computer science major student is:
Probability (Computer Science Major) = 15 / 140 ≈ 0.1071 or 10.71%
Probability of selecting a mathematics major calculus student:
There are 5 mathematics majors in calculus, so the probability of choosing a mathematics major student is:
Probability (Mathematics Major) = 5 / 140 ≈ 0.0357 or 3.57%
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Two cylinders, A and B, are created.
Cylinder A has volume V
Cylinder B has the same height as Cylinder A
Cylinder B has half the diameter of Cylinder A
Create and expression the represents the volume of Cylinder B in terms of V
Answers
just say answer, no need to explain! THANKSSS!
Answers
The exponent of the function and its parent function are same. The given function has an exponent equal to 3. This means, its parent function must also have the exponent equal to 3.
So, the parent function of given function is a cubic function.
Thus, option A is the correct answer.
Roger pushes a box on a 30° incline. If he applies a force of 60 newtons parallel to the incline and displaces the box 10 meters along the incline, how much work will he do on the box?
Answers
Force = m * a
m = 60 newtons
a = cos30 (since Roger applies force parallel to the incline, we will use cosine)
F = 60 * cos30
F = 51.9615... N
Work done = F * d
F = 51.9615... N
d = 10 meters
W = 51.9615... N * 10 meters
W = 519.6152... Joules or 520 J
Roger does 600 joules of work on the box when he applies a force of 60 newtons and displaces the box 10 meters along a 30° incline.
When Roger pushes a box on a 30° incline with a force of 60 newtons and displaces the box 10 meters along the incline, the work done on the box can be calculated.
Work is given by the equation W = F imes d imes cos(heta), where W is the work, F is the force applied, d is the displacement, and heta is the angle between the force and the direction of displacement. In this case, because the force is applied parallel to the incline and displacement is along the incline, the angle heta is 0°, making cos( heta) equal to 1.
To find the work done by Roger, we calculate it as:
W = 60 N imes 10 m imes cos(0°)
W = 60 N imes 10 m imes 1
W = 600 joules.
Hence, Roger will do 600 joules of work on the box.
The probability of a certain hockey player making a goal after hitting a slap shot is 1/5. How many successful slap shot would you expect her to make after 120 attempts?
-5
-20
-24
-60
I need help with Getting the answer! Help please!
Answers
Answer: 24
We know that the probability of a certain hockey player making a goal after hitting a slap shot is [tex]\frac{1}{5}[/tex].
We need to figure out the number of successful slap shots if she makes 120 attempts?
Since the player is able to make a goal once out of 5 attempts. Therefore, in order to find the number of goals that we can expect the player to make successfully if she attempts 120 slap shots we will multiply the probability with 120.
Number of successful goals = (Probability of making one goal)x(Number of attempts)
Number of successful goals = [tex]\frac{1}{5}\times 120 = 24[/tex].
Therefore, player will be able to make 24 goals out of 120 attempts.
Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer:
Sample Adventure Beach Cruise Ski
A 74 5 2 19
B 71 6 2 21
Which of the following inferences can be made based on the data?
A. More members prefer a cruise vacation and a ski vacation than an adventure
vacation.
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
C. Most members prefer a beach vacation.
D. Most members prefer a cruise vacation.
Answers
There are a total of 5+19+6+21 = 51 people that prefer either a beach or a ski vacation, while only 2+2=4 people prefer a cruise vacation.
Answer:
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
Briana wants to go to the movies. The price for a student ticket is 2.75 less than the price for the adult’s ticket. If you represent the price of the student ticket using the variable “x”, how would you write the algebraic expression for the adult’s ticket price?
Answers
Adult ticket= x+2.75