The coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1 is (6.75, -0.5). The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Let the line be represented as AB, therefore, the coordinates of points A and B are (3,-2) and (8,0), respectively. The coordinate of the point m that divides the line AB in a ratio of 3:1 is,
x = [(x₂×m)+(x₁×n)]/(m+n)
x = [(8×3)+(3×1)]/(3+1)
= (24+3)/4
= 6.75
y = [(y₂×m)+(y₁×n)]/(m+n)
y = [(0×3)+(-2×1)]/(3+1)
= (0-2)/4
= -0.5
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Final answer:
The coordinates of the point that divides the directed segment from (3,-2) to (8,0) in the ratio of 3:1 are a) (6.75, -0.5), using the section formula.
Explanation:
When finding the coordinates of a point on a directed segment that divides it into a specific ratio, such as 3:1, the formula for the section formula in coordinate geometry is used. This formula allows us to calculate the coordinates of the point that divides the segment internally or externally in a given ratio (m:n) using the coordinates of the endpoints (x1,y1) and (x2,y2). The formula for the point (x, y) that divides the segment internally in the ratio m:n is:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
For the directed segment from (3, -2) to (8, 0) and a ratio of 3:1, we find the point by this method:
x = (3×8 + 1×3) / (3 + 1) = (24 + 3) / 4 = 27 / 4 = 6.75
y = (3×0 + 1×(-2)) / (3 + 1) = (0 - 2) / 4 = -2 / 4 = -0.5
Thus, the coordinates of the point that divides the segment in the ratio 3:1 are a) (6.75, -0.5).
Which statements about the system are true? Select two options.
y= 2 x - 4
3y - x = -7
Answer:
Step-by-step explanation:
y= 2x - 4........(1)
3y - x = -7.......(2)
Putting (1) into (2)
3(2x - 4) - x = -7
6x - 12 - x = -7
6x - x = -7 + 12
5x = 5
x = 5/5
x = 1
And y = 2x - 4 ...(1)
y = 2(1) - 4
y = 2 - 4
y = -2
Answer:
first and third one
Step-by-step explanation:
did the test on edge
Simplify a^15/ a^5
Pleaaaaseeeeee
When you divide the same value raised to different powers keep the value and subtract the powers.
A^15 / a^5 = a ^(15-5) = a^10
Answer:
a^10
Step-by-step explanation:
7. Number Sense Rachel's family went
on a car trip. They traveled 68 miles
the first day. They traveled 10 fewer miles
the second day. They traveled 85 miles the
third day. How many miles did they travel?
Answer:
211
Step-by-step explanation:
The total miles that Rachel's family travelled can be found to be 211 miles.
How to find the total miles ?First day: 68 miles
Second day: 10 fewer miles than the first day, so:
= 68 miles - 10 miles
= 58 miles
Third day: 85 miles
Add up the miles traveled each day:
Total miles = 68 miles (first day) + 58 miles (second day) + 85 miles (third day)
Total miles = 211 miles
In conclusion, Rachel's family traveled a total of 211 miles over the three days of their car trip.
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A car company charges a $45 fee to use their vehicle. They also charge an additional $0.35 per mile 9 (m). write a function that models the total cost (c) of taking a passenger to the airport. What does C represents What does M represents what is the equation
The total cost function for taking a passenger to the airport is C = 45 + 0.35M, where C is the total cost and M is the number of miles driven. The $45 is a fixed fee, and $0.35 is the charge per mile.
The student is interested in creating a function that models the total cost of taking a passenger to the airport. This function includes a fixed fee and a variable fee that depends on the number of miles driven. To model this, let C represent the total cost and M represent the miles driven.
The total cost C can be represented by the equation C = 45 + 0.35M. Here, the $45 is a fixed fee for using the vehicle, and $0.35 is the additional charge per mile driven.
C represents the total cost of the trip to the airport and M represents the number of miles driven to the airport.
HELP!!!!!!!!!
I will give brainliest
In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and segment DF is congruent to segment BD. Point C is the point of intersection between segment AG and segment BD while point E is the point of intersection between segment AG and segment DF.
*look at image attached*
Prove ΔABC ≅ ΔGFE.
Answer:
∠ABC ≅ ∠DEC
∠DEC = ∠GEF
thus:
∠ABC = ∠GEF
∠GFE ≅ ∠DCE
∠DCE = ∠ACB
thus:
∠ACB = ∠GFE
If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.
thus: ΔABC ∼ ΔGEF by AA similar triangle postulate
I hope this helps
Prove [tex]\Delta ABC\cong \Delta GFE[/tex]
The sides opposite to equal angles are equal
∴[tex]DE=DC[/tex]
Subtract [tex]DC[/tex] and [tex]DE[/tex] from [tex]DB[/tex] and [tex]DF[/tex] respectively.
[tex]DB-DC=DF-DE[/tex]
We get, [tex]BC=EF[/tex]------Eq [tex]1[/tex]
[tex]\angle DEC\cong \angle DCE[/tex] (Given)
[tex]\angle DEC= \angle DCE[/tex] (Vertically opposite angle)
[tex]\angle DEC= \angle GEF[/tex] (Vertically opposite angle)
Hence, [tex]\angle ACB= \angle GEF[/tex]------Eq [tex]2[/tex]
In [tex]\Delta ABC[/tex] and [tex]\Delta GFE[/tex]
[tex]BC=EF[/tex] (From eq [tex]1[/tex])
[tex]\angle ACB= \angle GEF[/tex] ( From eq [tex]2[/tex])
[tex]\angle B\cong \angle F[/tex] (Given)
Therefore By AAS congruency [tex]\Delta ABC\cong \Delta GFE[/tex].
Hence Proved.
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You entered Kente invested a total of $8000. He invested part of the money for 2yr in a stock fund that earned the equivalent of 6.5% simple interest. He put the remaining money in an 18 month certificate of deposit that earned 2.5% simple interest. If the total interest from both investments was $855 , determine the amount invested in each account?
Step-by-step explanation:
Given,
Kente invested part of money for 2 yr in stock fund that earned the equivalent of 6.5 % simple interest.He put remaining money in a 18 month certificate of deposit that earn of 6.5%simple interest.
Let he invested in stock fund be$ x. Remaining money =$(8000-x)
∴He got interest from stock fund was = [tex]\frac{PRt}{100}[/tex]
=$[tex]\frac{x\times6.5\times2}{100}[/tex] [here P =x , R = 6.5% and t = 2 yr]
=$ [tex]\frac{{13 x}}{{100} }[/tex]
Again he got interest from deposit was = [tex]\frac{PRt}{100}[/tex]
=$ [tex]\frac{(8000-x)\times 2.5\times\frac{18}{12} }{100}[/tex] [here P = (8000-x), R=2.5% and t =[tex]\frac{18}{12} yr[/tex]]
=$ [tex]\frac{(8000-x) \times 7.5}{200}[/tex]
According to problem
[tex]\frac{{13 x}}{{100} }+\frac{(8000-x) \times 7.5}{200}= 855[/tex]
⇔[tex]\frac{26x + 60000 - 7.5}{200} =855[/tex]
⇔18.5 x =171000 - 60000
⇔x = [tex]\frac{11100}{18.5}[/tex]
⇔x = 6000
So he invested in stock fund was = $6000
and in certificate of deposit was =$(8000- 6000)= $ 2000
Two angles are supplementary if their sum is 180°. One angle measures five times the measure of a smaller angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
Answer:
30, 150
Step-by-step explanation:
One angle is x
The other angle is 5x
5x + x = 180
6x=180
180/6=30
x=30
5(30)=150
Mr. Elliot's class created a
mural about Martin Luther
King in their school. The
mural was 4 12 feet long by
3 14 feet wide. If it took the
class 30 minutes to paint 1
square foot of the mural,
| about how long did it take
them to complete the
whole thing?
Answer:
it would take 3881040 minutes to complete the entire mural
helpppppppp ! pleaseeeee !
Answer:
2v - 2u
Step-by-step explanation:
We are to subtract u from v.
⇒ We have to take away 'u' from 'v'.
⇒ v - u
Doubling some quantity means make it twice as much. so, we just multiply the result by 2.
We get: 2(v - u)
⇒ 2v - 2u which is the required result.
Car A is going 72km per Hour and Car B is going 90km per hour but started 140m behind Car A. How long will it take for Car B to reach Car A
Answer:
going into new york using the george washington bridge, consumers must pay a toll (there is not toll to return to New jersey). they can pay $6 cash or they can pay $5 (during peak hour) using the E Z pass system. The E Z pass system is a prepaid plan that also requires a one-time $12 account activation fee. How many trips to new york would a person need to make (during peak hours) so that the total amount spent with the E Z pass is equal to the amount spent for tolls without the E Z pass?
Step-by-step explanation:
how do you solve this?
Answer:
Sorry I can't help in this question
The sum of four consecutive multiples of 7 is 378. Find the numbers
Answer:i have no idea but go back to your math book and lesson and check :p
Step-by-step explanation:
Answer:
84, 91, 98, 105
Step-by-step explanation:
7x + 7 (x+1) + 7(x+2) + 7(x+3) = 378
28x + 42 = 378
28x = 336
x = 12
7x12, 7x13, 7x14, 7x15 i.e. 84, 91, 98, 105
check: 84 + 91 + 98 + 105 = 378
5. Write the number 81 as a power with a base of 3 and a base of 9.
Answer:
3^4 and 9^2
Step-by-step explanation:
A total of 631 tickets were sold for the school play. They were either adult tickets or student tickets. There were 69 fewer students tickets sold then adult tickets. How many adult tickets were sold?
Final answer:
To solve the problem, two equations were set up and solved for the number of adult tickets (A). The equations A + S = 631 and S = A - 69 led to finding that 350 adult tickets were sold for the school play.
Explanation:
The school play ticket problem is a basic algebraic question involving setting up and solving equations. We need to determine the number of adult tickets and student tickets sold, given the total tickets and the difference between them.
Let's denote the number of adult tickets as A and the number of student tickets as S. According to the information provided:
A + S = 631 (The total number of tickets sold)
S = A - 69 (There were 69 fewer student tickets sold than adult tickets)
By substituting the second equation into the first, we get:
A + (A - 69) = 631
2A - 69 = 631
2A = 631 + 69
2A = 700
A = 350
So, 350 adult tickets were sold.
What is the value of x?
Enter your answer in the box.
°
Answer:
x = 84
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 5, thus
sum = 180° × 3 = 540°
Sum the interior angles and equate to 540 for x
131 + 108 + 107 + 110 + x = 540, that is
456 + x = 540 ( subtract 456 from both sides )
x = 84
Person A can paint the neighbor's house 6 times as fast as Person B. The year A and B worked together it
took them 2 days. How long would it take each to paint the house?
Person A takes 2.3 days to paint the house working alone
Person B takes 13.8 days to paint the house working alone
Solution:
Let "x" be the number of days it takes person A to paint the house
Person A can paint the neighbor's house 6 times as fast as Person B
Therefore.
Number of days it takes person B to paint the house = 6x
Their rates of painting are added to get the rate working together
[tex]\frac{\text{1 house}}{\text{x days}} + \frac{\text{1 house}}{\text{6x days}} = \frac{\text{1 house}}{\text{2 days}}[/tex]
[tex]\frac{1}{x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{1 \times 6}{6x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{7}{6x} = \frac{1}{2}\\\\\ x = \frac{7}{3}= 2.3[/tex]
Thus person A takes 2.3 days to paint the house working alone
Person B = 2x = 6(2.3) = 13.8
Thus person B takes 13.8 days to paint the house working alone
How do you make a stem and leaf plot?
Answer:
How to Make a Stem-and-Leaf Plot
Step 1: Determine the smallest and largest number in the data. The game stats: ...
Step 2: Identify the stems. For any number, the digit to the left of the right-most digit is a stem. ...
Step 3: Draw a vertical line and list the stem numbers to the left of the line.
Step 4: Fill in the leaves. ...
Step 5: Sort the leaf data.
Step-by-step explanation:
A stem-and-leaf plot is a graphical representation in statistics that displays all data points in a dataset. It can be formed by ordering the data, separating each data point into a 'stem' and a 'leaf' and recording these on either side of a line on paper.
Explanation:Your question is about creating a stem and leaf plot, which is a form of graphical representation used in statistics to explore and summarize data. Here is how you make a stem and leaf plot:
First, order your data from least to greatest.Next, determine the 'stem' and the 'leaf'. The 'stem' is the first part of each data point, while the 'leaf' is the remaining part. For example, for the number 34, 3 is the stem, and 4 is the leaf.Draw a vertical line on your paper. Label the left side as 'Stem' and the right side as 'Leaf'.Then, you list down all the 'stems' on the left side, and for each stem, put the corresponding 'leaves' on the right side.In a stem-and-leaf plot, unlike histogram, all data values within a class are visible which gives a clear representation of the data distribution.Learn more about Stem and Leaf Plot here:https://brainly.com/question/32830750
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Crayons come in a carton a carton holds 6 packages each package holds 10 small boxes each small box holds 12 crayons how many crayons come in a carton
Answer:720
Step-by-step explanation: think about it, 6 packages, 10 per box hold 12 crayons, 10•12=120. 120•6 boxes equals 720. I may be wrong idk but try that. Im fully confident in that answer
Final answer:
To calculate the total number of crayons in a carton, multiply the number of crayons in a small box by the number of boxes in a package, and then by the number of packages in a carton. This results in 720 crayons per carton.
Explanation:
To find out how many crayons come in a carton, we need to do a series of multiplications. We start at the smallest unit, which is the crayon, and work our way up to the carton.
Each small box holds 12 crayons.Each package holds 10 small boxes, so 10 boxes × 12 crayons each = 120 crayons per package.A carton holds 6 packages, so 6 packages × 120 crayons each = 720 crayons in a carton.Therefore, there are 720 crayons in a carton.
Y=-3/4x+4 find it in slope intercept form
Answ
this is slope intercept form
Step-by-step explanation:
PLEASE HELP. I DON'T UNDERSTAND THESE PEOPLE.
EXPLAIN GOOD FOR BRAINLIEST.
Answer:
Step-by-step explanation:
As it is a square, length of all sides will be equal.
So OW = WV = VU = OU
Here, OU = a
so, W(a,o) because in x-axis y=0
V (a,a)
How can base-ten blocks be used to divide by a two-digit divisor? Explain.
Answer:
it can be shown that one ten base block is used to break down the number with one value blocks.
Step-by-step explanation:
Base ten blocks is used to divide a two digit divisor as follows.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
To use Base ten blocks to divide a two digit divisor.
Now,
Let an example as;
156 ÷ 13 = 12
Use Base ten blocks to divide as;
We start with a squares of 100 as 10 groups, then place 3 more groups below the hundred to make 13 groups.
We have 26 left to split evenly to each group.
We get, 12 in each group.
Thus, Base ten blocks is used to divide a two digit divisor as above example.
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How do you solve for h step by step?
Answer:
h = [tex]\frac{2A}{b_{1}+b_{2} }[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex](b₁ + b₂)h
Multiply both sides by 2 to clear the fraction
2A = (b₁ + b₂)h
Divide both sides by (b₁ + b₂)
[tex]\frac{2A}{b_{1}+b_{2} }[/tex] = h
Rebecca downloaded four times as many songs as Nigel. If X represents the number of songs downloaded by Nigel, write an expression for the number of songs downloaded by Rebecca.
Answer:
X = the number of songs downloaded by Nigel
Y = the number of songs downloaded by Rebecca
Rebecca downloaded four times as many songs as Nigel.
Y = 4X
Answer:
Step-by-step explanation:
Let Nigel songs be = x
Rebecca downloaded songs = 4x
============================================================== Don't delete please
Answer:
The First one To the right is The Correct Shape
Nike is having a sale $100 shoes is 30% off an additional 20% off what is the amount?
Answer:
50% off would be $50
Step-by-step explanation:
20% + 30% = 50% original price was $100 but now with 50% off it is $50
Nike is having a sale $100 shoes is 30% off an additional discount 20% off. The amount to be paid for shoes now is $56.
Discount is the amount of off offered by the seller to the customer on a certain product. It is always offered as a percentage of the marked price of the product to lure the customer to buy the product.
Selling price is the price at which the product is finally sold. It is the marked price of the product minus the discount given.
Marked price = $100
initial discount = 30%
price of shoes becomes = $100 - 30% of $100 = [tex]100 - \frac{30}{100} *100 = 100- 30 = 70[/tex]
Additional discount offered = 20%
selling price of shoes = $70 - 20% of $70 = [tex]70 - \frac{20}{100} *70 = 56[/tex]
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Find the surface area of the composite figure.
12 cm
11 cm
5 cm
7 cm
3 cm
4 cm
4 cm
12 cm
SA = [?] cm?
The student's question lacks necessary details to compute the surface area of the composite figure. Generally, surface area is calculated by summing the areas of each face. For cubes, multiply the area of one face by six and adjust for unexposed areas in composites.
Explanation:The question asks for the total surface area of a composite figure, but the question does not give enough details about the specific shape or composition of the figure. Typically, to find the surface area of any 3-dimensional shape, you'd sum the areas of all the individual faces. For example, for a cube, you'd calculate the area of one face (side length squared) and multiply by 6, because a cube has 6 faces.
In this scenario, if the composite figure was a combination of cubes, you would calculate the total surface area by finding the surface area of each cube separately (surface area of a cube = 6 x side length squared) and then adjust for any faces that are not exposed. The total surface area is the sum of the surface areas of each part of the composite figure minus any overlapping areas.
Without the complete details of the figure, I cannot provide a numerical answer, but I hope this explanation helps you understand the steps involved in computing surface area for composite figures.
Amazon was valued at 430 billion dollars. Write this number in scientific notation
Answer:
430 billion (430,000,000,000) is 4.3 x 10^11 in scientific notation
To convert 430 billion into scientific notation, express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion becomes 10^11. Therefore, the scientific notation of 430 billion is 4.3 x 10^11.
Explanation:The process of writing large numbers or small numbers in scientific notation involves expressing the number as a product of a number between 1 and 10 (inclusive) and a power of 10. To write 430 billion dollars in scientific notation, firstly express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion is 10^11. So, Amazon's worth in scientific notation is 4.3 x 10^11.
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Which of the following represents the graph of f(x) = 2x?
Answer:
I believe it is the fourth graph
Step-by-step explanation:
The only graph that correctly represents the exponential function f(x) = 2ˣ is the fourth graph
How to Identify the exponential function graph?The exponential function is given as:
f(x) = 2ˣ
Thus:
When x = -2, we have:
f(-2) = 2⁻²
f(-2) = 1/2² = 1/4
When x = -1, we have:
f(-1) = 2⁻¹
f(-1) = 1/2¹ = 1/2
When x = 0, we have:
f(0) = 2⁰
f(0) = 1
When x = 1, we have:
f(1) = 2¹
f(1) = 2
When x = 2, we have:
f(1) = 2²
f(1) = 4
Thus, the only graph that correctly represents these values is the fourth graph
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The following data pairs represent the average temperature x (in degrees Fahrenheit) and electricity
costs y (in dollars) for different homes
(65, 147), (59, 141), (71, 176), (78, 189), (82, 183), (85, 211),
(88,231), (91, 227), (84, 198) (79, 188), (63, 152), (59, 126)
Which of the following values is most likely the closest to the correlation coefficient of the data?
r=-1
r=-0.5
=0
r=0.5
Answer:
r=1
Step-by-step explanation:
The correlation coefficient r = 0.8694 suggests a strong positive relationship between the variables, supporting reliable predictions using the regression line.
The correlation coefficient r = 0.8694 indicates a strong positive relationship between the average temperature and electricity costs.
With a value of r = 0.8694 and comparing it to the critical values from the table, r is significant, suggesting a reliable prediction using the regression line.
Therefore, the most likely value closest to the correlation coefficient of the data is r = 0.9.
Find 7/9 of 1 and 2/7
Answer:
1
Step-by-step explanation:
bc theyre even