Point A is located at (4, 8) and point B is located at (14, 10) . What point partitions the directed line segment AB¯¯¯¯¯ into a 1:3 ratio?
(6 1/2, 8 1/2)
(11 1/2, 9 1/2)
(6, 6)
(9, 9)
Answers
Answer:
A is the answer or (6 1/2, 8 1/2) or (13/2, 17/2) or (6.5,8.5)
Step-by-step explanation:
Given : A line segment AB with
[tex]A= (x_1,y_1)=(4,8)[/tex] and [tex]B= (x_2,y_2)=(14,10)[/tex]
let C partitioned the line AB by 1:3 let m:n = 1:3
shown in the figure attached
Formula used:
[tex]C= (\frac{n x_1 + m x_2 }{m+n},\frac{n y_1+ m y_2 }{m+n})[/tex]
putting value in formula we get,
[tex]C= (\frac{(4) (3)+ (14)(1) }{1+3},\frac{(8)(3)+ (10)(1)}{1+3})[/tex]
[tex]C= (\frac{(13 }{2},\frac{17}{2})[/tex]
[tex]C= (6.5 ,8.5)[/tex]
[tex]C= ( 6 1/2,8 1/2)[/tex]
therefore, A is the answer
Related Questions
The sum of the digits of a two-digit number is 12. The number with the digits reversed is 15 times the original tens' digit. Find the original number.
I don't need the answer, just the equations! Thanks!
Answers
[tex]a-digit\ of\ tens\\b-digit\ of\ ones\\10a+b-the\ number\\10b+a-the\ number\ with\ reversed\ digits\\\\\left\{\begin{array}{ccc}a+b=12&\to b=12-a\\10b+a=15(10a+b)\end{array}\right\\\\\text{Substitute}\\\\10(12-a)+a=15(10a+12-a)\\10(12-a)+a=15(9a+12)\qquad\text{use distributive property}\\(10)(12)+(10)(-a)+a=(15)(9a)+(15)(12)\\120-10a+a=135a+180\\120-9a=135a+180\qquad\text{subtract 120 from both sides}\\-9a=135a+60\qquad\text{subtract 135a from both sides}\\-144a=60\qquad\text{divide both sides by (-144)}\\\\a=-\dfrac{60}{144}[/tex]
a is negative and it's not a digit.
Conclusion: Such a number does not exist.Zoe found a sweatshirt that she wanted at jcpenny when she went shopping the other day. it was 30% off. what was the original cost if the sale price was 21$
Answers
The sale price was 30% off the original price, which means it was on sale for 70% of the original cost ( 100% - 30% = 70%)
To find the original cost, divide the sale price by the percent of the original cost:
21 / 0.70 = 30
The original price was $30
check:
30 x 0.3 = 9 ( amount of discount)
30 - 9 = 21 ( sale price)
Final answer:
To find the original price of the sweatshirt that Zoe found, which was sold at a 30% discount, we use the sale price of $21 to calculate that the original price was $30 by dividing by 0.70. An example with sales tax involves an $85 jacket with 7.5% tax, where sales tax is rounded to $6.38 and added to the original price for a total of $91.38.
Explanation:
To determine the original cost of the sweatshirt that Zoe found, which was discounted by 30%, we need to work backwards from the sale price. The sale price represents 70% of the original cost since the item is 30% off. If the sale price is $21, we can set up the equation 0.70 * original price = $21 to find the original price.
Dividing both sides of the equation by 0.70 gives us the original price. Therefore, original price = $21 / 0.70. After performing this calculation, we find that the original cost of the sweatshirt was $30
Emily bought a jacket for $85. If the sales tax is 7.5%, the amount of sales tax would be calculated as 0.075 * $85, which equals $6.375. To get the total cost, we would round $6.375 to the nearest penny to get $6.38, and then add it to the original price of the jacket. The total cost is $85 + $6.38 = $91.38.
PLEASE ANSWER
consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
Answers
Answer:
r = 4b + 3
Step-by-step explanation:
As b is the independent variable, r must be the dependent variable which should be on the left by itself in function notation.
Rearranging 16b = 4r - 12
4r = 16b + 12
r = 4b + 3
Answer:
r = 4b + 3
Step-by-step explanation:
given equation 16b = 4r - 12
in function notation, dependent variable should be on the right n independent variable appears on the left
16b + 12 = 4r - 12 +12
16b + 12 = 4r
flip left n right
4r = 16b + 12
divide by 4
r= 4b + 3
Find the value of the polynomial:
6a^3–a^10+4a^3+a^10–8a^3+a for a=−3
Answers
-57
Step-by-step explanation:We can collect terms to simplify the arithmetic.
... = a^3(6 +4 -8) +a^10(-1 +1) +a
... = 2a^3 +a
... = a(2a^2 +1)
For a = -3, this is
... -3(2(-3)² +1) = -3(2·9 +1)
... = -3·19 = -57
find the measure of the missing side. 7.4 3.6
Answers
Check the picture below.
The length of the missing side (the other leg) is approximately 6.47 units.
To find the measure of the missing side of a right triangle when you know the hypotenuse and one of the other sides, you can use the Pythagorean Theorem. The theorem states:
a² + b² = c²
Where:
- a and b are the lengths of the two shorter sides (legs) of the right triangle.
- c is the length of the hypotenuse.
In this case, you know the hypotenuse (c) is 7.4 and one of the legs (height, let's call it 'a') is 3.6. You want to find the length of the other leg (b).
Plug the values into the Pythagorean Theorem:
3.6² + b² = 7.4²
Solve for b:
b² = 7.4² - 3.6²
b² = 54.76 - 12.96
b² = 41.8
To find b, take the square root of both sides:
b = √41.8
b ≈ 6.47 (rounded to two decimal places)
So, the length of the missing side (the other leg) is approximately 6.47 units.
To know more about length, refer here:
https://brainly.com/question/18425269
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A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
Answers
Answer:
8.3%
Step-by-step explanation:
What is the area of the rectangle shown on the coordinate plane? Enter your answer in the blank. Do not round at any steps.
Answers
12 units²
Step-by-step explanation:Counting half-squares around the perimeter of the rectangle, we find there are 10. Counting full squares inside the rectangle, we find there are 7. Then the total area is
... (1/2)·10 +7 = 12 square units
_____
Alternate calculation
The long side is the hypotenuse of a right triangle with legs 3, so has length 3√2. The short side is the hypotenuse of a right triangle with legs 2, so has length 2√2. The area is the product of these lengths, so is ...
.. area = (3√2)(2√2) = 6(√2)² = 6·2 = 12 . . . square units
Answer:
21
Step-by-step explanation:
A jacket is on sale for $68.00. There is 5% sales tax on the purchase. What is the total cost, including tax?
Answers
Answer:71.4
Step-by-step explanation:
At the community center nine boys and nine girls are playing singles at the community center nine boys and nine girls are playing singles table tennis. If each girl plays against east boys everyone’s how many games are played?
Answers
Answer:
81
Step-by-step explanation:
9girls x 9 boys to play each other
If Mary has ran 41 miles how many inches is that?
Answers
3. To combine the equations and solve for one of the variables, you need to eliminate the other variable. How can you change one equation so that one variable is eliminated when the two equations are added? Explain and write the new equation. 12x + 6y = 120
4x + y = 30
Combine the two equations to eliminate one of the variables, and then solve for the other.
Solve for the other variable.
Prove that your solutions are correct by substituting the values back into the original equations and verifying the answers.
Answers
4x + y = 30 -----(eq. 2)
4x + y = 30
4x = 30 - y
x = (30 - y)/4
Substituting this value of x in eq. 1, we get,
[tex]12( \frac{30 \: - \: y}{4} ) \: + \: 6y \: = \: 120[/tex]
[tex]3(30 \: - \: y) \: + \: 6y \: = 120[/tex]
[tex]90 \: - \: 3y \: + \: 6y \: = \: 120[/tex]
[tex]3y \: = \: 30[/tex]
[tex]y \: = \: 10[/tex]
[tex]x \: = \: \frac{30 \: - \: y}{4} [/tex]
[tex]x \: = \: \frac{30 \: - \: 10}{4} [/tex]
[tex]x \: = \: \frac{20}{4} [/tex]
[tex]x \: = \: 5[/tex]
Hence, x = 5, and y = 10.
To verify, substitute the values in the equation,
4(5) + (10) = 30
30=30
12(5) + 6(10) = 120
120=120.
Answer:
x=5
y=10
Step-by-step explanation:
2=-6x+4 solve for the variable x
Answers
Answer:
x=1
Step-by-step explanation:
so just plug 1 in and you wil get it
Answer:
16
Step-by-step explanation:
6(2)+4
6 x 2=12
12+4=16
Hailey, a chemistry student, is measuring samples of a metallic substance for an experiment on density, using a balance that measures to 1/10 of a gram. Which is the most accurate measurement based on the limitations of the balance that might be found in her recorded data? A) 9.01 grams B) 9.2 grams C) 9.24 grams D) 9.244 grams
Answers
Answer:
B) 9.2 g
Step-by-step explanation:
The balance measures only to 0.1 g.
So, the best measurement Hailey can make is to the nearest 0.1 g.
The most precise measurement she can make is 9.2 g.
The accuracy depends on the balance and on how carefully she works.
Nikita knows the following information about her food club that has 1111 members: 33 members like neither fruit nor vegetables. 44 members like fruit but not vegetables. 55 members in total like fruit. Can you help Nikita organize the results into a two-way frequency table?
Answers
Answer:
[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]
Step-by-step explanation:
You are given such information:
food club has 1111 members;33 members like neither fruit nor vegetables;44 members like fruit but not vegetables;55 members in total like fruit.Then 55 - 44 = 11 members like fruit and vegetables. Thus,
1111 - 55 - 33 = 1023 members like vegetables but not like fruit.
A two-way frequency table will take look
[tex]\begin{array}{cccc}&\text{ Like fruit }&\text{ Do not like fruit }&\text{ Total }\\\text{Like vegetables}&11&1023&1034\\\text{Do not like vegetables}&44&33&77\\\text{Total}&55&1056&1111\end{array}[/tex]
Nikita can organize her data into a two-way frequency table showing members' preferences for fruit and vegetables. The table identifies how many members like only fruit, only vegetables, both, or neither accordingly.
Nikita has the following data about her food club consisting of 1111 members:
33 members like neither fruit nor vegetables.44 members like fruit but not vegetables.55 members in total like fruit.We can organize this information into a two-way frequency table. Here are the steps:
Calculate the number of members who like both fruit and vegetables. Since 55 members like fruit, 44 like only fruit, and 33 like neither, we subtract the 44 members who like only fruit from the total 55 fruit-likers to find those who like both: 55 - 44 = 11.
Calculate the number of members who like vegetables only. The number of members who like either fruit or vegetables or both can be found by subtracting those who like neither from the total number of members: 1111 - 33 = 1078. We already know 55 like fruit, so those who like vegetables only: 1078 - 55 = 1023 (1111 total members - 33 neither - 55 fruit).
The two-way frequency table looks like this:
Fruit No Fruit Total
Vegetables 11 1023 1034
No Vegetables 44 33 77
Total 55 1056 1111
on a road map of pennsylvania, the distance from philaephia to washington d.c. is 6.8 centimeters. whatis the actual distance between the cities if the mape scale is 2 centimeters = 40 miles.
Answers
Answer:
136 miles
Step-by-step explanation:
The map distance is 3.4 times 2 cm, so the road distance will be 3.4 times 40 miles, or 136 miles.
Point D is between points S and T on ST. Given that SD = 2.9 and ST = 11.1, find the length of DT
Answers
D. 8.2
Step-by-step explanation:ST = SD + DT . . . . . segment addition theorem
11.1 = 2.9 + DT . . . . substitute the given lengths
8.2 = DT . . . . . . . . subtract 2.9
The length of segment DT is 8.2 units.
Answer:8.2
Step-by-step explanation:
I got it right on edginuity
Reid are 1/4 of pie. Vince ate 1/3 of same pie. How much of the pie is left?
Answers
Answer:
5/12
Step-by-step explanation: find common denominator
The table shows how long it took Melinda to do her math homework each day over four days.
Table) Monday:3/4, Tuesday:5/6, Wednesday:2/3, Thursday:1/2
What is the ratio of the time it took Melinda to do her math homework on Wednesday to the time it took her to do it on Tuesday.
Please help me, I struggle with this topic in school.
Answers
4/5
Step-by-step explanation:The question is asking you to find the ratio of Wednesday's time (2/3) to Tuesday's time (5/6). To do that, you divide the fractions:
... Wednesday / Tuesday = (2/3) / (5/6)
There are a couple of different methods you can use to divide fractions.
1. Invert the denominator and multiply.
When we invert 5/6, it becomes 6/5. So our division problem is now a multiplication problem:
... (2/3) × (6/5) = (2×6)/(3×5) = 12/15
This result can be reduced by removing a factor of 3 from numerator and denominator:
... Wednesday/Tuesday = 4/5
___
2. Make both fractions have the same denominator, then drop the denominators.
The denominators of the fractions in our ratio are 3 and 6. If we multiply 3 by 2, it becomes 6, so we can rewrite the numerator fraction as ...
... 2/3 = (2/3)×(2/2) = 4/6
Now, it has a denominator of 6 and our division problem is
... (2/3) / (5/6) = (4/6) / (5/6)
Dropping the (same) denominators gives ...
... Wednesday/Tuesday = 4/5
Which of the following equations is perpendicular to y = 2x + 5 and passes through the point (4 , 6)? A. y = – 1 2x + 8 B. y = 2x + 8 C. y = – 1 2x – 2 D. y = 2x – 2
Answers
Answer:
The equation would be y = -1/2x + 8
Step-by-step explanation:
To find the equation of the line, we start by find the slope. Perpendicular slopes have opposite and reciprocal slopes. since the original slope is 2, then the perpendicular slope is -1/2.
Now, using the point and the slope in point-slope form, we can find the equation.
y - y1 = m(x - x1)
y - 6 = -1/2(x - 4)
y - 6 = -1/2x + 2
y = -1/2x + 8
The equations that is perpendicular to y = 2x + 5 and passes through the point (4 , 6) is y = - 1/2 x + 8
For an equation to be perpendicular to the another line equation the product of there slope will be negative one. Therefore,
m₁m₂ = -1Therefore, the slope of y = 2x + 5 is 2. The equation should have the following slope:
2m₂ = - 1
m₂ = -1 / 2
A linear equation is represented as follows:
y = mx + bm = slope
b = y-intercept
Therefore,
let use the point (4 , 6) to find b
6 = - 1/2 (4) + b
6 = -2 + b
b = 6 + 2
b = 8
The equation will be as follows:
y = - 1/2 x + 8
read more; https://brainly.com/question/16236339?referrer=searchResults
please help me asap!
Answers
Answer:
Option d) 115 degrees
Step-by-step explanation:
We are given a trapezium ABDE in the picture. AB and ED are the parallel sides.
F is the mid point of AE and C the midpoint of BD. FC is joined.
We are also given that angle of AED = 65 degrees.
To find the measure of angle BAE.
Since sides AB and ED are parallel sides we find that AE is the transvesal intersecting the two parallel lines.
Hence by parallel lines axiom, the two interior angles namely Angle AED and BAE are supplementary.
i.e. 65 +angle BAE=180
Hence angle BAE = 115 degrees.
Option d is the answer.
Paul needs 8 equal-length sections of rope.After cutting these 8 sections,he has 28.9 inches of rope left over from an original length of 184.9 inches.What is the length of each of the sections?Be sure to define your variable(s)
Answers
19.5 inches
Step-by-step explanation:Let r represent the length of one of the sections of rope (in inches). Then the total length of the original rope is ...
... 8r +28.9 = 184.9
... 8r = 156 . . . . . . . . . . . . subtract 28.9; next, divide by 8
... 156/8 = r = 19.5
The length of each of the sections is 19.5 inches.
Please help me, due in 20 minutes and I need the work.
Answers
Answer:
When she mixes the clay she now had 3/2 and 3/4 added would be 6/4 and 3/4 so she has 9/4 pounds of clay. If each student needs 1/8 and she had 18/8 that means she can make 18 students finish.
Please mark brainliest as that would help alot/
Step-by-step explanation:
the ratio of students that take french to spanish is 20:19. How do the number of students taking french and the number of students taking spanish compare.
Answers
Answer:
More students take French than take Spanish.
Step-by-step explanation:
Effectively, out of every 39 students taking French and/or Spanish, 19 of them take Spanish and 20 of them take French. The number of French students in that group is higher. (20 is more than 19)
Derrick and Mark are brothers who live in the same house. Mark is home, and Derrick is 5 mi from home. Both boys begin riding their bikes at the same time. Derrick rides directly home at a constant rate of 15 mph, and Mark rides away from home at a constant rate of 18 mph. Let d represent distance from home, and let t represent time in hours. Which system models this situation? A. d = 5 − 15t d = 18t B. d = 15 − 5t d = 18t C. d = 5 + 15t d = 18t D. d = 5 − 15t d = 5 + 18t
Answers
A. d = 5 − 15t; d = 18t
Step-by-step explanation:Derrick's distance from home is initially 5 miles and is decreasing at the rate of 15 miles per hour. His distance from home can be modeled by ...
... d = 5 - 15t . . . . . . d in miles; t in hours
Mark's distance from home is initially zero and is increasing at the rate of 18 miles per hour. His distance from home can be modeled by ...
... d = 18t . . . . . . . . . d in miles; t in hours
Together, these equations form the pair ...
d = 5 -15td = 18t_____
Comment on the equations
There is nothing in the problem statement or definition of the variables to suggest that one distance is measured in the same direction as the other, or that one value of d has any relationship to the other.
Usually, a "system of equations" expresses relationships among variables that all have the same definition with respect to some problem statement. Here, both values of d are "distance from home", but they don't necessarily have any relationship to each other. Their being the same value doesn't mean the boys have met, for example.
Which equation can be used to find the area of the of the trapezoid?
A) A = 2(15 + 23)(9)
B) A = 2(15 + 23)(9)
C) A = 1/2(15 + 23)(9)
D) A = 1/2 (152 + 232)(92)
Answers
Answer:
C) 1/2(15 +23)(9)
Step-by-step explanation:
The formula for the area of a trapezoid in terms of base lengths b1 and b2 and height h is ...
... A = 1/2(b1 +b2)h
Substituting the values shown in the figure, this becomes ...
... A = 1/2(15 +23)(9) . . . . . matches selection C
a damsel in distress is being
Answers
Check the picture below.
make sure your calculator is in Degree mode.
A rock is pushed out of a six-story window that is 60 feet above the ground. What energy changes occur as the rock falls to the ground?
A)
The potential energy of the rock is destroyed as it falls.
B)
The potential energy of the rock is transformed into kinetic energy.
C)
The kinetic energy of the rock is transformed into potential energy.
Answers
Answer:
B) The potential energy of the rock is transformed into kinetic energy.
Step-by-step explanation:
Our understanding of Physics tells you the potential energy due to the rock's position in the gravitational field is transformed into kinetic energy as the rock gains speed (and loses height).
_____
Comment on the problem
There are additional effects not accounted for by this simplified answer, including thermal effects, radiation effects, and sound effects. (In this new age, there can also be energetic effects in dimensions we're not accustomed to considering, including emotional or other effects on—or due to—consciousness.)
Answer B)it goes from being still to moving
Which of the following expressions are polynomials and which are not (why?)
1/x^3 +x^2
Answers
Answer:
none shown
Step-by-step explanation:
1/x^3 = x^(-3) has a negative exponent. It does not match the requirement that exponents be a non-negative integer. Therefore, any expression containing 1/x^3 will not be a polynomial.
A basketball player attempts 15 baskets in a game, He makes 9 of the attempted basket. which ratio describe the number of basket the player made to the number of basket the player attempted?
Answers
Answer:
3:5
Step-by-step explanation:
We are looking for the ratio of baskets made to baskets attempted
made: attempted
9:15
We can divide each number by 3
9/3: 15/3
3:5
The ratio of baskets made: attempted is 3:5
The ratio that describes the number of baskets made to the number of baskets attempted by the basketball player is 9 to 15, which simplifies to 3 to 5.
The question pertains to the ratio of successful basket attempts to total attempts made by a basketball player in a game.
In this case, the player successfully made 9 baskets out of 15 attempts.
To express this as a ratio, we simply compare the number of made baskets to the total attempts,
thus the ratio is 9 to 15, which can also be simplified by dividing both numbers by their greatest common divisor, which is 3, resulting in a simplified ratio of 3 to 5.
HURRYYY 20 PTS
Mrs. Nygaard needs 12 hours to grade all of her students’ projects. She made a chart to show how much time she could spend grading the projects during the week.
How many hours will Mrs. Nygaard need to work over the weekend to finish grading the projects?
Answers
Add all the hours together:
1 3/4 + 1 1/4 = 3 + 1 1/2 = 4 1/2 + 1 1/5
To add fractions with different denominators, find the common denominator and rewrite the fractions
Common denominator of 2 and 5 is 10
1/2 becomes 5/10
1/5 becomes 2/10
now you have 4 5/10 + 1 2/10 = 5 7/10 + 2 = 7 7/10
Now subtract that from 12:
12 - 7 7/10 = 4 3/10 hours