Point E is located at (−2,4) and point F is located at (5,10) . What are the coordinates of the point that partitions the directed line segment EF⎯⎯⎯⎯⎯ in a 7:3 ratio? Enter your answer, as decimals, in the boxes.
Answers
Solution:
Coordinates of Point E and F are (-2,4) and (5,10).
Suppose the Point M(x,y), divides the Line Segment Joining E (-2,4) and F (5,10) in the 7:3 ratio.
So, EM: MF= 7:3
Formula for internal Division
So,we get
x= 2.9
and , y= 8.2
Related Questions
What's the answer please
Use the functions m(x) = 5x + 4 and n(x) = 6x − 9 to complete the function operations listed below.Part A: Find (m + n)(x). Show your work. Part B: Find (m ⋅ n)(x). Show your work. Part C: Find m[n(x)]. Show your work.
Which value is the eighth term in the sequence: an= - 1/125 (5^n-1)?-3125 -125 -625 -25
Two sides of a triangle are 15 mm and 10 mm. The perimeter of the triangle is 35 mm. What's the third side?
Answers
Answer: 4096
Step-by-step explanation: 1 gallon=128 ounces, 128x32=4096
Final answer:
32 ounces per day is equal to 0.25 gallons per day.
Explanation:
To convert 32 fluid ounces per day to gallons per day, we need to use the conversion factor that 1 gallon = 128 fluid ounces. Divide 32 by 128 to get the equivalent in gallons per day:
32 fl oz ÷ 128 fl oz/gal = 0.25 gallons/day
Therefore, 32 ounces per day is equal to 0.25 gallons per day.
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Answers
z=(x-μ)/σ
the z-score associated with 0.5% is 0
thus
0=
(8-μ)/0.4=0
solving for x we get:
μ=9
Answer: μ=9
Final answer:
The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:
The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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25/60 = 30/x
25
36
50
72
Answers
x = 30/25 * 60
x = 1800/25
x = 72
So, option D is your answer.
Hope this helps!
Answer:
d
Step-by-step explanation:
Answers
The Keller family spent a total of $63.04.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
First, let's find the cost of the meal before tax and tip.
We know that the total bill, including tax, is $55.35, which is equal to 100% + 8% (the tax rate) = 108% of the original meal cost.
We can set up an equation to solve for the original meal cost (let's call it x):
x + 0.08x = 55.35
Simplifying the left-hand side:
1.08x = 55.35
Dividing both sides by 1.08:
x = 51.25
So the cost of the meal before tax and tip was $51.25.
Next, let's calculate the amount of tax they paid:
0.08x = 0.08(51.25) = 4.10
So the tax they paid was $4.10.
Now let's calculate the tip they left for the server. They left a 15% tip on the original meal cost of $51.25:
0.15(51.25) = 7.69
So the tip they left was $7.69.
Finally, to find out how much they spent in total, we add up the cost of the meal, the tax, and the tip:
51.25 + 4.10 + 7.69 = 63.04
Therefore, the Keller family spent a total of $63.04.
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Complete question:
The Keller family's dinner bill is $55.35. This includes an 8% meal tax and a 15% tip on original meal for the server how much did they spend in total?
Then you find 15% of 55.35 which is 8.30
You add them together which equals 12.72
You then subtract 12.75 from 55.35 55.35-12.75=42.63
The original price was $42.63
system of equations?
(1) (3,0) is the solution to the system because it satisfies the equation
y = |x - 3|.
(2) (9,0) is the solution to the system because it satisfies the equation
3x + 3y = 27.
(3) (6,3) is the solution to the system because it satisfies both equations.
(4) (3,0), (9,0), and (6,3) are the solutions to the system of equations
because they all satisfy at least one of the equations.
Answers
3x + 3y = 27
3x + 3|x - 3| = 27
3x + 3|x - 3| = ±27
3x + 3|x - 3| = 27 or 3x + 3|x - 3| = -27
3x + 3(x - 3) = 27 or 3x + 3(x - 3) = -27
3x + 3(x) - 3(3) = 27 or 3x + 3(x) - 3(3) = -27
3x + 3x - 9 = 27 or 3x + 3x - 9 = -27
6x - 9 = 27 or 6x - 9 = -27
+ 9 + 9 + 9 + 9
6x = 36 or 6x = -18
6 6 6 6
x = 6 or x = -3
y = |x - 3| or y = |x - 3|
y = |6 - 3| or y = |-3 - 3|
y = |3| or y = |-6|
y = 3 or y = 6
(x, y) = (6, 3) or (x, y) = (-3, 6)
The two systems of equations of the graph is only equal to (6, 3). It is not equal to (-3, 6) because one of the systems of equations - y = |x - 3| - only has one solution to the function. So the answer to the problem is 3 - (6, 3) is the solution to the system because it satisfies both equations.
b. (34)4 and 38 ⋅ 38
c. 64 ⋅ 34 and 188
d. 43 ⋅ 53 and 203
e. (43)3 and 43 ⋅ 43 ⋅ 43
2. Choose an equivalent expression for 123 • 129 • 124 • 122.
a. 12^4
b. 12^18
c. 12^35
d. 12^216
3. Choose an equivalent expression for 106 ÷ 104.
a. 10^2
b. 10^3
c. 10^10
d. 10^24
4. Select all the expressions that are equivalent to 78 • 7.
a. 73 • 73
b. 7^18/7^9
c. (73)3
d. 74 + 75
e. 74 • 75
5. Is this equation correct?
63 ⋅ 73 = 423
A. Yes; 63 • 73 is equal to (6 • 7)3 or 423.
B. Yes; 63 • 73 is equal to (6 • 7 • 3) or (42 • 3).
C. No; 63 • 73 is equal to (6 • 7 • 3) or (42 • 3).
D. No; 63 • 73 is equal to (6 • 7)3 + 3 or 426.
Answers
This question was not properly written
Complete Question
Select all the pairs of equivalent expressions.
a. (4³)³ and 4³ ⋅ 4³
b. (3⁴)⁴ and 3⁸ ⋅ 3⁸
c. 6⁴ ⋅ 3⁴ and 18⁸
d. 4³ ⋅ 5³and 20³
e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³
2. Choose an equivalent expression for 12³ • 12⁹• 12⁴ • 12².
a. 12^4
b. 12^18
c. 12^35
d. 12^216
3. Choose an equivalent expression for 10⁶ ÷ 10⁴.
a. 10^2
b. 10^3
c. 10^10
d. 10^24
4. Select all the expressions that are equivalent to 7⁸ • 7.
a. 7³• 7³
b. 7^18/7^9
c. (7³)³
d. 7⁴ + 7⁵
e. 7⁴ • 7⁵
5. Is this equation correct?
6³⋅ 7³= 42³
A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.
B. Yes; 6³ • 7³is equal to (6 • 7 • 3) or (42 • 3).
C. No; 6³ • 7³ is equal to (6 • 7 • 3) or (42 • 3).
D. No; 6³ • 7³ is equal to (6 • 7)³+ 3 or 42⁶.
Answer:
1 The correct answer is
d. 4³ ⋅ 5³ and 20³
e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³
2b. 12^18
3 a = 10²
4a. 7³ • 7³
c. (7³)³
e. 7⁴ • 7⁵
5 A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.
Step-by-step explanation:
1) Select all the pairs of equivalent expressions.
These are the correct options
d. 4³ ⋅ 5³and 20³
4³ × 5³ = 8000
20³ = 8000
e. (43)3 and 43 ⋅ 43 ⋅ 43
2. Choose an equivalent expression for 12³ • 12⁹• 12⁴• 12².
For an Algebraic Expressions,
We have the rule
x^a × x^b = x ^a+ b
Hence: 12³ • 12⁹• 12⁴ • 12².
= 12^3+9+4+2 = 12^18
Hence, b. 12^18
3. Choose an equivalent expression for
10⁶ ÷ 10⁴.
For an Algebraic expressions
x^a ÷ x^b = x ^a - b
Therefore
10⁶÷ 10⁴ = 10²
a. 10^2 Is the correct option
4. Select all the expressions that are equivalent to 7⁸ • 7.
7⁸ . 7= 7^8+1
= 7^9 or 7⁹
The equivalent expressions are:
a. 7³ • 7³ = 7⁹
b. 7^18/7^9 = 7⁹
c. (7³)³ = 7⁹
e. 7⁴ • 7⁵ = 7⁹
5. Is this equation correct?
6³ ⋅ 7³ = 42³
A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³
1. There are equivalent expressions in options (a) and (e).(43)3 and 43 ⋅ 43, (43)3 and 43 ⋅ 43 ⋅ 43
2. The equivalent expression for 123 • 129 • 124 • 122 is 12^18. Option b
3. The equivalent expression for 106 ÷ 104 is 10^2.Option a
4. Equivalent expressions in options (a) and (c) represent 78 • 7.
5. The equation 63 ⋅ 73 = 423 is not correct; the correct result is 63 • 73 = 1369.Option C
1. Pairs of Equivalent Expressions:
a. (43)3 and 43 ⋅ 43: These are equivalent expressions because (43)3 means 43 raised to the power of 3, which is the same as 43 multiplied by itself 3 times.
e. (43)3 and 43 ⋅ 43 ⋅ 43: These are equivalent expressions because (43)3 means 43 raised to the power of 3, which is the same as 43 multiplied by itself 3 times.
2. Equivalent Expression for 123 • 129 • 124 • 122:
b. 12^18: This expression represents the product of 12 raised to the power of 18, which is equivalent to multiplying the given numbers.
3. Equivalent Expression for 106 ÷ 104:
a. 10^2: This expression represents 10 raised to the power of 2, which is equivalent to the given division.
4. Expressions Equivalent to 78 • 7:
a. 73 • 73: This expression represents the square of 7^3, which is equivalent to 78 • 7.
c. (73)3: This expression represents 7^3 raised to the power of 3, which is equivalent to 78 • 7.
5. Is the Equation Correct?
C. No; 63 • 73 is equal to (6 • 7 • 3) or (42 • 3). The equation 63 ⋅ 73 = 423 is not correct; the correct result is 63 • 73 = 1369. The provided equation does not accurately represent the multiplication of 63 and 73.
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