Answers
Given:
A line segment AB.
A point is [tex]\dfrac{3}{10}[/tex] of the way from A to B.
To find:
The coordinates of that point.
Solution:
Section formula: If a point divide a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
From the given figure, it is clear that the two end points of the line segment are A(-4,-5) and B(12,4).
Let the unknown point be P. The point is [tex]\dfrac{3}{10}[/tex] of the way from A to B. It means,
[tex]\dfrac{AP}{AB}=\dfrac{3}{10}[/tex]
Let AP and AB are 3x and 10x, then
[tex]\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3x}{10x-3x}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3x}{7x}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3}{7}[/tex]
It means, point P divided the line segment in 3:7.
Using section formula, we get
[tex]P=\left(\dfrac{3(12)+7(-4)}{3+7},\dfrac{3(4)+7(-5)}{3+7}\right)[/tex]
[tex]P=\left(\dfrac{36-28}{10},\dfrac{12-35}{10}\right)[/tex]
[tex]P=\left(\dfrac{8}{10},\dfrac{-23}{10}\right)[/tex]
[tex]P=\left(0.8,-2.3\right)[/tex]
Therefore, the coordinates of the required point are (0.8, -2.3).
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x=6
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If Jimmy boy here has 35 ropes and he washes 56 paper, how much wetlands will Johnny Boy own left.
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Answer:
All of what he had
Step-by-step explanation:
Answer: jimmy will have it all
Step-by-step explanation:
1.45 to 4.35 as a simplified fraction
Answers
Answer:
1/45 = 0.02
4/35 =0.1 142857
Step-by-step explanation:
The expression of 1.45 to 4.35 as a fraction in its simplified form is 1/3.
What is a simplified fraction?A simplified fraction is an improper fraction that can no longer be further divided by a divisor. An improper fraction is a fraction with both the numerator and the denominator.
From the information given, we are to express 1.45 to 4.35 as a simplified fraction.
i.e.
= 1.45 as a ratio of 4.35
= 1.45/ 4.35
= 1/3
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Step-by-step explanation:
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Some kind of evadence
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Answer:
Im pretty sure it would be C.
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Sine a signature, photograph and quotes are all pieces of evidence, you can rule them out and infer that c would be the most reliable answer.
The Valley Middle School library just added 250 books to the shelves. Of those books, 40% are fiction. How many of the new books are fiction?
Answers
Answer:
100
20 = 50
50 x2
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
250 books × 40%
= 100
other way to solve it is
250 × 0.40
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Find the value of z in parallelogram CDEF
Answers
Answer:
z = 13
Step-by-step explanation:
Opposite sides of a parallelogram are equal. Therefore:
3z = z + 26
Subtracf z from each side
3z - z = 26
2z = 26
z = 26/2
z = 13
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Answers
Answer:
-9Step-by-step explanation:
This would be -27/3 = -9
Please help me with this question what’s 84 + 6 1/3
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Answer:
90 1/3
Step-by-step explanation:
Answer: Mixed number form = 90 1/3
Decimal form = 90.3 with a repation bar
Actual Form = 271 / 3
Step-by-step explanation:
solve all 5 questions for 62 points if they are correct you will be marked brainiest
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Answer:
1.0.003
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Step-by-step explanation:
The area of a circle is 641 ft2. What is the circumference, in feet? Express your
answer in terms of
Answers
Step-by-step explanation:
Given
Area of a circle (A) = 641 ft²
Circumference (C) = ?
We know
πr² = 641
r² = 641 / 3.142
r² = 204
r = 14.28 ft
Now
Circumference
= 2πr
= 2 * 3.14 * 14.28
= 89.68 ft
Hope it will help :)
Answer:
The circumference is 89.68 ft.
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Answer:
Do not use, there's still one more piece of the puzzle missing.
X =
Step-by-step explanation:
Lets look everything over and compare the corresponding parts of the 2 triangles.
One side of each is shared between the two triangles.
Another side of each triangle is 13 on each triangle.
The included angle of one triangle is 80 degrees and the other is 110 degrees.
What is 2/7+7/8
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Answer:
65/56 = 1 9/56
Step-by-step explanation:
Answer:
Step-by-step explanation:
16/56 + 49/56 = 65/56= 1 9/56
Someone plz help been stuck on this question for the last 2 hours
Paul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?
7% interest =$?
13% interest =$?
Answers
Answer:
7% interest = $10000
13% interest = $20000
Step-by-step explanation:
Let the amount invested at 7% interest be x.
Let the amount invested at 13% interest be y.
Thus;
x + y = 30000 - - - (eq 1)
We want to find out how much Paul needs to invest in each option to make a total 11% return on his $30,000.
Thus;
0.07x + 0.13y = 0.11(30000)
Multiply through by 100 to get rid of the decimal;
7x + 13y = 0.11(30000 × 100).
7x + 13y = 330000 - - - (eq 2)
From eq 1, x = 30000 - y
Put this for x in eq 2 to get;
7(30000 - y) + 13y = 330000
210000 - 7y + 13y = 330000
6y = 330000 - 210000
6y = 120000
y = 120000/6
y = $20000
x = 30000 - 20000
x = $10000
Thus;
Amount invested at;
7% interest = $10000
13% interest = $20000
The graphs below have the same shape. What is the equation of the blue graph? 
Answers
Answer:
c
Step-by-step explanation:
Darby bought a rare baseball card for $2,000. Three years later, the value of the card had increased 35% of its original value. By how much did the value of Darby’s baseball card increase?
$___
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Answer:
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Find the length of AB when A(-4,1) and B(3,-1). Round to the nearest tenth (one decimal place) if necessary.
Answers
Answer:
7.3 units is the answer rounded
When A(-4,1) and B(3,-1), the length of AB is approximately 7.3 units.
What is distance formula?The distance formula is a mathematical formula that is used to compute the distance between two points in a coordinate plane.
This formula is derived from the Pythagorean theorem, which states that the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the other two sides.
We can use the distance formula to find the length of AB:
[tex]d = \sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Where (x1, y1) = (-4, 1) and (x2, y2) = (3, -1)
d = sqrt([tex](3 - (-4))^2 + (-1 - 1)^2[/tex])
= sqrt([tex]7^2 + (-2)^2[/tex])
= sqrt(49 + 4)
= sqrt(53)
≈ 7.3 (rounded to one decimal place)
Therefore, the length of AB is approximately 7.3 units.
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