The coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).
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.
Given that the ratio of the two lines is 3:1, therefore, we can write,
m:n = 3:1
Also, the coordinate of the endpoints of the line are,
A = (x₁, y₁) = (1, 7)
B = (x₂, y₂) = (5, 15)
Now, Using the Section formula the coordinate of the point P can be written as,
[tex]P = (\dfrac{mx_2+nx_1}{m+n}\ , \dfrac{my_2+yx_1}{m+n})\\\\P = (\dfrac{3(5)+1(1)}{4}\ , \dfrac{3(15)+1(7)}{4})\\\\P = (4, 13)[/tex]
Hence, the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).
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Solve the following proportion by cross multiplying:
( x - 3 ) / 4 = ( 2x + 2 ) / 6
Answer:
- 13
Step-by-step explanation:
Solving
[tex] \frac{(x - 3)}{4} = \frac{(2x + 2)}{6} \\ \\ cross \: multiplying \\ 6 \times (x - 3) = 4 \times (2x + 2) \\ 6x - 18 = 8x + 8 \\ 6x - 8x = 8 + 18 \\ - 2x = 26 \\ dividing \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{26}{ - 2} \\ x = - 13[/tex]
[tex] \implies \: \sf{ \dfrac{x \: - \: 3}{4} \: = \: \dfrac{2x \: + \: 2}{6} } \\ \\ \implies \: \sf{6( x \: - \: 3) \: = \:4(2x \: + \: 2)} \: \\ \\ \implies \: \sf{6 \times ( x \: - \: 3) \: = \: (2x \: + \: 2)}\\ \\ \implies \: \sf{6x \: - \: 18 \: = \:8x \: + \: 8}\\ \\ \implies \sf{6x \: - \: 8x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \: 26}\\ \\ \implies \sf{ - x \: = \: \dfrac{26}{2} }\\ \\ \implies \sf{ - x \: = \: \cancel{\dfrac{26}{2} }}\\ \\ \implies \sf{ - x \: = \: 13}\\ \\ \implies \red{\bf{ x \: = \: - 13}}[/tex]
Find an equation for the line that passes through the points (6,1) and (-4,3)
Answer: $$y=-2/3x+2$$
Explanation: Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Which type of parent function is f(x) = 1/x
Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.
What are rational functions?Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.
The most simple example is given by:
[tex]f(x) = \frac{1}{x}[/tex].
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Answer: Reciprocal
Step-by-step explanation:
Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.
Please help me solve this.
Answer:
I think that is a FORMULA.it can't be solved if we don't know the values of atleast one of the x and y.
Hope this helps.
Good luck ✅.
To estimate the number of bass in a lake, a biologist catches and tags 32 bass. several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. how many bass are in the lake?
If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.
Given Biologist catches and tags 32 bass, when sample of 55 bass is taken then 5 are found tagged.
Population is basically number of living thing exists in a particular area.
Number of bass which are tagged in lake=32
Sample size=55
Number of bass found tagged=5
means percentage of tagged bas found is 5/32*100=1.6%
We have to calculate number of times 5 is multiplied to get 32 which is 6.4.
Number of bass in the lake=55*6.4
=352 basses.
Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.
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How do the areas of the parallelograms compare? the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is equal to the area of parallelogram efgh. the area of parallelogram abcd is 2 square units less than the area of parallelogram efgh.
option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of the parallelogram is:
A = b×h
Here b is the base length and h is the height
In ABCD parallelogram:
A = (3)×(3)
A = 9 square units
EFGH parallelogram:
a = (3)×(3)
A = 9 square units
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
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Which set of systems of equations represents the solution to the graph?
an upward opening parabola decreasing from negative 3 comma 4 to a minimum at negative one comma zero and then increasing to 1 comma 4 and a downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3
The correct graph for the given sets of equation is given attached below.
Equation no 2 gives the perfect solution to the graph.
A parabola, is cross section cut out of the cone and represented by an equation [tex]Y=4ax^2[/tex]
Clearly, by property of the parabola, the curve of parabola should symmetric to its axis. From this property set of Equation (2) i.e. downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3 Holds the property of the parabola
Thus, the required solution for the sets of equation (2) is given in the attachment.
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A membership committee of three is formed from four eligible members. let the eligible members be represented by a, b, c, and d. the possible outcomes include s = {abc, abd, acd, bcd}. which statements about the situation are true? select three options.
The correct statements are:
There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If persons B and C must be on the committee, there are two ways to form the committee.
It is given that:
A membership committee of three is formed from four eligible members.
1)
There are four ways to choose the committee.
This statement is true.
since we have to choose 3 members out of the 4 members so we can use the method of combination.
2)
There are three ways to form the committee if person D must be on it.
This statement is also true.
since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.
3)
If seven members are eligible next year, then there will be fewer combinations.
This statement is wrong.
Since we have to choose 3 members out of 7 members so the number of possible combinations will be:
i.e. there are 35 combinations possible.
4)
If persons B and C must be on the committee, there are two ways to form the committee.
if B and C have to be in the committee then we have to choose just one person out of the two people left.
Hence, the statement is true.
5)
If persons A and C must be on the committee, then there is only one way to form the committee.
If A and C have to be in the committee then as in last option we have to choose any one of the two person left.
so possible number of ways are 2.
Hence, the statement is false.
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The point P(x, y) is on the terminal ray of angle Theta. If Theta is between Pi radians and StartFraction 3 pi Over 2 EndFraction radians and = Negative five-halves, what are the coordinates of P(x, y)?
P(Negative StartRoot 21 EndRoot, –2)
P (StartRoot 21 EndRoot, –2)
P(–2, StartRoot 21 EndRoot)
P(–2, Negative StartRoot 21 EndRoot)
The coordinates of P(x, y) is: A. P(Negative StartRoot 21 EndRoot, –2)
Coordinates of P(x, y)Given:
Radians=3π/2
theta=-5/2
Hence:
Hypotenuse = - 5
Altitude = 2
Using Pythagorean theorem
Hypotenuse² = Altitude² + Base²
-5²= 2² + Base²
25 ² - 4 ² = Base²
Base = √21
Thus P(x,y) :
= P(-√21 : -2)
Therefore the correct option is A.
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HELP ASAP
Given: ABCD is a parallelogram.
Prove: A is congruent to FCE.
Answer:
Step-by-step explanation:
C is equal to A. Because angle FCE is on the other side with C, it has to be equal to A
ABCD is a parallelogram (Given)
As opposite angles of a parallelogram are equal
<A=<BCD--(1)Also
<BCD=<FCE(Opposite angle)-(2)From (1) and (2)
<A is congruent to <FCE
if y= 2x-3 were chnged to y=2x+5 how would the graph of the new function compare with the original
The new function moved up by 8 units from the original.
The only difference in the functions is the y-intercept. The slope remained the same ([tex]2[/tex]), but the y-intercept went up by 8, meaning the function moved up 8 units.
See the attached image for a graph of both functions. The new function is the solid blue line.
Harry decided to buy some candy bars that
cost $2.19 each. He also bought a drink for
$3.55. Harry paid a total of $10.12. Write an
equation to find how many candy bars Harry
purchased.
Duane rode his bike at 14 miles per hour for 3 hours, then put the bike down and began walking at miles 2 per hour. Elizabeth started jogging at 5 miles per hour along the same path at the same time that Duane started biking. When she reached the bike, she began riding it at 10 miles per hour. How many hours will it have been since they started when Elizabeth catches up to Duane
Elizabeth will take 9 hours and 45 minutes to catch up with Duane using the given speed-distance-time values.
The speed-distance-time relations are:
Speed = Distance/Time, Distance = Speed*Time, and Time = Distance/Speed.
The distance traveled by Duane on the bike at 14 miles per hour for 3 hours = 14*3 miles = 42 miles.
The time that Elizabeth takes to cover 42 miles jogging at 5 miles per hour = 42/5 hours = 8.4 hours.
The distance traveled by Duane in the extra time which Elizabeth took to reach his bike (8.4 - 3 = 5.4 hours) walking at 2 miles per hour = 2*5.4 = 10.8 miles.
Now, the distance between Elizabeth and Duane is 10.8 miles, before Elizabeth starts riding the bike.
Keeping the distance constant, we calculate the relative speed to calculate the time to cover this distance.
Relative speed = Elizabeth's speed - Duane's speed {As Elizabeth is moving towards Duane, that is, covering the distance but Duane is moving away from Elizabeth, that is, increasing the distance}.
or, Relative speed = 10 - 2 = 8 miles per hour.
Time taken to cover the distance = 10.8/8 = 1.35 hours.
Therefore, the total time taken by Elizabeth to catch up with Duane = 8.4 + 1.35 hours = 9.75 hours or 9 hours and 45 minutes.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
Considering the given equation of the circle, the true statements are given as follows:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis.The circle has the same radius as the circle with equation x² + y² = 9.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation given is:
x2 + y² - 2x - 8 = 0.
Completing the squares, the equation is given as follows:
(x - 1)² + y² = 8 + 1
(x - 1)² + y² = 9.
Researching the problem on the internet, the true statements are:
The radius of the circle is of 3 units.The center of the circle lies on the x-axis([tex]y_0 = 0[/tex]).The circle has the same radius as the circle with equation x² + y² = 9.More can be learned about the equation of a circle at https://brainly.com/question/24307696
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Select the correct answer from each drop-down menu.
The slope of the line in the graph is [ ]. The y-intercept is [ ]. The equation of the line is y= [ ], and x is [ ]
BOX 1:
A. 2
B. 3
C. -2
D. -3
BOX 2:
A. -3
B. 3
C. 4
D. -4
BOX 3:
A. 2
B. 3
C. -2
D. -3
BOX 4:
A. -3
B. +3
C. +4
D. -4
For the linear function in the graph, we have that:
The slope is of 3.The y-intercept is of -4.The equation of the line is: y = 3x - 4.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line goes through point (0,-4), hence:
The y-intercept is of -4.
The function also goes through point (2,2), hence the slope is:
m = (2 - (-4))/(2 - 0) = 6/2 = 3.
Then, the equation of the line is:
y = 3x - 4.
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If the side lengths of a polygon are: 4x, 6x, 12, and 18 what is the value of x if the perimeter is 118?
The value of x for given polynomial is 8.8.
What is Polygon?The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
Here, the length of sides of given Polygon are:
4x, 6x, 12, 18
Perimeter of polygon = 118 units.
We know that,
Perimeter of polygon = Sum of all sides
118 = 4x + 6x + 12 + 18
118 = 10x + 30
118 - 30 = 10x
10x = 88
x = 88/10
x = 8.8
Thus, the value of x for given polygon is 8.8.
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I'm not very good at solving these problems
1 atom of C has a mass of 12 amu (atomic mass unit).
1 atom of O has a mass of 16 amu.
1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.
C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.
Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.
6) Stacie was solving the triangle below. Can you find her mistake?
Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Solution is supposed to be
[tex]tan_ (-1) (28/21) = 53.33[/tex]
Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
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20 points. The length of a rectangular room is 4.5 m and it’s width is 9.6 m. Find the area of the room
Answer:
43.2 m square is ur answer .
Answer:
43.2 m^2
Step-by-step explanation:
The area of a rectangle is the width times the length.
Area = (9.6 m)*(4.5 m)
Area = 43.2 m^2
what is the slope of this line?
y-9=1/5(x-2)
Answer: D) 1/5
Step-by-step explanation:
Format for point-slope form: y-y₁=m(x-x₁)
x1, y1 is a point on the line
m is the slope
So in this equation, m = 1/5
so, the slope is 1/5
hope this helps!
What is the radius of a hemisphere with a volume of 4635 ft 3 , 4635 ft 3 , to the nearest tenth of a foot?
Step-by-step explanation:
Hemisphere Formulas in terms of radius r:
V = (2/3)πr.
Hereof, What is the radius of a hemisphere? As latter is 4πr2 , curved surface area of a hemisphere of radius r is 2πr2 . and hence total surface area of hemisphere is 2πr2+πr2=3πr2 . Hence, radius of hemisphere is 4 cm.
In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide: . The graph shows a circle with three points, A is equal to (8, 15), B is equal to (12, 13), and C is equal to (8, 10). C is the center of the circle. A line is joining AC and BC A. 24 units B. 45 units C. 21 units D. 15 units E. 5 units Reset Next
The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.
What is Dilation?Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.
Applying the distance formula, we have:
BC = √[(8−12)² + (10−13)²]
BC = √(−4)² + (−3)²]
BC = √(16+9)
BC = √25
BC = 5 units
Applying the scale factor:
Length of C'B' = 3(5) = 15 units.
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Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 = 7
☐ A. x = -√7 +1
3
B. X=
=
C. x=
☐ D. x=
= 2√2
2√2
3
☐ E. X=
-√7
3
☐ F. x =
<=
X= √²+1
3
+1
+1
Step-by-step explanation:
therefore A is the correct answer
A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about the origin, ( 0 , 0 ) (0,0)left parenthesis, 0, comma, 0, right parenthesis.
The angle of rotation of triangle ABC to A'B'C is 105°
How to illustrate the information?It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.
Point B is also on the x axis and point B' is in the second quadrant.
In this case, the angle that depicts the second quadrant is 105°.
In conclusion, the correct option is D.
The complete question is:
Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)
Determine the angle of rotation
A. -105 degrees
B. -75 degrees
C. 75 degrees
D. 105 degrees
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Find the value of x.
The value of 'x' is 25.00
How to determine the value of xThe given figure is a triangle
To find the value of 'x', first find the value of the other side
Using
Hypotenuse square = opposite square + adjacent square
16^2 = 10^2 + y^2
256 = 100 + y^2
Make y subject of formula
y = √ 256- 100
y = √ 156
y= 12. 49
To find 'x'
28^2 = x^2 + 12.59^2
784 = x^2 + 158. 51
x^2 = 784 - 158. 51
x^2 = 625. 49
x =√ 625. 49
x = 25.00
Thus, the value of 'x' is 25.00
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Find the inverse of the function
y = log₂ (x-3)
Answer:
[tex]f^{-1}(x)=2^x+3[/tex]
Step-by-step explanation:
Given:
[tex]y=\log_2(x-3)[/tex]
To find the inverse of the given function, make x the subject.
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 2^y=x-3[/tex]
Add 3 to both sides:
[tex]\implies x=2^y+3[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=2^x+3[/tex]
una fracion reducicion a su minima expresion en igual a 1/8 . si la suma de sus terminos es 72. hallar la diferencia entre ellos
La diferencia entre el denominador y el númerador de la fracción es:
64 - 8 = 56.
¿Como encontrar la fracción?
Tendremos una fracción de la forma:
[tex]\frac{a}{b}[/tex]
Tal que:
[tex]\frac{a}{b} = \frac{1}{8}[/tex]
[tex]a + b = 72[/tex]
Eso es un sistema de ecuaciones
Primero, podemos reescribir la primer ecuación como:
[tex]8a = b[/tex]
Ahora podemos reemplazar "b" en la segunda ecuación por "8a", así obtenemos:
[tex]a + 8a = 72\\\\9a = 72\\\\a = 72/9 = 8[/tex]
Ahora podemos obtener el valor de b:
[tex]b = 8a = 8*8 = 64[/tex]
La diferencia entre a y b es:
[tex]b - a = 64 - 8 = 56[/tex]
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Mass (kg)
45
61
57
78
68
Length (cm)
112
138
133
180
175
Which of the options is the most appropiate to suow data in the table?
Pictogram
Pie chart
Bar chart
Line Graph
Scatter Graph
Answer:
Line or scatter graph.
Step-by-step explanation:
I prefer line, although some of the points deviate a bit. But the line shows a definite relationship between mass and length.
See attached graph.
Which set of data does not have a mode?
(A) 1, 2, 5, 6, 8
(B) 1, 3, 5, 5, 6
(D) 1, 1, 1, 2, 2
(C) 1, 5, 5, 5, 5
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\textbf{Which set of data does not have a mode?}[/tex]
[tex]\huge\textbf{The choices that you have provided:}[/tex]
[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]
[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]
[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]
[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]
[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]
[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]
[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\textbf{1, 2, 5, 6, 8}[/tex]
[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]
[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]
[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option D. }[/tex]
[tex]\textbf{1, 1, 1, 2, 2}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]
[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]
[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Kelly has 2 liters of milk in the refrigerator. she used 12 liters of milk in the morning with breakfast. she then used the same quantities of milk at both lunch and dinner, such that she used up all the milk. what quantity of milk did she use at dinner?
Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.
What is Volume?Each thing in 3-D takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.Given we have, Initial amount of milk is [tex]2[/tex] liters.
The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.
Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters
[tex]\frac{3}{2}[/tex] liters used in half:
[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.
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