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xenn [34]
3 years ago
10

Liam uses 2 quarts of yellow paint and adds 3 1/4 Jars of blue paint.Evan uses 1/2 quarts of yellow paint and adds 5 1/2 of red

paint.They end up with the same volume of paint.write an equation to show it.
Mathematics
1 answer:
EleoNora [17]3 years ago
7 0

Answer:

2 + (13/4)x = 1/2 + (11/2)y

Step-by-step explanation:

Let each jar of paint used by Liam be x

Let each jar of paint used by Evan be y.

Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have

2 + 3 1/4x

= 2 + (13/4)x

Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have

1/2 + 5 1/2y

= 1/2 + (11/2)y

Since they end up with the same volume of paint, we have

2 + (13/4)x = 1/2 + (11/2)y

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4 0
3 years ago
Find the distance between the two points rounding to the nearest tenth (if necessary).
QveST [7]

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

  • Distance: In Mathematics, physics or daily life, distance is a numerical or occasionally qualitative measurement of how far objects or points are from each other.
  • Coordinates: In geometry, coordinates are a pair of numbers that can uniquely determine the position of points or other geometric elements on a Euclidean or Cartesian Plane.

To learn more about Distances and Coordinates, click on the link below.

brainly.com/question/14364020

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5 0
1 year ago
4. will give brainliest
saul85 [17]

The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>

By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

  • a - Length of the major semiaxis.
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Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

To learn more on ellipses: brainly.com/question/14281133

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