Answer:
Step-by-step explanation:
The sum of the angles on a straight line is 180 degrees. Therefore,
Angle XYZ + angle MYZ = 180
Angle XYZ + 115 = 180
Angle XYZ = 180 - 115 = 65 degrees
The sum of the angles in a triangle is 180 degrees. It means that
Angle XZY + angle YXZ + angle MYZ = 180
Therefore,
4k + 5 + 6k + 10 + 65 = 180
4k + 6k + 5 + 10 + 65 = 180
10k + 80 = 180
10k = 180 - 80 = 100
Dividing the left hand side and the right hand side of the equation by 10, it becomes
10k/10 = 100/10
k = 10
If Fabio drinks 2 quarts of water each day, he would drink 8 cups of water in accordance with direct proportion.
<h3>What is a proportion?</h3>
A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented by the following equation:
y = kx
Where:
- y and x are the variables.
- k represents the constant of proportionality.
By applying direct proportion, we have:
1 quarts = 4 cups
2 quarts = X cups
Cross-multiplying, we have:
X = 4 × 2
X = 8 cups.
In conclusion, the quantity of water which Fabio drinks each day is equal to 8 cups.
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The width of the card to the nearest tenth of an inch is 6.15 inches
<h3>Area of rectangle</h3>
- Width = x
- Length = 2x + 1
- Area = 88 square inches
Area of a rectangle = Length × Width
88 = (2x + 2) × x
88 = 2x² + 2x
2x² + 2x - 88 = 0
x = -b ± √b² - 4ac / 2a
= -2 ± √2² - 4(2)(-88) / 2(2)
= -2 ± √4 - (-704) / 4
= -2 ± √708 / 4
= -1/2 ± √177/2
x = 6.15 or -7.15 inches
The width of the rectangle can not be negative, so, 6.15 inches is the width.
Learn more about rectangle:
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3/4 feet
You can set this up as an equation and solve

Answer:
<h2>

</h2>
Step-by-step explanation:
32base x means 
Similarly, 32base x+51base y equals to 
and 23base x +42 base y means 
As per the given condition, 
Putting,
in
, we get

