Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula:
Apply the : congruent (corresponding alternate exterior and alternate interior angles) and supplementary (consecutive interior angles) theorems
step-by-step explanation:
The property to apply here is : congruent (corresponding alternate exterior and alternate interior angles) and supplementary (consecutive interior angles)
1.h = 180°-120°=60°=e=d=a
f=120° = c=b
2.b=180°-105°=75°=c=f=g
a=105°=e=h
3. f=180°-36°=144°=g=c=b
a=36°=d=h
4. a=180°-161°=19°=e=h=d
c=161°=f=g
5. f=180°-145°=35°=g=c=b
a=145°=d=h
6. b=180°-25°=155°=c=f=g
25°=d=e=h
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Angles :brainly.com/question/13209798
Keywords: parallel lines, intersect, transversal, angle
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8b - 32
Hope it’s right
Best luck with your studying
Answer:
(3,-3)
y= -3
x= 3
Step-by-step explanation:
5x+2y=9
2x-3y=15
solve the equation
x=9/5-2/5y
2x-3y=15
substitute the value of x into an equation
2(9/5-2/5y)-3y=15
distribute
18/5-4/5y-3y=15
subtract -4/5 to -3
18/5-19/5y=15
subtract 18/5 from both sides
-19/5=57/5
divide both sides by -19/5
y= -3
substitute the value of y into an equation
x=9/5-2/5(-3)
distribute
x=9/5+6/5
add 9/5 to 6/5
x=3
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(3,-3)
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The gemstone has 22 edges.
We use Euler's formula on this:
F + V - E = 2
Substituting our information, we have:
14 + 10 - E = 2
Combining like terms,
24 - E = 2
Subtract 24 from both sides:
24 - E - 24 = 2 - 24
-E = -22
Divide both sides by -1:
-E/-1 = -22/-1
E = 22
