The area of the composite figure = area of square + area of triangle + area of rectangle = 58.5 ft²
<h3>What is the Area of the Composite Figure?</h3>
Area of the composite figure = area of square + area of triangle + area of rectangle = s² + 1/2(bh) + lw
Given the following:
- s = 3 ft
- b = 11 ft
- h = 3 ft
- l = 11 ft
- w = 3 ft
Area of the composite figure = (3²) + 1/2(11)(3) + (11)(3)
Area of the composite figure = 58.5 ft²
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A dependent variable is a value that depends on how the other variables are controlled or manipulated.
Meanwhile, an independent variable, is as what its name suggests, is independent and doesn't change based on the value of other variables.
a.) The dependent variable is the number of glitter markers
b.) The independent variable is the number of gift bags
c.) The number of glitter markers Teresa needs to buy depends on the number of gift bags she has. She has to multiply
d.) The relationship is additive. The more gift bags Teresa has, the more glitter markers she has to buy.
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Answer:
210 cm³
Step-by-step explanation:
RULE :
the volume of the triangular prism = the area of the base × the height
= 14 × 15
= 210
Answer: 1.375
Step-by-step explanation:
Im not good at it, but this may be right?
