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4 years ago

Write ratio as a fraction in simplest form. 24L to 56L

1 answer:

7 0

we would add the number up and that equals 80. so after you have 80, you put the numerators on top and simplify the fraction out. i simplified it and got

3/10

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Which of the following does NOT represent a function?

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3 years ago

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Brainliest will be given to the correct answer!

IrinaK [193]

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for $b_{1}$ . $b_{1} = \frac{2\cdot A}{h}-b_{2}$

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . $b = \frac{A}{h}$

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

$A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})$ (Eq. 1)

Where:

$h$ - Height of the trapezoid, measured in centimeters.

$b_{1}$ , $b_{2}$ - Lengths fo the bases, measured in centimeters.

$A$ - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}]$ Compatibility with multiplication/Commutative and associative properties.

4) $h = \frac{2\cdot A}{b_{1}+b_{2}}$ Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that $A = 91\,cm^{2}$ , $b_{1} = 16\,cm$ and $b_{2} = 12\,cm$ , then height of the trapezoid is:

$h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}$

$h = 6.5\,cm$

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for $b_{1}$ :

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})$ Compatibility with multiplication/Commutative and associative properties.

4) $2\cdot A \cdot h^{-1} = b_{1}+b_{2}$ Existence of multiplicative inverse/Modulative property

5) $\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}$ Definition of division/Compatibility with addition/Commutative and associative properties

6) $b_{1} = \frac{2\cdot A}{h}-b_{2}$ Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for $b_{1}$ .

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ( $A= 215\,cm^{2}$ , $h = 8.6\,cm$ and $b_{2} = 30\,cm$ )

$b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm$

$b_{1} = 20\,cm$

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . Now we present the procedure to clear $b$ below:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $b_{1} = b_{2}$ Given.