What constitutes a function
1 answer:
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Answer:
They are similar by the definition of similarity in terms of a dilation
Step-by-step explanation:
The given vertices of triangle ΔABC are;
A(1, 5), B(3, 9), and C(5, 3)
The vertices of triangle ΔDEF are;
D(-3, 3), E(-2, 5), and F(-1, 2)
Therefore, we get;
The length of segment, = √((9 - 5)² + (3 - 1)²) = 2·√5
The length of segment, = √((9 - 3)² + (3 - 5)²) = 2·√10
The length of segment, = √((5 - 3)² + (1 - 5)²) = 2·√5
The length of segment, = √((5 - 3)² + (-2 - (-3))²) = √5
The length of segment, = √((2 - 5)² + (-1 - (-2))²) = √10
The length of segment, = √((2 - 3)² + (-1 - (-3))²) = √5
∴ /
= 2·√5/(√5) = 2
/
= 2·√10/(√10) = 2
/
= 2·√5/(√5) = 2
The ratio of their corresponding sides are equal and therefore;
ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.
The amount of gas consumed by first and second car were 20 gallons and 15 gallons respectively.
<em><u>Explanation</u></em>
Suppose, gallons of gas were consumed by the first car.
As the total gas consumption in one week is 35 gallons, so the amount of gas consumed by second car will be: gallons.
The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas.
So, the <u>distance traveled by the first car</u> in gallons of gas
miles and the <u>distance traveled by the second car</u> in
gallons of gas
miles.
Given that, the two cars went a <u>combined total of 925 miles</u>. So, the equation will be.....
So, the amount of gas consumed by the first car is 20 gallons and the amount of gas consumed by the second car is: (35 - 20) = 15 gallons.