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3 years ago

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Select the correct answer. Given: AD = CF BC = DE Prove: AB = EF Statement Reason 1. AD = CF given 2. AD = AB + BC + CD CF = CD

+ DE + EF segment addition 3. AB + BC + CD = CD + DE + EF Transitive Property of Equality 4. AB + BC = DE + EF 5. BC = DE given 6. AB = EF Subtraction Property of Equality What is the reason for the fourth statement in this proof? A. definition of collinear points B. segment addition C. Subtraction Property of Equality D. Substitution Property of Equality

2 answers:

madreJ [45]3 years ago

8 0

Answer:

Step-by-step explanation: The answer is D- Substitution Property of Equality. I just did the test and it was right.

shutvik [7]3 years ago

7 0

Answer:

C. Subtraction property of equality.

Step-by-step explanation:

Given AD= CF

And BC=DE

To prove that AB=EF

Proof:

1.Statement: AD=CF

Reason: Given in question.

2. Statement: AD= AB+BC+ CD, CF= CD+DE+EF

Reason: Segment addition property because AB,BC,and CD are the segments of AB and CD,DE and DE are segments of CF.

3. Statement: AB+BC+CD=CD+DE+EF

Reason: Transitive property of equality

Transitive property: If ab=bc and bc=ca

Then , ab=ca

4.Statement: AB+BC= DE+EF

Reason: By using subtraction property of equality.

5. Statement:BC=DE

Reason: Given in question.

6. Statement: AB=EF

Reason: when we put BC=DE . Then we get AB+DE=DE+EF. By using subtraction property of equality .

Hence proved .

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One week Beth bought 3 apples and 8 pears for $14.50. The next week she bought 6 apples and 4 pears and paid $14. Find the cost

zalisa [80]

Let us assume the cost of 1 apple = x dollars
Let us also assume the cost of 1 pear = y dollars
Then we can form two equations from the details given in the question. Based on those details the required answer to the question can be easily deduced.
3x + 8y = 14.50
And
6x + 4y = 14
Dividing both sides of the equation by 2 we get
3x + 2y = 7
2y = 7 - 3x
y = (7 - 3x)/2
Putting the value of y from the second equation in the first equation we get
3x + 8y = 14.50
3x + 8[(7 - 3x)/2] = 14.50
3x + 4 (7 - 3x) = 14.50
3x + 28 - 12x = 14.50
- 9x = 14.50 - 28
- 9x = - 13.5
9x = 13.5
x = 13.5/9
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Putting the value of x in the second equation we get
6x + 4y = 14
(6 * 1.5) + 4y = 14
9 + 4y = 14
4y = 14 - 9
4y = 5
y = 5/4
   = 1.25
So we can find from the above deduction that the cost of 1 apple is 1.5 dollars and the cost of 1 pear is 1.25 dollars
Then
Cost of 2 apples = 2 * 1.5 dollars
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Answer:

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Step-by-step explanation:

An inequality is used to compare two values, showing that one value smaller than, larger than, or not equal to another value. x ≠ y means that x is not equal to y. x < y means that x is less than y and x > y means that x is greater than y.

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Vedmedyk [2.9K]

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Step-by-step explanation:

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A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t

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Answer:

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Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

$\frac{dP}{dt} =4.058e^{1.6t}$

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Where k is a constant of Integration.

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Therefore:

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