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9 days ago

In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF.

Mathematics

2 answers:

Inessa [3.9K]9 days ago

5 0

Answer:

The answer is option c.

Step-by-step explanation:

CD = EF -----> as given

CD + DE = EF + DE -----> adding DE to both sides

CE = CD + DE

DF = EF + DE

Consequently, CE = DF -----> due to the transitive property of equality, given that CD + DE = EF + DE

Since CE = DF and AB = CE (as given), it follows that AB = DF.

Svet_ta [4.3K]9 days ago

3 0

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Given: CD = EF and AB = CE

To Show: AB = DF

Following the steps outlined:

1. CD + DE = EF + DE by the (addition) Property of Equality.

This shows that the same value has been added to both sides of the equation.

2. CE = CD + DE and DF = EF + DE through (segment addition).

This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.

3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.

So, CE = EF + ED = FD (via substitution) Property of Equality.

4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.

This follows the rule that if x = y and y = z, then x = z.

Answer: 4

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Displayed Work:

$(g \circ h)(x) = g(h(x))$

$g(x) = x^2\\\\g(h(x)) = (h(x))^2 \ \text{replace every x with h(x)}\\\\g(h(x)) = (x-7)^2 \ \text{replace h(x) with x-7}\\\\(g \circ h)(x) = (x-7)^2$

Now substitute x = 5

$(g \circ h)(x) = (x-7)^2 \\\\(g \circ h)(5) = (5-7)^2 \\\\(g \circ h)(5) = (-2)^2\\\\ (g \circ h)(5) = 4$

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Alternative approach:

h(x) = x-7

h(5) = 5-7

h(5) = -2

Thus

g(h(5)) = g(-2)

and

g(x) = x^2

g(-2) = (-2)^2

g(-2) = 4

Thus giving

$g(-2) = g(h(5)) = (g \circ h)(5) = 4$

8 0

16 days ago

Read 2 more answers

What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?

tester [3916]

We have to calculate the result of the division problem.

$\frac{x^{3}-3x^{2}+3x-2}{x^{2}-x+1}$

To determine the result, long division will be employed.

$x^{2}-x+1$ ) $x^{3}-3x^{2}+3x-2$

Initially, we quotient with x since $x^{2}$ fits into $x^{3}$ , x times.

Thus, we have:

$x^{2}-x+1$ ) $x^{3}-3x^{2}+3x-2$ (x

$\text{..................}x^{3}-x^{2}+x$

After subtraction, we obtain:

$\text{....................}-2x^{2}+2x-2$

We can see that $x^{2}$ fits into $-2x^{2}$ , -2 times; therefore, the next addition to the quotient will be -2. This results in a final quotient of (x-2).