In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

NEED HELP I need to fill in the highlighted parts

Gemiola [76]

The statements and reasons why the given statements are true are presented in the following two column proofs;

Question 1

Given: 9·(x + 6) - 41 = 75

$Prove \ x = \dfrac{62}{9}$

Statement ${}$ Reason

S1. 9·(x + 6) - 41 = 75 ${}$ R1. Given

S2. 9·(x + 6) = 116 ${}$ R2. Addition property

S3. 9·x + 54 = 116 ${}$ R3. Distributive property

S4. 9·x = 62 ${}$ R4. Subtraction property

S5. $x = \dfrac{62}{9}$ ${}$ R5. Division property of equality

Question 2.

Statement ${}$ Reason

S1. m∠A + m∠B = m∠D ${}$ R1. Given

S2. ∠C and ∠D form a Linear Pair ${}$ R2. Definition of linear pair

S3. ∠C and ∠D are supplementary ${}$ R3. Linear pair ∠s are supplementary

S4. ∠C + ∠D = 180° ${}$ R4. Definition of supplementary

S5. m∠C + m∠A + m∠B = 180° ${}$ R5. Substitution property

Question 3.

Statement ${}$ Reason

S1. ∠BDA ≅ ∠A ${}$ R1. Given

S2. ∠BDA ≅ ∠CDE ${}$ R2. Vertical angle theorem

S3. ∠CDE ≅ ∠A ${}$ R3. Transitive property of congruency

S4. m∠CDE = m∠A ${}$ R4. Definition of congruency

S5. (13·x + 20)° = (14·x + 15)° ${}$ R5. Substitution Property of Equality

S6. 14·x° = 13·x + 5° ${}$ R6. Subtraction property

S7. x = 5 ${}$ R7. Subtraction property

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6 0

2 years ago

Find the inverse of f(x)=1/(x^3)

Pepsi [2]

Answer:

Step-by-step explanation:

y $f(x)^{-1} = inverse\\f(x)=y \\y = 1/(x^{3} \\Inverse: y=x ------------> x = 1/y^{3}\\y^{3} - \frac{1}{x} = 0\\y^{3} = \frac{1}{x}\\y = \sqrt[3]{\frac{1}{x}} \\y = \frac{\sqrt[3]{1} }{\sqrt[3]{x}} \\y = \frac{1}{\sqrt[3]{x}}$

4 0

2 years ago

Explain why 2a+3b=5ab

Ahat [919]

That's not correct. The terms 2a and 3b are not like terms, so we cannot combine them to get 5ab. We simply leave it as 2a+3b.

If you had 2a+3a, then it would simplify to 5a

Similarly, 2b+3b = 5b

Or you could have 2ab+3ab = 5ab

The key is that the variable portions must match up to be able to add them.

8 0

3 years ago

Read 2 more answers

Joan Messineo borrowed $47,000 at a 5% annual rate of interest to be repaid over 3 years. The loan is amortized into three eq

tester [92]

Answer:

a) The value of the Annual Payment is A=$17,258.80

b) Is the picture in the attachment file

c) As you can see it in the picture with each payment, balance comes down, due it is the interest base, Interest portion comes down too.

Step-by-step explanation:

Hi

a) First of all, we are going to list the Knowns: $VP=47000$ , $i=5$ % and $n=3$ , Then we can use $A=\frac{VP}{\frac{1-(1+i)^{-n} }{i} } =\frac{47000}{\frac{1-(1+0.05)^{-3} }{0.03} }=17258.80$ . So this is the value of the Annual Payment