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3 years ago

The proof shows that ABCD is a rectangle. Which of the following is the missing reason?

Mathematics

1 answer:

patriot [66]3 years ago

4 0

Answer:

Side-side-side postulate

Step-by-step explanation:

In the first statement, we are given that AC = BD ....... (1){It is given}

Now, in the second statement, we are given that AB = DC ...... (2){ Because the parallelogram has equal opposite sides}

Now, again we are given that AD = DA ........... (3) {From the symmetric property}

Now, conditions (1), (2), and (3) are applicable to say that Δ ABD and Δ ACD are congruent.

Since there are three sides involved to say Δ ABD ≅ Δ ACD, so it is by Side-side-side postulate. (Answer)

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Question 12

soldi70 [24.7K]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The tank for a car holds 17 gallons. The gasoline gauge shows the tank is 3/4 full. How much gas is still in the tank?

Give your answer as a whole number or as a mixed fraction reduced to lowest terms.

Answer:

$Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\$

Step-by-step explanation:

The tank for a car holds 17 gallons.

The gasoline gauge of the car shows that the tank is 3/4 full.

We are asked to find the remaining gasoline in the tank.

$Gas \: \:left = \frac{3}{4} \times 17 \\\\Gas \: \:left = \frac{51}{4} \\\\Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\$

Therefore, the remaining gas in the tank is $12\frac{3}{4}$ gallons.

Alternatively:

$1 - \frac{3}{4} = \frac{1}{4}$

Amount of gasoline consumed = $\frac{1}{4} \times 17 = \frac{17}{4}$

Amount of gasoline left = total - consumed

Amount of gasoline left = $17 - \frac{17}{4} = 12\frac{3}{4} \:\: gallons$

6 0

3 years ago

(c^3b^1a^4)^4 + 3a^16b^4c^12

azamat

Answer: 4a16b4c12

Step-by-step explanation:

5 0

3 years ago

Carmen is writing an article for a magazine. She will be paid a fee and also will be paid for each word that is published. The t

enot [183]

Answer:

The inverse function of f(x)=2.5*x+150 is f⁻¹(x)= $\frac{2}{5}x-60$

Step-by-step explanation:

An inverse or reciprocal function of f (x) is called another function f ⁻¹(x) that fulfills that:

If f(a)=b then f⁻¹(b)=a

That is, inverse functions are functions that do the "opposite" of each other. For example, if the function f (x) converts a to b, then the inverse must convert b to a.

To construct or calculate the inverse function of any function, you must follow the steps below:

Since f (x) or y is a function that depends on x, the variable x is solved as a function of the variable y. And since inverse functions swap the input and output values (that is, if f (x) = y then f⁻¹(y) = x), then the variables are swapped and write the inverse as a function.

You know that he function f(x) = 2.5*x + 150 or y=2.5*x +150

Solving for x:

2.5*x +150=y

2.5*x= y-150

$x=\frac{y-150}{2.5}$