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2 years ago

Match the reasons with the statement.

Mathematics

2 answers:

LuckyWell [14K]2 years ago

7 0

Answer: 1. 12 - x = 20 - 5 x

given

2. 12 + 4 x = 20

Division property of equality

3. 4 x = 8

Subtraction property of equality

4. x = 2

Addition property of equality

Firlakuza [10]2 years ago

3 0

To prove that x = 2 in the equation given, first, we write the given.
(4) Given: (A) 12 - x = 20 - 5x
Then, add 5x to both sides of the equation,
(3) Addition property of equality: (B) 12 + 4x = 20
Then, subtract 12 from both sides of the equation
(2) Subtraction property of equality: (C) 4x = 8
Lastly, divide both sides by 4
(1) Division property of equality : (D) x = 2

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A store sells three types of note cards. There are three sizes of each type. Show two ways to find the total number of notecards

bonufazy [111]

Answer: There are 9 different types of note cards that the store sells.

We can use the Fundamental Counting Principle to determine the total number of options.

There are two different events in this problem. First, there are 3 kinds of cards. Second, there are 3 sizes for each kind.

Simply, multiply the 3 by the other 3 and you have 9 different options.

Just think, each card would have a small, medium and larger option. So there are 3 groups of 3 or 9 total options.

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3 years ago

If the blue radius below is perpendicular to the green chord and the segment BC is 7.6 units long, what is the length of the cho

galina1969 [7]

Answer:

The correct answer is A. 15.2 units

Step-by-step explanation:

The segment AB is congruent to the segment BC eg AB≅BC Why?

We can prove it with the triangle congruent theorem, postulate side-side-angle

We are watching triangle ΔABO and triangle ΔCBO, they are congruent

first element side OB=OB - common side

second element side OA=OC=r - radius of the circle

third element angle ∡ABO≅∡CBO=90°

According to the postulate side-side-angle we can conclude that triangles

ΔABO≅ΔCBO (triangles are congruent)

If they are congruent all of their elements are also congruent and therefore also

side AB=BC => AB+BC=AC, which is chord => 7.6+7.6=15.2 units

AC= 15.2 units ( chord )

Good luck!!!

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3 years ago

Starlight tree farms sells douglas firs and noble first one December they sold 139 more douglas first than noble firs the total

Aloiza [94]

Part A:

Given that Starlight tree farms sells Douglas Firs and Noble First.

Let n be the number of Noble Fir trees sold, then if they sold 139 more Douglas First than Noble Firs, this means that the number of Douglas First trees sold is n + 139.

Given that the total number of trees sold was 377, then we have, n + n + 139 = 377, which means that 2n + 139 = 377

Therefore, the equation that could be used to solve for n, the number of Noble Fir trees sold is 2n + 139 = 377.

Part B:

Given that you are driving 55 miles per hour and you must drive a total of 440 miles. If you already driven 275 miles, then, the equation representing the number of hours, h, it will take to reach your destination is given by 55h + 275 = 440.

Subtracting 275 from both sides of the equation gives:

 $55h+275-275=440-275 \\ \\ \Rightarrow55h=165$

Dividing both sides by 55 gives:

 $\frac{55h}{55} = \frac{165}{55} \\ \\ \Rightarrow h=3$

Therefore, the time it will take you to reach your destination is 3 hours.

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