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andreyandreev [35.5K]
2 years ago
12

Rachel multiplied each side of x ≥ 2 by 3. She wrote the result as 3x ≤ 6. Explain the error Rachel made.

Mathematics
1 answer:
andrey2020 [161]2 years ago
6 0

Answer:

Her mistake was to change the inequality sign from ≥ to ≤.

The sign only changes when you multiply or divide both sides of an inequality by a negative number.

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What is the common difference in arithmetic sequence 10,8,6,4...? <br> 2<br> -2<br> 1/2<br> -1/2
Aleks04 [339]
10 - 8 = -2
  8 - 6 = -2
etc, so -2 is the common difference
5 0
3 years ago
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Prove: Quadrilateral ABCD is a parallelogram.
Brilliant_brown [7]

Answer:

Step 3.

m∠ AEB = m∠ CED .........By  Vertical Angles Theorem.

Step-by-step explanation:

Vertical Angles Theorem:

Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines,are congruent.

If two lines intersect each other we have two pair of vertical opposite angles. As shown in the figure.

Here,

∠ 1 and ∠ 2 are vertical opposite angles and also they are equal.

∠ 3 and ∠ 4 are also vertical opposite angles and also they are equal.

For,

step 3. m∠ AEB = m∠ CED

Therefore, the reason for step 3 of this proof is Vertical Angles Theorem.

6 0
3 years ago
Anais bought yards of ribbon. she had feet inches of ribbon left after trimming some curtains. how many inches of ribbon did ana
castortr0y [4]

<u>Anais bought </u><u>2 1/2 yards</u><u> of ribbon. She had </u><u>2 feet 8 inches</u><u> of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.</u>

What is Unit Conversion?

  • Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion.
  • The units are expressed using scientific notation and converted into numerical values as per the quantities.

Anais bought 2 1/2 yards of ribbon.

And she had 2 feet 8 inches left after trimming some curtains.

The first thing to do is to convert all units to inches;

From standard conversion rate.

1 yard  = 36 inches

As such  2 1/2 yards of ribbon in inches will be:

= 2 1/2 × 36 inches

= 5/2 × 36 inches

= 5 × 18 inches

= 90 inches of ribbon bought.

Similarly, since 1 foot  = 12 inches.

The amount of curtains left after trimming is:

= ( ( 2 × 12 ) + 8 )inches

= (24 + 8) inches

= 32 inches

If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.

It implies that the number of inches of ribbon that Anais used is:

= 90 inches - 32 inches

= 58 inches

Therefore, we can conclude that Anais used 58 inches of ribbon.

Learn more about  Unit Conversion

brainly.com/question/2495501

#SPJ4

<u>The complete question is-</u>

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Anais used _____ inches of ribbon.

6 0
1 year ago
5/7 = x/11 round your answer to the nearest tenth.
Scilla [17]

Answer:

7.9

Step-by-step explanation:

Multiply both sides of the equation by 11. This cancels out the fraction so 11 * 5/7 = x

lmk if I misunderstood the question or need to elaborate

6 0
3 years ago
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You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you fo
taurus [48]

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

  • Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

  1. 1+2+4+8+16+32+64+128+256+489=1000
  2. Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
  3. If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since x-489\leq511, by 2) we know that this would be possible.

4 0
3 years ago
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