Which equation represents the situation: The number s of students in the classroom increased by 2 equals 20?

In a word processing document or on a separate piece of paper, use the guide to construct a two-column proof proving AC > EF

VARVARA [1.3K]

<em>Answer:</em>

Complete proof is written below.

Facts and explanation about the segments shown in question :

As BC = EF is a given statement in the question
AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.

Below is the complete proof of the observation given in the question:

<em />

<em>STATEMENT REASON </em>

___________________________________________________

1. BC = EF 1. Given

2. AB + BC = AC 2. Betweenness

3. AC > BC 3. Def. of segment inequality

4. AC > EF 4. Def. of congruent segments

<em />

<em>Keywords: statement, length, reason, proof</em>

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4 0

3 years ago

How many solutions does the<br> equation have?<br> 3(7/3 + 4/3) - 2x + 8 = 5x + 12

Finger [1]

Answer: It only has one solution.

Step-by-step explanation:

Let's solve your equation step-by-step.

3( 7 /3 + 4 /3 )−2x+8=5x+12

Step 1: Simplify both sides of the equation.

3( 7 /3 + 4 /3 )−2x+8=5x+12

11+−2x+8=5x+12

(−2x)+(11+8)=5x+12(Combine Like Terms)

−2x+19=5x+12

Step 2: Subtract 5x from both sides.

−2x+19−5x=5x+12−5x

−7x+19=12

Step 3: Subtract 19 from both sides.

−7x+19−19=12−19

−7x=−7

Step 4: Divide both sides by -7.

−7x /−7 = −7 /−7

x=1

Answer:

x=1

4 0

3 years ago

Write the equation that is the translation of y = |x| right 7 units and down 9 units.

weqwewe [10]

Y=|x-7|-9 because up seven and down nine

3 0

4 years ago

Read 2 more answers

I’m so confused on what numbers l should put into the boxes

Serggg [28]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.

<h3>What is the equation of a line?</h3>

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The lines for the given statements can be plotted as shown below.

The coordinate grid can be filled as,

1)

x 0 3 1

y 3 0 2

2.)

x 0 1 -1

y 1 0 2

3.)

x 0 4 -1

y -2 0 2

4.)

x 0 1 1

y -2 0 -2

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3 0

2 years ago

tim has 74 socks, that are white or black. he has 1 more pair of white socks than black socks. how many individual socks of each

MAXImum [283]

Tim owns 74 socks, the colours of which are unknown.

He does, however, have an additional pair that is white rather than black.

Therefore, it suggests that we are working with the two hues white and black.

The result of dividing the total number of socks by two is:

= 74/2

= 37 socks, two pairs each for black and white.

But let's not forget that Tim has a pair of white socks in addition to his black pair.

The total number of white socks is equal to= 37+1= 38 socks.

Total black sock pairs= 37-1=36 socks.

Last but not least, the question asks us to count the number of single socks rather than pairs.

For white then:

There will be = (38x 2) socks per pair.

= 76 socks

For Black

The individual socks will be = (36 × 2)socks

= 72 socks

We can then deduce that there are 76 individual socks for white and 72 individual socks for black.

<h3>How many pairs of socks must you take to find a matching pair?</h3>

The solution would have to be four. Despite the large number of socks in the drawer, there are only three different colours, so if you take four socks, you will undoubtedly find at least one pair that matches.

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4 0

1 year ago