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uranmaximum [27]
3 years ago
6

Are the expressions 3/4a + 8 - 1/4a - 2 and 1/2(a + 12) equivalent? Show why or why not.

Mathematics
1 answer:
natta225 [31]3 years ago
4 0

Answer:Yes they are equivalent.

Step-by-step explanation:

3/4a + 8 - 1/4a - 2 1/2(a + 12)

Combine like terms Distributive property

2/4a+6 1/2a+6

2/4=1/2 (simplify)

1/2+6=1/2+6

You might be interested in
If m∠JKM = 43, m∠MKL = (8 - 20), and m∠JKL = (10x - 11), find each measure.
Brut [27]

Correct Question: If m∠JKM = 43, m∠MKL = (8x - 20), and m∠JKL = (10x - 11), find each measure.

1. x = ?

2. m∠MKL = ?

3. m∠JKL = ?

Answer/Step-by-step explanation:

Given:

m<JKM = 43,

m<MKL = (8x - 20),

m<JKL = (10x - 11).

Required:

1. Value of x

2. m<MKL

3. m<JKL

Solution:

1. Value of x:

m<JKL = m<MKL + m<JKM (angle addition postulate)

Therefore:

(10x - 11) = (8x - 20) + 43

Solve for x

10x - 11 = 8x - 20 + 43

10x - 11 = 8x + 23

Subtract 8x from both sides

10x - 11 - 8x = 8x + 23 - 8x

2x - 11 = 23

Add 11 to both sides

2x - 11 + 11 = 23 + 11

2x = 34

Divide both sides by 2

\frac{2x}{2} = \frac{34}{2}

x = 17

2. m<MKL = 8x - 20

Plug in the value of x

m<MKL = 8(17) - 20 = 136 - 20 = 116°

3. m<JKL = 10x - 11

m<JKL = 10(17) - 11 = 170 - 11 = 159°

3 0
2 years ago
Anton will be constructing a segment bisector with a compass and straightedge, while Maxim will be constructing an angle bisecto
elena-14-01-66 [18.8K]

A bisector is a line that divides either a line or an angle into <em>two</em><em> proportionate</em> parts or angles. Thus, Anton's <em>bisector</em> would divide the segment into two <u>equal parts</u>, while Maxim's <em>bisector</em> would divide the angle into two <u>equal angles</u>.

The <u>similarities</u> between their construction are:

  • <em>Intersecting</em> arcs through which the bisector would pass are required.
  • The arcs are dawn using <em>the same</em> radius of any measure.
  • The <em>edges</em> of the arc of the given angle, and the ends of the segment are used as <em>centers</em>.

The <u>differences</u> between their construction are:

  • Anton has to draw two intersecting arcs <u>above</u> and <u>below</u> the segment. While Maxim would draw two intersecting arcs <u>within</u> the lines forming the angles.
  • Anton's bisector would be <em>perpendicular</em> to the segment, while Maxim's bisector would be at <em>an angle</em> which is half of the initial angle.

Visit: brainly.com/question/17247176

3 0
2 years ago
Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)
Lisa [10]

Answer:

f(x) = 4x^2 - 3x + 6

Step-by-step explanation:

Quadratic function is given as f(x) = ax^2 + bx + c

Let's find a, b and c:

Substituting (0, 6):

6 = a(0)^2 + b(0) + c

6 = 0 + 0 + c

c = 6

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

f(x) = ax^2 + bx + c

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

16 - 6 = 4a + 2b + 6 - 6

10 = 4a + 2b

10 = 2(2a + b)

\frac{10}{2} = \frac{2(2a + b)}{2}

5 = 2a + b

2a + b = 5 => (Equation 1)

Substituting (3, 33), and c = 6

f(x) = ax^2 + bx + x

33 = a(3)^2 + b(3) + 6

33 = 9a + 3b + 6

33 - 6 = 9a + 3b + 6 - 6

27 = 9a + 3b

27 = 3(3a + b)

\frac{27}{3} = \frac{3(3a + b)}{3}

9 = 3a + b

3a + b = 9 => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

3a + b = 9

2a + b = 5

a = 4

Replace a with 4 in equation 2.

2a + b = 5

2(4) + b = 5

8 + b = 5

8 + b - 8 = 5 - 8

b = -3

The quadratic function that represents the given 3 points would be as follows:

f(x) = ax^2 + bx + c

f(x) = (4)x^2 + (-3)x + 6

f(x) = 4x^2 - 3x + 6

6 0
3 years ago
100,203 in expanded form
Paul [167]

Answer:

100,000 + 200 + 3

Step-by-step explanation:

5 0
3 years ago
What percent of 80 is 12?<br><br>what number is 75% of 52? ​
HACTEHA [7]

Answer:

<em>The answer for the first question is: </em>

<em>12/80 =</em>

<em>12 ÷ 80 =</em>

<em>0.15 =</em>

<em>0.15 × 100/100 =</em>

<em>0.15 × 100% =</em>

<em>(0.15 × 100)% =</em>

<h2><em>15%</em></h2>

<em>Then, the answer for the second question is: </em>

<em>75% × 52 =</em>

<em>(75 ÷ 100) × 52 =</em>

<em>(75 × 52) ÷ 100 =</em>

<em>3,900 ÷ 100 =</em>

<h2><em>39 </em></h2>

* Hopefully this helps:) Mark me the brainliest:)!!!

5 0
3 years ago
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