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STatiana [176]
3 years ago
10

Which expression is equivalent to 7a2b + 10a2b2 + 14a2b3?

Mathematics
2 answers:
Ugo [173]3 years ago
4 0
The given expression can be simplified in many ways by grouping like terms. The simplest form is obtained by factoring out a²b which gives us the following expression.

a²b(7 + 10b +14b²)
igomit [66]3 years ago
4 0

Answer:

a^2b(7 + 10b + 14b^2)

Step-by-step explanation:

Given : 7a^2b + 10a^2b^2 + 14a^2b^3

To Find: Which expression is equivalent to 7a^2b + 10a^2b^2 + 14a^2b^3

Solution:

7a^2b + 10a^2b^2 + 14a^2b^3

Take a^2 as common

a^2(7b + 10b^2 + 14b^3)

Now take b as common

a^2b(7 + 10b + 14b^2)

Hence a^2b(7 + 10b + 14b^2) is  equivalent to 7a^2b + 10a^2b^2 + 14a^2b^3

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8. In quadrilateral ABCD, AD is congruent to BC, and AD is parallel to BC. Andre has written a proof to show that ABCD is a para
luda_lava [24]

The correct choices to fill the blanks are listed below:

  1. AD
  2. BC
  3. AC
  4. CBA
  5. angle BAC
  6. CD

<h3>How to prove that a quadrilateral is a parallelogram</h3>

In this question we should fill the blanks based all information related to Euclidean geometry, especially concepts related to angles, triangles, parallelism and quadrilaterals.

The complete paragraph is shown below:

<em>Since </em><u><em>AD</em></u><em> is parallel to </em><u><em>BC</em></u><em>, alternate interior angles. </em>

<u><em>AD</em></u><em> and </em><u><em>BC</em></u><em> are congruent. </em>

<em>AC is congruent to </em><u><em>AC</em></u><em> since segments are congruent to themselves.</em>

<em>Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle </em><u><em>CBA</em></u><em> by the Side-Angle-Side Triangle Congruence. </em>

<em>Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to </em><u><em>angle BAC</em></u><em>.</em>

<em>Since those alternate interior angles are congruent. AB must be parallel to </em><u><em>CD</em></u><em>. </em>

<em>Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.</em>

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/25240753

8 0
2 years ago
g In 2013, the Pew Research Foundation reported that 43% of U.S. adults report that they live with one or more chronic condition
SOVA2 [1]

Answer:

We are 95% confident that the true proportion of U.S. adults who live with one or more chronic conditions is between 39.7% and 46.33%

Step-by-step explanation:

From the question we are told that

  The  sample  proportion is \r p = 43\%  = 0.43

   The  standard error is SE =  0.017

Given that the confidence level is 95%  then the level of significance is mathematically represented as  

      \alpha =  (100-95)\%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as

     E = Z_{\frac{\alpha }{2} } *  SE

=>    E = 1.96 *  0.017

=>     E = 0.03332

Generally 95% confidence interval is mathematically represented as

      \r p -E <  p <  \r p +E

=>   0.43 -0.03332 <  p <  0.43 + 0.03332

=>    0.39668 <  p <  0.46332

Converting to percentage

(0.39668 * 100)<  p <  (0.46332*100)        

39.7\% <  p < 46.33 \%    

7 0
3 years ago
Alejandro loves to go to the movies. He goes both at night and during the day. The cost of a matinee is 7 dollars. The cost of a
saw5 [17]

Answer:

<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>

<u>Our system of equations:</u>

<u>x + y = 12</u>

<u>7x + 12y = 104</u>

Correct statement and question:

Alejandro loves to go to the movies. He goes both at night and during the day. The cost of a matinee is 7 dollars. The cost of an evening show is 12 dollars.

Alejandro went to see a total of 12 movies and spent $ 104. How many of each type of movie did he attend? Write a system of equations.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

Step 1:

Let x to represent the number of matinee shows Alejandro went to.

Let y to represent the number of evening shows Alejandro went to.

Now, let's write our system of equations:

x + y = 12

7x + 12y = 104

*********************

x = 12 - y

*********************

7 (12 - y) + 12y = 104

84 - 7y + 12y = 104

5y = 104 - 84

5y = 20

y = 20/5

<u>y = 4 ⇒ x = 12 - 4 = 8</u>

<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>

4 0
3 years ago
What is the least common multiple of 8 and 32
Viefleur [7K]
The least common multiple is 32
6 0
3 years ago
What’s the answer to 4x+3=15
Anastasy [175]

Answer: 4.500

Step-by-step explanation:

4x - 18  =   2 • (2x - 9)

2   =  0

 2x-9 = 0

 2x = 9

x = 9/2 = 4.500

3 0
3 years ago
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