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nekit [7.7K]
3 years ago
12

Complete the square y=x^2+6x+8

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

Answer:

y = (x+3)² - 1

Step-by-step explanation:

To complete the square take the middle term b and divide by 2. Then square the value.

Here b = 6.

So 6/2 = 3

3² = 9

Add 9 to both sides of the equation.

x² + 6x + 8 = 0

x² + 6x + 9 + 8 = 9

(x+3)² - 1 = y

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Find the coefficient of x^7 in the expansion of (3x+4)^11
devlian [24]

Use the binomial theorem:

(a+b)^n=\displaystyle\sum_{k=0}^n\binom nka^{n-k}b^k

In this case,

(3x+4)^{11}=\displaystyle\sum_{k=0}^{11}\binom{11}k(3x)^{11-k}4^k

The x^7 term occurs for k=4:

\dbinom{11}4(3x)^{11-4}4^4=\dfrac{11!}{4!(11-4)!}3^74^4x^7=184,757,760x^7

6 0
3 years ago
Given that the circles are congruent, can you conclude that YZ=BC?<br> Answer options: yes, no
Anastasy [175]

Answer:

Answer is yes

Step-by-step explanation:

Given in the picture are two circles which are congruent.

This suggests that the radii of the two circles are equal.

Also the central angle of the two circles are congruent (given)

Consider triangles ABC and XYZ,

AC =XY:  AB = YZ:

Angle A = Angle X

By SAS theorem, the two triangles are congruent.

Hence BC = YZ

So yes is answer.

4 0
3 years ago
What is the value of 5 in 756? write and draw to explain how you know
Dennis_Churaev [7]
The value of 5 is 10 because it is in the tens place. If you draw a place value chart it shows that 5 is in the tens place. You could also draw it with 5 blocks with ten cubes.

Happy studying ^_^
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3 0
3 years ago
Read 2 more answers
Turn this fraction into a decimal. Show your work. 13/16.
Lady bird [3.3K]

Answer:

0.8125

Step-by-step explanation:

First , we all know that fraction is like division.

So I divided 13 by 16

Then I got my answer

7 0
3 years ago
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FIND M∠R (GIVING BRAINLIEST, 25 PTS)
riadik2000 [5.3K]

Answer:

<h2>76</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • triangles
  • equation
  • PEMDAS
<h3>given:</h3>
  • M\angle T=2x+2
  • M\angle R=3x+1
<h3>tips and formulas:</h3>
  • this is an isosceles triangle since two sides are equal therefore \angle T=\angle S
  • a triangle contains 180°
<h3>let's solve:</h3>

according to the question

2x+2+2x+2+3x+1=180

solve:

  1. collect like terms:7x+5=180
  2. substract 5 from both sides:=>7x+5-5=180-5=>7x=175
  3. divide both sides by 7: =>7x/7=175/7
  • x=25

given:

M∠R=3x+1

substitute the value of x

3×25+1

75+1

76

7 0
3 years ago
Read 2 more answers
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