MATHEMATICS HIGH SCHOOL

What is the solution of the following question?
x^2+10x+25=12

Answers

Answer 1
Answer: make equal to 0
minus 12from both sides
x^2+10x+13=0
we can't factor so use quadratic formula

x= \frac{-b+/- \sqrt{b^(2)-4ac} }{2a}
x= \frac{-10+/- \sqrt{10^(2)-4(1)(13)} }{2(1)}
x= (-10+/- √(100-52) )/(2)
x= (-10+/- √(48) )/(2)
x= (-10+/- 4√(3) )/(2)
x= -5+/- 2√(3)


x= -5+ 2√(3) or -5- 2√(3)

aprox
x=-1.5359 or -8.4641
Answer 2
Answer:

Answer: - 1.536  or - 8.464  

Step-by-step explanation:

Step 1: Rearrange the equation, by putting everything on the left hand side of the equation so that the quadratic formula can be applicable to the equation  

x^2-10*x+25-(12)=0  

Step 2: the quadratic formula

                       

           - B  ±  √ B2-4AC

 x =   ————————

                     2A    

Where A= 1

B = 10

C = 13

B2  -  4AC =  100 - 52  

= 48

            10 ± √ 48  

  x  =    —————

                   2

      -   √ 48  

x =(10-√48)/2=5-2√ 3 =  - 1.536  

x =(10+√48)/2=5+2√ 3 = - 8.464  

Are the two solutions

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In the two-column proof below, provide a reason for each statement.

Answers

The ∠4 (which is equal to ∠2) and ∠13 are congruent (∠4 ≅ ∠13) because they both form part of the angles that add up to 180 degrees. In the given conditions, we have ∠2 ≅ ∠1 (given), and ∠7 and ∠13 are supplementary angles.

Supplementary angles add up to 180 degrees, so we can conclude that ∠7 + ∠13 = 180 degrees.

Now, we can use the fact that ∠2 ≅ ∠1 to deduce that ∠2 = ∠1.

Since ∠7 and ∠13 add up to 180 degrees and ∠2 = ∠1, we can deduce that ∠2 + ∠13 = 180 degrees.

This means that ∠4 (which is equal to ∠2) and ∠13 are congruent (∠4 ≅ ∠13) because they both form part of the angles that add up to 180 degrees.

Learn more about angle:

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In the two-column proof below, provide a reason for each statement. Given: ∠ 2 ≅ ∠7 and ∠7  and ∠13 are supplementary angles Prove: ∠4 ≅ ∠13

which one of following statement expresses a true proportion 3:4=9:12 b. 2:1=1:2 c. 7:9=8:9 d. 54:9=6:3

Answers

a is the right one:
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    3×3:4×3=9:12

solve the triangle. round lengths to the nearest tenth and angle measures to the nearest degree a=7 b=7 c=5

Answers

Hello,

a,b,c are the sides.

1) first idea
Theorem of Al' Kashi (genralized pythagorean theorem) will help us

a²=b²+c²-2bc cosA  ==>49=49+25-2*7*5*cos A
==>cos A=25/70=5/14 ==>
A=69,075167572361683699967605141899 °≈69°

b²=a²+c²-2ac cos B ==> 49=49+25-2*7*5 * cos B==>cos B=5/14
B=A (triangle is isocele ==> a second method)

C=180-2*69=42°

II)
The triangle isocele is formed with 2 right triangles.
(base=5/2 hypotenuse=7)

cos B=(5/2)/7=5/14 (the same) ==>B=69°
A=B=69°
C=42°

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Answers

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Answers

Answer:

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Step-by-step explanation:

Answer:

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