Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or the theorem you used.
If not, explain.
2 answers:
Answer: Both the pairs of triangles (a) and (b) are similar.
(a) By AA similarity statement.
(b) By proportionality statement.
Step-by-step explanation: We are given to check whether the pairs of triangles in cases (a) and (b) are similar or not.
(a) We see that in triangles ABC and PQR, we have
m∠A = m∠P = 41°, m∠B = m∠Q = 85° and m∠C = m∠R = 54°.
So, ΔABC and ΔPQR are similar by AA similarity statement.
(b) We see that in triangles ABC and DEF, we have
AB = 4, BC = 5, CA = 3, DE = 24, EF = 30 and FD = 18.
So, we have
That is, the corresponding sides of two triangles are proportional.
Thus, ΔABC and ΔDEF are similar by proportionality statement.
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Answer:
x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i
x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
0-(3*x^2+3*x+7)=0
Step by step solution:
Step 1:
Equation at the end of step 1 :
0 - (( + 3x) + 7) = 0
<u>Step 2:</u>
Pulling out like terms:
2.1 Pull out like factors:
- 3x - 7 = -1 • (
+ 3x + 7)
Trying to factor by splitting the middle term
2.2 Factoring + 3x + 7
The first term is, its coefficient is 3 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 3 • 7 = 21
Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is 3 .
-21 + -1 = -22
-7 + -3 = -10
-3 + -7 = -10
-1 + -21 = -22
1 + 21 = 22
3 + 7 = 10
7 + 3 = 10
21 + 1 = 22
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 3 :
- 3x - 7 = 0
<u>Step 3:</u>
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = -3x-7
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -0.5000
Plugging into the parabola formula -0.5000 for x we can calculate the y -coordinate :
y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0
or y = -6.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = -3x-7
Axis of Symmetry (dashed) {x}={-0.50}
Vertex at {x,y} = {-0.50,-6.25}
Function has no real roots
Solve Quadratic Equation by Completing The Square
3.2 Solving -3x-7 = 0 by Completing The Square .
Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:
+3x+7 = 0 Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :
+x+(7/3) = 0
Subtract 7/3 from both side of the equation :
+x = -7/3
Now the clever bit: Take the coefficient of x , which is 1 , divide by two, giving 1/2 , and finally square it giving 1/4
Add 1/4 to both sides of the equation :
On the right hand side we have :
-7/3 + 1/4 The common denominator of the two fractions is 12 Adding (-28/12)+(3/12) gives -25/12
So adding to both sides we finally get :
+x+(1/4) = -25/12
Adding 1/4 has completed the left hand side into a perfect square :
+x+(1/4) =
(x+(1/2)) • (x+(1/2)) =
(x+(1/2))2
Things which are equal to the same thing are also equal to one another. Since
+x+(1/4) = -25/12 and
+x+(1/4) = (x+(1/2))2
then, according to the law of transitivity,
(x+(1/2))2 = -25/12
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(1/2))2 is
(x+(1/2))2/2 =
(x+(1/2))1 =
x+(1/2)
Now, applying the Square Root Principle to Eq. #4.2.1 we get:
x+(1/2) = √ -25/12
Subtract 1/2 from both sides to obtain:
x = -1/2 + √ -25/12
√ 3 , rounded to 4 decimal digits, is 1.7321
So now we are looking at:
x = ( 3 ± 5 • 1.732 i ) / -6
Two imaginary solutions :
x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i
or:
x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i
Answer:
422332423fund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.
Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spacfund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.
Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spac
Step-by-step explanation:
fund-raising project. The cost of paint color needed is php 1,200 plus php 45 each pot. She estimates that your class will design 80 pots and sell designed pots for php 100 each.
Direction: answer the following questions below then, decide if you are in favor of camie's plan. write your answers on the spac
