Which statements can be used to prove that ABC and A’B’C are congruent?

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

7 0

Answer:

O A.

Step-by-step explanation:

Option A identifies two angles (sufficient for similarity) and one side, sufficient (with similarity) for congruence. The applicable congruence theorem is AAS.

Option B identifies two sides and the angle not between them. The two triangles will be congruent in that case only if the angle is opposite the longest side, which is not true in general.

Option C same deal as Option A.

Option D identifies three congruent angles, which will prove the triangles similar, but not necessarily congruent.

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Solve for a.

tamaranim1 [39]

The correct answer is: [C]: " a = ± $\sqrt{25 - b^2}$ " .
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Explanation:
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We are given:
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 → " 25 = a² + b² " ; Solve for "a" ;
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→ To solve for "a" ; we want to isolate "a" on one side of the equation.
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We can rewrite: " 25 = a² + b² " ;

as: " a² + b² = 25 " .

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Then, we can subtract " b² " from each side of the equation; as follows:
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→ " a² + b² − b² = 25 − b² " ;

to get:
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→ " a² = 25 − b² " ;
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→ Now, take the square root of EACH SIDE of the equation ;
to isolate "a" on one side of the equation; & to solve for the value(s) of "a" ;
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→ √(a²) = $\sqrt{25 - b^2}$ ;

to get:
_____________________________________________________
 → a = | $\sqrt{25 - b^2}$ | ;

→ a = ± $\sqrt{25 - b^2}$ ;

 → which is: Answer choice: [C]: " a = ± $\sqrt{25 - b^2}$ " .
______________________________________________________

8 0

3 years ago

Sami purchased 5 comic books priced as shown.

kati45 [8]

Answer:

$19.23

Step-by-step explanation:

First, add the prices of all 5 comics together. That should equal $17.63. The tax is 9% so that would be 1.5867 or $1.60. In total, Sami paid $19.23.

6 0

3 years ago

Read 2 more answers

. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i

KIM [24]

Answer:

Error of Andrew: Made incorrect factors from the roots

Step-by-step explanation:

Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:

(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.

Simplifying the brackets, we get:

(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.

This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.

So, the polynomial would be:

$(x - 3)(x - 2 - 2i)(x - 2+2i)=0\\\\ (x-3)(x^{2}-2x+2xi-2x+4-4i-2xi+4i-4i^{2})=0\\\\ (x-3)(x^{2}-4x+4+4)=0\\\\ (x-3)(x^{2}-4x+8)=0\\\\ x^{3}-4x^{2}+8x-3x^{2}+12x-24=0\\\\ x^{3}-7x^{2}+20x-24=0$