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2 years ago

What theorem can be used to prove that the two triangles are congruent?

Mathematics

2 answers:

Sergio [31]2 years ago

4 0

SSS is my best answer.

Nuetrik [128]2 years ago

3 0

The SSS Triangle Congruency Postulate.

The two triangles have corresponding, congruent sides. Side QR corresponds to and is congruent to MN as denoted by the single hash mark. Sides QS and MP are corresponding and congruent sides as denoted by the three hash marks. Sides RS and NP are corresponding, congruent sides as denoted by the two hash marks. Therefore, as the SSS postulate states, if three sides in one triangle are corresponding, congruent sides to another triangle, the two triangles are congruent. In both triangles, the three corresponding sides are congruent; therefore, the triangles are congruent.

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AveGali [126]

18 11 25 8 4 !!!!!!!!

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3 years ago

F(x) = 2x + 3g(x) = 2x² + 6x + 13Find: (gºf)(x)

Butoxors [25]

Answer:

The function (gof)(x) is;

$(g\circ f)(x)=8x^2+36x+49$

Explanation:

Given the functions;

$\begin{gathered} f(x)=2x+3 \\ g(x)=2x^2+6x+13 \end{gathered}$

Solving for the function;

$(g\circ f)(x)=g(f(x))$

so, we have;

$\begin{gathered} g(f(x))=2(f(x))^2+6(f(x))+13 \\ g(f(x))=2(2x+3)^2+6(2x+3)+13 \\ g(f(x))=2(4x^2+12x+9)^{}+6(2x)+6(3)+13 \\ g(f(x))=8x^2+24x+18^{}+12x+18+13 \\ g(f(x))=8x^2+24x^{}+12x+18+18+13 \\ g(f(x))=8x^2+36x+49 \end{gathered}$

Therefore, the function (gof)(x) is;

$(g\circ f)(x)=8x^2+36x+49$

5 0

1 year ago

A 31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third

Nostrana [21]

Answer:

The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

Step-by-step explanation:

Total length of the steel = 31 inches

Let the length of the first piece = x

let the length of the second piece = y

Let the length of the third piece = z

So,

y = 2x

z = 4x + 3

x + 2x + 4x +3 = total length of the steel = 31

7x + 3 + 31

7x = 31 - 3

7x = 28

x= 4 inches

Thus; y = 2x = 2 × 4 = 8 inches

z = 4x +3 = 4×4 +3 =19 inches

∴The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

6 0

3 years ago

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Amanda purchased a 30 year $10,000 bond at par value with a 4% coupon. What is the total value of the coupons

klasskru [66]

Amanda purchased a 30 year $10,000 bond at par value with a 4% coupon.

We find the coupon amount each year

Coupon amount = actual amount of bond * 4%

= 10,000 * 0.04 = 400

Coupon amount for every year = 400

Total value of coupons for 30 years = 400 * 30 = 12000

$12,000 is the total value of the coupons

8 0

3 years ago

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142=10x+8x+2. Please show steps as well.

mel-nik [20]

Answer:

x=7.78

Step-by-step explanation:

142=10x+8x+2

Move all numbers with the same variables to each side to separate them.

142-2=10x+8x

140=18x

Divide by 18.

x= 140/18

x=7.78

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3 years ago

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