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Free_Kalibri [48]
4 years ago
5

For the function f(x)=x2−24÷3+12 f(1) ​f(0)​ ​f(−1)​

Mathematics
1 answer:
LuckyWell [14K]4 years ago
3 0

Put the values of x to the equation of the function.

f(x)=\dfrac{x^2-24}{3}+12

f(1)=\dfrac{1^2-24}{3}+12=\dfrac{1-24}{3}+12=\dfrac{-23}{3}+12=-7\dfrac{2}{3}+12=4\dfrac{1}{3}\\\\f(0)=\dfrac{0^2-24}{3}+12=\dfrac{-24}{3}+12=-8+12=4\\\\f(-1)=\dfrac{(-1)^2-24}{3}+12=\dfrac{1-24}{3}+12=\dfrac{-23}{3}+12=-7\dfrac{2}{3}+12=4\dfrac{1}{3}

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Given: S is the midpoint of QR, QR¯⊥PS¯ and ∠RSP and ∠QSP are right angles.<br><br> Prove: PR≅PQ
tigry1 [53]

ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.

<h3>What is the CPCTC Theorem?</h3>

If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.

Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)

∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)

SP ≅ SP based on the reflexive property (one pair of congruent sides)

Therefore, ΔRSP ≅ ΔQSP by SAS.

Conclusively, PR ≅ PQ by CPCTC theorem.

Learn more about the CPCTC theorem on:

brainly.com/question/6076251

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The solution to given system of equations is x = 2 and y = -5

<em><u>Solution:</u></em>

<em><u>Given the system of equations are:</u></em>

4x + y = 3 ---------- eqn 1

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We have to find the solution to above system of equations

<em><u>We can solve the system by substitution method</u></em>

From eqn 1,

4x + y = 3

Isolate y to one side

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<em><u>Substitute eqn 3 in eqn 2</u></em>

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Combine the like terms

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Divide both sides of equation by -14

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<em><u>Substitute x = 2 in eqn 3</u></em>

y = 3 - 4(2)

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<h3>y = -5</h3>

Thus the solution is x = 2 and y = -5

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Answer B

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