What operation would you do first to simplify 4 × 3 - 3 to the second power + 1 × 8

Mathematics

1 answer:

True [87]2 years ago

6 0

Answer:

4 × 3 - 3^2 + 1 × 8 = 11/1 = 11

Step-by-step explanation:

Multiple: 4 * 3 = 12

Exponentiation: 3 ^ 2 = 9

Subtract: the result of step No. 1 - the result of step No. 2 = 12 - 9 = 3

Multiple: 1 * 8 = 8

Add: the result of step No. 3 + the result of step No. 4 = 3 + 8 = 11

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Given: △ACM, m∠C=90°, CP ⊥ AM

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Answer: The answer is $3\dfrac{4}{7}.$

Step-by-step explanation: Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

$AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.$

Now,

$AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)$

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

$CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)$