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2 years ago

5

Which expression is equivalent to -8x -2 (5 + 4x) ?

1 answer:

Brrunno [24]2 years ago

5 0

Answer: -16x-10

-2(8x+5)

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It helps to add decimals because it means one out of ten

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3 years ago

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Given: △ACM, m∠C=90°, CP ⊥ AM

larisa86 [58]

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,

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

Comparing equations (A) and (B), we have

$5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.$

Thus,

$AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.$

8 0

3 years ago

Paul has $30,000 to invest. His intent is to earn 15% interest on his investment. He can invest part of his money at 8% interest

jeka94

Answer:

Amount invested at 8% is $9000 and amount invested at 18% is $21000.

Step-by-step explanation:

Let amount invested at 8% be x.

Let amount invested at 18% be y.

We get the 1st equation as:

$x+y=30000$ ........(1)

We get the second equation as:

$0.08x+0.18(y)=0.15\times30000$

=> $0.08x+0.18y=4500$

or getting rid of the decimal by multiplying by 100 on both sides.

$8x+18y=450000$ ........(2)

Multiplying (1) by 8 and subtracting from (2) we get

$10y=210000$

So, y = 21000

And $x+21000=30000$

$x = 30000-21000$

So, x = 9000

Therefore, amount invested at 8% is $9000 and amount invested at 18% is $21000.

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Step-by-step explanation:

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