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4 years ago

The function p is defined as p(x)=x2+4x-12

Mathematics

1 answer:

Ira Lisetskai [31]4 years ago

4 0

Given the function $p(x)=x^2+4x-12.$

Part A.

To write the expression that defines $p(x-6)+5,$ you have to substitute x-6 instead of x into the function expression and then add 5 to the function:

$p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.$

Part B.

1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).

2 transformation is translation 5 units up (+5 determines this transformation).

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Rewrite the equation in exponential form, and show how you got there:

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Answer: $13^0=1$

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Logarithms are in the format $log_{b} a=c$ while exponential form is in the format $b^c=a$

So we can transfer a,b, and c from the log form to the exponential form

$log_{13} 1=0\\\\13^0=1$

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3 years ago

A Tom bought these 3 t shirts at the sale price of $ 14. 50. How much money did he save compared to the original total of the t

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3 years ago

Anita works for a dog-walking service. She earns a one-time fee of $10 plus an additional $2 for each dog she walks. If Anita wa

ahrayia [7]

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Hope this helps :)

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3 years ago

Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000

AleksandrR [38]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

First, we determine the value of the 5 installments using a 5% annual compounded rate.

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

Now, if the annual rate is 6% continuously compounded.

First, we need to calculate the effective interest rate:

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

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3 years ago

To get the paint colour you want you mix 2 parts red with 3 parts cream and 1 part blueHow much cream and blue will you need to

oksian1 [2.3K]

Red : Cream : Blue
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You need 6 parts of Cream and 2 parts of Blue

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3 years ago