Match the situation to the correct expression. The sum of n and 40

Multiply. (d+7)(d-7) Simplify your answer.

romanna [79]

Answer:

$\huge\boxed{(d+7)(d-7)=d^2-49}$

Step-by-step explanation:

$\bold{METHOD\ 1:}\\\\(d+7)(d-7)\qquad|\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=d^2-7^2=d^2-49\\\\\bold{METHOD\ 2:}\\\\(d+7)(d-7)\qquad|\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(d)(d)+(d)(-7)+(7)(d)+(7)(-7)\\\\=d^2-7d+7d-49\qquad|\text{combine like terms}\\\\=d^2+(-7d+7d)-49\\\\=d^2-49$

7 0

3 years ago

Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop

xxMikexx [17]

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

f(x)=log (3 x) +5 x²

$f'(x)=\frac{1}{3x}+10 x$

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248$

$x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012$

$x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057$

$x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052$

So, root of the equation =0.205 (Approx)

Approximate relative error

$=\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41$

Approximate relative error in terms of Percentage

=0.41 × 100

= 41 %

7 0

3 years ago

A rental car company charges $35 a day plus $.15/mi for a mid-size car. A customer owes $117.25 for a three-day rental. How many

Molodets [167]

The base charge is 35 dollars per day. He rented the car for 3 days, so before you add in the mileage you have to multiply 35 x 3 days for 105 dollars. Then you have to take the remaining charge and divide it by the charge per mile to get the number of miles driven. Lets set up the equation.

d= number of days rented
m= number of miles driven

35(d) + .15(m) = 117.25
35(3) + .15m = 117.25
105 + .15m = 117.25
.15m = 117.25 - 105
.15m = 12.25
m = 12.25/.15
m = 81.67

So he drove 81.67 miles

8 0

3 years ago

What is 1+1. 100 points to whoever gets it first. Answer fast!

Anni [7]

Answer:

da answer iz two cause wen u add one plus one u get answer two

Step-by-step explanation:

let mi hope dat it useful

4 0

3 years ago

Read 2 more answers

Use the distributive property to fill in the blanks below. 2 x (8 - 7) = x 8) - (x7)