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3 years ago

Use the geometric model to factor x^2-9

Mathematics

1 answer:

inysia [295]3 years ago

8 0

Answer:

(x - 3)(x + 3)

Step-by-step explanation:

a² - b² = (a - b)(a + b)

x² - 9 = (x - 3)(x + 3)

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If all the sides of a triangle get 2 times as big, how much does the area change?

KIM [24]

Answer:

Step-by-step explanation:

area becomes 2²=4 times.

4 0

3 years ago

Jennifer wants to net $35,000 on her house. Her closing costs will be 7,500 plus a 7% commission. She owes $185,000 on her loan.

GenaCL600 [577]

7,500 plus the commision is 525 now you add it to the 7,500 that will leave you with 8,025 now you subtract it from 185,000 so the answer will be 176,975

I'm glad if it helps :)

3 0

3 years ago

Read 2 more answers

I'm not sure how to solve the systems of equations problem below

Viefleur [7K]

Solve the lower equation first

+12 on each side
7x=51
divide by 7
x=51/7

then use that to solve the upper equation

3 0

2 years ago

Calculus 2

FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

$\displaystyle \int_1^47\sqrt{\ln(x)}\, dx$

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

The trapezoidal rule is given by:

$\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)$

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

$\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}$

Therefore, the trapezoidal approximation is:

$\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)$

Evaluate:

$\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337$

The midpoint rule is given by:

$\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x$

Thus:

$\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)$

Simplify:

$\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319$

Simpson's Rule is given by:

$\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)$

So:

$\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)$

Simplify:

$\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834$

6 0

3 years ago

14-16 and 17-20 <br>I need help figuring this out or answers.

Temka [501]

14 -16=-2 17-20=-3 it's just regular problems backwards

3 0

3 years ago