What property justifies that 6 x + 9 3 = 2 x + 3 ?

(x-1)/2=2 please help

Lilit [14]

Answer:

x = 5

Step-by-step explanation:

5 - 1 = 4

4/2 =2

Hope this helps!

7 0

2 years ago

Read 2 more answers

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by

Whitepunk [10]

$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\\y(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\\\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^{\pi/2}\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^{\pi/2}\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{\pi\sin^23}{864}}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

5 0

2 years ago

The scale of a map is 1 inch : 9.5 miles.

DedPeter [7]

Answer:

2.526 in
4.211 in

Step-by-step explanation:

To find the number of inches, divide miles by 9.5.

__

a) 24 miles = (24 mi)×(1 in)/(9.5 mi) = (24/9.5) in ≈ 2.526 in

__

b) 24 miles + 16 miles = 40 miles = (40 mi)×(1 in)/(9.5 mi) = 40/9.5 in ≈ 4.211 in

_____

Comment on units conversion

I find it convenient to work units conversion problems by writing a fraction that is equal to 1 and multiplying by that to change units. My fraction has the "to" units in the numerator, and the "from" units in the denominator. That way, the unwanted units cancel when the multiplication is carried out.

The fraction is equal to 1 because the measurement in the numerator is equal to the measurement in the denominator.

__

Some folks prefer proportions. If you do it that way, be sure "like" is matched with "like".

map inches/ground miles = 1/9.5 = x/24

route inches/scale inches = route miles/scale miles = x/1 = 24/9.5

6 0

2 years ago

HELP ASAP ILL GIVE BRAINLIST

Mila [183]

Answer:

Part A) ΔCGB and ΔPBE are similiar

Part B) They are similar because they are Vertical Angles/Alternate Interior Angles

Part C) Distance from B to E is 125; Distance from P to E is 275.

Step-by-step explanation:

5 0

2 years ago

A family built a house in a beach resort area. In 1990, the house was 430 ft from the water. With erosion, the house was 400 ft

neonofarm [45]

We develop an equation for the given situation by first writing the general equation for lines,

y = mx + b

Substituting to this given the values given above,

(1990) 430 = b

(2000) 400 = m(10) + 430

The value of m from the equation in 2000 is -3. Thus, the equation of that relates the variables is,

y = -3x + 430

8 0

2 years ago