Use the method of substitution to solve this: 9x+4y=9/2 and y=2x-1

4.6 is what percent of 23? Can someone give me the answer please

lukranit [14]

Answer:

20%

Step-by-step explanation:

Ratios:

$\frac{x}{100} =\frac{4.6}{23} \\\\23x=460\\x=20$

Double check:

20% = 0.2

23(0.2) = 4.6

5 0

2 years ago

Find the differential of the function w=xsin(2yz^4).

SCORPION-xisa [38]

The differential of

$w = x \sin(2yz^4)$

is

$\mathrm dw = \dfrac{\partial w}{\partial x}\,\mathrm dx + \dfrac{\partial w}{\partial y}\,\mathrm dy + \dfrac{\partial w}{\partial z}\,\mathrm dz$

where the partial derivatives are

$\dfrac{\partial w}{\partial x} = \sin(2yz^4) \\\\ \dfrac{\partial w}{\partial y} = x \cos(2yz^4) \times 2z^4 = 2xz^4 \cos(2yz^4) \\\\ \dfrac{\partial w}{\partial z} = x \cos(2yz^4) \times 8yz^3 = 8xyz^3 \cos(2yz^4)$

So the differential dw is

$\mathrm dw = \boxed{\sin(2yz^4)}\,\mathrm dx + \boxed{2xz^4 \cos(2yz^4)}\,\mathrm dy + \boxed{8xyz^3 \cos(2yz^4)}\,\mathrm dz$

5 0

2 years ago

3. What is the exact area of triangle ABC? Use special right triangles to help find the base of the triangle. Show your work.

Oduvanchick [21]

The exact area of triangle ABC is 93.51 cm².

The given parameters;

Height of the triangle, h = 18 cm

The base of the triangle is calculated by using trigonometry ratio as follows;

$tan (30) = \frac{b}{18} \\\\$

where;

b is the base of the triangle ABC

$b = 18 \times tan(30)\\\\b = 10.39 \ cm$

The area of the triangle ABC with the calculated base and given height is calculated as follows;

$A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2$

Thus, the exact area of triangle ABC is 93.51 cm².

Learn more about area of a triangle here: brainly.com/question/23945265

3 0

1 year ago

Stanley Bank offers a money market account that earns 1.85% compounded continuously: a) If $10,000 is invested in this type of a

Alexxx [7]

Answer:

a) $1056.33 b) 23 years

Step-by-step explanation:

a) 10000(1+1.85/100)^3=10565.33 (2d.p.)

b) let x be the no. of years

15000 = 10000(1+1.85/100)^x

1.5 = 1.0185^x

ln both sides

ln 1.5 = x ln 1.0185

x = ln 1.5/ln 1.0185

=22.11

=23 years (rounded up)

5 0

2 years ago

Find the angles of a parallelogram in which an exterior angle is one-third that its interior angle.

iogann1982 [59]

Answer:

The angles of a parallelogram are 135°-45°-135°-45°

Step-by-step explanation:

we know that

In a parallelogram opposites angles are congruent and consecutive angles are supplementary

Remember that

The sum of a exterior angle and its interior angle is equal to 180 degrees

Let

x ----> the measure of one interior angle of parallelogram

y ----> the measure of the other interior angle of parallelogram

we have that

$x+\frac{x}{3}=180^o$

solve for x

$\frac{4}{3}x=180^o\\\\x=(180^o)3/4\\\\x=135^o$

Find the measure of the other interior angle of parallelogram

Remember that consecutive interior angles are supplementary

$x+y=180^o$

substitute the value of x

$135^o+y=180^o$

solve for y

$y=45^o$

therefore

The angles of a parallelogram are 135°-45°-135°-45°

3 0

3 years ago