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3 years ago

Which expression is equivalent to 1/3(5x+3y)+2/5y+7?

Mathematics

2 answers:

Pepsi [2]3 years ago

5 0

D is the answer because all you have to do is solve

nikklg [1K]3 years ago

3 0

Answer:

Option A is correct.

The expression which is equivalent to $\frac{1}{3}(5x+3y)+\frac{2}{5}y +7$ is, $\frac{5}{3}x + \frac{7}{5}y + 7$

Step-by-step explanation:

Given the expression: $\frac{1}{3}(5x+3y)+\frac{2}{5}y +7$

The distributive says that:

$a\cdot(b+c) = a\cdot b+ a\cdot c$

Apply distributive property on [1] we have;

$\frac{5}{3}x + y + \frac{2}{5}y + 7$

Like terms are those terms which have same variables to the same power.

Combine like terms, we have;

$\frac{5}{3}x + \frac{7}{5}y + 7$

Therefore, the expression which is equivalent to $\frac{1}{3}(5x+3y)+\frac{2}{5}y +7$ is, $\frac{5}{3}x + \frac{7}{5}y + 7$

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Given: ABCD parallelogram BK ⊥ AD , AB = 6, AK = 3 Find: m∠A, m∠B, m∠C, m∠D

Troyanec [42]

Answer: Angle A = 60°, angle B = 120°, angle C = 60°, angle D = 120°

Step-by-step explanation: Please refer to the attached diagram for further details.

The question has given the parallelogram ABCD as having side AB measuring 6 units, side AK measuring 3 units and line BK has been drawn perpendicular to line AD. This means line AK forms a right angle at the point where it meets line AD. From the information provided and the figure derived from that, we have right angled triangle ABK with the right angle at point K, line AB equals 6 units and line AK equals 3 units.

Using angle A as the reference angle, line AK is the opposite (side facing the reference angle), line AB is the hypotenuse (line facing the right angle) and line AK is the adjacent (side that lies between the right angle and the reference angle).

Hence, using the trigonometric ratios,

Cos A = adjacent/hypotenuse

Cos A = 3/6

Cos A = 0.5

Checking with the calculator, (that is second function of Cos 0.5)

A = 60

The opposite sides of a parallelogram are equal (that is line AD is parallel to line BC) and therefore opposite angles are equal (that is angle A is equal to angle C).

Similarly, angle B is equal to angle D. However, angles in a quadrilateral equals 360 degrees.

Therefore, angles in parallelogram ABCD is derived as;

A + B + C + D = 360

60 + B + 60 + D = 360

120 + B + D = 360

Subtract 120 from both sides of the equation

B + D = 240

Having known that angle B equals angle D, angles B and D is derived as each half of the value 240

Angle B = 240/2

Angle B = 120

and angle D = 120

Therefore, the angles are;

A = 60, B = 120, C = 60, D = 120

3 0

3 years ago

4,750meters to kilmeters

Stella [2.4K]

4.75 Kilometers, you just divide by 1000

7 0

3 years ago

Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

6 0

4 years ago

4x - 30x3 -3x2 what is the answer to this problem

AnnyKZ [126]

Answer

4x-84

Solve This Problem Step By Step

6 0

4 years ago

What is the length of the missing leg? If necessary, round to the nearest tenth.

Marrrta [24]

Answer:

The length of the hypotenuse is 33 yards.

Step-by-step explanation:

We can solve for 'a' using Pythagoras theorem. Let's solve it.

65² = b² + 56²
=> 4225 = b² + 3136
=> b² = 1089
=> b = 33

Hence, the length of the hypotenuse is 33 yards.

Hoped this helped.

$BrainiacUser1357$

7 0

2 years ago