5×-3(4×-8)=-11 helppppppp

When solving a system of two equations via substitution, there will always be only one answer.

sertanlavr [38]

No false.
Remember the solution(s) to a system of equations is where the graphs all intersect if at all.
For the case of say a system of 2 lines, you can see the different possible outcomes..
-- If the two lines intersect at some point (x,y), that is one unique solution
-- If the two lines are parallel to each other, you see there are no intersection points and therefore this system of two parallel lines has no solutuion.
-- If the two lines overlap, really the same line written as a multiple of the other line, then you see they intersect at all points along the line, here there are infinite solutions.

6 0

3 years ago

Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

3 years ago

If I get on at the bottom of the ferris wheel, in how many degrees will it take for my car to get to the top of the ferris wheel

Keith_Richards [23]

It would take 180* to get to the top.

5 0

3 years ago

Read 2 more answers

You purchased $132.49 worth of wheels and bearings for your skateboards. The shop charges $15 per board to install them. The tot

Thepotemich [5.8K]

Answer:

4

Step-by-step explanation:

192.49-132.49=60

60÷15=4

5 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

svet-max [94.6K]

Answer:

tan (C) = 2.05

Step-by-step explanation:

Given:

A right angled triangle CDE right angled at ∠D.

Side CD = 39

Side DE = 80

Side CE = 89

We know, from trigonometric ratios that, the tangent of any angle is equal to the ratio of the opposite side to the angle and the adjacent side of the angle.

Therefore, tangent of angle C is given as:

$\tan(\angle C)=\frac{DE}{CD}$

Plug in the given values and solve for angle C.This gives,

$\tan(\angle C)=\frac{80}{39}\\\\\tan(\angle C)=2.051\approx 2.05(Rounded\ to\ nearest\ hundredth)$

Therefore, the measure of tangent of angle C is 2.05.

4 0

3 years ago