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3 years ago

What is the solution to this system of equations?

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

8 0

3x+y=−11

3x+y+−3x=−11+−3x(Add -3x to both sides)

y=−3x−11

2x+2y=−10

2x+2(−3x−11)=−10

−4x−22=−10(Simplify both sides of the equation)

−4x−22+22=−10+22(Add 22 to both sides)

−4x=12

−4x

−4

(Divide both sides by -4)

x=−3

y=−3x−11

y=(−3)(−3)−11

y=−2(Simplify both sides of the equation)

Answer:

x=−3 and y=−2

D.(-3,-2)

You might be interested in

A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width

rodikova [14]

perimeter = 2L +2w

L = w+11

70 = 2(w+11) +2w

70 = 2w+22+2w

70= 4w + 22

48 = 4w

w=48/4 = 12

width = 12

length = 12+11 = 23

2x12 = 24

2x23 = 46

46+24 = 40

length = 23 inches, width = 12 inches

Answer is D

5 0

3 years ago

Read 2 more answers

How many odd 2-digit positive integers greater than 30 are there?

alexgriva [62]

Answer:

There are 70 two digit numbers that are greater than or equal to 30

Step-by-step explanation:

hope it helps you

6 0

2 years ago

Read 2 more answers

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

7 0

3 years ago

Solve -4x ≥ -8. Graph the solution.

Semmy [17]

Answer:

do its ??

Step-by-step explanation:

7 0

3 years ago

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing t

azamat

The glass will contain <u>89.086 milliliters</u> of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.

In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y = -29.202x + 293.5.

We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.

To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.

Thus,

y = -29.202x + 293.5,

or, y = -29.202(7) + 293.5 {Substituting x = 7},

or, y = -204.414 + 293.5,

or, y = 89.086.

Thus, the glass will contain <u>89.086 milliliters</u> of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.

Learn more about the equation of the line of best fit at

brainly.com/question/1564293

#SPJ1

4 0

2 years ago