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3 years ago

Tell wheather the system has one solution, infinitely many solutions, or no solution.

Mathematics

1 answer:

ipn [44]3 years ago

5 0

<h3>Answer:</h3>

One solution: (x, y) = (2, 0)
Infinitely many solutions: 2x -5y = 17

<h3>Step-by-step explanation:</h3>

1. When you put the second equation in standard form, it is ...

... 5x +3y = 10

This is a different equation than the first one, so there will be one solution where the lines interect. (Adding the two equations gives 10x=20 ⇒ x=2. Since adding or subtracting y gives the same result, y must be zero.)

2. When you put the second equation in standard form, it is the same as the first:

... 2x -5y = 17 . . . . . divide the equation by 3

That is, any (x, y) values that satisfy the first equation will also satisfy the second equation (since they are the same). There are an infinite number of (x, y) values that do so.

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Given y=2x^2-6x+3. X=-1

konstantin123 [22]

Y=2(-1)^2-6(-1)+3
y=2+6+3
y=8+3
y=11

5 0

3 years ago

Three water storage containers have the same volume in the shape of a cylinder, a cone, and a sphere. The base radius of the cyl

fredd [130]

Answer:

- The ratio of the height of the cone to the height of the cylinder is 3:1

- The ratio of the height of the cone to radius of the sphere is 4:1

Step-by-step explanation:

Note that the radii of all the structures are the same.

Let the height of the cone be H and the height of the cylinder be h

The volume of each of the shapes are given below as

Volume of cylinder = πr²h

Volume of a cone = (1/3)πr²H

Volume of a sphere = (4/3)πr³

1) The ratio of the height of the cone to the height of the cylinder

To obtain this, we equate the volume of those two structures

Volume of the cone = Volume of the cylinder

(1/3)πr²H = πr²h

πr² cancels out on both sides and we're left with

(H/3) = h

H = 3h

(H/h) = (3/1)

So, The ratio of the height of the cone to the height of the cylinder is 3:1

2) The ratio of the height of the cone to radius of the sphere

Similarly equating the volumes of the cone and the sphere

(1/3)πr²H = (4/3)πr³

(1/3)πr² cancels out on both sides and we're left with

H = 4r

(H/r) = (4/1)

The ratio of the height of the cone to radius of the sphere is 4:1

Hope this Helps!!!

8 0

3 years ago

The amount Cami raised during last year’s charity walk, $45.50, is StartFraction 7 over 10 EndFraction of the amount she raised

barxatty [35]

Answer:

The equation is given by:

$n = \frac{7}{10} \times 45.50$

Step-by-step explanation:

During last years's charity walk, she raised $45.50.

During this years walk, she raised n, which is 7/10 of this amount. So, the equation is given by:

$n = \frac{7}{10} \times 45.50$

3 0

3 years ago

Volume of right trapezoid cylindar whole bases are B 16m, b 8m, height is 4m and length is 32m

viktelen [127]

Answer:

$volume = 1536 m^3$

Step-by-step explanation:

given data;

B = 16m

b =8 m

height H = 4 m

length L = 32 m

volume of any right cylinder = (Area of bottom) \times (length)

Volume = A* L

The area of a trapezoid is

$A=\frac{1}{2} H*(b+B)$

$A =\frac{1}{2} 4*(8+16)$

$A = 48 m^2$

therefore volume is given as

volume = 48*32

$volume = 1536 m^3$

6 0

3 years ago

The temperature at 12 am was 44 degrees. The temperature dropped steadily for the next 8 hours to reach the daytime low of 20 de

adelina 88 [10]

Answer:

62 degrees

Step-by-step explanation:

Points (12,440 and (20,20)

Slope = -3

Equation of line: y - 44 = -3(x - 12)

Plug in x = 6 to get y = 62.

6 0

2 years ago