All categories

2 years ago

How many solutions does the system 2y=10x-14 and 5x-y=7 have ?

1 answer:

7 0

I find it of tremendous use to convert to the slope intercept form to easily visualize the lines. The first is:
y = 5x - 7 [Dividing both sides by 2] and the second is:
-y = -5x + 7 [Subtracting 5x from each side]
y = 5x - 7 [Dividing each side by -1]

These two equations represent the same line. If the lines were parallel, there would be no solution. If the lines intersected, there would be only one unique solution satisfying both equations (the point of intersection).

In this case, where the two equations represent the same line, the number of solutions is infinite.

The answer is: ∞

You might be interested in

Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less tha

cupoosta [38]

Answer:

Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

Let the height of the box, h = x feet

Therefore, length is, l = ( 9+x ) feet

And width is, b = ( x-4) feet

so volume of the box is

V = l x b x h

$180= (x+9) \times (x-4) \times (x)$

$x^3 +5x^2-36x -180 =0$

Factorizing we get

(x+5)(x-6)(x+6)=0

Therefore,

x = -5, -6, 6

Now since the height of the box cannot be negative, so taking the positive value of x, we get

Height of the box, h = x = 6 feet

Length , l = ( 9+x ) = 9+6 = 15 feet

Width , b = ( x-4) = 6-4 = 2 feet

8 0

3 years ago

A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg. What is the densi

Rashid [163]

<h2>Density of ethyl alcohol is 56.25 lbm/ft³ </h2>

Step-by-step explanation:

We have 1 lbm = 0.454 kg

1 kg = 2.203 lbm

1 m = 3.28 ft

Density of ethyl alcohol = 9.01 x 10² kg/m³

$\texttt{Density = }\frac{9.01\times 10^2\times 2.203}{3.28^3}=56.25lbm/ft^3$

Density of ethyl alcohol = 56.25 lbm/ft³

3 0

2 years ago

The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?

Travka [436]

--------------------------------------------------
Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

--------------------------------------------------
Formula
--------------------------------------------------
Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
--------------------------------------------------
62 = 2(2x + 4 + x)
62 = 2(3x + 4) ← combine like terms 
62 = 6x + 8 ← remove bracket 
62 - 8 = 6x ← minus 8 on both sides 
6x = 54 ← swap sides 
x = 54 ÷ 6 ← divide by 6 on both sides
x = 9 m

--------------------------------------------------
Find Length and Width
--------------------------------------------------
Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

--------------------------------------------------
Answer: Length = 22m
--------------------------------------------------

3 0

2 years ago

Read 2 more answers

11x + 10y - 8x - 12y (a) x + -2y (b) 3x + 2y (c) -x + 2y (d) 3x + -2y

svetoff [14.1K]

Answer:

d) 3x+-2y

Step-by-step explanation:

combine like terms of x and y

11x-8x=3x

10x-12x=-2y

brainliest?

8 0

3 years ago

Which of the following best describes the English expression five more than the quantity of a number minus six?

klasskru [66]

5 + x - 6 hopes this helps

8 0

2 years ago