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Helen [10]
2 years ago
14

Which statement is true about the equations –3x + 4y = 12 and 1/4x –1/3 y = 1?The system of the equations has exactly one soluti

on at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
Mathematics
1 answer:
iren [92.7K]2 years ago
4 0

Answer:

The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation:

The equations have the same slope. In standard form, this can be seen as the same coefficients for x and y. We will multiply the second equation by -12 to reveal this.

\frac{1}{4} x-\frac{1}{3}y=1 \\-12(\frac{1}{4} x-\frac{1}{3}y=1)\\\frac{-12}{4} x-\frac{-12}{3}y=-12\\-3x+4y=-12

This means the equations are parallel and will never cross. There is no solution.

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3 years ago
1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?
ziro4ka [17]

PART A (1 in diagram)

Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.

1. The domain of the given function f(x) is the set {10, 20, 30}.

All we can say about

{f}^{ - 1} (x)

is that, it has a range of {10, 20, 30}.

This is because the domain of a function becomes the range of its inverse function.

2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,

{f}^{ - 1} (x)

will contain the point (0,3).

Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.

In simple terms the domain of the function becomes the range of the inverse function and vice versa.

3. If the first term in an arithmetic sequence is 2.

Then we have a=2.

If the twelfth term is 211, then

a + 11d = 211...(1)

Put a=2 into this equation.

2 + 11d = 211

Solve for d.

11d = 211 - 2

11d = 209

d =  \frac{209}{11}  = 19

If

a_n = 135

then

a + (n - 1)d = 135

Substitute a=2 and d=19

2 + (n - 1)19 = 135

19(n - 1) = 133

(n - 1) =  \frac{133}{19}

n - 1 = 7

n = 7 + 1 = 8

Therefore n=8

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3 years ago
How does multiplying both the dividend and the divisor by a factor of 10 sometimes make a problem easier to solve?
Mandarinka [93]
Because the divider and dividend are actually smaller then factors
5 0
3 years ago
Find the equation of the line using the point-slope formula. Write all the final equations
vivado [14]

Answer:

y=\frac{1}{2}x+\frac{5}{2}

Step-by-step explanation:

We are going to find the slope by lining up the points vertically and subtract, then put 2nd difference over first.

Also you could just use \frac{y_2-y_1}{x_2-x_1}.  It is the same thing.

(  5  ,   5)

-(  1  ,   3)

--------------

  4      2

So the slope is 2/4 or 1/2 after reducing.

The point-slope form a line is

y-y_1=m(x-x_1) with a point on the line (x_1,y_1)=(1,3) given and with slope m=\frac{1}{2} given.

y-3=\frac{1}{2}(x-1)

We are going to solve this for y and simplify what we can because our goal is y=mx+b; this is slope-intercept form.  It is called that because it tells us the slope,m, and the y-intercept,b.

Distribute:

y-3=\frac{1}{2}x-\frac{1}{2}

Add 3 on both sides:

y=\frac{1}{2}x-\frac{1}{2}+3

Simplify:

y=\frac{1}{2}x+\frac{5}{2}

4 0
3 years ago
Alex is making puppets for a show. He bought all the string needed for $125.It costs $18 for the remaining materials to make eac
strojnjashka [21]

Answer:

900

Step-by-step explanation:

3 0
3 years ago
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