Plz help. Which problem is a linear equation?

When are absolute values and the opposite of a rational number equal

miskamm [114]

When the rational number is negative

7 0

3 years ago

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Hey Guys...I need help again... Which graph represents a proportional relationship?

sukhopar [10]

Answer:

A

Step-by-step explanation:

For a graph to be representative of a proportional relationship, it must meet the following criteria:

1) It is a straight line.

2) It passes through the origin point (0,0).

3) It is neither horizontal nor vertical*.

We can see that D is not a line. So, D is not a proportional relationship.

We can also see that B and C are vertical and horizontal, respectively. They also do not cross the origin.

The only choice that is a straight line and also crosses through the origin point is A.

So, our answer is A.

And we're done!

*Note: Vertical lines are not proportional because they are not a function.

Horizontal lines are not proportional because they has a constant of proportionality of 0, which can't be the case.

8 0

3 years ago

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Simon and his niece Marcie are comparing their ages to see if there is a Mathematical connection. They find that Simon is three

Rom4ik [11]

Answer:

Simon's Age = 47

Marcie's Age = 11

Step-by-step explanation:

The question is to find Simon's age and Marcie's age.

Let Simon's age be x and Marcie's age be y

Simon is 3 years more than 4 times marcie, so we can write:

x = 4y + 3

Also,

Sum of their ages is 58, so we can write:

x + y = 58

or x = 58 - y

Now, we substitute this into 1st equation and solve for y first:

$x = 4y + 3\\58-y = 4y + 3\\58-3=4y+y\\55=5y\\y=\frac{55}{5}\\y=11$

We know

x = 58 - y

so,

x = 58 - 11

x = 47

So,

Simon's Age = 47

Marcie's Age = 11

3 0

2 years ago

#1: 36 in.=__________ft?

KatRina [158]

1. 3 foot
2. 4 yard
3. 1 yard
4. 4 foot
5. 6 foot
6. 108 inch
7. 7.5 foot
8. 66 inch
9. 216 inch
10. 36 foot
11. 3.75 foot
12. 30 yard

3 0

2 years ago

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

is

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

2 years ago