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11Alexandr11 [23.1K]
3 years ago
11

Which of the algebraic expressions are not linear expressions? Select all that apply. a. 3x - 2 b. -9y c. -7x^2^ + 4x d. -1/2x^2

^ e. 8xy (The ^2^ means squared!)
Mathematics
1 answer:
Sedaia [141]3 years ago
6 0

Answer:

c, d and e

Step-by-step explanation:

A linear expression is an expression in which sum of exponents of variables is at most 1 in each of its terms.

Option a: 3x - 2

Here, the exponent of the variable is 1.

So, it is a linear expression.

Option b: -9y

Here, the exponent of the variable is 1.

So, it is a linear expression.

Option c: -7x^2 + 4x

Here, the highest exponent of the variable is 2.

So, it is NOT a linear expression.

Option d: -\frac{1}{2} x^2

Here, the exponent of the variable is 2.

So, it is NOT a linear expression.

Option e: 8xy

Here, sum of exponents of variables is 2.

So, it is NOT a linear expression.

Hence, c, d and e are NOT algebraic expressions.

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Let's say side length is s. 
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4 sides needed, total length thus 4*s.

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HELP!!!!
ss7ja [257]
<h3>3 Answers: Choice D, Choice E, Choice F</h3>

============================================================

Explanation:

The inequality 6x - 10y ≥ 9 solves to y ≤ (3/5)x - 9/10 when you isolate y.

Graph the line y = (3/5)x - 9/10 and make this a solid line. The boundary line is solid due to the "or equal to" as part of the inequality sign. We shade below the boundary line because of the "less than" after we isolated for y.

Now graph all of the points given as I've done so in the diagram below. The points in the blue shaded region, or on the boundary line, are part of the solution set. Those points are D, E and F.

We can verify this algebraically. For instance, if we weren't sure point E was  a solution or not, we would plug the coordinates into the inequality to get...

6x - 10y ≥ 9

6(5) - 10(2) ≥ 9 .... plug in (x,y) = (5,2)

30 - 20 ≥ 9

10 ≥ 9 ... this is a true statement

Since we end up with a true statement, this verifies point E is one of the solutions. I'll let you check points D and F.

-----------

I'll show an example of something that doesn't work. Let's pick on point A.

We'll plug in (x,y) = (-1,1)

6x - 10y ≥ 9

6(-1) - 10(1) ≥ 9

-6 - 10 ≥ 9

-16 ≥ 9

The last inequality is false because -16 is smaller than 9. So this shows point A is not a solution. Choices B and C are non-solutions for similar reasons.

3 0
2 years ago
How are y-intercepts of y=(1/3)^x and y=5(1/3)^x different?
loris [4]
Remark.
The easiest way to do this question is to graph it. Start with that.
The red line is y = (1/3)^x
The blue line is y = 5*(1/3)^x

Comment
The red line's y intercept is (0,1)
The blue line's y intercept is (0,5)

Why
If the x value is 0 then (1/3)^0 = 1
y = (1/3)^0 = 1 * 1 = 1 and for the blue graph
y =  5*(1/3)^0 = 5*1 = 5

In other words, in this set of equations, the 5 makes the y intercept 5 times larger than the 1 in front of y = (1/3)^x

If you have choices, could you please list them? I may be giving you the right answer but not in the form required.

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3 years ago
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-x - y = 8
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Ok, we are going to solve this in 2 parts.  First we have to solve for one of the variables in one of the equation in terms of the other variable.  I like to take the easiest equation first and try to avoid fractions, so let's use the first equation and solve for x.

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So now we have a value for x in terms of y that we can use to substitute into the other equation.  In the other equation we are going to put -8 - y in place of the x.

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Now we have a value for y.  We need to plug it into either of the original equations then solve for x.  I usually choose the most simple equation.

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Answer:

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