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Umnica [9.8K]
3 years ago
12

Write an inequality and solve each problem.

Mathematics
1 answer:
astra-53 [7]3 years ago
5 0
For all of these, let n = the unknown number. 

25) "Five less than a number" becomes 5 - n 
"At least" tells you your number is greater than or equal to - 2.
Put it all together.

5 - n ≥ - 2
- n ≥ - 2 - 5
- n ≥ - 7
Divide by - 1 to isolate the variable. This flips the operation.

n ≤ 7

26) "The difference between a number and 6" tells you to do n - 6
"no more than" means this is a less than or equal to sign. 

n - 6 ≤ 5
n ≤ 5 + 6

n ≤ 11

27) "The sum of a number and 7" becomes n + 7
"more than" is a greater than sign

n + 7 > 1
n > 1 - 7

n > - 6

28) "The difference between a number and 10" becomes n - 10
Obvious one, "greater than" is... just that.

n - 10 > 9
n > 9 + 10

n > 19

29) "Four less than a number" is 4 - n
Another obvious one in "less than" 

4 - n < 11
- n < 11 - 4
- n < 7
Divide by - 1 on both sides to isolate the variable

n > - 7
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What is partial derivative of z=(2x+3y)^10 with respect to x,y?
maw [93]
Not sure if you mean to ask for the first order partial derivatives, one wrt x and the other wrt y, or the second order partial derivative, first wrt x then wrt y. I'll assume the former.

\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9

\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9

Or, if you actually did want the second order derivative,

\dfrac{\partial^2}{\partial y\partial x}(2x+3y)^{10}=\dfrac\partial{\partial y}\left[20(2x+3y)^9\right]=180(2x+3y)^8\times3=540(2x+3y)^8

and in case you meant the other way around, no need to compute that, as z_{xy}=z_{yx} by Schwarz' theorem (the partial derivatives are guaranteed to be continuous because z is a polynomial).
3 0
3 years ago
Read 2 more answers
A line segment has an end point of ( -4,-6) which reflection will produce an image with endpoints (-4, 6) and (-6,-4)
HACTEHA [7]
The given point is (-4, -6)

First reflected point is (-4, 6).
Note that the x coordinate is same and y coordinate has opposite sign. Above x-axis, y is positive and below x-axis y is negative. This shows that the reflection was across x-axis which resulted in the change of sign of y coordinate.

Second reflected point is (-6, -4)
Notice that in comparison to the original point, the location of x and y coordinate has been interchanged. This can only happen when the reflection is across the line y = x. The reflection of a graph across y = x also results in the inverse of that graph, with x values and y values interchanging their positions.

So,
1st Answer: Reflection across x-axis
2nd Answer: Reflection across the line y = x
4 0
3 years ago
MY LAST QUESTION PLEASE HURRY, SORRY FOR RUSHING BY THE WAY
77julia77 [94]

Answer:40

Step-by-step explanation:

dividing 1200 by 600 is 2

so you would do the same for 80

6 0
3 years ago
How many different 6 letter words can be made from the word SMOOTH?
shutvik [7]

Answer:

0

Step-by-step explanation:

But you can make 5 letter words, 4, 3, and 2, just no 6 letters.

8 0
3 years ago
What is the y- intercept of the graph of 2x + y = -4?
Brrunno [24]

First write the equation in slope-intercept form which is more commonly known as <em>y = mx + b</em> form where the <em>m </em>or the coefficient of the x term represents the slope of the <em>b</em> or the constant term represents the y-intercept.

Subtract 2x from both sides to get <em>y = -2x - 4</em>.

I put the x term first because that's how it is in y = mx + b form.

Now we can see that the <em>b</em> or the constant term is -4.

We can write this as the ordered pair (0, -4).

Keep in mind when writing a y-intercept as an ordered pair, your x-coordinate will always be 0 in the ordered pair.

8 0
3 years ago
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