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nordsb [41]
3 years ago
5

Do you prefer to express solutions to inequalities using interval notation or as an inequality ? Do you think it’s important to

know both formats ? How could each be used ?
Mathematics
1 answer:
docker41 [41]3 years ago
8 0

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of <em>'x>3 or x<-3' </em>which is more confusing.

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A line passes through the point, (−8,7) and has a slope of −5/4. Please help...
o-na [289]

Answer:

5x + 4y + 12 = 0

Step-by-step explanation:

Start with the point-slope equation of a straight line:  y - k = m(x -  h):

Here we are given the point (h, k):  (-8, 7) and the slope m = -5/4.  Inserting this info into the equation give above, we get:        y - 7 = (-5/4)(x + 8).

We must put this equation into "standard form" Ax + By + C = 0.

Multiply all three terms by 4 to remove fractions:  4y - 28 = -5(x + 8), or

4y - 28 + 5x + 40 = 0

Rearranging these terms, we get 5x + 4y + 12 = 0, which is the desired equation in standard form.

8 0
3 years ago
Explain proportionality to me 7th grade math ​
kari74 [83]

If two quantities <em>a</em> and <em>b</em> are directly proportional to one another, then both <em>a</em> and <em>b</em> change in the <u>same direction</u>.

For example, if the amount/volume of coffee I have in a cup is directly proportional to the total volume of the cup, then the larger the cup gets, the more coffee I can fill it with. On the other hand, if the cup gets smaller, the amount of coffee it can hold also gets smaller.

Both <em>a</em> and <em>b</em> don't necessarily change at the same rate, though, which means one of these needs to get appropriately scaled by some factor <em>k</em>, so that

<em>a</em> = <em>kb</em>

Continuing the coffee example: Suppose I only fill my cup halfway. If the total volume of the cup is <em>a</em>, then the amount of coffee I pour in is <em>b</em> = 1/2 <em>a</em>. So the relationship of these two quantities is governed by the equation,

<em>a</em> = 2<em>b</em>

and in this case, <em>k</em> = 2.

If instead <em>a</em> and <em>b</em> are inversely proportional, this means as one quantity changes, the other changes in the <u>opposite direction</u>.

Suppose I have two cups that I use for coffee that can both hold the same amount <em>k</em> if they are filled completely, but one cup is taller than the other. In order for both cups to be able to hold the same volume of coffee, the taller cup must have a thinner profile.

The cups are cylindrical, so that their volumes are equal to the products of the area of their base <em>a</em> and their height <em>b</em>. If one cup is twice as tall as the other, then for the smaller cup we could have

<em>ab</em> = <em>k</em>

and for the taller one,

<em>a</em> (2<em>b</em>) = <em>k</em>

But in order to get the same volume, the quantity <em>a</em> for the shorter cup must be cut in half to preserve equality:

(1/2 <em>a</em>) (2<em>b</em>) = <em>ab</em> = <em>k</em>

So one quantity is doubled (increases), while the other gets halved (decreases).

5 0
3 years ago
Carly bought a new house for $125,000. The value of the house appreciates approximately 3.5% each year. What will be the value o
mixer [17]
For 1 year, the house appreciates $4375 (3.5% of 125,000). Therefore after 10 years, $4375(10) = $43750. $125,000+ $43750 = $168,750.
6 0
2 years ago
Read 2 more answers
Difference between cylinder and cone
lord [1]
A cylinder has two bases and a height that (unless oblique) runs right along a side, while a cone has one base and whose height begins at the center of its base and goes straight up to the peak.
7 0
3 years ago
which of the following could be represented by -8? a dropof 8 meters, 8 T-shirt, sea level in 8 places of the world, 8 c above z
Liula [17]
A drop of 8 meters can be represented as -8
3 0
2 years ago
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