Answer:
Step-by-step explanation:
Here,
y
∝
x
⇒
y
=
k
x
where k is constant.
⇒
1
=
k
.2
[put y =1,x=2]
⇒
k
=
1
2
Again, y = kx
⇒
y
=
1
2
×
4
[put x = 4]
⇒
Y
=
2
Answer:
y
=
2
Answer: cools rapidly
Step-by-step explanation:
Some igneous rocks contain crystals of very different sizes. These
rocks formed from magma that started cooling within Earth and then
erupted onto the surface. The large crystals grew as the magma cooled
slowly. The small crystals grew as the lava cooled quickly.
Hope this helps!
Answer:
A. g(x) = (2x)²
Step-by-step explanation:
From the diagram of the two functions graph f(x) is the parent function and g(x) is the transformed function. you can see that the graph of g(x) is stretched vertically compared to the graph of g(x). The Parent function has y =1 corresponding to x =1 while for the transformed function when x = 1, y = 4 the graph is vertically stretched by a factor of 4, and horizontally The Parent function has y =1 corresponding to x =1. while for the transformed function when x = 0.5, y = 1, it is stretched horizontally by 2 (√4), i.e
This means that g(x) = 4x² = (2x)²
There are several ways to do this.
I'll show you two methods.
1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.
slope = m = (y2 - y1)/(x2 - x1)
Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.
Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.
Plug in values into the formula:
m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4
The slope is -1/4
2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.
Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4
As you can see we got the same slope using both methods.
Answer : Greatest number of identical dental care bags the dentist can make with the least items leftover is 1.
Number of bags will be 2,4,3 respectively.
Explanation:
Number of tubes of toothpaste = 56
Number of packets of floss = 112
Number of toothbrushes = 85
So, Greatest number of identical dental care bags the dentist can make with the least amount of items leftover from toothbrush = H.C.F of 56,112, 85= 1 ( ∵ as they are coprime to each other )
Since there is no common factor among 56,112,85 but there is common factor between 56 and 112 i.e. 56 remaining bags from toothbrushes will be 85-56=29 .
So we consider 28 ,
Now, 56 can be written as 28×2
112 can be written as 28×4 and
84 can be written as 28× 3
So, there can be 28 bags in which all the three materials can be present and there is no leftover from toothpaste and floss but there is leftover from toothbrushes only as we consider 84 instead of 85 to get divisible by 28 so we get the common factor easily.
so, there will be 2 two bags for toothpastes and 4 bags for floss and 3 bags for toothbrushes.
