Answer:
3
Step-by-step explanation:
The constant of proportionality (or the slope) is 3. Observe that if x increases by 2 (from 1 to 3), y increases by 6 from 3 to 9, so that m = rise/run = 6/2, or 3.
Answer:
![a=7.5](https://tex.z-dn.net/?f=a%3D7.5)
Step-by-step explanation:
Given the function
and the output
when
, we can write the equation:
![6a-15=30](https://tex.z-dn.net/?f=6a-15%3D30)
![6a=45](https://tex.z-dn.net/?f=6a%3D45)
![a=7.5](https://tex.z-dn.net/?f=a%3D7.5)
We can insert the value of
into the function to verify the output equals
:
![f(a) = 6a-15](https://tex.z-dn.net/?f=f%28a%29%20%3D%206a-15)
![= 6(7.5)-15](https://tex.z-dn.net/?f=%3D%206%287.5%29-15)
![=30](https://tex.z-dn.net/?f=%3D30)
∴ We have verified that ![a=7.5](https://tex.z-dn.net/?f=a%3D7.5)
Hope this helps :)
<u>Answer:</u>
If the circumference of a circle is changed from 9 cm to 3 cm, then the diameter decreases by a factor of 3.
<u>Solution:</u>
Given, the circumference of a circle is changed from 9 cm to 3 cm,
We have to find how will the diameter change from the given equations?
We know that, diameter = 2
radius and circumference = 2π
radius.
![\text { Now, circumference }=\pi \times(2 \times \text { radius }) \rightarrow \text { circumference }=\pi \times \text { diameter }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Now%2C%20circumference%20%7D%3D%5Cpi%20%5Ctimes%282%20%5Ctimes%20%5Ctext%20%7B%20radius%20%7D%29%20%5Crightarrow%20%5Ctext%20%7B%20circumference%20%7D%3D%5Cpi%20%5Ctimes%20%5Ctext%20%7B%20diameter%20%7D)
![\text { At initial stage } \rightarrow \text { circumference }=9 \rightarrow \pi \times \text { diameter }=9 \rightarrow \text { diameter }=\frac{9}{\pi}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20At%20initial%20stage%20%7D%20%5Crightarrow%20%5Ctext%20%7B%20circumference%20%7D%3D9%20%5Crightarrow%20%5Cpi%20%5Ctimes%20%5Ctext%20%7B%20diameter%20%7D%3D9%20%5Crightarrow%20%5Ctext%20%7B%20diameter%20%7D%3D%5Cfrac%7B9%7D%7B%5Cpi%7D)
![\text { Now, after change } \rightarrow \text { circumference }=3 \rightarrow \pi \times \text { diameter }=3 \rightarrow \text { diameter }=\frac{3}{\pi}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Now%2C%20after%20change%20%7D%20%5Crightarrow%20%5Ctext%20%7B%20circumference%20%7D%3D3%20%5Crightarrow%20%5Cpi%20%5Ctimes%20%5Ctext%20%7B%20diameter%20%7D%3D3%20%5Crightarrow%20%5Ctext%20%7B%20diameter%20%7D%3D%5Cfrac%7B3%7D%7B%5Cpi%7D)
![\text { Now, for finding change in factor }=\frac{\text { new diameter }}{\text { old diameter }}=\frac{\frac{3}{\pi}}{\frac{9}{\pi}}=\frac{3}{9}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Now%2C%20for%20finding%20change%20in%20factor%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20new%20diameter%20%7D%7D%7B%5Ctext%20%7B%20old%20diameter%20%7D%7D%3D%5Cfrac%7B%5Cfrac%7B3%7D%7B%5Cpi%7D%7D%7B%5Cfrac%7B9%7D%7B%5Cpi%7D%7D%3D%5Cfrac%7B3%7D%7B9%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Hence, the diameter decreases by a factor of 3.
Answer:
x = 125.44
Step-by-step explanation:
you multiply both side by 7
so 7 • 17.92 = 7 • x/7
125.44 = x