Answer:
(1,6)
x = 1, y = 6
See attachment for the graph
Step-by-step explanation:
y=x+5
y=-x+7
Using the elimination process
y=x+5
- y=-x+7
----------------
0=2x-2
2=2x
1=x
x=1
Substitute x = 1
y = x + 5
y = 1 + 5
y = 6
Answer:
Option (2)
Step-by-step explanation:
x = 1 is represented by a solid point on a number line.
x > 1 is represented by an arrow starting from x = 1 towards infinity
If we mix both the properties, x ≥ will be represented by an arrow starting from a solid point at x = 1 and moving towards the values greater than one.
From the options given,
Arrow mentioned in Option (2) will be the correct representation of the inequality.
Answer:
![\text{ 78\%}](https://tex.z-dn.net/?f=%5Ctext%7B%2078%5C%25%7D)
Explanation:
Here, we want to get the percentage of the gross pay is the take-home pay
Mathematically, we have to divide the take-home pay by the gross pay and multiply it by 100%
Her take-home pay is the difference between her gross pay and her deductions
We have this as:
![\text{ 4633 - 1009.13 = \$3,623.87}](https://tex.z-dn.net/?f=%5Ctext%7B%204633%20-%201009.13%20%3D%20%5C%243%2C623.87%7D)
We have this as:
Answer : The length of the wire is, 8533 cm
Step-by-step explanation :
As the iron sphere is beaten and drawn into a wire. That means, their volume will be equal.
Volume of iron sphere = Volume of cylindrical wire
The formula will be:
![\frac{4}{3}\pi r_1^3=\pi r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r_1%5E3%3D%5Cpi%20r_2%5E2h)
where,
= radius of sphere = ![\frac{Diamtere}{2}=\frac{8cm}{2}=4cm](https://tex.z-dn.net/?f=%5Cfrac%7BDiamtere%7D%7B2%7D%3D%5Cfrac%7B8cm%7D%7B2%7D%3D4cm)
= radius of cylindrical wire = ![\frac{Diamtere}{2}=\frac{2mm}{2}=1mm=0.1cm](https://tex.z-dn.net/?f=%5Cfrac%7BDiamtere%7D%7B2%7D%3D%5Cfrac%7B2mm%7D%7B2%7D%3D1mm%3D0.1cm)
h = height of cylindrical wire or length of wire
Now put all the given values in the above formula, we get:
![\frac{4}{3}\pi r_1^3=\pi r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r_1%5E3%3D%5Cpi%20r_2%5E2h)
![\frac{4}{3}\times r_1^3=r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ctimes%20r_1%5E3%3Dr_2%5E2h)
![\frac{4}{3}\times (4)^3=(0.1)^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ctimes%20%284%29%5E3%3D%280.1%29%5E2h)
![h=8533.33cm\approx 8533cm](https://tex.z-dn.net/?f=h%3D8533.33cm%5Capprox%208533cm)
Therefore, the length of the wire is, 8533 cm
Answer: 10350
Step-by-step explanation:
Amount invested = Principal = 180,000
Interest rate = 5.75%
Time = 1 year
The interest that is earned at the end of the first year will be:
= PRT
= 180,000 × 5.75% × 1
= 180,000 × 0.0575 × 1
= 10350