Answer:
14.24 foot far is the mirror from the base of the statue.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the statement:
See the diagram as shown below:
Height of a boy = 5.9 foot tall
Height of a statue = 12 foot.
Distance of a boy from the mirror = 7 feet.
Let x be the distance of the mirror from the base of the statue.
then by definition of proportion we have;
![\frac{\text{Height of a boy}}{\text{Distance of a boy from the mirror}}= \frac{\text{Height of a statues}}{\text{Distance of mirror from the base of the statue} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BHeight%20of%20a%20boy%7D%7D%7B%5Ctext%7BDistance%20of%20a%20boy%20from%20the%20mirror%7D%7D%3D%20%5Cfrac%7B%5Ctext%7BHeight%20of%20a%20statues%7D%7D%7B%5Ctext%7BDistance%20of%20mirror%20from%20the%20base%20of%20the%20statue%7D%20%7D)
Substitute the given values we have;
![\frac{5.9}{7} =\frac{12}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B5.9%7D%7B7%7D%20%3D%5Cfrac%7B12%7D%7Bx%7D)
By cross multiply we have;
![5.9x = 84](https://tex.z-dn.net/?f=5.9x%20%3D%2084)
Divide both sides by 5.9 we have;
x = 14.24 ft
Therefore, 14.24 foot far is the mirror from the base of the statue.
A. Answer: y = 32.913(1.126)ˣ
<u>Step-by-step explanation:</u>
You are given two coordinates (2, 53) and (9, 122). Use these to create a system of equations:
53 = a(b)² and 122 = a(b)⁹
122 = a(b)²· (b)⁷
122 = 53 · (b)⁷
![\dfrac{122}{53}=b^7](https://tex.z-dn.net/?f=%5Cdfrac%7B122%7D%7B53%7D%3Db%5E7)
![\sqrt[7]{\dfrac{122}{53}}=b](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7B%5Cdfrac%7B122%7D%7B53%7D%7D%3Db)
1.126 = b
Substitute the b-value into either of the equations to solve for "a":
53 = a(1.126)²
![\dfrac{53}{(1.126)^2}=a](https://tex.z-dn.net/?f=%5Cdfrac%7B53%7D%7B%281.126%29%5E2%7D%3Da)
32.913 = a
Input the a- & b-values into the general form of an exponential equation:
y = a(b)ˣ
y = 32.913(1.126)ˣ
***********************************************************************************
B. Answer: 23 minutes
<u>Step-by-step explanation:</u>
Substitute y = 500 into the equation above to solve for x:
500 = 32.913(1.126)ˣ
![\dfrac{500}{32.913}=(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=ln(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=x\cdot ln(1.126)\\\\\\\dfrac{ln\bigg(\dfrac{500}{32.913}\bigg)}{ln(1.126)}=x\\\\\\\boxed{23 = x}](https://tex.z-dn.net/?f=%5Cdfrac%7B500%7D%7B32.913%7D%3D%281.126%29%5Ex%5C%5C%5C%5C%5C%5Cln%5Cbigg%28%5Cdfrac%7B500%7D%7B32.913%7D%5Cbigg%29%3Dln%281.126%29%5Ex%5C%5C%5C%5C%5C%5Cln%5Cbigg%28%5Cdfrac%7B500%7D%7B32.913%7D%5Cbigg%29%3Dx%5Ccdot%20ln%281.126%29%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bln%5Cbigg%28%5Cdfrac%7B500%7D%7B32.913%7D%5Cbigg%29%7D%7Bln%281.126%29%7D%3Dx%5C%5C%5C%5C%5C%5C%5Cboxed%7B23%20%3D%20x%7D)
Answer:
$150
Step-by-step explanation:
Annual Real Estate Tax Rate =1.8%
Value of Bonnie's House = $100,000
Annual Tax= 1.8 % × $100,000 =0.018 × $100,000 = $1,800
Therefore, tax payment on a monthly basis
= $1,800÷12 Months
= $150 per month.
Real estate tax will add $150 per month to Bonnie's mortgage payment.
y=400+50x
y=300+25x
Step-by-step explanation:
x is the number of minutes and y is the total cost