Answer:
78
Step-by-step explanation:
a
The trapeze area is:
A = (1/2) * (B + b) * (h)
Where,
B: major base
b: minor base
h: height
Substituting values:
A = (1/2) * (8.5 + 4) * (2)
A = 12.5 feet ^ 2
For two gallons of paint the number of trapezoids is:
N = (2 * 350) / (12.5)
N = 56
Answer:
Lillian can paint with 2 gallons of paint 56 front frames of a podium
Answer:
This is easy -- it's just a list of steps. At this level, the problems are pretty simple.
Let's just do one, then I'll write out the list of steps for you.
Find the inverse of f( x ) = -( 1 / 3 )x + 1
STEP 1: Stick a "y" in for the "f(x)" guy:
y = -( 1 / 3 )x + 1
STEP 2: Switch the x and y
( because every (x, y) has a (y, x) partner! ):
x = -( 1 / 3 )y + 1
STEP 3: Solve for y:
x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3
STEP 4: Stick in the inverse notation, f^( -1 )( x )
f^( -1 )( x ) = -3x + 3
Step-by-step explanation:
Answer: $785
Step-by-step explanation:
A VA loan is a mortgage loan program established by the United States department of veteran affairs. The main objective of VA loans is to assist veterans,
Eligible surviving spouses and service members to have their own houses.
In many states, property tax reduction are offered to veterans including other additional benefits.
The appraised value is the value of a property as determined by the loan underwriting team.
VA loans are made on appraised value
Therefore, The origination fee of 1/2% equals :
(0.5/100) * $157,000 = $785
Answer:
The zeros are
![x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=x%3D-2%2C%5C%3Ax%3D3%2C%5C%3Ax%3D-%5Cfrac%7B1%7D%7B2%7D%2Bi%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%5C%3Ax%3D-%5Cfrac%7B1%7D%7B2%7D-i%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
Step-by-step explanation:
We have been given the equation x^4-6x^2-7x-6=0
Use rational root theorem, we have
![a_0=6,\:\quad a_n=1](https://tex.z-dn.net/?f=a_0%3D6%2C%5C%3A%5Cquad%20a_n%3D1)
![\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Adividers%5C%3Aof%5C%3A%7Da_0%3A%5Cquad%201%2C%5C%3A2%2C%5C%3A3%2C%5C%3A6%2C%5C%3A%5Cquad%20%5Cmathrm%7BThe%5C%3Adividers%5C%3Aof%5C%3A%7Da_n%3A%5Cquad%201)
![\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}](https://tex.z-dn.net/?f=%5Cmathrm%7BTherefore%2C%5C%3Acheck%5C%3Athe%5C%3Afollowing%5C%3Arational%5C%3Anumbers%3A%5Cquad%20%7D%5Cpm%20%5Cfrac%7B1%2C%5C%3A2%2C%5C%3A3%2C%5C%3A6%7D%7B1%7D)
![-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B1%7D%5Cmathrm%7B%5C%3Ais%5C%3Aa%5C%3Aroot%5C%3Aof%5C%3Athe%5C%3Aexpression%2C%5C%3Aso%5C%3Afactor%5C%3Aout%5C%3A%7Dx%2B2)
![=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\](https://tex.z-dn.net/?f=%3D%5Cleft%28x%2B2%5Cright%29%5Cfrac%7Bx%5E4-6x%5E2-7x-6%7D%7Bx%2B2%7D%5C%5C)
![=x^3-2x^2-2x-3](https://tex.z-dn.net/?f=%3Dx%5E3-2x%5E2-2x-3)
Again factor using the rational root test, we get
![=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)](https://tex.z-dn.net/?f=%3D%5Cleft%28x%2B2%5Cright%29%5Cleft%28x-3%5Cright%29%5Cleft%28x%5E2%2Bx%2B1%5Cright%29)
Using the zero product rule, we have
![x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=x%2B2%3D0%3A%5Cquad%20x%3D-2%5C%5Cx-3%3D0%3A%5Cquad%20x%3D3%5C%5Cx%5E2%2Bx%2B1%3D0%5C%5C%5C%5Cx_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A1%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%5C%5C%5C%5C%3D-%5Cfrac%7B1%7D%7B2%7D%2Bi%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%5C%3Ax%3D-%5Cfrac%7B1%7D%7B2%7D-i%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
Therefore, the zeros are
![x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=x%3D-2%2C%5C%3Ax%3D3%2C%5C%3Ax%3D-%5Cfrac%7B1%7D%7B2%7D%2Bi%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%5C%3Ax%3D-%5Cfrac%7B1%7D%7B2%7D-i%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)