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3 days ago

Georgia’s gross pay was $35,600 this year. She is to pay a federal income tax of 16%. How much should Georgia pay in federal inc

ome tax this year? Round to the nearest dollar. $29.90 $569.00 $5,696.00 $29,904.00

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If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, and , which condition needs to be met to prove ?

Zina [12379]

The answer
the full question is
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) create two line segments, and AB ⊥ CD, what condition must be satisfied to establish that AB ⊥ CD?

Let A(x1, y1) and B(x2, y2) represent the first line, while C(x3, y3) and D(x4, y4) represent the second line.

The slope for the first line is given by m = (y2 - y1) / (x2 - x1).
For the second line, the slope is m' = (y4 - y3) / (x4 - x3).

The necessary condition to demonstrate that AB ⊥ CD is

(y2 - y1) * (y4 - y3)
m × m' = --------- × ------------ = -1
(x2 - x1) (y4 - y3)

5 0

3 months ago

Read 2 more answers

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o

Svet_ta [12734]

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ both yield the same result.

Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Insert $x=1$ in $g(x)=-x+6$ to find the value of $g(1)$ .

$g(1)=-1+6\\g(1)=5$

Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

$g(2)=-2+6\\g(2)=4$

Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

$g(4)=-4+6\\g(4)=2$

Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

$g(5)=-5+6\\g(5)=1$

Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Also, substitute $x=6$ in $g(x)=-x+6$ to obtain the value of $g(6)$ .

$g(6)=-6+6\\g(6)=0$

Step 7:

According to the provided condition $f(x)=g(x)$ .

(a). Insert $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ into the previously mentioned equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply through by $-1$ on both sides.

$x^{2} -4x-12=x-6$

(c). Move the term $x-6$ to the left side of the equation.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6$

From the analysis above, it is noted that for $x=6$ both functions $f(x)$ and $g(x)$ yield the same outcome.

Using a direct approach:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0

1 month ago

Island A is 150 miles from island B. A ship captain travels 240 miles from island A and then finds that he is off course and 200

babunello [11817]

Applying the cosine law, we can determine:

c² = a² + b² - 2abcos(C) 
where: 
a, b, and c represent the sides of the triangle and C indicates the angle opposite to side c

Thus, we have:
150² = 240² + 200² - 2(240)(200)cos(C) 

Now we solve for C

22,500 = 57,600 + 40,000 - 96,000cos(C) 
22,500 - 57,600 - 40,000 = -96,000cos(C)
-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)→ C=38.53°

Therefore, the direction the captain should head towards island B is
180 - 38.53 = 141.47 degrees

4 0

2 months ago

Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur

tester [12383]

It appears you've gathered most of the relevant information, but a critical element is missing. The surface represented is parameterized by... and has a normal vector corresponding to this representation with a specified norm. Thus, the integral of... is...

6 0

1 month ago