Find the distance from the point (9, -2) to the line y= 3/2x+ 4.
A)117 units
B)85 units
C)6 units
D)177 units

Answer:

[tex](-3,4/375)[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{6}(\frac{2}{5})^x[/tex]

Reflection: Across y-axis

Required

The ordered pair on g(x)

The rule of reflection across y-axis is:

[tex](x,y) = (-x,y)[/tex]

So, we have:

[tex]g(x) = f(-x)[/tex]

f(-x) is:

[tex]f(-x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

Recall that:

[tex]g(x) = f(-x)[/tex]

Hence:

[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

From the options (missing in the question), the ordered pair is:

[tex](-3,4/375)[/tex]

To check this, we have:

[tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x[/tex]

[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{--3[/tex]

[tex]g(-3) = \frac{1}{6}(\frac{2}{5})^{3[/tex]

Expand

[tex]g(-3) = \frac{1}{6}(\frac{8}{125})[/tex]

Simplify

[tex]g(-3) = \frac{1}{3}(\frac{4}{125})[/tex]

Open bracket

[tex]g(-3) = \frac{4}{375}[/tex]

Answer:

nt ooooo

o

Step-by-step explanation:

Answer:

x = V(X + 8) + 4

Step-by-step explanation:

Switch sides

x - 4 = V(X + 8\)

Add\ 4 to both sides

x - 4 + 4 = V(X + 8\) + 4

Simplify

x = V(X + 8) + 4

Answer:

122

Step-by-step explanation:

Angle ABE = angle ABF + EBF

11x - 31 = 6x + 26 + 2x - 9 add like terms

11x - 31 = 8x + 17 transfer like terms to the same side of the equation

11x - 8x = 17 + 31 add/subtract like terms

3x = 48 divide both sides by 3

x = 16 now replace x with 16 in the equation

16*6+26 = 122

Answer:

Alternate interior angles theorem

Step-by-step explanation:

Hope it helps you in your learning process.

options b is not correct

Answer:

B is right option

Step-by-step explanation

A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees.

Answer:

y-25 = 2(x-10)

Step-by-step explanation:

First find the slope using the points (10,25) and (20,45)

m = ( y2-y1)/(x2-x1)

m = (45 - 25)/(20-10)

   = 20/10

   = 2

Then using point slope form of a line

y-y1 = m(x-x1)

y-25 = 2(x-10)

Answer:

WX = WZ

Step-by-step explanation:

Given

See attachment for triangles

Required

Additional information to prove the congruence of the triangles

Congruence by SAS means 1 angle and 2 sides of each triangles are equal.

The mark on angle W means that <XWY = <ZWY--- This represent the A in SAS

Both triangles share line WY.

So, WY = WY

Lastly, to complete the proof, lines WX must equal line WZ

Answer:

9/2

Step-by-step explanation:

For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0.

-9/2 + 9/2 = 0

Answer:

9/2.

Step-by-step explanation:

If x is the additive inverse then

x + (-9/2) = 0

x - 9/2 = 0

so x = 9/2.

75 cents *2 / 3 = 50 cents

75 crnts + 50 cents = 125 cents

Answer:

The modal age is 11

The range is the highest minus the Lowe's which is 19-9=10

by using Pythagoras theorem c2= a2 + b2

so let's say c= 17 and a= 7, let's calculate for b

(17)^2 = (7)^2 + b2

289= 49+b2

289 - 49 = b2

240 =b2

√249 = b

b = 15 . 49

Answer:

[tex]3x^2-3x\left(x-2\right)-12=0[/tex]

[tex]3x^2-3x\left(x-2\right)-12+12=0+12 \longleftarrow (\mathrm{Add\:}12\mathrm{\:to\:both\:sides})[/tex]

[tex]3x^2-3x\left(x-2\right)=12[/tex]

[tex]-3x\left(x-2\right)=-3xx-\left(-3x\right)\cdot \:2[/tex]

[tex]=-3xx+3\cdot \:2x[/tex]

[tex]-3xx+3x^{2}[/tex]

[tex]=3x^{1+1}[/tex]

[tex]=3x^2[/tex]

[tex]3\cdot \:2x=6x[/tex]

[tex]=-3x^2+6x[/tex]

[tex]3x^2-3x^2+6x=12\Longleftarrow Add\:similar\:elements[/tex]

[tex]6x=12[/tex]

[tex]\frac{6x}{6}=\frac{12}{6} \Longleftarrow Divide[/tex]

[tex]x=2[/tex]

✧✧✧✧✧✧✧✧

OAmalOHopeO

✧✧✧✧✧✧✧✧

Answer: 12 units²

Step-by-step explanation:

To find the area of a parallelogram, we use the formula A=l×w. To find the length and width, let's graph out the parallelogram to get a better view. Let's refer to the picture attached to see what the graph looks like. The length is 4 units while the width is 3 units. Therefore we multiply.

A=4×3=12 units²

Now, we know the area is 12 units².

Answer:

24 is the answer because 18/3=6 6x4 is 24

Hello,

Here are the solution in excel files

par la méthode de Gauss

Answer:

(1/2×6×8)+(π×4^2/2)

=49.12 ft^2

☆○☆○☆○☆○☆○

Hope it helps..

Have a great day!!!

Wait sorry ignore this I'm still getting used to brainly and I did the question wrong sorry

Answer:

The answer is Tonya's phone had the greater initial trade-in value.

Leo's phone decreases at an average rate slower than the trade in value of Tonya's phone.

Step-by-step explanation:

Given

Tonya

[tex]f(x) = 490 * 0.88^x[/tex]

Leo

[tex]x \to g(x)[/tex]

[tex]0 \to 480[/tex]

[tex]2 \to 360[/tex]

[tex]4 \to 470[/tex]

Solving (a): The phone with greater initial value

The initial value is when x = 0. So, we have:

[tex]f(x) = 490 * 0.88^x[/tex]

[tex]f(0) = 490 * 0.88^0[/tex]

[tex]f(0) = 490 * 1[/tex]

[tex]f(0) = 490[/tex]

From Leo's table

[tex]g(0) = 480[/tex]

By comparison;

[tex]f(0) > g(0)[/tex]

i.e.

[tex]490 > 480[/tex]

So: Tonya's had the greater initial trade-in value

Solving (b): The phone with lesser rate

An exponential function is:

[tex]y = ab^x[/tex]

Where:

[tex]b \to rate[/tex]

For Tonya

[tex]b = 0.88[/tex]

For Leo, we have:

[tex](x_1,y_1) = (0,480)[/tex]

[tex](x_2,y_2) = (2,360)[/tex]

So, the equation becomes:

[tex]y = ab^x[/tex]

[tex]480 = ab^0[/tex] and [tex]360 = ab^2[/tex]

Solving [tex]480 = ab^0[/tex], we have:

[tex]480 = a * 1[/tex]

[tex]480 = a[/tex]

[tex]a= 480[/tex]

[tex]360 = ab^2[/tex] becomes

[tex]360 = 480 * b^2[/tex]

Divide both sides by 480

[tex]0.75 = b^2[/tex]

Take square roots

[tex]0.87 = b[/tex]

[tex]b=0.87[/tex] -- Leo's rate

By comparison; Leo's rate is slower i.e. 0.87 < 0.88

Answer:

Step-by-step explanation:

use the slope formula Faith,  

point P1 (-2a,0)  in the form (x1,y1)

point P2(0,-2b)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

m = (-2b - 0 ) / (0-(-2a))

m = -2b  / 2a

m = - b/a

they are trying to confuse  you with the  "a" and "b" variables in the problem, but just use the rules you know to solve what you can :)

Answer:

The correct answer is -7.5 years.

Step-by-step explanation:

Given:

Principle amount = 12000

Interest = 4320

time = ?

rate = 4.8 simple interest

Solution:

We know that simple Interest I = (P*t*r)/100

then t = I*100/p*r

putting values in formula:

t = 4320*100/4.8*12000

= 432000/57,600

= 7.5 years

Answer:

Step-by-step explanation:

Answer:

sin x

Step-by-step explanation:

sin ^2  x + sin x + cos ^ x -1

sin ^2  x + cos ^ x   + sin x-1

We know that sin^2 x + cos ^2 x = 1

1 + sin x -1

sin x

Hi!

[tex]\sin^2x+\sin x+\cos^2 x-1=\\\\=\underline{\sin^2x+\cos^2x}+\sin x-1=\\\\=1+\sin x-1=\boxed{\sin x}[/tex]

Answer:

woa

i  n

Step-by-step explanation:

Answer:

k = 1/4

Step-by-step explanation:

81y² - k = (9y)² - (1/2)²

(9y)² - k = (9y)² - (1/2)²

k =   (1/2)² = 1/4

Answer: $21, 600

Step-by-step explanation:

Given:

Original cost (when the shop owner brought it) = $20,000

Profit amount = 20% of original cost

Discount rate = 10%

Solve:

First Step: Find the market price (before discount)

Second Step: Find the discount price

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Area of triangle1/2b*h Now you can do

The area of the triangle is 9000 square centimeters

Let the sides in order of length be represented as:

x, y and z.

So, we have:

z = 80 + y

z = 130 + x

P = 540

The perimeter is calculated as:

P = x + y + z

So, we have:

x + y + z =540

Substitute z = 130 + x

x + y + 130 + x =540

Evaluate the like terms

2x + y = 410

Substitute z = 130 + x in z = 80 + y

130 + x  = 80 + y

Evaluate the like terms

x - y = -50

So, we have:

2x + y = 410

x - y = -50

Add both equations

3x = 360

Divide by 3

x = 120

Substitute x = 120 in z = 130 + x

z = 130 + 120

z = 250

Substitute z = 250 in z = 80 + y

250 = 80 + y

y = 170

So, we have:

x = 120

y = 170

z = 250

The area is then calculated as:

[tex]Area = \sqrt{s * (s -x) *(s - y) * (s -z)[/tex]

Where

s = P/2 = 540/2

s = 270

So, we have:

[tex]Area = \sqrt{270 * (270 -120) *(270 - 170) * (270 -250)[/tex]

Evaluate

Area = 9000

Hence, the area of the triangle is 9000 square centimeters

Read more about areas at:

https://brainly.com/question/24487155

#SPJ6

Answer:

Distributive property

Step-by-step explanation:

The question is not properly formatted.

From the available detail, I will re-write the question as follows

[tex]45x + 3(25x + 75y)[/tex]

Required

The property used

Distributive property is stated as follows:

[tex]a(b \± c) = ab \± ac[/tex]

So, we have:

[tex]45x + 3(25x + 75y) = 45x + 75x + 225y[/tex]

Evaluate like terms

[tex]45x + 3(25x + 75y) = 120x + 225y[/tex]

Answer:

x = 25.2

Step-by-step explanation:

[tex]\frac{5}{18} =\frac{7}{x}[/tex]

5x = 126

x = 25.2