3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
a) Show that x = 3.
b) Given that y = 1/2 determine the value of k.

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:

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:

x = 9

y = 9

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

This is really simple once you get the hang of it. Promise. Remember this:

IF YOU HAVE THE OPPORTUNITY TO CHOOSE A POINT FROM THE TABLE WHERE X = 0, THEN DO IT!

This gives you the a value in your equation and you don't have to solve for it. I'll show you how this looks in the first table of values and then we won't have to do it going forward.

I'm using the coordinates (0, 1) and (1, .5) from the first table. Filling in the equation with the first set of coordinates:

[tex]1=a(b)^0[/tex] and since anything to the 0 power is 1, we know a = 1 (this happens every time we have a coordinate in an exponential table where the x value is 0. a always equals whatever y is!)

Now that we know a = 1, we use that along with the next coordinate pair and solve for b:

[tex].5=1(b)^1[/tex] which simplifies to

.5 = b and the equation is

[tex]y=1(.5)^x[/tex]

For the next table use the coordinate (0, 50) and 1, 25). From the above explanation, I know that a = 50 (because x = 0). Use that along with the next coordinate pair to solve for b:

[tex]25=50(b)^1[/tex] which simplifies to

b = .5 and the equation is

[tex]y=50(.5)^x[/tex]

Lastly, use the points (0, 192) and (1, 768) and we know that a = 192; and it follows that

[tex]768=192(b)^1[/tex] so

b = 4 and the equation is

[tex]y=192(4)^x[/tex]

The first 2 of these are exponential decay because the number inside the parenthesis is less than 1 but greater than 0; the last one is exponential growth since the number inside the parenthesis is greater than 1. That's how you can tell.

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: A

Step-by-step explanation:

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:

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:

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:

x = 25.2

Step-by-step explanation:

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

5x = 126

x = 25.2

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

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](-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:

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.

Answer:

Does the answer help you?

Answer:

nt ooooo

o

Step-by-step explanation:

Answer:

Option a (4 MPa) is the right answer.

Step-by-step explanation:

The given values are:

Force,

F = 8 kN

Area,

A = 2 cm²

The stress will be:

⇒ [tex]\sigma = \frac{Force}{Area}[/tex]

By substituting the given values, we get

       [tex]=\frac{8}{2}[/tex]

       [tex]= 4 \ MPa[/tex]

Answer:

15.3 cm² is the correct answer for that question

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: 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.

Hello,

Here are the solution in excel files

par la méthode de Gauss

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:

woa

i  n

Step-by-step explanation:

Answer:

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

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:

[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:

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