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4 years ago

Given the system of linear equations:

Mathematics

1 answer:

Vanyuwa [196]4 years ago

3 0

Answer:

Step-by-step explanation:

hello :

Part A : x+6y =6 means : 6y = - x+6

so : y = (-1/6)x+1 an equation for the line (D)

y = (1/3)x -2 is the line (D')

PartB : solution of the system : y = (-1/6)x+1 ....(1) color red

y = (1/3)x -2 ....(2) color bleu

is the intersection point : (6 ; 0)

PartC : Algebraically by (1) and (2) : (-1/6)x+1 = (1/3)x -2

(-1/6)x - (1/3)x = -2-1

(-x-2x)/6= -3

-3x = -18

so : x = 6 put this value in (1) or (2) : y = (-1/6)(6)+1 =0 the solution is : (6 ;0)

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Korri plotted three vertices of a rectangle on a coordinate plain at (-3,3) (1.5,3), (-3, -21/2.) Wha t is the 4rth point of the

otez555 [7]

Answer:

$(x_4,y_4) = (1.5,-2\frac{1}{2})$

Step-by-step explanation:

Given

$(x_1,y_1) = (-3,3)$

$(x_2,y_2) = (1.5,3)$

$(x_3,y_3)=(-3,-2\frac{1}{2})$

Required

Determine the coordinate of the 4th point

From the given parameters, we can see that the rectangle is either horizontal or vertical.

This is because:

$x_1 = x_3 = -3$

and

$y_1 = y_2 = 3$

To calculate the fourth point, we simply make use of:

$x_2 = x_4$ and $y_3 = y_4$

Substitute 1.5 for x2 in $x_2 = x_4$

$1.5= x_4$

$x_4=1.5$

Substitute -2 1/2 for y3 in $y_3= y_4$

$-2\frac{1}{2}= y_4$

$y_4 = -2\frac{1}{2}$

Hence, the 4th point is:

$(x_4,y_4) = (1.5,-2\frac{1}{2})$

8 0

3 years ago

Find (a) the amplitude, (b) the wavelength, (c) the period, and (d) the speed of a wave whose displacement is given by y= 1.5 co

leonid [27]

Answer with Step-by-step explanation:

We are given that displacement of wave

$y=1.5cos(0.68x+37t)$

Where y in cm and t in sec.

a.Compare it with

$y=Acos(kx+\omega t)$

Amplitude of wave=A

We get A=1.5

Amplitude=A=1.5 cm

b.k=0.68

$\frac{2\pi}{\lambda}=0.68$

$\lambda=\frac{2\times 3.14}{0.68}=9.2 cm$

Using $\pi=3.14$

Wavelength of the wave=9.2 cm

c.Period= $\frac{2\pi}{T}=\omega$

$\frac{2\pi}{T}=37$

$T=\frac{2\times 3.14}{37}=0.17 s$

The period of the wave=0.17 s

Speed of the wave= $\nu \lambda=\frac{\lambda}{T}=\frac{9.2}{0.17}$

Speed of the wave=54.1 cm/s

8 0

3 years ago

Simplify the expression: x2+x(x-5) -x+7

Veronika [31]

Hi mate!

The answer after simplifying is: 2x^2-6x+7

Please let me know if you need further assistance! Have a terrific evening.
~Brooke❤️

8 0

3 years ago

Evaluate each expression:<br> I-3|=

mote1985 [20]

The value of the modulus function |-3| is 3.

<h3>What is the value of modulus?</h3>

'Modulus' exists a Latin word, which signifies 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value designates only the numeric value and does not contain the sign of the numeric value. The modulus of any vector quantity exists ever taken as positive and exists in its absolute value.

The absolute value (or modulus) | x | of a real number x stands as the non-negative value of x without regard to its sign.

For example, the absolute value of 5 stands at 5, and the absolute value of −5 exists also at 5. The absolute value of a number may be considered as its distance from zero along a real number line.

Therefore, the value of the modulus function |-3| is 3.

To learn more about the value of modulus refer to:

brainly.com/question/271574379

#SPJ9

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2 years ago

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lakkis [162]

Its either (top to bottom) 1 or 4

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3 years ago