All categories

3 years ago

Pls help me will give brainliest

Mathematics

1 answer:

maksim [4K]3 years ago

3 0

Answer:

1. Because they are Vertically opposite

2. 2 lines that form a straight line and form 180 degrees when added are called a linear pair.

3. Because angle 1 and 2 is a linear pair and forms 180 degrees. The same goes for angles 2 and 3.

4. Because when they are a linear pair and together they form 180 degrees.

5. Angle 1 and 2, angles 2 and 3 are linear pairs. And linear pairs always form 180 degrees. So, they are both equal.

6. Because they are vertically opposite angles.

7. Because they are vertically opposite angles.

:) :) :) :) :) :) :)

You might be interested in

Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.

jarptica [38.1K]

$y''-y'+y=\sin x$

The corresponding homogeneous ODE has characteristic equation $r^2-r+1=0$ with roots at $r=\dfrac{1\pm\sqrt3}2$ , thus admitting the characteristic solution

$y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x$

For the particular solution, assume one of the form

$y_p=a\sin x+b\cos x$

${y_p}'=a\cos x-b\sin x$

${y_p}''=-a\sin x-b\cos x$

Substituting into the ODE gives

$(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x$

$-b\cos x+a\sin x=\sin x$

$\implies a=1,b=0$

Then the general solution to this ODE is

$\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}$

$y''-3y'+2y=e^x\sin x$

$\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2$

$\implies y_c=C_1e^x+C_2e^{2x}$

Assume a solution of the form

$y_p=e^x(a\sin x+b\cos x)$

${y_p}'=e^x((a+b)\cos x+(a-b)\sin x)$

${y_p}''=2e^x(a\cos x-b\sin x)$

Substituting into the ODE gives

$2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x$

$-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x$

$\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12$

so the solution is

$\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}$

$y''+y=x\cos(2x)$

$r^2+1=0\implies r=\pm i$

$\implies y_c=C_1\cos x+C_2\sin x$

Assume a solution of the form

$y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)$

${y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)$

Substituting into the ODE gives

$(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)$

$-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)$

$\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49$

so the solution is

$\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}$

7 0

3 years ago

The sum of three numbers is 24. Twice the middle number is 2 more than the largest number, and the largest number is equal to th

harina [27]

Answer:

x = 5, y = 7, z = 12

Step-by-step explanation:

Let the numbers be x, y and z

x + y + z = 24
2y = z + 2
z = x + y

Solving by substitution:

x + y + z = z + z = 24
2z = 24
z = 12

2y = z + 2
2y = 12 + 2
2y = 14
y = 7

z = x + y
x = z - y
x = 12 - 7 = 5

The answer:

x = 5, y = 7, z = 12

8 0

3 years ago

Find the distance between each pair of points

dolphi86 [110]

Answer: the correct answer is 20

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the graph given,

x2 = - 7

x1 = 5

y2 = - 7

y1 = 9

Therefore,

Distance = √(- 7 - 5)² + (- 7 - 9)²

Distance = √(- 12²) + (- 16)²

= √(144 + 256) = √400

Distance = 20

5 0

3 years ago

Solve for y when x =0 -9x-2y=-20

madam [21]

substitute 0 for x in the equation.

-9(0) - 2y= -20

0 - 2y = -20

-2y= -20 (divide by -2)

y = 10

5 0

3 years ago

Read 2 more answers

Convert 30 feet per second to miles per minute.

Amanda [17]

We know that:

1 mile = 5280 ft

1 minute = 60 sec

Therefore to convert this we simply use the conversion factors:

(30 ft / s) * (60 s / 1 min) * (1 mi / 5280 ft) = 0.34 mi / min

So we got 0.34 miles per minute.

8 0

3 years ago