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2 years ago

Write an equation in slope-intercept form for the line parallel to y = 2x – 2

Mathematics

2 answers:

ValentinkaMS [17]2 years ago

7 0

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

$y=\stackrel{\stackrel{m}{\downarrow }}{2}x-2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of al ine whose slope is 2 and passes through (5,-4)

$(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4}) \qquad \qquad \stackrel{slope}{m}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{2}(x-\stackrel{x_1}{5})\implies y+4=2(x-5) \\\\\\ y+4=2x-10\implies y=2x-14$

astra-53 [7]2 years ago

5 0

Y = 2x-14
you can use the point slope formula as you have a coordinate given to you. Y - Y1 = m ( X - X1)
Y + 4 = 2 ( X - 5)
Y + 4 = 2X - 10
Y = 2X - 14

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Find x<br> A. 22√2<br> B. 22<br> C. 11√3/3<br> D. 11√3

mel-nik [20]

Answer

$22\sqrt{2}$

Step-by-step explanation:

First we gave a name to the side that is common for both triangles, can be Y for example.

Using trigonometric functions we can make a relationship between the two angles that we have and the magnitud of the side.

$sin(45)=\frac{11}{Y} \\$ , Because sin(x)= op/hip

$cos(60)=\frac{Y}{x}$ , Because con(x)=ad/hip

Having this equations, we can solve the system and find x

$Y=\frac{11}{sin(45)} \\Y=cos(60)*x$

we equal Y and solve

$\frac{11}{sin(45)}=cos(60)*x\\ x=\frac{11}{sin(45)*cos(60)} \\x=\frac{11}{\frac{\sqrt{2} }{2} *\frac{1}{2} } \\x=\frac{11}{\frac{\sqrt{2} }{4} } \\x=\frac{44}{\sqrt{2} }\\$

Then we rationalize

$x=22\sqrt{2}$

Hope you like it!

7 0

3 years ago

Read 2 more answers

The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −20 3x

tester [92]

Answer:

Option D is correct.

13x = 39

Step-by-step explanation:

The system of equation is given:

$2x-y = -4$ ....[1]

$3x+5y = 59$ .....[2]

Multiply equation [1] by 5 to both sides we have;

$10x-5y = -20$ .....[3]

Using elimination method:

Add [2] and [3] equations to eliminate y and solve for x, we have;

$13x = 39$

Divide both sides by 13 we get;

x = 3

Substitute x in [1] we have;

2(3)-y = -4

6-y = -4

Subtract 6 from both sides we have;

-y = -10

Divide both sides by -1 we have;

y = 10

⇒Solution: (3, 10)

Therefore, an equation can replace 3x+5y = 59 in the original system and still produce the same solution is,

13x = 39

6 0

3 years ago

Read 2 more answers

Subtract: 6/2x^+8x - x/4x^+12x-16 = 6/2x(x+4) - x/4(x+4)(x-1) = 6•2(x-1)/2x(x+4)•2(x-1) - x•x/4(x+4)(x-1)•x

ss7ja [257]

Answer:

$\frac{-x^2+12x-12}{4x(x+4)(x-1)}$

Step-by-step explanation:

$\frac{6}{2x(x+4)}- \frac{x}{4(x+4)(x-1)}$

$\frac{6\cdot2(x-1)}{2x(x+4)\cdot2(x-1)}- \frac{x\cdot x}{4(x+4)(x-1)x}$

$\frac{12(x-1)}{4x(x+4)(x-1)}- \frac{x^2}{4x(x+4)(x-1)}$

$\frac{12(x-1)-x^2}{4x(x+4)(x-1)}$

$\frac{-x^2+12x-12}{4x(x+4)(x-1)}$

5 0

4 years ago

Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

7 0

3 years ago

If a yard of fabric cost $12.99 then how much will 2 feet cost

Ratling [72]

We know that 1 ft= 1/3 yd.

2 ft* (1/3 yd/ 1 ft)* ($12.99/ 1 yd)= $8.66
(Note that the units cancel out so you get the answer)

2 ft of fabric will cost $8.66~

5 0

3 years ago