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3 years ago

What is the equation of a line perpendicular to why=2x-6 that passes through (5,4)

Mathematics

1 answer:

almond37 [142]3 years ago

4 0

Answer:

y = ½(13- x)

Step-by-step explanation:

Step 1. Find the<em> slope (m₁) of the original line </em>

The equation for the original line is

y = 2x - 6

slope = m₁ = 2

Step 2. Find the <em>slope (m₂) of the perpendicular line </em>

m₂ = -1/m₁ Substitute the value of m₁

m₂ = -1/2

Step 3. Find the <em>equation for the perpendicular line</em>

y = mx + b Substitute the value of m₂

y = -½x + b

The line passes through (5, 4).

4 = -½(5) + b Add 5/2 to each side

4 = -5/2 + b Add 2 to each side

b = 13/2

y = -½x + 13/2

y = ½(13 – x)

In the image, below, the red line is the graph of your original equation.

The blue line passing through (5, 4) is the perpendicular line.

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If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm

natulia [17]

Answer:

Step-by-step explanation:

This problem is borers on elasticity of materials.

according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>

$F= ke$

where F is the applied force in N

k is the spring constant N/m

e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters= $\frac{15}{100}$ = $0.15m$

we can solve for the spring constant k

we also know that the force F = mg

assuming $g=9.81m/s^{2}$

therefore

$24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\$

We can use this value of k to solve for the mass that will cause an extension of $10cm= 0.1m$

$x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg$

5 0

3 years ago

GIVING THE BRAINLIEST ANSWER

Ahat [919]

Answer:

(6,3)

Step-by-step explanation:

y=2/3 x - 1

y=-1/2 x + 6

Since both equations are equal to y, we can set them equal

2/3 x - 1 =-1/2 x + 6

We have fractions, so I will multiply by 6 to clear the fractions

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

Distribute

4x -6 = -3x +36

Add 3x to each side

4x+3x -6 = -3x+3x +36

7x -6 = 36

Add 6 to each side

7x-6+6 = 36+6

7x = 42

Divide each side by 7

7x/7 = 42/7

x =6

Now we need to find y

y =2/3x -1

y = 2/3(6) -1

y = 4-1

y=3

(6,3)

5 0

3 years ago

Y-2=-3(x-7) written in standard form

uysha [10]

Y=2-3(x-7)
You just add +2 to each side and the positive and negative cancel out and it switches it over

8 0

3 years ago

Two California landmarks, Mt Whitney and Death Valley, are the highest and lowest points in lower 48 states. The difference in e

Varvara68 [4.7K]

We can find out he answer to the question by using the information given.
Since we know that Death Valley is the lower of the two spots, we can assume that we can add the difference in elevation to Death Valley to get the elevation of Mt Whitney.
-86+4,504=4,418
Th elevation of Mt Whitney is 4,418 meters above ground.
Hope this helps!

5 0

3 years ago

what is the value of the x variable in the solution to the following system of equations? 2x 2y = 6 x 3y = −1 a. −2 b. 2 c. 5 d.

tatuchka [14]

2x + 2y = 6 . . . . . (1)
x + 3y = -1 . . . . . (2)

(1) x 3 => 6x + 6y = 18 . . . . . (3)
(2) x 2 => 2x + 6y = -2 . . . . . (4)

(3) - (4) => 4x = 20
x = 20/4 = 5

7 0

3 years ago