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2 years ago

Find the distance between parallel lines whose equations are y = x - 6 and y = x + 8.

Mathematics

1 answer:

Sidana [21]2 years ago

8 0

Answer:

Step-by-step explanation:

Distance between y2 = x + 8 and y1 = x - 6

y2 - y1 = (x + 8) - (x - 6) = 14

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A quadratic equation is shown below:

sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

$3x^{2}-11x+10=0$ has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

$\frac{d}{dx}(3x^{2}-11x+10)=6x-11$

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

$x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}$

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

$x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}$

6 0

2 years ago

How many real solutions does the following equation have?

kolbaska11 [484]

Answer: A

Step-by-step explanation:

X=(2±√4-12)/2

X=(2±2i√2)/2

x1=1+i√2

x2=1-i√2

4 0

2 years ago

For what real value of $v$ is $\frac{-21-\sqrt{301}}{10}$ a root of $5x^2+21x+v$?

Degger [83]

Answer:

v = 7

is the value for which

x = (-21 - √301)/10

is a solution to the quadratic equation

5x² + 21x + v = 0

Step-by-step explanation:

Given that

x = (-21 - √301)/10 .....................(1)

is a root of the quadratic equation

5x² + 21x + v = 0 ........................(2)

We want to find the value of v foe which the equation is true.

Consider the quadratic formula

x = [-b ± √(b² - 4av)]/2a ..................(3)

Comparing (3) with (2), notice that

b = 21

2a = 10

=> a = 10/2 = 5

and

b² - 4av = 301

=> 21² - 4(5)v = 301

-20v = 301 - 441

-20v = -140

v = -140/(-20)

v = 7

That is a = 5, b = 21, and v = 7

The equation is then

5x² + 21x + 7 = 0

6 0

2 years ago

How to find the area

Virty [35]

Just like you drew those dotted lines. You know how to find the areas of rectangles which is A=length x width

The answer would be 20cm^2+6cm^2+18cm^2=44 cm^2

7 0

3 years ago

Read 2 more answers

Camp Canine is a kennel for boarding dogs while their owners are on vacation. The graph shows three tiers of boarding pricing. I

kondaur [170]

Answer:

yeha

Step-by-step explanation:

8 0

2 years ago