Write an equation in slope-intercept form for the line that passes through (4,5) and parallel to the to the line described by y=5x+10

Answers

Answer 1
Answer:

Answer:

y = 5x-15

Step-by-step explanation:

Parallel ⇒ So the slopes will definitely be equal

So,

Slope = m = 5

Now,

Point = (x,y) = (4,5)

So, x = 4, y = 5

Putting these in the slope intercept form to get b

y = mx +b \n

5 = (5)(4) + b

5 = 20 + b

b = -20+5

b = -15

So, Putting m and b in the slope intercept form to get the required equation,

y = 5x-15


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A state's license plates consist of four letters followed by three numerals, and 246 letter arrangements are not allowed. how many plates can the state issue?

Answers

The state will issue 4,56,97,354 plates

What is exponents and powers?

When anumber is multiplied by itself a finite number of times, the number being multiplied is called the base number, and the number of times it is being multiplied is called the exponent. Suppose a number is being multiplied by itself n number of times, then this expression is called the nth power of the given number.

  • An exponent is the number of times a given number is being multiplied by itself.
  • The expression when a number is being multiplied by itself n number of times is called the nth power of the given number.

Given:

Number of letters = 4

Number of numerals = 3

As 246 letter arrangements are not allowed.

So, we have total 26 letters.

and numbers from 0 to 9.

So, the number of plates  will be

= 26*26*26*26*10*10

=(26)^4 * (10)^2

= 45697600

Now, deducted those 246 letter arrangements which are not allowed

= 45697600 - 246

= 4,56,97,354

Hence, the state will issue 4,56,97,354 plates.

Learn more about this concept here:

brainly.com/question/14881584

#SPJ2

There are 26 letters in the alphabet, there are also 10 numbers 1-10. You multiply that and it would be 260.

Whoever answers correctly gets brainlist

Answers

Answer:

So now D would be at (-4 , 2)

Step-by-step explanation:

From D, you can calculate every other letter’s location. Yeah.

Answer:

Please mark me as brainliest!

Step-by-step explanation:

The coordinates:

D: ( 2,6 )

A: ( 2, 1 )

B: ( 5, 1 )

C: ( 5, 6 )

You want to translate this down 4 units and left 6 units.

So what you would do is this:

Formula = ( x - 6 , y - 4 )

D: ( -4, 2 )

A: ( -4, -3 )

B: ( -1, -3 )

C: ( -1, 2 )

Factor the trigonometric expression. 5sin^2x-8sinx-4

Answers

(sin(x)-2)(5 sin(x)+2)
4(5sin^2(x)cos^2(x)-2sin(x)-1)

What is the value of -(3/4) to the power of -4

Answers

The answer would be -3 13/81 (simplified)

Write the equation of a parabola whose directrix is y=9.75 and has a focus at (8, 0.25).

Answers

Answer:

y = (-1/19)(x - 8)² + 1521/76

Step-by-step explanation:

A parabola moves in such a way that it's distance from it's focus and directrix are always equal.

Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4

If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;

√((x - 8)² + (y - ¼)²)

Distance from that point to the directrix is; (y - 39/4)

Thus;

√((x - 8)² + (y - ¼)²) = (y - 39/4)

Taking the square of both sides gives;

((x - 8)² + (y - ¼)²) = (y - 39/4)²

(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²

Simplifying this gives;

(x - 8)² - (39/4)² = (½ - 39/2)y

(x - 8)² - 1521/4 = -19y

(x - 8)² - 1521/4 = -19y

Divide both sides by -19 to get;

y = (-1/19)(x - 8)² + 1521/76

The base diameter and the height of a cone are both equal toX units.
Which expression represents the volume of the cone, in
cubic units?
Piex2
2piex3
o 1/3piex?
o 1/12piex

Answers

Answer:

For this case we know that the diameter and height of a cone are both equal. That means:

h = D=x

With D =2r with r the radius. The volume of a cone is given by:

V =(1)/(3) \pi r^2 h

And for this case we know that h =x and x =2r so then r= (x)/(2)

And replacing we got:

V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3

And the best option would be:

1/12pix^3

Step-by-step explanation:

For this case we know that the diameter and height of a cone are both equal. That means:

h = D=x

With D =2r with r the radius. The volume of a cone is given by:

V =(1)/(3) \pi r^2 h

And for this case we know that h =x and x =2r so then r= (x)/(2)

And replacing we got:

V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3

And the best option would be:

1/12pix^3