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madam [21]
3 years ago
6

Graph two more functions in the same family for witch the parameter being changed is the y-intercept, b

Mathematics
1 answer:
Trava [24]3 years ago
3 0

Answer:

The equation of line having slope m and y-intercept b is

 y = m x + b

The other two equations of line in the same family having intercepts p and q are,keeping the slope same i.e m , described in the question are

→ y= m x + p

→ y = m x  + q

As both the equation have same slope i.e m , so lines will be parallel, but their Y - intercept are different i.e distance from the origin where it cuts the y-axis are different i.e at a distance of p and q from origin.




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HELP!!
leonid [27]

Answer:

The focus point is (2 , 0) ⇒ answer D

Step-by-step explanation:

* Lets revise the equation of the parabola in standard form

- The standard form is (x - h)² = 4p(y - k)

- The focus is (h, k + p)

- The directrix is y = k - p

- If the parabola is rotated so that its vertex is (h , k) and its axis of

 symmetry is parallel to the x-axis, it has an equation of

 (y - k)² = 4p(x - h)

- The focus is (h + p, k)

- The directrix is x = h - p

* Lets solve the problem

∵ The equation of the parabola is y = 1/8(x² - 4x - 12)

- Lets make x² - 4x completing square

∵ √x² = x  

∴ The 1st term in the bracket is x

∵ 4x ÷ 2 = 2x

∴ The product of the 1st term and the 2nd term is 2x

∵ The 1st term is x

∴ the second term = 2x ÷ x = 2

∴ The bracket is (x - 2)²

∵  (x - 2)² = (x² - 4x + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out  

  the bracket to keep the equation as it

∴ (x² - 4x + 4) - 4 = (x - 2)² - 4

- Lets put the equation after making the completing square

∴ y = 1/8 [(x - 2)² - 4 - 12]

∴ y = 1/8 [(x - 2)² - 16] ⇒ multiply both sides by 8

∴ 8y = (x - 2)² - 16 ⇒ add 16 to both sides

∴ 8y + 16 = (x - 2)² ⇒ take from the left side 8 as a common factor

∴ 8(y + 2) = (x - 2)²

∴ The standard form of the equation of the parabola is

   (x - 2)² = 8(y + 2)

∵ The standard form of the equation is (x - h)² = 4p(y - k)

∴ h = 2 , k = -2 , 4p = 8

∵ The focus is (h , k + p)

∵ h = 2

∵ 4p = 8 ⇒ divide both sides by 4

∴ p = 2

∴ The focus = (2 , -2 + 2) = (2 , 0)

* The focus point is (2 , 0)

6 0
3 years ago
2. C is at (-5.1) & D is at (7.6). Where is the midpoint on segment CD?​
topjm [15]

Answer:

1.25

Step-by-step explanation:

Find the average.

-5.1+7.6=2.5

2.5/2

1.25

6 0
3 years ago
Matthew is packing 120 pencils and 108 notebooks
Rasek [7]

9514 1404 393

Answer:

  • 12 boxes
  • 10 pencils, 9 notebooks

Step-by-step explanation:

a) The number of boxes will be the greatest common divisor (GCD) of the numbers 120 and 108. That number is 12.

  120 = 12×10

  108 = 12×9 . . . . 12 is the greatest common divisor

Matthew can make 12 boxes with equal numbers of the items.

__

b) 120 pencils divided by 12 will be 10 pencils per box.

108 notebooks divided by 12 will be 9 notebooks per box.

_____

<em>Additional comment</em>

It helps to be familiar with multiplication tables up to about 12×12.

The GCD can always be found using Euclid's algorithm. Look at the remainder when the larger number is divided by the smaller. If it is not zero, then replace the larger number with the remainder and repeat. If the remainder is zero, the divisor is the GCD.

Here, we have ...

  120/108 = 1 r 12.

  108/12 = 9 r 0   ⇒   12 is the GCD

7 0
3 years ago
Abc is bisected by bd for what value of x will dx= day be true?
Reil [10]

Answer:

x=3\\

Step-by-step explanation:

Note that because BD is an angle bisector, then angle XBD and angle DXY are equal. Also note that BYD and BXD are equal because they are both right angles. Also, by the transaitive property, BD = BD. Therefore, it can be concluded that BXD is congruent to BYD.

Therefore, we must solve 5x+4=19 \Longrightarrow 5x = 15 \Longrightarrow x=3.

5 0
3 years ago
Find all polar coordinates of point P = (6, 31°).
alex41 [277]
(6,(31pi/180)+2 n pi) (-6,(31pi/180)+2 n pi) <span>
</span>
3 0
3 years ago
Read 2 more answers
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