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4 years ago

How is the distributive property used to expand expressions? provide an example

1 answer:

8 0

Yes the distributive property is used to expand expressions, but it is also used to make it simpler.
For an example

3(x+4) + 3(y-8)
This is the same thing as
3x + 12 + 3y -8

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This table Shows the number of cars sold by some salespeople over 4weeks.

insens350 [35]

Answer:

6.75

Step-by-step explanation:

4+8+6+9=27

27/4(people)= 6.75

3 0

3 years ago

Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y

Shkiper50 [21]

Answer:

Part 1) $y+8=3(x+2)^{2}$ -----> $y=-8.08$

Part 2) $y-14=-(x-3)^{2}$ ----> $y=14.25$

Part 3) $y+7.5=2(x+2.5)^{2}$ ----> $y=-7.625$

Part 4) $y-17=-(x-3)^{2}$ -----> $y=17.25$

Part 5) $y+7=(x-4)^{2}$ ----> $y=-7.25$

Part 6) $y-6=-(x-1)^{2}$ ----> $y=6.25$

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y-k=\frac{1}{4p}(x-h)^{2}$

where

(h,k) is the vertex

The directrix is

$y=k-p$

case 1) we have

$y+8=3(x+2)^{2}$

the vertex is the point (-2,-8)

$\frac{1}{4p}=3$

$p=\frac{1}{12}$

The directrix is equal to

$y=-8-\frac{1}{12}=-8.08$

case 2) we have

$y-14=-(x-3)^{2}$

the vertex is the point (3,14)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=14+\frac{1}{4}=14.25$

case 3) we have

$y+7.5=2(x+2.5)^{2}$

the vertex is the point (-2.5,-7.5)

$\frac{1}{4p}=2$

$p=\frac{1}{8}$

The directrix is equal to

$y=-7.5-\frac{1}{8}=-7.625$

case 4) we have

$y-17=-(x-3)^{2}$

the vertex is the point (3,17)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=17+\frac{1}{4}=17.25$

case 5) we have

$y+7=(x-4)^{2}$

the vertex is the point (4,-7)

$\frac{1}{4p}=1$

$p=\frac{1}{4}$

The directrix is equal to

$y=-7-\frac{1}{4}=-7.25$

case 6) we have

$y-6=-(x-1)^{2}$

the vertex is the point (1,6)

$\frac{1}{4p}=-1$

$p=-\frac{1}{4}$

The directrix is equal to

$y=6+\frac{1}{4}=6.25$

5 0

3 years ago

Triangle FGH is an equilateral triangle with sides measuring units.

dolphi86 [110]

Draw an equilateral triangle FGH so that FH is the horizontal base. Draw a vertical line GR from G to line FH to represent the height of the triangle.

Let a = length of a side of the equilateral triangle (all sides are equal).
Each angle is 60° because the three angles add up to 180°.

Let h = GR, the height of the triangle.
Because the triangle is equilateral, triangle FGR is a right triangle, with
m∠F = 60° ,
m∠R = 90°,
FG = a.

By definition,
sin(F) = h/a
That is,
h = a*sin(F) = a*sin(60) = a*(√3/2).

Answer:
The height of the equilateral triangle is (a/2)√3,
where a = length of a side of the triangle.

4 0

4 years ago

Read 2 more answers

I need help guyssss.. anyybodyyy

larisa [96]

Answer:

1/2

Step-by-step explanation:

thats the answer

7 0

3 years ago

Read 2 more answers