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MakcuM [25]
3 years ago
8

24 POINTS!!!!!!!!!!!!!!!!!! Factor the expression. 4d + 12

Mathematics
1 answer:
marin [14]3 years ago
5 0
Hi there.

Factor
4d + 12
4( d + 3)


I hope that's help ! 

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Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?
Lubov Fominskaja [6]

Answer:

  yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

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For the first parabola, the point of intersection is ...

  y^2 = 4(-y-1)

  y^2 +4y +4 = 0

  (y+2)^2 = 0

  y = -2 . . . . . . . . one solution only

  x = -(-2)-1 = 1

The point of intersection is (1, -2).

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For the second parabola, the equation is the same, but with x and y interchanged:

  x^2 = 4(-x-1)

  (x +2)^2 = 0

  x = -2, y = 1 . . . . . one point of intersection only

___

If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

7 0
3 years ago
What is the measure of an angle if the measures of its two adjacent supplementary angles add up to 100°?
Sindrei [870]
<h3>Answer:  130</h3>

Explanation:

Let x be the unknown angle we want to find.

Let y be adjacent and supplementary to x. This means x+y = 180

Let z also be adjacent and supplementary to x. So x+z = 180 also

Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.

Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z

y+z = 100

z+z = 100

2z = 100

z = 100/2

z = 50

Therefore,

x+z = 180

x+50 = 180

x = 180-50

x = 130

8 0
3 years ago
Solve the equation 3(2x+2)=3x-15<br>x=-7<br>x=-17/3<br>x=3<br>x=7​
Nady [450]

3(2x+2)=3x-15

mutiply the bracket by 3

(3)(2x)(3)(2)= 6x+6

6x+6= 3x-15

move 3x to the other side

sign changes from +3x to -3x

6x-3x+6= 3x-3x-15

6x-3x+6= -15

3x+6= -15

move +6 to the other side

sign changes from +6 to -6

3x+6-6= -15-6

3x= -21

divide by 3 for both sides

3x/3= -21/3

x= -7

Answer: x= -7

4 0
3 years ago
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Which is the set of all y-values or the outputs?<br> Range<br> Function<br> Relation<br> Domain
alina1380 [7]

Answer:

Step-by-step explanation:

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3 0
3 years ago
Three friends order a pizza. Danny eats 1/2 of the pizza, Mike eats 1/3 of the pizza, and Chris eats 1/6 of the pizza. The next
xenn [34]

Answer:

It Mike who ate the most pizza

Step-by-step explanation:

7 0
3 years ago
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