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Katarina [22]
2 years ago
11

Is there a way to come to the answer that

tle="\frac{4x+14}{x+3}" alt="\frac{4x+14}{x+3}" align="absmiddle" class="latex-formula"> is equivalent to \frac{2}{x+3}+4 just using methods to look at transformations? Not using other methods like partial fractions or anything.
Mathematics
1 answer:
babymother [125]2 years ago
4 0

You can use a bit algebraic manipulation like so

(4x+14)/(x+3)

(4x+12 + 2)/(x+3)

((4x+12) + 2)/(x+3)

(4(x+3) + 2)/(x+3)

4(x+3)/(x+3) + 2/(x+3)

4 + 2/(x+3)

2/(x+3) + 4

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(0, -2) is a solution of the equation 2x - 3y = 6. true or false
lisov135 [29]

Answer:

It is a solution of the ordered pair.

Step-by-step explanation:

The y intercept is (0,-2)

5 0
3 years ago
32% of 1600 = 512
yaroslaw [1]

Answer:

  • 64%: 1024
  • 96%: 1536
  • 132%: 2112
  • 232%: 3712

Step-by-step explanation:

<u>64% of 1600</u>

  64% of 1600 = 2 × (32% of 1600) = 2×512

  64% of 1600 = 1024

<u>96% of 1600</u>

  96% of 1600 = 3 × (32% of 1600) = 3×512

  96% of 1600 = 1536

<u>132% of 1600</u>

  132% of 1600 = (100% of 1600) + (32% of 1600) = 1600 + 512

  132% of 1600 = 2112

<u>232% of 1600</u>

  232% of 1600 = (100% of 1600) + (132% of 1600) = 1600 +2112

  232% of 1600 = 3712

3 0
3 years ago
Read 2 more answers
I beg please help :(
Aloiza [94]

Answer:

(2.8, 0.8)

(0.8, -1.8)

Step-by-step explanation:

1. Home (Xa, Ya)= (8, 6)

San Antonio (Xb, Yb)=(-5, -7)

Xa-Xb=8-(-5)=13

Ya-Yb=6-(-7)=13

Emily  starts at 2/5 of the road, make it  (Xc, Yc)

Xc= Xa-(Xa-Xb)2/5=8-5.2=2.8

Yc=Ya-(Ya-Yb)2/5=6-5.2=0.8

=> Emily starts at (2.8, 0.8)

2.

Emily ends at 3/5 of the road, , make it  (Xd, Yd)

Xd= Xa-(Xa-Xb)3/5=8-7.8=0.8

Yd=Ya-(Ya-Yb)3/5=6-7.8=-1.8

=> Emily ends at (0.8, -1.8)

6 0
3 years ago
A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours
qaws [65]

Answer:

  • The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.
  • Below are all the steps explained in detail.
  • The graph is attached.

Explanation:

<u />

<u>1. Name the variables:</u>

  • x: number of smaller lifts
  • y: number of larger lifts

<u></u>

<u>2.  Build a table to determine the number of hours each lift requires from each department:</u>

<u></u>

Number of hours

                                        small lift    large lift   total per department

Welding department            1x             3y                x + 3y

Packaging department        2x             1y                2x + y

<u></u>

<u>3. Constraints</u>

  • 150 hours available in welding:         x + 3y ≤ 150
  • 120 hours available in packaging:   2x + y ≤ 120
  • The variables cannot be negative:    x ≥ 0, and y ≥ 0

Then you must:

  • draw the lines and regions defined by each constraint
  • determine the region of solution that satisfies all the constraints
  • determine the vertices of the solution region
  • test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

<u></u>

<u>4. Graph</u>

See the graph attached.

Here is how you draw it.

  • x + 3y ≤ 150
  • draw the line x + 3y = 150 (a solid line because it is included in the solution set)
  • shade the region below and to the left of the line

  • 2x + y ≤ 120
  • draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
  • shade the region below and to the left of the line

  • x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

  • the solution region is the intersection of the regions described above.

  • take the points that are vertices inside the solutoin region.

<u>5. Test the profit function for each vertex</u>

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

  • (0,0)
  • (0,50)
  • (42,36)
  • (60,0)

The profits with the vertices are:

  • P(0,0) = 0
  • P(0,50) = 25(0) + 90(50) = 4,500
  • P(42,36) = 25(42) + 90(36) = 4,290
  • P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

3 0
2 years ago
Select all the pairs that represent alternate exterior angles.
Leno4ka [110]

Answer: 3rd option : Angle 2 and 7

Step-by-step explanation:

Alternate exterior angles are located on the outside of the parallel line on opposite sides.

Therefore, the alternate exetrior angles are 1 and 8 and 2 and 7.

Since there is no option for angle 1 and 8, the correct answer is the 3rd option --> Angle 2 and 7.

8 0
2 years ago
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