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In-s [12.5K]
3 years ago
11

Please help. Don’t understand this math problem!

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0

Answer:

  { 4 }

Step-by-step explanation:

First you need to solve the equation. Then you need to write the solutions as a set.

__

I like to use a graphing calculator to solve equations involving roots. That helps avoid extraneous solutions. Here, the graph of the left side intersects the graph of the right side at x=4. There is exactly one solution, so the solution set is ...

  { 4 }

__

Solving this algebraically, you would isolate the radical, then "undo" it by squaring both sides of the equation. Then solve the resulting quadratic. That will have 2 solutions, only one of which will work in the original equation.

  √(5x +16) -2 = 3x -8 . . . . given

  √(5x +16) = 3x -6 . . . . . .  add 2

  5x +16 = (3x -6)^2 . . . . .  square both sides

  5x +16 = 9x^2 -36x +36 . . . . expand the square

  9x^2 -41x +20 = 0 . . . . . . subtract (5x+16) to put into standard form

Factors of 9·20 = 180 that have a sum of 41 are 5 and 36, so we can rewrite this equation as ...

  9x^2 -36x -5x +20 = 0

  9x(x -4) -5(x -4) = 0 . . . . . . factor by pairs

  (9x -5)(x -4) = 0

The values of x that make this equation true are the values that make the factors be zero: 5/9 and 4. Trying these in the equation, we find ...

  √(5(5/9) +16) -2 = 13/3 -2 = 2 1/3 . . . . value of the left side for x = 5/9

  3(5/9) -8 = -6 1/3 . . . . . . value of the right side for x=5/9; not the same

  x = 5/9 is NOT A SOLUTION

__

  √(5(4)+16) -2 = √36 -2 = 4 . . . . value of the left side for x = 4

  3(4) -8 = 12 -8 = 4 . . . . . . value of the right side for x=4. These are the same, so ...

  x = 4 is a solution

The set of solutions is then ...

  { 4 } . . . . . solution set

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A hotel room cost $79 per night. Meg's family is getting 2 rooms for 5 nights for their trip.
SCORPION-xisa [38]
$790 because it would be 79 times 10
6 0
2 years ago
There are 24 girls on the track team. First race2/3 girl ran.only1/4 girl ran in second race. 1/6 on third race. Hiw many more g
alukav5142 [94]

Answer:

10 more girls

Step-by-step explanation:

So here 2/3 of 24 ran for first race

Then it gives us that 16 girls ran for first race.

Next, 1/4 of 24 ran for second race

That is 6 girls

The remaining girls ran for the third race,

24 - 22

2 girls

16 - 6 = 10

So for first race 10 more girls ran

5 0
3 years ago
John made a triangle with all three sides the same length, 1 \frac{2}{3} ft. What is the perimeter of the triangle?
UNO [17]

Answer:

5 ft

Step-by-step explanation:

If all sides are of the same length, we can multiply the value of one side by 3, because a triangle has three sides (and the perimeter is all sides added together), to find the perimeter.

1\frac{2}{3} × 3

1\frac{2}{3} can be rewritten as \frac{5}{3}, so:

\frac{5}{3} × \frac{3}{1}

= \frac{15}{3}

The numerator & denominator share a common factor of 3, so:

5 ft is the final answer/perimeter.

hope this helps!

7 0
2 years ago
Draw a model to represent the following problem 42 divide 7 Answer
hodyreva [135]

We have to draw the model for 42 divide 7 . In order to draw the model we use below steps.

  • Draw 7 boxes to represent 7 groups.
  • Assume 42 as the number which represents the total of these 7 groups.
  • Put a question mark at the first box.

Attached is the model to represents 42 divide 7 .

In the question mark we should put 6. Hence, when we add 6 to 7 times that will be equal to 42.


5 0
3 years ago
What is the answer for this 8k−5(−5k+3)
Helen [10]

Answer:

33k-15

Step-by-step explanation:

8k−5(−5k+3)

8k+25k-15 because -5(-5) equals=25. Two negatives equal a positive.

-5(3)= -15

So the equation changes to 8k+25k-15.

Combine like terms, and you get:

33k-15

Hope this helps, have a good day. c;

6 0
3 years ago
Read 2 more answers
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