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san4es73 [151]
3 years ago
15

3x squared -42x+9=-5 for completing the square

Mathematics
1 answer:
enot [183]3 years ago
8 0
3x^2 -42x + 9 = -5

Subtract 9 from both sides
3x^2 -42x  = -5 - 9

3x^2 -42x  = -14

Divide by 3 through
x^2 -14x  = - \dfrac{14}{3}

Add (b/2)^2 to form perfect square
x^2 -14x +  (\dfrac{14}{2})^2  = - \dfrac{14}{3} +  (\dfrac{14}{2})^2

Form perfect square
(x -7)^2  =  \dfrac{7}{3}

square root both sides
(x -7) = \pm \sqrt{\dfrac{7}{3}}

Add 7 to both sides
x  =   \pm \sqrt{\dfrac{7}{3}}  + 7

Rewrite the answer into 2 different answers
x  =   7 +  \sqrt{\dfrac{7}{3}}  \ or \  7 - \sqrt{\dfrac{7}{3}}



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I need help. this is due in less than 10 min and i have no clue how to solve. any tips appreciated
babymother [125]

Answers:

  • a) x = 9
  • b) arc JK = 68
  • c) arc MJ = 112
  • d) arc LMK = 248

================================

Explanation:

Arcs JK and KL form a semicircle, so they add to 180 degrees

(arcJK) + (arcKL) = 180

(5x+23) + (17x-41) = 180

22x-18 = 180

22x = 180+18

22x = 198

x = 198/22

x = 9

Then you'll use this x value to find arc JK and arc KL

arc JK = 5x+23 = 5*9+23 = 68

arc KL = 17x - 41 = 17*9-41 = 112

Since central angles MNJ and KNL are vertical angles, this means minor arcs MJ and KL are congruent arcs. So arc MJ is also 112 degrees

Arc LMK is basically nearly everything of the full circle, but we exclude out the portion from L to K (the shorter distance)

arc LMK = (full circle) - (measure of minor arc LK)

arc LMK = 360 - 112

arc LMK = 248

8 0
3 years ago
Expand the following expression: 4 (2k + j)
Nadya [2.5K]

Answer:

4(2k + j) = 8k + 4j

Step-by-step explanation:

4(2k + j)

Distribute in the 4.

4 * 2k + 4 * j

Multiply 4 and 2k.

8k + 4 * j

Multiply 4 and j.

8k + 4j

3 0
1 year ago
Read 2 more answers
A restaurant has 9 pounds of onion. The restaurant's manager ordered 4 more pounds of onion. The onions then were mixed and kept
Iteru [2.4K]

Answer:

6.5

Step-by-step explanation:

9 + 4 = 13 divide by 2 = 6.5 is your answer.

4 0
3 years ago
If f(x) is the total cost, in dollars, of x cupcakes, which of the following statements best describes the meaning of f(5) = 12?
dezoksy [38]

Answer:

  • See below

Step-by-step explanation:

<u>This a form of the proportional relationship:</u>

  • f(x) = kx, where f(x) - total cost, k- cost of each item, x - number of items

<u>We have:</u>

  • f(5) = 12

<u>It means:</u>

  • Total cost of 5 cupcakes is $12
5 0
2 years ago
Can someone help me with this
jolli1 [7]

Answer:

  4 sides

Step-by-step explanation:

A lot of math is about pattern matching. Here, you're asked if sides are the same length (one side matches another), if there are right angles (square corners), and if the number of angles or sides is 4.

You might make the observations ...

  <u>pink</u>: 2 pairs of parallel sides that are the same length (4 sides). Adjacent sides are different length.

  <u>orange</u>: all 4 sides are congruent and at right angles

  <u>blue</u>: 2 pairs of parallel sides that are the same length (4 sides). Adjacent sides are different length.

  <u>green</u>: 2 pairs of parallel sides that are the same length--4 sides and 4 right angles. Adjacent sides are different length.

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The only feature in common is "4 sides."

5 0
2 years ago
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