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ozzi
3 years ago
6

What are the solutions?8x^2-12x-23=-5​

Mathematics
1 answer:
erastova [34]3 years ago
4 0

Answer:

x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4

Step-by-step explanation:

Solve for x over the real numbers:

8 x^2 - 12 x - 23 = -5

Divide both sides by 8:

x^2 - (3 x)/2 - 23/8 = -5/8

Add 23/8 to both sides:

x^2 - (3 x)/2 = 9/4

Add 9/16 to both sides:

x^2 - (3 x)/2 + 9/16 = 45/16

Write the left hand side as a square:

(x - 3/4)^2 = 45/16

Take the square root of both sides:

x - 3/4 = (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4

Add 3/4 to both sides:

x = 3/4 + (3 sqrt(5))/4 or x - 3/4 = -(3 sqrt(5))/4

Add 3/4 to both sides:

Answer:  x = 3/4 + (3 sqrt(5))/4 or x = 3/4 - (3 sqrt(5))/4

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pickupchik [31]
I’m pretty sure the answer is b because the triangles are congruent
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3 years ago
Which set of angle measures could be the measures of the interior angles of a triangle?
satela [25.4K]

Answer:

B

Step-by-step explanation:

The sum of the 3 interior angles of a triangle = 180°

Check the sums of the given sets of angles

90° + 42° +58° = 190° ≠ 180° ← not valid

60° + 60° + 60° = 180° ← Valid

100° + 48° + 42° = 190° ← not valid

31° + 75° + 70° = 176° ← not valid

7 0
3 years ago
Read 2 more answers
Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a buildi
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They will be forming a right triangle. 

long leg is the height of Lyra. 22 meters high from the entrance.
short leg is the distance of Donna. 50 meters from the entrance.
We need to solve for the hypotenuse or the range of communication.

a² + b² = c²
22² + 50² = c²
484 + 2500 = c²
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√2,984 = √c²
54.63 = c

The range of communication for the two radios is 55 meters.
8 0
3 years ago
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 678 babies were​ born, a
suter [353]

Answer:

We are 99% confident that the true proportion of female babies is captured by the interval from

0.8001

to

0.8999

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Step-by-step explanation:

7 0
3 years ago
Please help with #6 need it very soon
gregori [183]

Answer:

If this is a proof then here is the answer.

Angle ABD is Congruent to Angle CBD = Given

Angle BDA is Congruent to Angle BDC = Given

Angle ABD is Congruent to Angle CBD = Definition of Angle Bisector

Line Segment BD is Congruent to Line Segment BD = Reflexive Property

Line Segment AB is Congruent to Linge Segment CB = Angle-Side-Angle or ASA

Step-by-step explanation:

Lucky for you, I just learned this also ;)


Since you are given your first two directions, put them down as GIVEN in the proof.

Next, Since ABD and CBD are congruent angles, you can assume that it is an angle bisector since angle bisectors always bisect equally.

Then, (This one is obvious), since Line Segment BD shares a side with itself, it is equal by the Reflexive Property (EX: AB is congruent to AB).

Finally, Since there is two angles with a congruent side in the middle, you can confirm that it is equal by Angle-Side-Angle.

Hope this helped!


5 0
3 years ago
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