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salantis [7]
3 years ago
12

For what values of a are the following expressions true? |a+5|=−5−a

Mathematics
1 answer:
Fed [463]3 years ago
5 0

Answer:

a can be any real number less than equal to -5

Step-by-step explanation:

When a+5 is negative,

a + 5 = -(-5 - a)

a + 5 = a + 5

All values satisfy the equation

So a < -5

When a + 5 is greater than/equal to 0,

a + 5 = -a - 5

2a = -10

a = -5

a can be any real number less than equal to -5

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1 point
pantera1 [17]

Answer:

The answer is undefined

Because it passes through x

3 0
2 years ago
Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a 20%, percent ch
stira [4]

Answer:

30%

Step-by-step explanation:

If Justin has a 20% chance and Cam has a 50% chance that adds up to 70%

But you need to get to 100% so all you do is

70 - 100 = 30

30%

4 0
2 years ago
A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake's population of water
taurus [48]

Quadratic function ( in standard form ):

y = a x² + b x + c

x = 0:

635 = 0 + 0 + c

c = 635

x = 1:

644 = a + b + 635

a + b = 9

x = 2:

719 = 4 a + 2 b + 635

4 a + 2 b = 84

and now we have a system:

a + b = 9   /  * ( - 2 )

4 a + 2 b = 84

-------------------------

- 2 a + 2 b = - 18

+

 4 a + 2 b  = 84

-------------------------

  2 a = 66

 a = 33;   b = - 24;

 Function is:

 f ( x ) = 33 x² - 24 x + 635

f ( 8 ) = 33 * 64 - 24 * 8 + 635 = 2,112 - 192 + 635 = 2,555

 Answer: The number of waterfowl on week 8 would be 2,555.

 

8 0
3 years ago
Four times a number added to seven times the number equals 55
VLD [36.1K]
Its 12 because 4 times 12 is 48 if you add 7 to 48 you get 55
5 0
3 years ago
Read 2 more answers
Given: ABCD parallelogram BK ⊥ AD , AB = 6, AK = 3 Find: m∠A, m∠B, m∠C, m∠D
Troyanec [42]

Answer: Angle A = 60°, angle B = 120°, angle C = 60°, angle D = 120°

Step-by-step explanation: Please refer to the attached diagram for further details.

The question has given the parallelogram ABCD as having side AB measuring 6 units, side AK measuring 3 units and line BK has been drawn perpendicular to line AD. This means line AK forms a right angle at the point where it meets line AD. From the information provided and the figure derived from that, we have right angled triangle ABK with the right angle at point K, line AB equals 6 units and line AK equals 3 units.

Using angle A as the reference angle, line AK is the opposite (side facing the reference angle), line AB is the hypotenuse (line facing the right angle) and line AK is the adjacent (side that lies between the right angle and the reference angle).

Hence, using the trigonometric ratios,

Cos A = adjacent/hypotenuse

Cos A = 3/6

Cos A = 0.5

Checking with the calculator, (that is second function of Cos 0.5)

A = 60

The opposite sides of a parallelogram are equal (that is line AD is parallel to line BC) and therefore opposite angles are equal (that is angle A is equal to angle C).

Similarly, angle B is equal to angle D. However, angles in a quadrilateral equals 360 degrees.

Therefore, angles in parallelogram ABCD is derived as;

A + B + C + D = 360

60 + B + 60 + D = 360

120 + B + D = 360

Subtract 120 from both sides of the equation

B + D = 240

Having known that angle B equals angle D, angles B and D is derived as each half of the value 240

Angle B = 240/2

Angle B = 120

and angle D = 120

Therefore, the angles are;

A = 60, B = 120, C = 60, D = 120

3 0
3 years ago
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