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4 years ago

When does expanding and simplifying a(b+c) result in a positive value for ac

Mathematics

1 answer:

TiliK225 [7]4 years ago

7 0

Answer:

Step-by-step explanation:

(ab + bc)(ab + bc)

Simplifying

(ab + bc)(ab + bc)

Multiply (ab + bc) * (ab + bc)

(ab(ab + bc) + bc(ab + bc))

((ab * ab + bc * ab) + bc(ab + bc))

Reorder the terms:

((ab2c + a2b2) + bc(ab + bc))

(ab2c + a2b2 + (ab * bc + bc * bc))

(ab2c + a2b2 + (ab2c + b2c2))

Reorder the terms:

(ab2c + ab2c + a2b2 + b2c2)

Combine like terms: ab2c + ab2c = 2ab2c

(2ab2c + a2b2 + b2c2)

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To get the volume of a ___, multiply 4/3 by pi and then by the cube of radius

Sladkaya [172]

Answer:

To get the volume of a SPHERE, multiply 4/3 by pi and then by the cube of radius.

Step-by-step explanation:

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4 years ago

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A train leaves boston at 2:00 pm. a second train leaves the same city in the same direction at 6:00 pm. the second train travels

AURORKA [14]

$\boxed {\boxed { \text {Distance = Speed x Time}}}$

First Train:
Time taken = 9 hours (2pm to 11pm)
Let the speed be x
Distance = Time x Speed = 9x

Second Train:
Time taken = 5 hours (6pm to 11pm)
Speed = x + 48
Distance = Time x Speed = 5(x + 48)

Since both the distance they traveled are the same, we equate the distance to solve for x.

Solve for x:
9x = 5(x + 48)
9x = 5x + 240
4x = 240
x = 60

Find the speed:
x = 60 mph
x + 48= 108 mph

Answer: The spend of the two trains are 60 mph and 108 mph.

3 0

4 years ago

Another simple question.

AURORKA [14]

Answer:

Answer is B

Step-by-step explanation:

4 0

3 years ago

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A robot can complete 7 tasks in 5/6 hour. Each task takes the same amount of time. How long does it take the robot to complete o

tester [92]

Answer:

5/42

Step-by-step explanation:

To solve this problem, you have to divide 7 and 5/6 to find the unit rate (how much hours it takes to do one task).

Write what you know into a ratio

7 tasks

5/6 hour

2. You want to know how many hours one task takes, so make that a ratio as well.

7 tasks 1 task

5/6 hour ? hour

Ask yourself what do you do to the 7 in the numerator to get to one.

That's right! you divide by 7! And whatever you do to the numerator you do to the denominator (and vise-versa). Therefore if you divide the numerator(7) by 7 to get 1, you divide the denominator (5/6) by 7 as well.

5/6 divided by 7 is 5/42 meaning it takes the robot 5/42 hour to complete one task.

1 task

5/42 hour

6 0

3 years ago

The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape

Pie

Answer:

vertex: (-5/8, 7/16)
axis of symmetry: x = -5/8

Step-by-step explanation:

For quadratic ax²+bx+c, the axis of symmetry is located at x=-b/(2a).

Here, we have a=4, b=5, so the axis of symmetry is ...

... x = -5/(2·4) = -5/8

_____

The vertex y-value will be f(-5/8).

... f(-5/8) = (4·(-5/8) +5)·(-5/8) +2 = (5/2)·(-5/8) +2 = -25/16 +32/16

... f(-5/8) = 7/16

_____

The axis of symmetry is x = -5/8; the vertex is (-5/8, 7/16).

3 0

3 years ago