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Brilliant_brown [7]
3 years ago
5

The equation |ax + b| = c must have ?

Mathematics
2 answers:
NARA [144]3 years ago
8 0

Answer: Option c

Step-by-step explanation:

1. By definition |ax + b| = c can be written as:

-ax-b=c if ax+b is greater than zero (ax+b>0)

ax+b=c if ax+b is equal or greater than zero (ax+b\geq0)

This means that this function has two solutions.

2. Then, |ax + b| is always greater than zero. Therefore, if c is less than zero, then the equation has no solution.

3. Therefore, the function can have two solutions if c>0 and no solution is c<0.

Then, the function can have 0,1 or 2 solutions.

ArbitrLikvidat [17]3 years ago
4 0

Answer:

0, 1, or 2 solutions

Step-by-step explanation:

The equation |ax + b| = c

The equation have absolute value symbol

Absolute value always gives us the positive number.

For absolute value function , we need to consider two cases

positive and negative.

|x|=x  for positive ,  and |-x|=x for negative case

For negative case we include negative sign

So  |ax + b| = c can be written as 2 equations

(ax+b)=c                                  (ax+b)=-c

So we will get maximum of 2 solutions

The equation |ax + b| = c must have 0, 1, or 2 solutions

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Conditional probabilities are based on some event occurring given that something else has already occurred?
alex41 [277]

The answer is true. A conditional probability is a measure of the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A in the condition B", is usually written as P (A|B). The conditional probability of A given B is well-defined as the quotient of the probability of the joint of events A and B, and the probability of B.

8 0
3 years ago
A rectangular park is 85 yards wide and 120 yards long.
ki77a [65]

Answer:

A=10506.25 Sq.yards

Step-by-step explanation:

Width of the park=85 yds

Lenght of the park=120 yds

Now,

A=L*W

A=120*85

A=10200 square yards. This is the area of your given rectangle.

Now,

P=2(L+W)

P=2(120+85)

P=2(205)

P=410 this is the perimeter of your given rectangle.

Now,

a=410/4=102.5

Now,calculate the area of newly given distance of each side:

A=a^2

A=102.5^2

A=10506.25 Sq. Yards

This is the new area and is larger than the area of the given rectangle which was 10200 square yards.

3 0
3 years ago
The region bounded by y=(3x)^(1/2), y=3x-6, y=0
Ganezh [65]

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is y = (3x)^{\frac{1}{2} }

⇒ y^{2} = 3x ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

y^{2} - y - 6 = 0

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = \int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx

= \sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}

= [\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} }  }{3}] - [13.5 - 18 - 6 + 12]

= 6 - 1.5

= 4.5 sq. units. (Answer)

7 0
2 years ago
On a standardized exam, the scores are normally distributed with a mean of 165 and astandard deviation of 40. Find the z-score o
vladimir1956 [14]

The Z-score is calculated by the formula below

\begin{gathered} z-score=\frac{(x-\mu)}{\sigma}_{} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \\ x=\text{score} \end{gathered}

Step 2: Substitute the given parameters in the formula

\begin{gathered} z-\text{score}=\frac{145-165}{40} \\ Z=-\frac{20}{40} \\ Z=-\frac{1}{2} \\ Z=-0.5 \end{gathered}

Hence, the z-score of a person who scored 145 on the exam is -0.5

8 0
1 year ago
Solve |4| + |11 - 6| - |-2|
Pie

Answer:

...........the answer is 7?!

5 0
3 years ago
Read 2 more answers
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