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Tema [17]
3 years ago
9

State the domain, the range, and the intervals on which function is increasing decreasing, or constant in interval notation. Sta

te the domain and range using interval notation.
Mathematics
1 answer:
MariettaO [177]3 years ago
6 0

Answer:

Domain = (-\infty, \infty)

Range = (-\infty, 4]

Increasing interval is: (-\infty, 0)

Decreasing interval is: (0, \infty)

Constant at no interval

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The domain

From, the attached graph, we have:

y = -x^2 + 4

The degree of the polynomial (i.e 2) is even.

Hence, the domain is the set of all real numbers, i.e.

Domain = (-\infty, \infty)

Solving (b): The range

The curve of y = -x^2 + 4 opens downward, and the maximum is:

y_{max} = 4

This means that the minimum is:

y_{mi n} = -\infty

Hence, the range of the set is:

Range = (-\infty, 4]

Solving (c): Interval where the function increases/decreases/constant

In (a), we have:

Domain = (-\infty, \infty)

Split to 2 (at vertex x = 0)

(-\infty, 0) and (0, \infty)

So:

The increasing interval is: (-\infty, 0)

The decreasing interval is: (0, \infty)

<em>The function has a tangent at </em>x = 0<em> but at no interval, was the function constant</em>

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Juliette [100K]

50 + x ≥ 268

X ≥ 218

STEP BY STEP WORK

50 + x ≥268
-50 -50

x ≥218

Jan needs to save at least $218 for camp


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8 0
3 years ago
Answer please thanks ^^^
Thepotemich [5.8K]

Answer:

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Step-by-step explanation:

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Answer: The state with the second lowest population has the lowest population density.

Step-by-step explanation:

Since, Density = Population / Area

The population of state A = 1,055,173

Its area = 2677 square km

Thus, the density of state A = \frac{1055173}{2677} = 394.162495,

The population of state B = 1,333,089

Its area = 36,418 square km

Thus, the density of state B = \frac{1,333,089}{36,418} = 36.6052227,

The population of state C = 3,596,677

Its area = 5543 square km

Thus, the density of state C = \frac{3,596,677}{5543} = 648.868302,

The population of state D =6,745,408

Its area = 10555 square km

Thus, the density of state D = \frac{6,745,408}{10555} = 639.072288,

Since, by the above explanation,

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3 0
3 years ago
Does 2 1/3-1 3/4 need require renaming
ANEK [815]

Answer:

\frac{7}{12}

Step-by-step explanation:

2 \frac{1}{3}  - 1 \frac{3}{4}

The fractions above are known as mixed numbers (that is, fractions that contain the combination of a whole number and proper fraction). The mixed numbers can equally be renamed as improper fractions. However, renaming can only occur the the mixed numbers are being transformed as below:

\frac{7}{3}  -  \frac{7}{4}

The transformation occur through a simple approach thus: for the first mixed number; 2 1/3 = 2 multiplied by 3 plus 1 divide by 3 equals 7/3. Similarly, mixed number 1 3/4 is transformed by this: 1 multiplied by 4 plus 3 divide by 4 equals 7/4.

Simplifying further to arrive at final result implies,

\frac{7}{3}  -  \frac{7}{4}

Take the LCM of the denominators (4 × 3 =12) and simplify thus:

=   \frac{28 - 21}{12}

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Step-by-step explanation:

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480=3x

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F=160-20

Next problem

102+31+x=180

133+x=180

x=180-133

x=47

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3 years ago
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