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Dovator [93]
2 years ago
10

What is the range of the function

Mathematics
1 answer:
alexandr1967 [171]2 years ago
7 0

Answer: Choice B

Range = {-3, 1, 5}

============================================

Explanation:

The domain is the set of all possible input x values. The range is the set of all possible y outputs.

Plug in each x value from the domain, one at a time, to get its corresponding range y value.

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

Start with x = -3

f(x) = 2x+3

f(-3) = 2(-3)+3

f(-3) = -6+3

f(-3) = -3

So -3 is in the range.

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

Move onto x = -1

f(x) = 2x+3

f(-1) = 2(-1)+3

f(-1) = -2+3

f(-1) = 1

1 is also in the range

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

Finally plug in x = 1

f(x) = 2x+3

f(1) = 2(1)+3

f(1) = 2+3

f(1) = 5

The value 5 is the final value in the range.

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

All of those values form the set {-3, 1, 5} which is the complete range.

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A man comes into a store and steals $100 from the register without the owner knowledge. Comes back and buys $70 worth of stuff a
emmainna [20.7K]

Answer

The owner lose is $100 .

Reason

As given

A man comes into a store and steals $100 from the register without the owner knowledge.

Comes back and buys $70 worth of stuff and the owner gives him $30 in change.

i.e First man steals $100  than give back to owner when he buys  $70 worth of stuff and  the owner gives him $30 in change.

Therefore the total owner lose is the sum of  $70 worth of stuff and  $30 in change.

Total owner lose = $70 + $30

                            = $100

Therefore the owner lose be  $100 .

Hence proved


4 0
3 years ago
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What is the area of the donut?
mrs_skeptik [129]

6 x 4=24 so the area of the donut 24 which is the answer to the question

8 0
2 years ago
What is the circumference of the circle? Assume pi = 3.14
mezya [45]

Answer:

5 x 2 x 3.14 = 31.4

Formula of circumference:

radius(half of your diameter or given radius) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x 2(just always there when finding circumference)

6 0
2 years ago
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Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.
siniylev [52]

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

\displaystyle S = \frac{n}{2}\left(a + x_n\right)

Where <em>n</em> is the number of terms, <em>a</em> is the first term, and <em>x</em>_<em>n</em> is the last term.

We know that the initial term <em>a</em> is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find <em>n</em>.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

x_n=a+d(n-1)

Since the initial term is 13 and the common difference is 7:

x_n=13+7(n-1)

Substitute:

\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)

We are given that the initial term is 13 and the sum is 2613. Substitute:

\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))

Solve for <em>n</em>. Multiply both sides by two and combine like terms:

5226 = n(26+7(n-1))

Distribute:

5226 = n (26+7n-7)

Simplify:

5226 = 7n^2+19n

Isolate the equation:

7n^2+19n-5226=0

We can use the quadratic formula:

\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, <em>a</em> = 7, <em>b</em> = 19, and <em>c</em> = -5226. Substitute:

\displaystyle x  =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}

Evaluate:

\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}

Evaluate for each case:

\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

6 0
2 years ago
Events A and B are mutually exclusive. Find the missing probability.
Luden [163]

Answer:

B, 7/20

Step-by-step explanation:

If two events are mutually exclusive that means that there is no intersection

so in the union formula: AUB=A+B-A∩B

A∩B=0

we can write P(a)=x

7/10=7/20+x+0

7/10-7/20=x

x=7/20

8 0
3 years ago
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