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e-lub [12.9K]
3 years ago
5

Last year, the school library had a total of x books. Over the summer, the library acquired another 42 books and now has a total

of 2,402 books. Which equation could be used to find x, the number of books the library had last year?
A.2,402 + x = 42
B.x + 42 = 2,402
C.42x = 2,402
D.x - 42 = 2,402
Mathematics
1 answer:
natta225 [31]3 years ago
4 0
B.x + 42 = 2,402 letter b
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-/2 points
Rom4ik [11]

Answer:

Part 1) The domain of the quadratic function is the interval  (-∞,∞)

Part 2) The range is the interval  (-∞,1]

Step-by-step explanation:

we have

f(x)=-x^2+14x-48

This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)

step 1

Find the domain

The domain of a function is the set of all possible values of x

The domain of the quadratic function is the interval

(-∞,∞)

All real numbers

step 2

Find the range

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have a vertical parabola open downward

The vertex is a maximum

Let

(h,k) the vertex of the parabola

so

The range is the interval

(-∞,k]

Find the vertex

f(x)=-x^2+14x-48

Factor -1 the leading coefficient

f(x)=-(x^2-14x)-48

Complete the square

f(x)=-(x^2-14x+49)-48+49

f(x)=-(x^2-14x+49)+1

Rewrite as perfect squares

f(x)=-(x-7)^2+1

The vertex is the point (7,1)

therefore

The range is the interval

(-∞,1]

6 0
3 years ago
Name a pair of alternate interior angles in the diagram. <br> -a.<br> -b.<br> -c.<br> -d.
FrozenT [24]

Answer:

c

Step-by-step explanation:

the answer is c

alernate angles are angles that take the shape of z

8 0
3 years ago
PLEASE HELP GIVING 50 POINTS!!
PSYCHO15rus [73]

Answer:

  y = 18

Step-by-step explanation:

Direct variation means y will change by the same factor x does. When x changes by a factor of 15/10 = 1.5, the value of y will change by that same factor

  x = 10, y = 12

  x= 15, y = 1.5×12 = 18

The new value of y is y = 18.

_____

Written as a proportion, you have ...

  y/15 = 12/10

  y = 15×12/10 = 18

__

Written as a direct variation equation, you have ...

  y = kx

  12 = k·10   ⇒   k = 1.2

  y = 1.2·15 = 18 . . . . for x=15

4 0
2 years ago
State which of the following sets of ordered pairs represent a function.
anastassius [24]

Answer:

d. Set A and Set B

Step-by-step explanation:

We have been given three sets:

Set A: (5, 2), (4, 3), (3, 4), (2, 5)

Set B: (-1, -6), (0, 2), (1, 2), (3, 6)

Set C: (2, 1), (4, 2), (2, 3), (8, 4)

Now we need to state about which of the following sets of ordered pairs represent a function.

We know that a function can't have repeated values in domain that is x-value can't repeat.

we see that set C has repeated x-value "2".

Then set C is not a function.

Hence correct choice is:

d. Set A and Set B

8 0
3 years ago
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Darina [25.2K]

Answer:

About 6,810,000 results (0.79 seconds)  

wait a moment and scrole down!

your question will be answered

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