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wariber
11 days ago
8

The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of ch

ange between the points (–3, 0) and (–2, –5)?
Mathematics
2 answers:
Zina [12.3K]11 days ago
8 0

Solution:

The change in rate between the coordinates (–3, 0) and (–2, –5) is:

                          -5

Comprehensive explanation:

The rate of change from the coordinates (-5, 10) to (-4, 5) equals -5.

Next, we need to calculate the average rate of change for the points (-3,0) and (-2,-5)

For two points (a,b) and (c,d), the formula for the average rate of change is given by:

  Rate\ of\ change=\dfrac{d-b}{c-a}

Here, we have:

(a,b)=(-3,0) and (c,d)=(-2,-5)

Thus, the average rate of change is:

 Rate\ of\ change=\dfrac{-5-0}{-2-(-3)}\\\\\\Rate\ of\ change=\dfrac{-5}{-2+3}\\\\\\Rate\ of\ change=-5

It's important to note that for any linear function, the average rate of change remains constant across any two points.

           Thus, the result is:

                        -5

lawyer [12.5K]11 days ago
7 0

Solution:

The change rate amounts to -5

Detailed explanation:

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How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]
lawyer [12517]

Answer:

Step-by-step explanation:

Considering the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Dividing throughout by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The solution range is

0<θ<2π which means 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n=5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 surpasses the θ range

Thus, the solutions range from n =0 to n=9

Therefore, there are 10 solutions within the interval 0<θ<2π

4 0
22 days ago
By law, all businesses outside the Parkville city limits must fence their lots. How many inches of fence will be needed to fence
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8 0
7 days ago
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils left over. How many pencils were i
tester [12383]

Answer:

12 pencils per package.

Step-by-step explanation:

Details provided:

Ethan purchased 4 packages of pencils.

Number of Packages = 4

Number of pencils shared with friend = 8 pencils

Pencils remaining = 40 pencils

∴Total Number of Pencils = Pencils given to friend + Pencils remaining = 40+8 =48

Total Pencils in each package = \frac{\textrm{Total Number of Pencils}}{\textrm{No Of Packages}}= \frac{48}{4}= 12 \ pencils

8 0
1 month ago
Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan
lawyer [12517]

Answer:

The graph for the prepaid plan will exhibit a steeper slope and a lower y-intercept.

I trust this information is correct.

Step-by-step explanation:

prepaid plan: y =.20x

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3 0
1 month ago
Read 2 more answers
What is 3.242424 as a mixed number
Zina [12379]

Response:

Detailed explanation:

The final result is 3 /8/33.

step by step breakdown

Initially, we write:

x

=

3

.

¯¯¯¯

24

After that, we will multiply each side by

100

leading to:

100

x

=

324

.

¯¯¯¯

24

Subsequently, we will subtract the first equation from the second equation:

100

x

−

x

=

324

.

¯¯¯¯

24

−

3

.

¯¯¯¯

24

We can then solve for

x

in the following manner:

100

x

−

1

x

=

(

324

+

0

.

¯¯¯¯

24

)

−

(

3

+

0

.

¯¯¯¯

24

)

(

100

−

1

)

x

=

324

+

0

.

¯¯¯¯

24

−

3

−

0

.

¯¯¯¯

24

99

x

=

(

324

−

3

)

+

(

0

.

¯¯¯¯

24

−

0

.

¯¯¯¯

24

)

99

x

=

321

+

0

99

x

=

321

99

x

99

=

321

99

99

x

99

=

3

×

107

3

×

33

x

=

3

×

107

3

×

33

x

=

107

33

Next, we convert this improper fraction to a mixed numeral:

x

=

107

33

=

99

+

8

33

=

99

33

+

8

33

=

3

+

8

33

=

3

8

33

3

.

¯¯¯¯

=

3

8

33

6 0
1 month ago
Read 2 more answers
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