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Bogdan [553]
2 years ago
14

wanting to cut down his television-watching time slowly, Vince decides to watch 30 fewer minutes of television each week after t

he first.If Vince watches 6 hours of television during the first week,which of the following equations predicts vince's hours of television n weeks after the first
Mathematics
1 answer:
Effectus [21]2 years ago
7 0

Answer:

f(n) = - 0.5n + 6

Step-by-step explanation:

Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.

Slope-intercept form is y=mx+b. In this case, we are choosing to use f(n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f(n)=mn+b.

We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or -0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of -0.5 and is represented by m.

We substitute b=6 and m=0.5 into our form to get f(n)=-0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.

f(n)=-0.5(1)+6=-0.5+6=5.5

We can substitute for any n week and find the amount.


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It would depend on how large the rectangle is
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2 years ago
The difference between a number and 8 is 11
quester [9]

Answer:

The difference between 19 and 8 is 11.

Step-by-step explanation:

Given:

The difference between a number and 8 is 11

Find the number.

Solution:

Let the unknown number be =x

The difference between the unknown number can be written as:

x-8

We are given that the difference =11

So we can write the equation to find x as :

x-8=11

Using additive property to solve for x

Adding 8 to both sides to isolate x on one side.

x-8+8=11+8

∴ x=19

∴ The unknown number = 19

6 0
3 years ago
Read 2 more answers
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse
Drupady [299]

Answer:

a'(d) = \frac{d}{5} + \frac{3}{5}

a(a'(d)) = a'(a(d)) = d

Step-by-step explanation:

Given

a(d) = 5d - 3

Solving (a): Write as inverse function

a(d) = 5d - 3

Represent a(d) as y

y = 5d - 3

Swap positions of d and y

d = 5y - 3

Make y the subject

5y = d + 3

y = \frac{d}{5} + \frac{3}{5}

Replace y with a'(d)

a'(d) = \frac{d}{5} + \frac{3}{5}

Prove that a(d) and a'(d) are inverse functions

a'(d) = \frac{d}{5} + \frac{3}{5} and a(d) = 5d - 3

To do this, we prove that:

a(a'(d)) = a'(a(d)) = d

Solving for a(a'(d))

a(a'(d))  = a(\frac{d}{5} + \frac{3}{5})

Substitute \frac{d}{5} + \frac{3}{5} for d in  a(d) = 5d - 3

a(a'(d))  = 5(\frac{d}{5} + \frac{3}{5}) - 3

a(a'(d))  = \frac{5d}{5} + \frac{15}{5} - 3

a(a'(d))  = d + 3 - 3

a(a'(d))  = d

Solving for: a'(a(d))

a'(a(d)) = a'(5d - 3)

Substitute 5d - 3 for d in a'(d) = \frac{d}{5} + \frac{3}{5}

a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}

Add fractions

a'(a(d)) = \frac{5d - 3+3}{5}

a'(a(d)) = \frac{5d}{5}

a'(a(d)) = d

Hence:

a(a'(d)) = a'(a(d)) = d

7 0
2 years ago
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zvonat [6]
∠4 = 90  (verticallyopposite)
∠2 = 68 (verticallyopposite)

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∠6 = 68 + 90 = 158°

Answer: 158°
7 0
2 years ago
How many zeros in x^4 + 3x2 + 12
barxatty [35]

Answer:

We know that ,

Number of zeroes in a polynomial = degree of the polynomial

( degree of polynomial = the highest power in the polynomial )

therefore ,

\bold\blue{number \:of \:zeroes \:of\: the \:given} \\\bold\blue{polynomial\: = \:4}

hope helpful~

3 0
2 years ago
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