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ziro4ka [17]
3 years ago
6

The explicit rule for the arithmetic sequence shown in the graph is a↓n=9.5+2(n-1)

Mathematics
1 answer:
Virty [35]3 years ago
5 0

Answer:

True.

Step-by-step explanation:

The explicit form for an arithmetic sequence is:

a_n=a_1+d(n-1)

where a_1 is the first term and d is the common difference.

The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.

Yes, the common difference is the slope.

So we have d=2.

The first term is 9.5 because that is what happens when x=1.

x is n.

y is a_n.

So the answer is true.

----

You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:

Let n=1:

a_1=9.5+2(1-1)

a_1=9.5+2(0)

a_1=9.5+0

a_1=9.5

Let n=2:

a_2=9.5+2(2-1)

a_2=9.5+2(1)

a_2=9.5+2

a_2=11.5

Let n=3:

a_3=9.5+2(3-1)

a_3=9.5+2(2)

a_3=9.5+4

a_3=13.5

Let n=4:

a_4=9.5+2(4-1)

a_4=9.5+2(3)

a_4=9.5+6

a_4=15.5

Let n=5:

a_5=9.5+2(5-1)

a_5=9.5+2(4)

a_5=9.5+8

a_5=17.5

Let n=6:

a_6=9.5+2(6-1)

a_6=9.5+2(5)

a_6=9.5+10

a_6=19.5

We have confirmed that we get all 6 of the mentioned points using the equation they gave.

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The question is below
Viktor [21]

Answer:

sin I = \frac{80}{89}

Step-by-step explanation:

sin I = \frac{opposite}{hypotenuse} = \frac{KJ}{JI} = \frac{80}{89}

6 0
2 years ago
A model airplane is shot up from a platform 1 foot above the ground with an initial upward velocity of 56 feet per second. The h
scoray [572]

Answer:

Option B. 1.8 seconds

Step-by-step explanation:

h=-16t^2+56t+1

This is a quadratic equation, and its graph is a parabola

h=at^2+bt+c; a=-16, b=56, c=1

Like a=-16<0 the parabola opens downward, and it has a maximum value (height) at the vertex, at the abscissa:

t=-\frac{b}{2a}

Replacing the known values:

t=-\frac{56}{2(-16)}\\ t=-\frac{56}{(-32)}\\ t= 1.75

Approximately 1.8 seconds.

Answer: It takes approximately 1.8 seconds the airplane to reach its maximum height.


5 0
3 years ago
Read 2 more answers
Which rule represents a linear​ function?<br><br> y=5x² y=5x
nevsk [136]

Answer:

The answer is y=5x²

Step-by-step explanation:

If you put y=5x² on a graph paper it will be in a staright line.

7 0
2 years ago
I can’t figure out how to do a and b for 33
Monica [59]
A)
original rectangle P = 2(w+l)
so 
18 = 2(w+l) (1)

new rectangle 
doubling width w, so its 2w
tripling length l, so its 3l
46 = 2(2w + 3l) (2)

now you have
18 = 2(w+l) (1)
9 = w + l so w = 9 - l

46 = 2(2w + 3l) (2)
23 = 2w + 3l

substitute w = 9 - l into 23 = 2w + 3l
23 = 2w + 3l
23 = 2(9 - l) + 3l
23 = 18 - 2l + 3 l
23 - 18 = l
5 = l or l = 5
w = 9 - l = 9 - 5 = 4

answer
original rectangle, length = 5 in and width = 4 in

b)new rectangle
length = 3l = 3(5) = 15 in
width = 2w = 2(4) = 8 in

6 0
3 years ago
F(x)=2x^3+ax^2-37x-60<br><br> The binomial x-4 is a factor of f(x). Find the value of a.
jekas [21]

Given:

The function is

f(x)=2x^3+ax^2-37x-60

The binomial x-4 is a factor of f(x).

To find:

The value of a.

Solution:

If x-c is a factor of f(x), then f(c)=0.

It is given that, x-4 is a factor of f(x), then f(4)=0.

We have,

f(x)=2x^3+ax^2-37x-60

Substituting x=4, we get

f(4)=2(4)^3+a(4)^2-37(4)-60

f(4)=2(64)+a(16)-148-60

f(4)=128+16a-208

f(4)=16a-80

Now,

f(4)=0

16a-80=0

16a=80

a=\dfrac{80}{16}

a=5

Therefore, the value of a is 5.

6 0
2 years ago
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