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3 years ago

Tell whether the data in the table can be modeled by a linear equation. Explain.

Mathematics

1 answer:

anastassius [24]3 years ago

8 0

Answer:

y = -3x + 7

Step-by-step explanation:

Choosing two points from the given table:

Let (x1, y1) = (-3, 16)

(x2, y2) = (-1, 10)

Plug these given values into the slope formula:

m = (y2 - y1)/(x2 - x1)

= (10 - 16) / (-1 - (-3))

= -6 / (-1 + 3)

= -6/2

= -3

Therefore, the slope is -3.

Next, choose one of the points and plug into the <u>point-slope form</u>:

Let's use (-1, 10) as (x1, y1):

y - y1 = m(x - x1)

y - 10 = -3(x - (-1))

y - 10 = -3(x + 1)

y - 10 = -3x - 3

Add 10 on both sides to isolate y:

y - 10 + 10 = -3x - 3 + 10

y = -3x + 7

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Pls help meeee!!! I have benchmarks monday

quester [9]

Answer:

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.

Step-by-step explanation:

i) the cost of an automobile is given by the equation is

C(t) = $28000\times(0.73)^{t}$ , where C(t) represents the cost and t represents the time in years

ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.

ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.

iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.

5 0

3 years ago

Determine as a linear relation in x, y, z the plane given by the vector function F(u, v) = a + u b + v c when a = 2 i − 2 j + k,

Ostrovityanka [42]

Answer:

2x - y - 3z = 0

Step-by-step explanation:

Since the set

{i, j} = {(1,0), (0,1)}

is a base in $\mathbb{R}^2$

and F is linear, then

would be a base of the plane generated by F.

F(1,0) = a+b = (2i-2j+k)+(i+2j+k) = 3i+2k

F(0,1) = a+c = (2i-2j+k)+(2i+j+2k) = 4i-j+3k

Now, we just have to find the equation of the plane that contains the vectors 3i+2k and 4i-j+3k

We need a normal vector which is the cross product of 3i+2k and 4i-j+3k

(3i+2k)X(4i-j+3k) = 2i-j-3k

The equation of the plane whose normal vector is 2i-j-3k and contains the point (3,0,2) (the end of the vector F(1,0)) is given by

2(x-3) -1(y-0) -3(z-2) = 0

or what is the same

2x - y - 3z = 0

3 0

4 years ago

Assuming that a soap bubble is a perfect sphere, what is the diameter of a bubble containing 1,000 cm3 of air? Round to the near

Minchanka [31]

Answer:

17.85 cm

Step-by-step explanation:

1) Area of a sphere formula: $A=4\pi r^{2}$

2) Plug in A: 1000 = $4\pi r^{2}$

3) Simplify: 1000 = 12.56 $r^{2}$

4) Divide Each Side By 12.56: 79.61783439 = $r^{2}$

5) Take the Square Root of 79.61783439 to Solve for $r$ : 8.922882628 = $r$

6) Double $r$ to get the diameter: 8.922882628*2= 17.84576486

7) Round to the Nearest Tenth: 17.85 cm

8 0

3 years ago

Write an expression to represent this situation: seven less than the product of four and a number please help me

Studentka2010 [4]

4x-7: "seven less than" means you're going to subtract it from the upcoming value, which is "the product of four and a number". "a number" refers to an unknown variable, which I chose to be x. So put it all together and you get 4x-7

3 0

3 years ago

Employees at Counting Sheep Mattress Company earn 40% commissions on each mattress they sell. Jason sold a mattress for $1,149.

vampirchik [111]

Answer:

Commission earned = $459.6

Step-by-step explanation:

40% of 1149 = 0.4 x 1149 = $459.6

8 0

4 years ago

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