A'mari has finished 60% of an art project

ki77a [65]

Answer:

(0,20)

Step-by-step explanation:

1) we can represent the situation as coordinates

lets have # of texts be "x" variable

lets have bill be "y" as the y variable is always the dependant variable and the cost of the phone bill is dependant upon the number of texts so

y=mx+b-slope-intercept form

coordinates: (50,25) and (100,30)

slope: (30-25)/(100-50)

5/50=1/10

hence slope=1/10

y=1/10x+b

substitute in a coordinate pair into this equation

25=50*1/10+b

25=5+b

b=20

hence y intercept is (0,20)

8 0

2 years ago

Annika is selling art prints at a comic convention.The convention charged her $50 for her table space, and she is selling her pr

asambeis [7]

If she wants to make 130.00, she should sell 90 prints. She is charged at first so she starts at -$50.00. And I don’t understand the first question.

5 0

3 years ago

Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer

agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming: the function is $f(x)=x^{2}$ in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

$g'(0)=g'(1)$

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

$g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0$

$g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2$

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

$f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]$

This is what the Bilateral Theorem says:

$\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L$

4 0

3 years ago

katie bought 4 sweaters that each cost the same amount and 1 skirt that costs 20$. The items she bought cost a total of 160$ bef

Alika [10]

Hello, in order to solve this you first need to take $20 subtracted from 160 that leaves you with 140 next because she bought 4 sweaters you need to divide your remaining cash spent by 4 to get a total of $35 a sweater.

I hope this is what you were looking for, have a great day!

8 0

3 years ago

Dilbert invests a total of $33 000 in two accounts paying 6% and 10\% interest, respectively. How much was invested in each acco

vladimir1956 [14]

Answer:

In the 6% account, 13,000 was deposited

In the 10% account, 20,000 was deposited

Step-by-step explanation:

Here, we are interested in calculating how much invested in each account

.

Let the amount invested be $x and $y

Mathematically;

x + y = 33,000 ••••(i)

Now let’s work with interest

6% of x + 10% of y = 2780

6/100 * x + 10/100 * y = 2780

Multiply through by 100

6x + 10y = 278000 •••••••••(ii)

From i, x = 33,000 -y

Put this into ii

6(33,000 -y) + 10y = 278000

198,000-6y + 10y = 278000

4y = 80000

y = 80,000/4 = 20,000

But x = 33,000 -y = 33,000 -20,000 = 13,000

3 0

3 years ago