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2 years ago

6

The selling price of a textbook is

1 answer:

padilas [110]2 years ago

6 0

Answer:

198.43. dollars is the answer

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The sunglasses cost €70

Westkost [7]

Answer:

70 * 0.895 = 62.65

OR

1 0.895

70 x

-Cross-multiply

$\frac{70 * 0.895}{1}$ = 62.65

3 0

3 years ago

When working with integers, when do you add?

7nadin3 [17]

Answer: Ello mate, this image I provided below should help you out, let me know if you need anything else.

Step-by-step explanation:

5 0

3 years ago

Find the equation of the line.<br> hurryyyyyy

Natalija [7]

Answer:

y=-2x+1

Step-by-step explanation:

3 0

3 years ago

Find the recursive quadratic formula of the sequence: 1, 3, 7, 13, 21

Anika [276]

The sequence

1, 3, 7, 13, 21, ...

has first-order differences

2, 4, 6, 8, ...

Let $a_n$ denote the original sequence, and $b_n$ the sequence of first-order differences. It's quite clear that

$b_n=2n$

for $n\ge1$ . By definition of first-order differences, we have

$b_n=a_{n+1}-a_n$

for $n\ge1$ , or

$a_{n+1}=a_n+2n$

By substitution, we have

$a_n=a_{n-1}+2(n-1)$

$\implies a_{n+1}=(a_{n-1}+2(n-1))+2n$

$\implies a_{n+1}=a_{n-1}+2(n+(n-1))$

$a_{n-1}=a_{n-2}+2(n-2)$

$\implies a_{n+1}=(a_{n-2}+2(n-2))+2(n+(n-1))$

$\implies a_{n+1}=a_{n-2}+2(n+(n-1)+(n-2))$

and so on, down to

$a_{n+1}=a_1+2(n+(n-1)+\cdots+2+1)$

You should know that

$1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2$

and we're given $a_1=1$ , so

$a_{n+1}=1+n(n+1)=n^2+n+1$

or

$a_n=(n-1)^2+(n-1)+1\implies\boxed{a_n=n^2-n+1}$

Alternatively, since we already know the sequence is supposed to be quadratic, we can look for coefficients $a,b,c$ such that

$a_n=an^2+bn+c$

We have

$a_1=a+b+c=1$

$a_2=4a+2b+c=3$

$a_3=9a+3b+c=7$

and we can solve this system for the 3 unknowns to find $a=1,b=-1,c=1$ .

4 0

4 years ago

If f(x) is a linear function, f(- 3) = - 3 , and f(5) = 4 , find an equation for f(x)

uysha [10]

$f(x)=mx+b$

$f(-3)=-3$ meaning that (-3,-3)

$f(5)=4$ meaning that (5,4)

(1 ) Find slope.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{4+3}{5+3}\\m=\frac{7}{8}$

The slope is 7/8

(2) Substitute any ordered pairs in the equation.

I'll use (5,4)

$f(x) = \frac{7}{8}x+b\\4=\frac{7}{8}(5)+b\\4=\frac{35}{8}+b\\32=35+8b\\32-35=8b\\-3=8b\\-\frac{3}{8}=b\\b=-\frac{3}{8}$

Therefore the equation for f(x) is $f(x)=\frac{7}{8}x-\frac{3}{8}$

8 0

3 years ago