Please help i'll give brainliest HELP PLLLLEEEEEEEEAAAAAAAASEEEEEEE

Can someone help me with my quadratics and equations questions? I need to show my work :)

Dvinal [7]

Y = x^2 +2x
y = 3x +20

so:
x^2 + 2x = 3x + 20

subtract 3x from both side:

x^2 +2x -3x = 20

combine like terms:
x^2 -x = 20

subtract 20 from each side:
x^2 -x -20 = 0

factor the polynomial:

(x-5) (x+4) = 0

solve for x
x = 5 and x = -4 ( 5-5 = 0 and -4 +4 = 0 )

replace x = 5 in 2nd equation: y = 3(5) +20
y = 15 +20
y = 35

replace x with -4 in same equation:
y = 3(-4) +20
y = -12 +20
y = 8
so solution is (5,35) and (-4,8)

6 0

3 years ago

Insect flies 20ft in 1sec. What is that in miles per hour?

vladimir2022 [97]

20 ft in 1 sec
60 x 20ft in 1 min
60 x 60 x 20ft in 1 hr
72000 ft in 1 hr
5280ft = 1 mile
speed = 72000/5280 mph

6 0

3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

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

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

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

Then

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

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

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

A recipe includes 6 cups of flour and three fourths cup of butter butter. Write the ratio of the amount of flour to the amount o

vodka [1.7K]

Iejejejsjhdhbdnjdjdjdfuucjdjdndjd

4 0

4 years ago

By definition, future value is?

Yuki888 [10]

Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, the rate of return; it is the present value multiplied by the accumulation function.

3 0

3 years ago

Read 2 more answers