Use the distributive property to remove the parentheses. 5(8+x)

Two princesses, Nat and Kat, are gifted with a savings account from their royal parents, Matt and Pat, when they turn 5 years ol

Arte-miy333 [17]

Answers and Step-by-step explanations:

(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:

m = (21200 - 6200) / (7 - 2) = 3000

Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:

y = 3000x + b

6200 = 3000 * 2 + b

b = 200

Nat's equation is y = 3000t + 200.

(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:

y = a(x - h)² + k, where (h, k) is the vertex

Plug in our vertex:

y = a(x - 20)² + 44100

We also have the point (9, 32000), so put that in to find a:

32000 = a(9 - 20)² + 44100

-12100 = a * 121

a = -100

So Kat's equation is y = -100(t - 20)² + 44100.

(c) In order to find the age when they have the same amount, we set the two equations equal:

3000t + 200 = -100(t - 20)² + 44100

-100(t² - 40t + 400) + 44100 = 3000t + 200

-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0

-100t² + 1000t + 3900 = 0

t² - 10t - 39 = 0

(t - 13)(t + 3) = 0

t = 13 or t = -3 -- obviously, years can't be negative, so t = 13.

Note, however, that t is the number of years <em>after</em> Kat and Nat are 5, so we need to add 13 to 5:

13 + 5 = 18

The age is 18.

4 0

3 years ago

Read 2 more answers

If a seed is planted, it has a 80% chance of growing into a healthy plant.

AlladinOne [14]

Answer:

0.336

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, n = 8, r = 7, p = 0.8, and q = 0.2.

P = ₈C₇ (0.8)⁷ (0.2)⁸⁻⁷

P = 0.336

3 0

3 years ago

Leah is writing an equivalent equation which solves for y. What should be her next step? 3x+4y=8 Add 4y to both sides of the equ

ratelena [41]

The given equation is

$3x+4y=8$

And we have to solve for y.

Solving for y, means isolating y . And to isolate y, we need to get rid of 4 that is with y .

It means we have to separate 4 from y, and for separation , we have to perform division. That is, we have to divide both sides by 4, and that will be the next step .

So out of the four options, correct option is the last option .

4 0

2 years ago

Read 2 more answers

Round to the nearest hundredth if necessary. <br> 2 qt =______ mL<br> help me pleaseeeee

Rasek [7]

It would be 1892.71

6 0

3 years ago

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5, find the ratio of the smaller number to the larger nu

IgorC [24]

Answer: