Use the x-intercept method to find all real solutions of the equation. x^3-10x^2+29x-20=0

Scenario: Does the age at which babies learn to crawl depend on the time of the year that the babies were born? Data were collec

sweet-ann [11.9K]

The age for when babies learn to crawl is different for Januar,May, and September.. so I guess yes?

4 0

2 years ago

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

barxatty [35]

Step-by-step explanation:

I assume that "ground" is at 0 ft height. which is in an actual scenario not airways the case.

y = -16x² + 64x + 89

shows us that the tower is 89 ft tall (the result for x = 0, at the start).

anyway, if the original assumption is correct, then we need to solve

0 = -16x² + 64x + 89

the general solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/)2a)

in our case

a = -16

b = 64

c = 89

x = (-64 ± sqrt(64² - 4×-16×89))/(2×-16) =

= (-64 ± sqrt(4096 + 5696))/-32 =

= (-64 ± sqrt(9792))/-32

x1 = (-64 + 98.95453501...)/-32 = -1.092329219... s

x2 = (-64 - 98.95453501...)/-32 = 5.092329219... s

the negative solution for time is but useful here (it would be the time calculated back to ground at the start).

so, x2 is our solution.

the rocket hits the ground after about 5.09 seconds.

5 0

2 years ago

Anisha invested $8,000 in an account that earns 10% interest How much money will she have in 15 years of the interest is compoun

tamaranim1 [39]

Answer:

A = $35,198.32

Step-by-step explanation:

Use the formula to calculate compound interest:

A = P(1 + i)ⁿ

"A" for total amount after the time period

"P" for principal, or starting money

"i" for the interest rate in a compounding period

To calculate "i":

i = r / c

"n" for the number of compounding periods

To calculate "n":

n = tc

So, we can combine the formulas into:

$A = P(1+\frac{r}{c})^{tc}$

"c" is the compounding periods in a year. (quarterly = 4)

We know:

P = 8000

r = 10% / 100 = 0.1

t = 15

c = 4

Substitute the information in the formula.

$A = P(1+\frac{r}{c})^{tc}$

$A = 8000(1+\frac{0.1}{4})^{15*4}$ Solve "i" and "n"

$A = 8000(1+0.025)^{60}$ Solve inside the brackets

$A = 8000(1.025)^{60}$ Do the exponent before multiplying by 8000

A = 35198.318 Exact answer

A ≈ 35198.32 Round to two decimal places for money

Therefore she will have $35,198.32 after 15 years.

5 0

3 years ago

Six and four fifths divided by three and two ninths

ahrayia [7]

Its going to be 4 .............

4 0

3 years ago

Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coord

ElenaW [278]

Answer:

(0, -1)

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.

Hence for parallelogram RSTU, RS // TU and RU // ST

Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:

Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5

Slope of ST = (2 - 4) /[6 - 3] = -2/3

Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)

Slope of TU = (y - 2) /[x - 6]

Slope of RU = Slope of ST

(y - 1) / (x + 3) = -2/3

3y - 3 = -2x -6

2x + 3y = -6 + 3

2x + 3y = -3 (1)

Slope of RS = Slope of TU

0.5 = (y - 2) /[x - 6]

0.5x - 3 = y - 2

0.5x - y = 1 (2)

Solving 1 and 2 simultaneously gives:

x = 0, y = -1

Therefore the coordinates of U = (0, -1)

8 0

2 years ago