If triangle DEF is congruent to triangle MNO, then angle E is congruent to angle ?

The height H of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 9

mariarad [96]

Answer:

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

Step-by-step explanation:

Statement is incorrect. Correct form is presented below:

The height $h(t)$ of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 90 feet per second is given by equation $h(t) = 3 +90\cdot t -16\cdot t^{2}$ , where $t$ is time in seconds. After how many seconds will the ball be 84 feet above the ground.

We equalize the kinematic formula to 84 feet and solve the resulting second-order polynomial by Quadratic Formula to determine the instants associated with such height:

$3+90\cdot t -16\cdot t^{2} = 84$

$16\cdot t^{2}-90\cdot t +81 = 0$ (1)

By Quadratic Formula:

$t_{1,2} = \frac{90\pm \sqrt{(-90)^{2}-4\cdot (16)\cdot (81)}}{2\cdot (16)}$

$t_{1} = 4.5\,s$ , $t_{2} = 1.125\,s$

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

3 0

3 years ago

A cage holds two litter of rats. One litter comprises one female and five males. The other litter comprises seven females and tw

timurjin [86]

Answer:

The probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.

Step-by-step explanation:

Since a cage holds two litter of rats, and one litter comprises one female and five males, while the other litter comprises seven females and two males, and a random selection of two rats is done, to find the probability that the two rats are from the same litter the following calculation must be performed:

6/15 x 5/14 = 0.1428

9/15 x 8/14 = 0.3428

Therefore, the probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.

4 0

3 years ago

The daily production cost, C, for x units is modeled by the equation: C = 200 – 7x + 0.345x2

lina2011 [118]

C(x) = 200 - 7x + 0.345x^2

Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.

Range is the set of possible results for c(x), i.e. possible costs.

You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.

You can substitute some values for x to help you, for example:

x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + .345 (4) = 187.38
3 200 - 21 + .345(9) = 182.105
4 200 - 28 + .345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42

10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745

The functions does not have real roots, then the costs never decrease to 0.

The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.

Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.

8 0

3 years ago

What is 2h+(6+h)+6•2

Romashka-Z-Leto [24]

2h+6+h+6*2

3h+6+12

3h+18

8 0

3 years ago

Read 2 more answers

PLSS HELP ASAP What slope- intercept form equation represents the line

scZoUnD [109]