A ball is launched into the sky at 54.4 feet per second from a 268.8 meter tall building. The equation for the ball’s height, h, at time t seconds is h = -3.2t^2 + 54.4t + 268.8. When will the ball strike the ground?

Given:

In [tex]\Delta ABC, \overline{CA}=\overline{CB}[/tex].

[tex]\overline{CD}[/tex] is an altitude drawn from C to [tex]\overline{AB}[/tex].

To prove:

[tex]\overline{CD}[/tex] bisects [tex]\overline{AB}[/tex].

Proof:

In [tex]\Delta ABC[/tex], [tex]\overline{CD}[/tex] is an altitude drawn from C to [tex]\overline{AB}[/tex].

It means, [tex]\Delta ACD\text{ and }\Delta BCD[/tex] are right angle triangles.

In [tex]\Delta ACD\text{ and }\Delta BCD[/tex],

Hypotenuse : [tex]\overline{CA}=\overline{CB}[/tex]       [Given]

Leg : [tex]\overline{CD}=\overline{CD}[/tex]       [Common]

If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then by HL postulate both triangles are congruent.

[tex]\Delta ACD\cong \Delta BCD[/tex]        [HL postulate]

[tex]\overline{AD}\cong \overline{BD}[/tex]       [CPCTC]

[tex]\overline{AD}=\overline{BD}[/tex]

It means, point D is the midpoint of [tex]\overline{AB}[/tex].

So, [tex]\overline{CD}[/tex] bisects [tex]\overline{AB}[/tex].

Hence proved.

Answer:

The answert is "$0.007 / bottle".

Step-by-step explanation:

Please find the complete question in the attachment file.

[tex]\to R(x) =7.5x^{0.7}[/tex]

The  average income:

[tex]\to A(x) = \frac{R(x)}{x} =7.5 x^{-0.3}[/tex]

The change rate on the average revenue:

[tex]\to A'(x) =7.5(-0.3)x^{-1.3}[/tex]

when 81 bottles were produced , then the rate of change in average revenue

[tex]\to =A'(81)\\\\\to -0.007 \ / \ bottle[/tex]

The average income  is decreasing at rate = $0.007 / bottle

Answer:

4/9 to 5/9

Step-by-step explanation:

So, out of every 9 students, 4 are boys. Therefore, 4/9 of the students are boys. The ratio of boys to girls is 4:5. So let 4x be the number of boys and 5x be the number of girls.

Answer:

I can't read the words the picture is to grainy

Answer:

10% would be 6

Step-by-step explanation:

First you want to find the 100 percent amount  to turn 40 into 100 you need to multiply it by 2.5 so you want to take 24 and multiply by 2.5 which equal 60 and 60 divided by 10  is 6

Answer:

True

Step-by-step explanation:

Principle = Interest * Time

So if time doesn't change, You'll get more money when Interest is higher!

Answer:

The sum of the exterior angles of a regular polygon will always equal 360 degrees.

Answer:

Step-by-step explanation:

Answer:

See answers below:

Answer:

6y + 6x

Step-by-step explanation:

the expanded form would be 6 multiplied to each item in the parenthesis

this gets you 6x + 6y

Answer:

369 m²

Step-by-step explanation:

Area of Triangle (sides): 1/2bh

=1/2(bh)

=1/2 (9•16)

=1/2 (144)

=72

There are four sides of the prism:

72•4=288

Area of Square (base): l•w

=9•9

=81

Surface Area = 288+81=369 m²

Answer:

369 m²

Step-by-step explanation:

Answer:

$1.03

Step-by-step explanation:

7/8 = 0.875

then

43 7/8 = 43.875%

43.875/100 = 0.43875

2.35 * 0,43875 = 1.031

Round to the neares cent:

1.03

Step-by-step explanation:

[tex]43 \frac{7}{8} \% \: of \: 2.35 \\ \frac{351}{8} \% \: of \: 2.35 \\ \frac{351}{8 \times 100} \times 2.35 \\ \frac{824.85}{800} = \boxed{\$1.0310625}[/tex]

the answer will be 10 just multiply the numbers

Answer: The answer is -9

Step-by-step explanation:-8 - 1 = -9

Answer:

5/8

Step-by-step explanation:

Answer:

$13,622.4

Step-by-step explanation:

$1,135.2(what she gets paid per month) *12 (months per year)

9514 1404 393

Answer:

  30°

Step-by-step explanation:

The angle a line makes with the x-axis is arctan(slope). Here, that is ...

  angle with x-axis = arctan(√3) = 60°

So, the angle made with the y-axis is the complement of this:

  angle with y-axis = 90° -60° = 30°

Answer:

Where is the picture of the figure ?

Answer:

where’s pic

Step-by-step explanation:

?

Answer:

8.25 minutes

Step-by-step explanation:

31 minutes-6.25 minutes=24.75 remaining miutes between the last 3 miles so then you take 24.75 minutes÷ 3 miles remaining= 8.25 minutes each last 3 miles

Answer:

[tex]\boxed{\boxed{\pink{\sf Option \ C \ is \ correct .}}}[/tex]

Step-by-step explanation:

Given to us is , 5 ( x + 12 ) and we need to find which is its equivalent in the given options .

So,

[tex]\bf = 5 ( x + 12 ) \\\\=\bf 5x + 5\times 12 \\\\=\boxed{\red{\bf 5x + 60 }}[/tex]

Answer:

the number is 4

Step-by-step explanation:

4 times 3=12

12-10=2

hope this helps!

Answer:

it's 7!

Step-by-step explanation:

Answer:

yasssssss queen/king

Step-by-step explanation:

Answer:

Step-by-step explanation: Do rise and run

Anwser would be -1

Hope this helps

Answer:

Step-by-step explanation:

1. isosceles

2. right scalene

3. obtuse scalene

4. equilateral

5. right isosceles

6. acute scalene

7. equilateral

8. isosceles

The average rate of change of h(t) = -16t ² + 40t + 4 between t = 0 and t = 2 is

(h (2) - h (0)) / (2 - 0) = ((-16×2² + 40×2 + 4) - (-16×0² + 40×0 + 4)) / 2

… = ((-64 + 80 + 4) - 4) / 2

… = 16 / 2

… = 8

h(t) is measured in feet, so the average rate of change is measured in feet per second, so it's 8 feet per second.

Answer:

16x-6

Step-by-step explanation:

well in order to do so

u have to multiply 2 to 8x to get 16x

and then, multiply the 2 to -3 to get -6

this is the distributive property form. and that's how u get ur answer

Answer:

m=42

Step-by-step explanation:

because all straight line equal 180, we can find angle C

180-98=82

now, all triangles add up to 180. If we add up all the values we can find x

82+6x+8+5x+2=180

92+11x=180

11x=88

x=8

Now, just plug the variable into the angle measure

5(8)+2

40+2

42