An object is thrown upward from the top of 96​-foot building with an initial velocity of 80 feet per second. The height h of the object after t seconds is given by the quadratic equation h=16t^2+80t+96. When will the object hit the​ ground?

Answer:

m<BAC = 85°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

m<BAC = 170°/2

m<BAC = 85°

Answer:

First, find the time when Jackie and her friend meet.

Using:

[tex]\sf s=ut+\dfrac12at^2[/tex]

where:

Jackie and her friend are not accelerating, so a = 0, which means the formula can be reduced to:

[tex]\sf s=ut[/tex]

Create equations

Jackie:  [tex]\sf s_1= 3t[/tex]

Friend:  [tex]\sf s_2 = 12t[/tex]

As the distance covered by Jackie and her friend at the time they meet equals 3 miles:

[tex]\sf s_1+s_2=3 \ miles[/tex]

[tex]\sf \implies 3t + 12t = 3[/tex]

[tex]\sf \implies 15t = 3[/tex]

[tex]\sf \implies t = 0.2 \ hr[/tex]

[tex]\sf \implies t=0.2 \times 60=12 \ mins[/tex]

Therefore, they meet 12 mins after they both start moving.

3 mph = 3 ÷ 60 = 0.05 miles per min

12 mph = 12 ÷ 60 = 0.2 miles per min

Therefore,

Jackie traveled:  0.05 x 12 = 0.6 miles

Her friend traveled: 0.2 x 12 = 2.4 miles

when they meet.

To find the speed Jackie's brother must walk to catch up with her at the same time she meets her friend, use s = 0.6 miles (as this is the distance Jackie walked) and t = 12 - 4 = 8 mins (since he left 4 mins after Jackie left):

[tex]\sf s=ut[/tex]

[tex]\sf \implies u = \dfrac{s}{t}[/tex]

[tex]\implies \sf u = \dfrac{0.6}{8}[/tex]

[tex]\implies \sf u = 0.075 \ miles \ per \ min[/tex]

[tex]\sf \implies u = 0.075 \times 60 = 4.5 \ mph[/tex]

So Jackie's brother needs to walk faster than 4.5 mph to catch up with Jackie before she meets her friend.

(If he walks at 4.5 mph, he will catch up to Jackie at the instant she meets her friend.  If he walks slower than 4.5 mph, he will not catch up with Jackie before she meets her friend).

Answer:

27.2

Step-by-step explanation:

sin 54 = opposite / hyp = 22 / x

sin 54 = 22/x

x = 22/sin54 = 27.2

Answer:

Parallelogram

Step-by-step explanation:

Instead of one pair of parallel sides like in a trapezoid, a parallelogram has two pairs of opposite sides (for example a rectangle)

Answer:

19 and 13

Step-by-step explanation:

width = x

length = x + 6

2x + 2(x + 6) = 64

2x + 2x + 12 = 64

4x = 64 - 12

4x = 52

x = 13

x + 6 = 19

Answer:

19 and 13

Step-by-step explanation:

Step-by-step explanation:

120 ÷ 1.6 = 75.

so 75 miles per hour.

75 × 2 = 150

therefore 150 miles in 2 hours

Answer:

120 km/ 1 hour

We need to convert kilometers into miles, so given the information below (1 mile = 1.6 km), we divide 120 km by 1.6 km because 1.6 km is equivalent to 1 mile.

120km/1.6km

= 75 miles, so therefore the cars rate will be:-

75 miles/ 1 hour

To see how many miles are in 2 hours, we must multiply the unit rate(75 miles/ 1 hour) by 2.

75 miles/ 1 hour x 2/2 hours

75 x 2

______ = 150/2, so the car will travel 150 miles in 2 hours.

 1 x 2

Answer:

(x−4)(x−2)(x+5)

Step-by-step explanation:

Answer:

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

This probability is the pvalue of Z when X = 136 subtracted by the pvalue of Z when X = 128. So

X = 136

has a pvalue of 0.8849.

X = 128

has a pvalue of 0.3446.

0.8849 - 0.3446 = 0.5403

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Apply Pythagorean theorem

[tex]\\ \rm\rightarrowtail B^2=2.2^2-2^2[/tex]

[tex]\\ \rm\rightarrowtail B^2=5-4[/tex]

[tex]\\ \rm\rightarrowtail B^2=1[/tex]

[tex]\\ \rm\rightarrowtail B=1[/tex]

Area:-

Answer:6

Step-by-step explanation:

I did the test

Answer:

3991680 or 792

Step-by-step explanation:

12P7 = 3991680

or

12C7 = 792

P = permutation

C = combination

Sorry, I am not sure which answer is correct or if any of the answers are correct.

[tex]\left\{\begin{matrix}x=4\\y=10\\\end{matrix}\right.[/tex]

[tex]\left\{\begin{matrix}-5x+y=-10\\-4x-y=-26\\\end{matrix}\right.[/tex]

_____________________________________

[tex]-5x+y+(-4x-y)=-10+(-26)[/tex]

____________________________

[tex]-5x+y-4x-y=-10-26[/tex]

_________________________________________________

[tex]-5x-4x=-10-26[/tex]

___________________________________________

[tex]-9x=-10-26[/tex]

______________________________________________

[tex]-9x=-36[/tex]

________________________________________________

Divide both sides of the equation by the coefficient of variable

[tex]x=\frac{-36}{-9}[/tex]

____________________________________________________

Determine the sign for multiplication or division

[tex]x=\frac{36}{9}[/tex]

_________________________________________

Cross out the common factor

[tex]x=4[/tex]

[tex]-4\times4-y=-26[/tex]

____________________________________________________

Calculate the product or quotient

[tex]-16-y=-26[/tex]

______________________________________________________

Rearrange variables to the left side of the equation

[tex]-y=-26+16[/tex]

_____________________________________________

Calculate the sum or difference

[tex]-y=-10[/tex]

_________________________________________-

Divide both sides of the equation by the coefficient of variable

[tex]y=10[/tex]

I hope this helps you

:)

Answer:

[tex]\sf \dfrac29[/tex]

Step-by-step explanation:

From the table:

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(Girl)=\dfrac{18}{30}[/tex]

[tex]\sf \implies P(Freshman \cap Girl)=\dfrac{4}{30}[/tex]

[tex]\begin{aligned}\sf P(Freshman|Girl)& = \sf\dfrac{P(Freshman \cap Girl)}{P(Girl)}\\\\ & = \sf \dfrac{4}{30} \div \dfrac{18}{30}\\\\ & \sf=\dfrac{4}{30} \times \dfrac{30}{18}\\\\ & = \sf \dfrac29\end{aligned}[/tex]

Answer: A = and then below is incorrect then state how to find the correct answer and why it is correct.

Step-by-step explanation: hope it helps

Answer:

$4.75

Step-by-step explanation:

To find the unit price (price for one), just divide $9.30 by 2. You get that one clay pot (the price for one unit) is $4.75.

Hopefully this helps- let me know if you have any questions!

Answer:

Step-by-step explanation:

let the eq. be

y=a(x-2)(x-4)+b

x=0,y=-2

-2=a(0-2)(0-4)+b

-2=8a+b

when x=6,y=-2

-2=a(6-2)(6-4)+b

-2=8a+b

when x=8,y=-6

-6=a(8-2)(8-4)+b

-6=24a+b

16a=-4

a=-1/4

-2=-2+b

b=0

y=-1/4(x-2)(x-4)

y=-1/4(x^2-6x+8)

y=-1/4x^2+3/2x -2

when x=1

y=-1/4(1-2)(1-4)

y=-3/4

[tex]\qquad\qquad\huge\underline{{\sf Answer♪}}[/tex]

If the given triangles are congruent, then their corresponding sides are equal as well ~

So, let's use this condition

[tex]\qquad \sf  \dashrightarrow \:2y + 5 = 3y + 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:3y - 2y = 5 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 3[/tex]

and

[tex]\qquad \sf  \dashrightarrow \:2x + 7 = 15[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 4[/tex]

Answer:

Width=28 1/3 Length=51 2/3

Step-by-step explanation:

1. Create an equation

x+(2x-5)=80

2. Solve

x+(2x-5)=80

3x-5=80

3x-5+5=80+5

3x/3=85/3

x=28 1/3

So, if x=28 1/3

85/3x2=170/3

56 2/3-5

So, Length=51 2/3

Answer:

B is the answer

Step-by-step explanation:

Hope it helps.

Answer:

4 squares

Step-by-step explanation:

If the rectangle is only 3 cm wide, only one square will be able to fit in a row. Since the square is 12 cm long, 4 squares can fit. This can be found by 12/3 which = 4

Answer:

See attached graph

Step-by-step explanation:

We need to convert the polar coordinates into Cartesian coordinates using the rules [tex]x=r\:cos\theta[/tex] and [tex]y=r\:sin\theta[/tex] (see table in attached file).

The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation [tex]r=4\:cos\theta[/tex].

Answer:

5m - 10

Step-by-step explanation:

Use distributive property;

5(m - 2)

(5 x m) (5 x -2)

5m - 10

Answer:

Θ = (π/6) + πn

Θ = (5π/6) + πn

Step-by-step explanation:

4sin²Θ + 4 = 5

            -4    -4

4sin²Θ = 1

÷4         ÷4

sin²Θ = (1/4)

√sin²Θ = √(1/4)

sinΘ = (1/2), (-1/2)

-------------------------

Θ = arcsin (1/2)

Θ = (π/6)

to find the quadrant subtract π

Θ = π - (π/6)

Θ = (5π/6)

Find the period

2π / |b|

b = 1

2π/1 = 2π

The sin Θ function is 2π, so values will repeat 2π in both directions.

Θ = (π/6) + 2πn (n is the variable)

Θ = (5π/6) + 2πn

-------------------------------------------------------------------------------------------------------

sin Θ = (-1/2)

Θ = arcsin (-1/2)

Θ = (-π/6)

To find the second function add π

Θ = 2π + (π/6) + π

Θ = (7π/6)

Find the period

2π/|b|

2π/1

2π

(-π/6) + 2π

2π       6         π

----- ×  ----- -  -----

1           6        6

Θ = (11π/6) will repeat every 2π in both directions

-------------------------------------------------------------------------------------------------------

Θ = (π/6) + 2πn

Θ = (5π/6) + 2πn

Θ = (7π/6) + 2πn

Θ = (11π/6) + 2πn

(π/6) + π = (7π/6)

(5π/6) + π = (11π/6)

Θ = (π/6) + πn

Θ = (5π/6) + πn

----------------------------------------------------------------------------------------------------------

I hope this helps!

Answer:

a=20

Step-by-step explanation:

a-10+a=30

a+a-10=30

2a-10=30

2a=30+10

2a=40

a=20

Answer:

Ans is mean .because mean means average.

Answer:

ok

Step-by-step explanation:

Answer:

Hi shelp >//<

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Answer:

Hi shelp >//<

[tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][/tex]

Step-by-step explanation:

enebe eeeHAHAHA

Answer:

1/4 is the correct answer

Step-by-step explanation:

Even after replacing the marble the propability will not chance.