a ball begins rolling down a hill. after 5 seconds, its velocity is 10 meters per second. what is the acceleration of the ball?


5m/s/s
10m/s/s
15m/s/s
2m/s/s​

Answer:

x in all equations just normally means 1

Step-by-step explanation:

x is always 1

Given:

In triangle ABC, m∠A=(8x-2)°, m∠B=(2x-8)° and m∠C=(94-4x)°.

To find:

The sides of the triangle ABC in order from shortest to  longest.

Solution:

In triangle ABC,

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]              (Angle sum property)

[tex](8x-2)^\circ+(2x-8)^\circ+(94-4x)^\circ=180^\circ[/tex]

[tex](6x+84)^\circ=180^\circ[/tex]

[tex]6x+84=180[/tex]

[tex]6x=180-84[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=\dfrac{96}{6}[/tex]

[tex]x=16[/tex]

Now,

[tex]m\angle A=(8(16)-2)^\circ[/tex]

[tex]m\angle A=(128-2)^\circ[/tex]

[tex]m\angle A=126^\circ[/tex]

Similarly,

[tex]m\angle B=(2(16)-8)^\circ[/tex]

[tex]m\angle B=(32-8)^\circ[/tex]

[tex]m\angle B=24^\circ[/tex]

And,

[tex]m\angle C=(94-4(16))^\circ[/tex]

[tex]m\angle C=(94-64)^\circ[/tex]

[tex]m\angle C=30^\circ[/tex]

In a triangle the smaller angle has shorter opposite side and larger angle has longer opposite side.

[tex]24^\circ<30^\circ<126^\circ[/tex]

[tex]m\angle B<m\angle C<m\angle A[/tex]

[tex]AC<AB<BC[/tex]

List the sides of triangle ABC in order from shortest to  longest is AC:AB:BC.

Therefore, the correct option is A.

Answer:

180º

Step-by-step explanation:

All the interior angles add up to 180º degrees.

Answer:

180 degrees

Step-by-step explanation:

In a Euclidean space, the sum of angles of a triangle equals the straight angle

The answer is b bbbbbbbbbbbbbbb

Answer:

The answer is B

Step-by-step explanation:

I hope this helps! :D

Answer:

The answer is 646.02 tell me if you need an explaination

Answer:

{0, infinity)

Step-by-step explanation:

range is always the y coords

Answer:

96 feet squared

Step-by-step explanation:

to find the triangles area you would have to multiply 16 times 12 which would get you 192 then you would have to divide it by 2. Therefore the answer is 96.

Answer:

Step-by-step explanation:

$8.75

hope it helps

Answer:

24

Step-by-step explanation:

half 32 and half it again u get 8 then u do 32-8

Answer:

B

Step-by-step explanation:

Okay, so we know they can run 1/4 a mile in 25 seconds. Now we want to know how far they can run in a minute ( 60 sec.). Because there is 25 seconds in 60 seconds 2.4 times, we multiply 1/4 by 2.4. We get 0.6. We know that there is 60 minutes in an hour, so we multiply 0.6 by 60. Now we know they can run 36 miles in an hour/ 36 miles per hour. So that eliminates C and D.

Anyways, B is correct because if you divide 1/4 by 25 you get 0.01. Multiply that by 60 to get a minute. (Because there is 60 seconds in a minute) Which is 0.6. Then multiply it again by 60 for an hour( because there is 60 minutes in an hour), and you get 36 hours.

Answer:

Step-by-step explanation:

((((((.5 mile = .25 hour<<<<<<<<<<<<<<<<<<<<<<<<<<

Multiply both sides by 4, because there are 4 quarters in 1 hour

(4)(.5) = (.25)(4)

2 miles =1 hr

Multiply both sides of the original equation by 3 to figure out how far in 3/4 of an hour

(3)(.5) = (3)(.25)

1.5 miles = 3/4 of an hour

now add the two answers together to figure out that the person walked 3.5 miles in 1 3/4 hours

***You also could have multiplied both sides of the original equation by 7, recognizing that that there are 7 quarters in 1.75 hours.

Answer:

Step-by-step explanation:

ΔSRQ and ΔVTU are similar Triangle.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, ΔRQS and ΔVUT such that,

RS = 16, QR= 64 and VT = 8, UT = 32

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

From the above condition since,

∠R = ∠T

and

[tex]\frac{QR}{SR} = \frac{UT}{VT} = \frac{4}{1}[/tex]

Thus,

ΔSRQ and ΔVTU are similar from the congruency  property of SAS.

Learn more about congruent triangles here:

https://brainly.com/question/22062407

#SPJ7

Answer:

Step-by-step explanation:

I HOPE IT HELPS :)

Step one: (((x2)+x)+1)+((0-(2x23•x))+5)

Step two: Check for a perfect cube.  2.1    -2x24+x2+x+6  is not a perfect cube.

2.2      Factoring:  -2x24+x2+x+6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x+6

Group 2:  -2x24+x2

Pull out from each group separately :

Group 1:   (x+6) • (1)

Group 2:   (2x22-1) • (-x2)

The groups have no common factor and can not be added up to form a multiplication.

So the answer would be,  -2 (x24) + (x2) ++ 6.

Answer:

By opting for the second option, Alice would save $ 15,740.00  in total mortgage cost

Step-by-step explanation:

In order to determine the better of the two options available, we need to determine the total cost under each option as follows:

Option 1:

cost of house=$625,000

loan amount=$625,000-(20%*$625,000)=$500,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=4%/12=0.33333333%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.33333333% )^-360/0.33333333%

500,000=monthly payment*(1-0.301795869 )/0.003333333

500,000=monthly payment*0.698204131 /0.003333333

monthly payment=500,000*0.003333333 /0.698204131

monthly payment=$ 2,387.08  

total monthly payments=$ 2,387.08*360=$859,348.80

Option 2:

upfront fee=$10,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=3.75%/12=0.3125%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.3125%  )^-360/0.3125%

500,000=monthly payment*(1-0.325222459  )/0.003125

500,000=monthly payment*0.674777541  /0.003125  

monthly payment=500,000*0.003125  /0.674777541=$2,315.58  

Total cost=total monthly payments+upfromt fee

total cost=($2,315.58 *360)+$10,000=$843,608.80  

savings by opting for the second option=$859,348.80-$843,608.80  

Answer: Numbers of servings: 10 and 13, Liters of punch: 14

Step-by-step explanation:

Number of servings - 6 = Liters of punch.

Answer:

I need  a picture or something else to give answer

Step-by-step explanation:

Answer:

220 possible ways

Step-by-step explanation:

Given

[tex]n = 12[/tex] --- people

[tex]r = 3[/tex] -- posts [tex](President, Vice\ President\ and\ Secretary)[/tex]

Required

Determine the number of selection

Since there is no condition attached, the number of selection is:

[tex]Selection = ^nC_r[/tex]

Substitute values for n and r

[tex]Selection = ^{12}C_3[/tex]

Apply combination formula

[tex]Selection = \frac{12!}{(12-3)!3!}[/tex]

[tex]Selection = \frac{12!}{9!3!}[/tex]

[tex]Selection = \frac{12*11*10*9!}{9!*3*2*1}[/tex]

[tex]Selection = \frac{12*11*10}{6}[/tex]

[tex]Selection = \frac{1320}{6}[/tex]

[tex]Selection = 220[/tex]

Hence, there are 220 possible ways

Answer:

30+(−17) is the answer

Step-by-step explanation:

my name is jeff   Step-by-step explanation:

Answer:

A will be at 6,6

Step-by-step explanation:

I think this because the graph is the same so it most likely will be the at the same position. Hope this is right !

Answer:

70 units

Step-by-step explanation:

Answer: Angle ABD is 39°

Step-by-step explanation:

Angle CBA is 90° (given by "box" on the corner of the right triangle)

Angle CBD is given as 51°

Subtract:

90° - 51° = 39°

Answer:

The toll on a bridge is $1.00 \:for\: cars\: and\: $2.50 for trucks. In one hour, a tollbooth operator collects a total of $105 in tolls.

Equation :---

[tex]\boxed{c + 2.5t = 105}[/tex]

Above equation represents the relationship between the number of cars, c, and the number of trucks, t, which could have passed by this tollbooth.

Answer:

3 feet

Step-by-step explanation:

720ft

1ft:240ft

720/240=3

3ft:720ft

Answer:

(a)

A single avocado costs $1

A single tomato costs $0.5

(b)

An avocado costs twice as much as a tomato

Step-by-step explanation:

Represent the tomatoes with T and the avocados with A.

So, we have:

[tex]4T + 8A = 10[/tex] --- (1)

[tex]6T + 14A = 17[/tex] --- (2)

Solving (a): The price of each

Multiply (1) by 1.5

[tex]1.5(4T + 8A = 10)[/tex]

[tex]6T + 12A = 15[/tex] --- (3)

Subtract (3) from (2)

[tex](6T + 14A = 17) - (6T + 12A = 15)[/tex]

[tex]6T - 6T + 14A - 12A = 17 - 15[/tex]

[tex]14A - 12A = 17 - 15[/tex]

[tex]2A = 2[/tex]

Divide both sides by 2

[tex]A = 1[/tex]

Substitute 1 for A in (1)

[tex]4T + 8A = 10[/tex]

[tex]4T + 8(1) = 10[/tex]

[tex]4T + 8 = 10[/tex]

Make 4T the subject

[tex]4T = 10 - 8[/tex]

[tex]4T = 2[/tex]

Divide both sides by 4

[tex]T = \frac{2}{4}[/tex]

[tex]T = 0.5[/tex]

Solving (b): Analysis

In (a), we have:

[tex]T = 0.5[/tex]

[tex]A = 1[/tex]

We can say that an avocado costs twice as much as a tomato

Answer:

1) Emilio's total saving - $127.5

2) 33.6ft

Step-by-step explanation:

1) $63.75 x 2 = $127.5

2) 308ft - 274.4ft = 33.6ft