One of the construction workers likes to listen to music on the job. Unfortunately, he
also has a bad habit of accidentally dropping his music player into the ravine! Luckily,
his daughter is good with physics and has built a safety balloon for his latest music
player that will release after the music player has been falling for 1 second.
The time it takes for the music player to fall from the bridge to the bottom of the
ravine can be modeled by the following equation:
1-
81 +24
16
where tis the amount of time since the construction worker dropped his music
player
Will the safety balloon release in time?
6. First, how long will it take for the music player to fall to the bottom of the ravine?
Solve the equation and find the values of t. (2 points: 1 point for each value)

Answer:

18 freshmen, 18 sophomores, 30 juniors, 30 seniors

Step-by-step explanation:

Given ratio

  freshman : sophomores : juniors : seniors

= 320 : 300 : 500 : 510

320 ≈ 300  and  500 ≈ 510

Therefore, 300 : 300 : 500 : 500

Ratio of 300 : 500 = 18 : 30

So  18 : 18 : 30 : 30 best represents the population

Given nos

Ratio:-

Round out

Option A

Step-by-step explanation:

6y×100=24

600y=24

600y/600=24/600

y=4/100

y=0.04

Answer:

the answer is D:5040

Step-by-step explanation:

The answer to your question would be D. 5040! Hope this helps - Have an amazing rest of your day :)

[tex]f(x)=\cfrac{x^2+x-42}{x^2+3x-28}\implies \stackrel{f(x)}{0}=\cfrac{x^2+x-42}{x^2+3x-28}\implies 0 = x^2+x-42 \\\\\\ 0=(x+7)(x-6)\implies x= \begin{cases} 6\\ -7 \end{cases}[/tex]

Answer:

∠s = ∠v

Step-by-step explanation:

Supplementary angles add up to 180°

∠s + ∠v = 180

90 + ∠v = 180

     ∠v = 180 - 90

      ∠v = 90°

⇒∠s ≅ ∠v

Answer:

a = 7

Step-by-step explanation:

3x + 4 = 57 ÷ 3

3x + 4 = 19

3x = 15

x = 5

2x + 2 =  2(5) + 2 = 10 + 2 = 12

19 - 12 = 7

a = 7

hope this helps!! p.s. i really need brainliest :)

Answer: D

Step-by-step explanation:

16+18+19+21+21=95

95/5 is 19
95+37=132

132/6=22

Answer: 40 minutes

Step-by-step explanation:

First, break this down into minutes. 1 1/4 hours is 75 minutes. 75 divided by 5 is 15. he spends 15 minutes taking a shower. 75 divided by 3 is 25. he spends 25 minutes eating breakfast. 25 plus 15 is 40. he spends 40 minutes to shower and eat breakfast.

Answer:

y=-1/3 x+1

Step-by-step explanation:

Answer:

a little confusing, but i think its a fake quiz that asks for your pledge so you put true, and integrity: the quality of being honest and having strong moral principles; moral uprightness

Step-by-step explanation:

Lets have Anisah be x right now.

4 years ago, Adrian was (x-4) + 28 = x+24
Right now, Adrian is 3x.

Knowing those two pieces of information, we can say that x+24 is equal to 3x-4. (This is because Adrian is 3x right now, and for 4 years ago, you subtract 4.)

x+24=3x-4
24=2x-4
28=2x
x=14

Right now Anisah is 14, and in 4 years he will be 14+4 = 18.

Answer:

[tex]\fbox{\fbox{Circumference = 226.08 feet}}[/tex]

Step-by-step explanation:

Given:

distance from center to the edge(Radius) of playground = 36 feet

To find:

Circumference of playground=?

Solution:

we know that,

Circumference of circle = 2πr

substituting the radius value in above formula,

[tex]2 \pi r = 2 \times 3.14 \times 36 = 226.08 \: ft[/tex]

[tex]\fbox{\fbox{Circumference = 226.08 feet}}[/tex]

Thanks for joining brainly community!

Answer: 226.08ft

Step-by-step explanation: we are finding the circumference of a circle so we will make 3.14 times 2 times 36 as it is a radius I think .

3.14 ×2×36=226.08 and the units is feet . Hope it helps buddy

Answer:

first one is b, second one is c

Step-by-step explanation:

3-4x<=11

-4x<=11-3

-4x<=8/:(-4)

x>=-2

Answer:

2.75

Step-by-step explanation:

When x = 4, y = 11

when x = 1, y = 2.75

k = 2.75

Since, there are 36 inches in 1 yard, multiply 3 1/3 by 36

So, 3 1/3 yards = 120 inches

Answer:

120 inches

Step-by-step explanation:

To convert 3 1/3 yards to inches, you first need to figure out how many inches are in one yard. 1 yard=36 inches.

After this, you would turn your mixed fraction into an improper fraction and then multiply by 36 inches. It would look like this:

10/3 * 36/1

Here, you would cancel out the common factors by factoring 36 by 3.

12*3=36 ----> 10/3 * [tex]\frac{3(12)}{1}[/tex] ----->

Lastly, multiply 10 by 12 and your answer would be 120 inches.

Part a)

The home value is $120,000 and they get a loan for $90,000.

This must mean the down payment was 120,000 - 90,000 = 30,000 dollars. This is the payment made up front.

The mortgage has a monthly payment of $786.60 which is done for 25 years = 25*12 = 300 months. They pay back 786*300 = 235,800 dollars.

Therefore, the total amount they pay for the house is:

downPayment + loanRepayment = 30,000 + 235,800 = 265,800

=======================================================

Part b)

Refer to the previous part. Laura and Martin pay back $235,800 after being loaned $90,000

The total amount of interest is 235,800 - 90,000 = 145,800 dollars.

=======================================================

Part c)

The annual interest rate is 9.5% which converts to the decimal form 0.095

Divide this over 12 to get the monthly interest rate in decimal form.

0.095/12 = 0.00791667 approximately

Then multiply this with the initial balance of $90,000

90,000*0.00791667 = 712.5003

This rounds to 712.50 and this represents the interest for the first month.

This leads to:

principal = monthlyPayment  - interest

principal = 786.60 - 712.50

principal = 74.10

It is unfortunately common practice that the starting monthly payments will be mostly interest. As time goes on, the increase payments decrease because they are tied directly to the remaining balance.

Answer:

6.856

Step-by-step explanation:

8² + x² = 17

8² - 17 = -x²

64 - 17 = -x²

-47 = -x²

x² = 47

x = 6.856

Answer:

a=5, a=-2.5

Step-by-step explanation:

Given:

[tex]2 a^2 - 5 a - 25 = 0[/tex]

Solution:

[tex]a_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-25\right)}}{2\cdot \:2}[/tex]

[tex]a_{1,\:2}=\frac{-\left(-5\right)\pm \:15}{2\cdot \:2}[/tex]

[tex]a_1=\frac{-\left(-5\right)+15}{2\cdot \:2},\:a_2=\frac{-\left(-5\right)-15}{2\cdot \:2}[/tex]

[tex]a=5,\:a=-2.5[/tex]

~Lenvy~

missing angle:

180° - 90° - 30°

180° - 120°

60°

missing sides:

(a)

[tex]\rightarrow \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

[tex]\rightarrow \sf tan(30)= \dfrac{4}{adjacent}[/tex]

[tex]\rightarrow \sf adjacent= \dfrac{4}{tan(30)}[/tex]

[tex]\rightarrow \sf adjacent= 4\sqrt{3}[/tex]

[tex]\rightarrow \sf adjacent= 6.93 \ cm[/tex]

(b)

[tex]\sf \rightarrow sin(x)= \dfrac{opposite}{hypotensue}[/tex]

[tex]\sf \rightarrow sin(30)= \dfrac{4}{hypotensue}[/tex]

[tex]\sf \rightarrow hypotensue= \dfrac{4}{ sin(30)}[/tex]

[tex]\sf \rightarrow hypotensue= 8 \ cm[/tex]

Answer:

m∠X = 60°

BX = 8 cm

BM = 4√3 cm

Step-by-step explanation:

The sum of the interior angles of a triangle is 180°

Given:

⇒ m∠B + m∠M + m∠X = 180°

⇒ 30° + 90° + m∠X = 180°

⇒ 120° + m∠X = 180°

⇒  m∠X = 180° - 120°

⇒  m∠X = 60°

Using the sine rule to find the side lengths:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

(where A, B and C are the angles, and a, b and c are the sides opposites the angles)

Given:

[tex]\implies \dfrac{4}{\sin 30\textdegree}=\dfrac{BX}{\sin 90\textdegree}=\dfrac{BM}{\sin 60\textdegree}[/tex]

[tex]\implies BX=\sin 90\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]

              [tex]=1 \cdot \dfrac{4}{\frac12}[/tex]

              [tex]=1 \cdot 4 \cdot 2[/tex]

              [tex]=8 \textsf{ cm}[/tex]

[tex]\implies BM=\sin 60\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]

              [tex]=\dfrac{\sqrt{3}}{2}\cdot \dfrac{4}{\frac12}[/tex]

              [tex]=\dfrac{\sqrt{3}}{2}\cdot 4 \cdot 2[/tex]

              [tex]=4\sqrt{3} \textsf{ cm}[/tex]

Answer:

7.5% compounded continuously yields the greatest return after 9 years

Step-by-step explanation:

Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.

7.6% compounded semiannually:

I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09

7.5% compounded continuously:

Since it is compounded continuously, we use the mathematical constant e.

I = 11000e = $29901.01

Answer:

  see attached

  cost = 33

Step-by-step explanation:

Kruskal's Algorithm is a "greedy" algorithm that adds the next minimum-weight edge to the tree, provided that it does not create a loop.

__

The minimum-weight edge in the graph is DF, with weight 1.

The next minimum-weight edge is GH, with weight 2.

The next minimum-weight edge is AB, with weight 3.

The next minimum-weight edge is EF, with weight 4.

Edge DE is the next lowest-weight, but it creates a loop (DEF), so we ignore it.

BC is the next edge we'll add to our tree.

FG is the next edge we'll add to the tree.

Edge DG creates a loop, so we ignore it.

Edge FH creates a loop, so we ignore it.

CF is the next edge we'll add to the tree. This completes the minimum spanning tree using Kruskal's Algorithm.

Included edges are AB, BC, CF, DF, EF, GF, GH.

The cost of the tree is 3+6+10+1+4+7+2 = 33.

Answer:

the answer in the question mark that was in the green box ???

Answer:

3+1.20c > 13.50

Step-by-step explanation:

hope this helps

Answer:

  4 mph

Step-by-step explanation:

Travel time is proportional to distance and inversely proportional to speed. If c represents the speed of the current in miles per hour, an equation for the total trip time is ...

  825/(29 -c) +825/(29 +c) = 58 . . . . . . hours travel time

  825(29 +c) +825(29 -c) = 58(29 -c)(29 +c)

  58c² -928 = 0 . . . . . . . rearrange to standard form

  58(c -4)(c +4) = 0 . . . . factor

Values of c that satisfy this equation are 4 and -4. For the purpose here, we'll choose the positive solution.

The speed of the current is 4 miles per hour.

Answer:

Step-by-step explanation:

17) In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠A +  ∠D = 180

5x + 30 + x = 180  

5x +x + 30 = 180    {Combine like terms}

     6x + 30 = 180 {Now, subtract 30 from both sides}

6x + 30 - 30 = 180 - 30

             6x  = 150

Now divide both sides by 6

              x = 150/6

              x = 25

∠A = 5x + 30

     = 5*25 + 30

     = 125 + 30

     = 155

In parallelogram, opposite angles are congruent.

∠C = ∠A

∠C = 155°

18)In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠A +  ∠D = 180

3x + 4 + x = 180  

3x +x + 4 = 180    {Combine like terms}

     4x + 4 = 180 {Now, subtract 4 from both sides}

4x + 4 - 4 = 180 - 4

             4x  = 176

Now divide both sides by 4

              x = 176/4

x =44

19) In parallelogram, adjacent angles are supplementary (add up to 180)

⇒∠GAC +  ∠ACF = 180

125 + ∠ACF  = 180  

       Now, subtract 125 from both sides

∠ACF = 180 - 125

∠ACF = 55

21) In parallelogram, adjacent angles are supplementary (add up to 180)

∠CFG + ∠ACF = 180

2w +30 + w + 15 = 180

2w +w + 30+ 15 = 180

          3w + 45   = 180

                      3w  = 180 - 45

                      3w = 135

                        w = 135/3

w = 45

∠ACF = w + 15

           = 45 + 15

∠ACF =  60

21) In parallelogram, opposite sides are congruent.

GF = AC

4x - 14 = 2x + 2

       4x = 2x + 2 + 14

       4x = 2x +  16

4x - 2x  = 16

    2x    = 16

          x = 16/2

         x = 8

22) In parallelogram, the diagonals bisect each other.

XC = GX

3y - 3  =2y + 2

       3y = 2y + 2 + 3

       3y = 2y + 5

  3y - 2y= 5

         y = 5

23) The length of the  middle segment of trapezium is half the sum of the two parallel sides.

[tex]\dfrac{b_{1}+b_{2}}{2}=110\\\\\\b_{1}+b_{2}=110*2\\[/tex]

square two sides

x+8=(x+8)2

x+8=x2+16x+64

x2+16x+64-x-8=0

x2+15x+56

then rule a2+-l

Answer:

18 I believe

Step-by-step explanation:

when you do 2.70 divided by 15% you get 18 and if you do 18 times 15% you get 2.70 so I think it is 18