a rock fell from a cliff at 108 feet high and landed on an embankment feet from the ground. find the amount if time it would have taken the rock to fall.

The elevation of Smallville is calculated by multiplying the elevation of Longfield by 4. Longfield's elevation is -144 1/2 feet, which is equivalent to -289/2 as an improper fraction. Multiplying this by 4 gives the elevation of Smallville as -578 feet.

To find Smallville's elevation, we first take the elevation of Longfield, which is -144 1/2 feet below sea level. Since Smallville is 4 times farther below sea level than Longfield, we have to multiply the elevation of Longfield by 4.

First, convert -144 1/2 to an improper fraction: -144 1/2 = -289/2.

Now, multiply by 4:

(-289/2) × 4 = -289 × 2 = -578 feet

So the elevation of Smallville is -578 feet below sea level.

C

the equation of a line in ' slope- intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

y = [tex]\frac{3}{4}[/tex] x is in this form

with slope m = [tex]\frac{3}{4}[/tex] → C

The slope of the line is  [tex]m=\dfrac{3}{4}[/tex].

Given,

Equation of line is,

[tex]y=\dfrac{3}{4} x[/tex].

The line is passes through point,(2,1) .

We know that the slope form of equation is,

[tex]y=mx+c[/tex]

here m is the slope of the line and c is its y intercept.

On comparing the given equation of line with the general equation we get,

[tex]m=\dfrac{3}{4}[/tex].

Hence the correct option is C.

For more details on slope follow the link:

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Answer:

B is your best Bet

Step-by-step explanation:

for this problem, you would have to do B because thats the best bet compared to the other answers

the answer is x > -2

x is greater then -2 and that is the 3 one

uhhhhh, your question seems a bit unclear. could you make it a bit more readable?

The total area is 21 (15+6=21)

Answer:

Area of the given figure is 21 square units

Step-by-step explanation:

Area of the rectangle formula is length times width

Area of the top rectangle  

Length = 5 and width = 3

So area of top rectangle =5 times 3 is 15 square units

Area of bottom rectangle  

length =2 and width =3

So area of bottom rectangle is 2 times 3 is 6 square units

Total area =[tex]15+6= 21[/tex] square units

Combine like terms:

4x, 7x, -10x

-10, 14, 2

4x + 7x - 10x = x

-10 + 14 + 2 = 6

6 + x should be the correct answer.

To find f(2), look and see where the line crosses the Y axis, when The line is on X 2.

The line is on Y = -2, so the answer would be -2.

On Saturday Nikki and Tyler walked to the local farmers market Nikki bought 8 apples for $6 dollars and Tyler brought 3 fewer apples than Nikki. How much did Tyler spend on apples?​

Tyler brought 8 apples - 3 apples = 5 apples.​

​To calculate the price of 5 apples we have to establish a proportion :

If 8 apples cost $6​

Then 5 apples will cost $X​

​X = 5apples * $6/8apples = $3.75

​Answer : Tyler spent on apples $3.75

​Hope this helps!​​​​

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

Answer:

log(bsae(3))27=c

Step-by-step explanation:

a p e x

The logarithm equation is equivalent to the exponential equation is c = log₃27

A logarithm is the power to which a number must be raised in order to get some other number.

Given that, exponential equation, [tex]3^{c}[/tex]=27

By the exponential form of logarithm:

[tex]x^{a} =m[/tex] then logarithm form is a = logₓ m

Therefore,

[tex]3^{c}[/tex]=27

Taking logarithm both sides,

[tex]3^{c}[/tex]=27

c = log₃27

Hence, the logarithm equation is equivalent to the exponential equation is c = log₃27

Learn more about logarithm, click;

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The answer would be D) 50, because you would have to add 14+36 which equals 50

Answer:

The medium-sized can is the cheaper by the oz, and is $0.005 per oz. cheaper.

Step-by-step explanation:

Medium can:  $0.92/(46 oz) = $0.020/oz

Large can:   $3.60 / (144 oz) = $0.025/oz

Surprisingly, the medium can price per oz. is lower than that of the large can.  The difference is $0.005 per oz.

The medium can of tomato juice has the lower unit price at $0.02 per ounce, which is $0.005 lower per ounce than the large can's unit price of $0.025 per ounce.

To determine which can of tomato juice has the lower unit price, we need to calculate the cost per ounce for each can. For the medium can, we divide the cost by the number of ounces:

Medium can unit price = $0.92 / 46 ounces = $0.02 per ounce

For the large can, we perform a similar calculation:

Large can unit price = $3.60 / 144 ounces = $0.025 per ounce

The medium can has a lower unit price of $0.02 per ounce compared to the large can's unit price of $0.025 per ounce. The difference in unit price is $0.025 - $0.02 = $0.005, or half a cent per ounce.

25/6 hope this helps

He washes 7 cars and gets $4.00 for each one :

So it's the number of cars times the money he gets for each one - 7 times 4 = 28

He fills 10 bags of leaves and gets $1.00 for each bag:

So it's the number of bags times the money he gets for each one - 10 times 1 = 10

Than you add the money from the cars to the money of bags : $10 + $28 =

$38 total

Answer: $38.00

why; live

1 a) Yogurt : Orange Juice : milk

      50 : 100 : 250

      (50 : 100 : 250 ) / 50

  ans=       1  :   2    :     5

b)  1 l = 1000 ml  of milk

      so  1000/250    = 4

       ans= 4 regular smoothies.

 c)   3 regular and 1 small

        (50 : 100 : 250 ) *3  +    (50 : 100 : 250 ) / 2

=  (150 : 300 : 750 ) +  (25: 50: 125)

ans =  175 ml yogurt, 350 ml orange juice, 875 ml milk          

a = 7

Because we are looking for the area we would times the length times width. What times 6 would be equal to 42? 7!

Answer: The rate of interest per annum is 1.3%.

Step-by-step explanation:

Given  Principal P= $1000

time period n=3

Amount A=$1040,40

To find rate of interest per annum r

We know that

[tex]A=P(1+\frac{r}{100} )^3\\\Rightarrow\ 1040=1000(1+\frac{r}{100})^3\\\Rightarrow\ 1.040=(1+\frac{r}{100})^3\\\text{taking log on both sides}\\log(1.040)=3log(1+\frac{r}{100})\\\Rightarrow0.039=3log(1+\frac{r}{100})\\\Rightarrow0.013=log(1+\frac{r}{100})\\\\\Rightarrow\ e^{0.013}=(1+\frac{r}{100})\\\Rightarrow\ 1.013=(1+\frac{r}{100})\\\Rightarrow\ \frac{r}{100}=1.013-1=0.013\\[/tex]

⇒  r = 1.3%.

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Final answer:

The surface area of the paper coffee filter with a radius of 6 centimeters and a slant height of 12 centimeters is approximately 339 square centimeters when rounded to the nearest whole number.

Explanation:

Finding the Surface Area of a Coffee Filter

To find the surface area of the paper coffee filter, we need to consider it as a part of a cone because a coffee filter is shaped like a cone with a circular base. The surface area of a cone is calculated by the formula Surface Area = πr(r + l), where r is the radius and l is the slant height. Given that the radius of the coffee filter is 6 centimeters and the slant height is 12 centimeters, the formula should be filled in as follows:

Radius (r) = 6 cm

Slant Height (l) = 12 cm

The calculation will then be:

Surface Area = π x 6 cm x (6 cm + 12 cm)

Surface Area = π x 6 cm x 18 cm

Surface Area = π x 108 cm²

Surface Area ≈ 3.14159 x 108 cm²

Surface Area ≈ 339.29 cm²

Rounding to the nearest whole number:

Surface Area ≈ 339 cm²

The surface area of the paper coffee filter is approximately 339 square centimeters.

it will be 14 more minuted because she has completed 5/19 minutes it takes to reach the beach.. we can get this answer by taking the total number of minuted to get to the beach (19) and subtract the number of minutes she has already walked (5)..... our answer is that she has 14 minutes left till she reaches the beach.

Answer

It is Going To Take 14 Minutes

1. expand using place value.

337,060 = 300,000 + 30,000 + 7,000 + 000 + 60 + 0

Next, we will use exponents:

300,000 = 3 * 10^5

30,000 = 3 * 10^4

7,000 = 7 * 10^3

000 = 0 * 10^2

60 = 6 * 10

0 = 0 * 10^0

then after combing these exponents, we can write the number as:

337,060 = 3 * 10^5 + 3 * 10^4 + 7 * 10^3 + 0 * 10^2 + 6 * 10 + 0 * 10^0

Finally, removing the meaningless zeroes, we would end up with:

337,060 = 3 * 10^5 + 3 * 10^4 + 7 * 10^3 + 6 * 10

5x-5=30

Add 5 to both of the sides

5x=35

Divide 5 to both of the sides

X=7

9) [tex]3 + 5n = 1 + 8n + 2[/tex]  | subtract 5 on both sides, and solve 8n and -5n

[tex]3 = 1 + 3n + 2[/tex]  | combine like terms, add 2 and 1

[tex]3 = 3n + 3[/tex]  | subtract 3 on both sides, and solve 3 and -3

[tex]0 = 3n[/tex]  | divide by 3n

[tex]0 = n[/tex]  | final answer

10)  [tex]5x + 12 = 4x + 6[/tex]  | subtract 4x on both sides, solve -4x and 5x

[tex]x + 12 = 6[/tex]  | subtract 12 on both sides, solve -12 and 6

[tex]x = -6[/tex]  | final answer

11)   [tex]-8x - 4 = 7 (-2 - 4x) + 4x[/tex]  | distribute 7 into the parentheses

[tex]-8x - 4 = -14 - 28x + 4x[/tex]  | combine like terms

[tex]-8x - 4 = -14 - 24x[/tex]  | add 8x on both sides, and solve 8x and -24x

[tex]-4 = -14 - 16x[/tex]  | add -14 on both sides, and solve 14 and -4

[tex]10 = -16x[/tex]  | divide by -16 on both sides, and solve

[tex]-0.625 = x[/tex]  | final answer

12)   [tex]16 - 2n = - 8 + 4 (n - 3)[/tex]  | distribute 4 into the parentheses

[tex]16 - 2n = -8 + 4n - 12[/tex]  | combine like terms

[tex]16 - 2n = 4n - 4[/tex]  | add 2n on both sides, and solve 2n and 4n

[tex]16 = 6n - 4[/tex]  | add 4 on both sides, and solve 4 and 16

[tex]20 = 6n[/tex]  | divide by 6 on both sides, and solve

[tex]3.33333 = n[/tex] | final answer (repeated)

13)  [tex]-6 (3 - 6r) = -18 + 4r[/tex]  | distribute -6 into the parentheses

[tex]-18 + 36r = -18 + 4r[/tex]  | subtract 4r on both sides, solve 36r and -4r

[tex]-18 + 32r = -18[/tex]  | add -18 on both sides, solve -18 and 18

[tex]32r = 0[/tex]  | divide by 32 on both sides, and solve.

[tex]r = 0[/tex]  | final answer

14)   [tex]4 (3b - 1) = 9 - b[/tex]  | distribute 4 into the parentheses

[tex]12b - 4 = 9 - b[/tex]  | add -b on both sides, solbe 12 and b

[tex]13b - 4 = 9[/tex]  | add -4 on both sides, solve 9 and 4

[tex]13b = 13[/tex]  | divide 13 on both sides, solve

[tex]b = 1[/tex]  | final answer

15)   [tex]-6x + 7 (1 - x) = -4 (x - 4)[/tex]  | distribute 7 into parentheses

[tex]-6x + 7 - x = -4 (x - 4)[/tex]  | distribute -4 into the parentheses

[tex]-6x + 7 - x = -4x + 16[/tex]  | combine like terms

[tex]-5x + 7 = -4x + 16[/tex]  | add -4x on both sides, solve -5x and 4x

[tex]-x + 7 = 16[/tex]  | subtract 7 on both sides, solve 16 and -7

[tex]-x = 9[/tex]  | divide by -1 on both sides, solve

[tex]x = -9[/tex]  | final answer

16)   [tex]5 - (8v + 5) = -4 (1 + 3v)[/tex]  | distribute the - and -4 into the parentheses

[tex]5 - 8v - 5 = -4 - 12v[/tex]  | combine like terms

[tex]10 + 8v = -4 - 12v[/tex]  | add 12v on both sides, solve 12v and 8v

[tex]10 + 20v = -4[/tex]  | subtract 10 on both sides, solve -4 and -10

[tex]20v = - 14[/tex]  | divide 20 on both sides, and solve

[tex]v = -0.7[/tex]  | final answer

17)   [tex]-8 (4 + 4n) = 8 (n + 6)[/tex]  | distribute -8 and 8 into the parentheses

[tex]-32 - 32n = 8n + 48[/tex]  | add -32n to both sides, solve 32n and 8n

[tex]-32 = 40n + 48[/tex]  | subtract 48 on both sides, solve -32 and -48

[tex]-80 = 40n[/tex]  | divide -80 on both sides, and solve

[tex]-2 = n[/tex]  | final answer

UNDER CONSTRUCTION (I WILL EDIT WHILE YOU RECIEVE THE ANSWERS)

How to Get Answer for Number 9:

3+5n = 1+8n+2

5n+3=(8n)+(1+2)(Combine Like Terms)

5n+3=8n+3

Step 2: Subtract 8n from both sides.

5n+3−8n= 8n+3−8n

−3n+3=3

−3n+3−3=3−3

−3n=0

Answer: n = 0

[tex]\frac{-3n}{-3} =\frac{0}{-3}[/tex]

10.

5x + 12 − 4x = 4x + 6 − 4x

x + 12 = 6

x + 12 − 12 = 6 − 12

Answer: x = −6

11. Answer is also x = 0

(More answers will come as edited)

First, subtract 44 from the 96. You get 52. Then, divide 52 by 7 to figure out what each shirt costs. The answer is 52/7, or $7.43. She spent 7 dollars and 43 cents on each shirt.

I believe it's a segment.

342,489 is your answer.

multiply both sides of the equation by 3.

2x+3y=9

move variable to the right side and change its sign

2x=9-3y

divide both sides of the equation by 2

x=9/2-3/2y

Answer : C) 12.8 cubic cm

The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p)

If y is  inversely proportional to x then [tex]y=\frac{k}{x}[/tex]

where k is constant of proportionality

v is  inversely proportional to p then [tex]v=\frac{k}{p}[/tex]

the volume of a gas is 24 cubic centimeters when the pressure is 16 pounds

Given : v= 24  and p = 16. We need to find out k

[tex]24=\frac{k}{16}[/tex]

Multiply by 16 on both sides

k = 384

Now we find out the volume under a pressure of 30 pounds

[tex]v=\frac{384}{30}[/tex]

[tex]v=\frac{128}{10}[/tex]= 12.8 cubic cm

Under a pressure of 30 pounds, the gas would occupy a volume of 12.8 cubic centimeters, as determined by applying Boyle's law, which states that volume and pressure are inversely proportional in conditions of constant temperature.

The volume (v) of a gas in a container at a constant temperature varies inversely as the pressure (p). This is a demonstration of Boyle's law, which states that pressure and volume are inversely proportional (P = k/V) when temperature is held constant. To find the new volume when the pressure changes, we can set up a proportion based on the original conditions provided: 24 cm³ at 16 pounds pressure. We set the initial volume and pressure as 24 cm³ and 16 lbs, respectively, and then solve for the new volume when the pressure is 30 lbs.

To find the volume under a pressure of 30 pounds, we use the equation:

V1 * P1 = V2 * P2

Where V1 is the original volume, P1 the original pressure, V2 the new volume, and P2 the new pressure. Plugging in our known values:

24 cm³ * 16 lbs = V2 * 30 lbs

Solving for V2, we get:

V2 = (24 cm³ * 16 lbs) / 30 lbs

V2 = 384 cm³ / 30 lbs

V2 = 12.8 cm³

Therefore, under a pressure of 30 pounds, the gas would occupy a volume of 12.8 cubic centimeters.