Water flows from a bathroom tap at a rate of 2 gallons every 6 seconds. At this rate, how many minutes will it take to fill an 80-gallon tub?

Answer:

a) X + X + 1 = 11

Step-by-step explanation:

Em matemática, a soma de consecutivos é expressa matematicamente como:

X + (X + 1) + (X + 2) + (X + 3) .............

Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11

Portanto, esta expressão algébrica é dada como:

X + (X + 1) = 11

X + X + 1 = 11

Portanto, a opção a) X + X + 1 = 11 é a opção correta

Answer:

1) The ship is closer

2) 675.73 m

Step-by-step explanation:

1) The given parameters are;

The initial angle between the ship's course and the lighthouse = 32°

The final angle between the ship's course and the lighthouse = 72°

The distance traveled by the sip between he two positions = 1500 m

Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b

Where;

a = The initial distance fro the lighthouse

b = The final distance fro the lighthouse

The angles of the triangle are

32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°

By sine rule we have;

1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =

Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m

b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m

Therefore, a  > b

The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer

2) By cosine rule we have

a² = b² + c² - 2× b×c×cos(A)

Where the given measurements by Kendra are;

410 m and 805 m with an included (in between) angle of 57°, we have;

Let b = 410 m, c = 805 m, and A  = 57°, we have;

a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²

a = The length of the stream = 675.73 m.

Answer:

20

Step-by-step explanation:

Since you can use the Pythagorean theorem to calculate the length of the hypotenuse, each side can be found to be 5. There are four equal sides, so it is 20.

Answer:

22.02

Step-by-step explanation:

14.8+6.25+0.97 is 22.02

don't know what you mean by simplify

Answer:

x > 16/5 or x < -3/4

Step-by-step explanation:

Equation 1: 5x - 4 > 12

Equation 2: 12x + 5 < -4

Equation 1: 5x - 4 > 12

add 4 to both sides

5x > 16

divide by 5 on both sides

x > 16/5

Equation 2: 12x + 5 < -4

subtract 5 on both sides

12x < -9

divide by 12 on both sides

x < -9/12

simplify

x < -3/4

Answer:

Alice will have to pay $13.33

Ben will have to pay $23.33

Kelvin will have to pay $43.33

Step-by-step explanation:

Given that

Alice destination is 20 miles away

Ben destination is 30 miles away

Calvin destination is 40 miles away.

For a mile, taxi costs 2 dollars.

To find:

How much each person has to pay if they share the same taxi to their respective destinations?

Solution:

For the first 20 miles, the taxi will be shared by all 3 of them.

Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40

This $40 will be shared among all 3.

Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33

Charges for Calvin = $13.33

For the next 10 miles, the taxi will be shared by Ben and Calvin.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be shared between Ben and Calvin.

Each will pay = [tex]\frac{20}{2} = \$10[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33 + 10 = $23.33

Charges for Calvin = $13.33 + 10 = $23.33

For the next 10 miles, Calvin travels alone.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be paid by Calvin alone.

Charges for Alice = $13.33

Charges for Ben = $23.33

Charges for Calvin = $23.33 + 20 = $43.33

Work Shown:

A = P*(1+r/n)^(nt)

A = 500*(1+0.04/1)^(1*3)

A = 562.432

A = 562.43

Answer: $562.43

Step-by-step explanation:

The initial start up amount is 500  and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.

So 100%  + 4 % = 104% = 1.04  

The common difference is 1.04.

so  500 * 1.04^n= A where n is the number of years and A is the total amount.

A = 500 * [tex]1.04^{3}[/tex]  

A= 562.43

Answer:

£600

Step-by-step explanation:

1 months= 30 days

here,

money made in 1 day= £20

now,

money made in 30 days= 20×30

= 600

[:• In one month you earn £600]

Answer:560 pounds

Step-by-step explanation:

If 1 day is equal to 20 pounds, to find how much pounds will you have a month, first check how many days are there in a month. Then multiply the number of days in a month to the given pound in one day.

So =1 month = 28 days

=1 day = 20 pounds

So= 20 pounds × 28 = 560 pounds

Answer:

4775.9 [tex]cm^3[/tex]

Step-by-step explanation:

To find the volume of a cone use the expression [tex]\pi r^2\frac{h}{3}[/tex]

r = radius

h = height

Now substitute h for 27 and r for 13, [tex]\pi 13^2\frac{27}{3}[/tex]

First do 13 x 13 (because of the exponent), then divide 27 and 3, which is 9

169 x 9 = 1521

Lastly multiply by pi or use 3.14

1521 x 3.14 = 4775.94

Since it asks to round to the tenth it is just 4775.9

Answer:

4778.4 cm^3

Step-by-step explanation:

The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3} \\[/tex].

In this case, the height is 27 and the radius is 13, so we plug in the values and get [tex]V = \pi (13)^2 \frac{27}{3}\\[/tex].

We solve and get the volume of the cone as [tex]1521\pi[/tex] or 4778.4 cm^3.

The correct answer is D. ​No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.

Answer:

  x = 11/9

Step-by-step explanation:

Eliminate parentheses, add 16x, subtract 21.

  7(3 -x) = 8(4 -2x) . . . . given

  21 -7x = 32 -16x . . . . . eliminate parentheses using the distributive property

  9x +21 = 32 . . . . . . . . add 16x

  9x = 11 . . . . . . . . . . . . subtract 21

  x = 11/9 . . . . . . . . . . . .divide by the coefficient of x

Answer:

6 (2 x + 1)

Step-by-step explanation:

Simplify the following:

4 (3 x + 2) - 2

Hint: | Distribute 4 over 3 x + 2.

4 (3 x + 2) = 12 x + 8:

12 x + 8 - 2

Hint: | Group like terms in 8 + 12 x - 2.

Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):

12 x + (8 - 2)

Hint: | Subtract 2 from 8.

8 - 2 = 6:

12 x + 6

Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.

Factor 6 out of 12 x + 6:

Answer: 6 (2 x + 1)

Answer:

well just do area, and since it's the same in each side 12×4= 144

Answer:

Below

Step-by-step explanation:

The sum of the 5 angles is 540°

● b+(b+45)+90+(2b-90)+(3/2)b = 540

3/2 is 1.5

● b+b+45+90+2b-90+1.5b = 540

● 2b +45+2b+1.5b = 540

● 5.5 b +45 = 540

● 5.5b = 495

● b = 495/5.5

● b = 90°

Answer:

b = 90

Step-by-step explanation:

b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540

b + b + 45 + 90 + 2b - 90 + (3/2)b - 90 = 540 - 90

b + b + 45 + 2b - 90 + (3/2)b = 450

2b + 2b + (45 * 2) + (2 *2b) - (90 * 2) + (2 * (3/2)b) = 450 * 2

2b + 2b + 90 + 4b - 180 + 3b = 900

11b - 90 = 900

11b - 90 + 90 = 900 + 90

11b = 990

b = 990 / 11

b = 90

check:

b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540

90 + (90 + 45) + 90 + (2*90 - 90) + (3/2)*90 = 540

90 + 135 + 90 + 90 + 135 = 540

540 = 540  --- OK

Answer:

the terms of any of the 2 terms should have been given

Answer:

y- intercept = - 39

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = 12x + 2 ← is in slope- intercept form

with slope m = 12

Parallel lines have equal slopes, thus

y = mx + c ← is the partial equation

To find c substitute (4, 9) into the partial equation

9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept

Answer:

y-intercept = -39

Step-by-step explanation:

if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line

y=mx+c

y=12x+2

comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use

y-y1=m(x-x1)

y1=9 and x1=4

y-9=12(x-4)

y-9=12x-48

y=2x-48+9

y=2x-39

comparing to the default equation of a line y=mx+c where c is the y-intercept

therefore the y-intercept is -39

Answer:

[tex] \boxed{\sf Perimeter \ of \ semicircle = 3 \pi \ cm} [/tex]

Given:

Radius of semicircle (r) = 3 cm

Step-by-step explanation:

[tex]\sf Perimeter \ of \ semicircle = \pi r [/tex]

[tex] \sf = 3 \pi \: cm[/tex]

Answer:

The end balance is $910.62 and the total interest $660.62. (That is without tax or inflation rate) I hope this helps.

Step-by-step explanation:

Answer:

without tax: interest total=$660.62

Step-by-step explanation:

I multiplied...

Answer:

1176in^2

Step-by-step explanation:

find the surface area of the cube

(14*14)6=1176 inches cubed

14*14 is finding the area of one side and then we multiply it by six because that's how many congruent sides there are

Answer:

[tex]\large\boxed{1,176 in^{2} }[/tex]

Step-by-step explanation:

The cube is 14 inches tall

All of the sides in a cube are the same, which means:

Length = 14 inches

Width = 14 inches

Height = 14 inches

There are 6 sides in a cube. Each side has a length and a width.

We can use the following formula to find the surface area (SA) of the cube, or how much wrapping paper Jayde will use.

SA = # of Sides(Length(Width))

Plug in known values

SA = 6((14)(14))

The 14s represent the length and width while the 6 represents the number of sides in the cube.

Solve/Simplify

SA = 6(196)

SA = 1,176 inches²

Jayde will need to use 1,176 in² of wrapping paper to wrap the whole present.

Hope this helps :)

Answer:

z=-3

Step-by-step explanation:

z=(-3)^2 - 3(4)

z=9 - 12

z=-3

━━━━━━━☆☆━━━━━━━

▹ Answer

3² * a² - b²

▹ Step-by-Step Explanation

9a² - b²

Break down each coefficient and variable:

9 = 3²

a² = a²

b² = b²

Combine everything together:

3² * a² - b²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Since both terms are perfect squares, factor using the difference of squares formula,  a^2-b^2=[a+b][a-b] where a=3a and b=b

Answer:

1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]

Step-by-step explanation:

i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13  

Step-by-step explanation:

5x² + 13x - 6 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a = 5 , b = 13 c = - 6

We have

[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]

[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]

[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]

[tex]x = \frac{ - 13±17}{10} [/tex]

[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]

3x² + 5x + 1 = 0

a = 3 , b = 5 , c = 1

[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]

[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]

[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]

[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]

Hope this helps you

Answer: 18

Do Keep Change Flip (KCF)

Keep: 9/2

Change: ÷ into ×

Flip: 1/4 into 4/1

Your new problem should be 9/2×4/1

Multiply

9/2×4/1=36/2

36/2=18

Final Answer: 18

Answer:

4 quarts

Hope it helps!

Step-by-step explanation:

Answer: 5 gallons= 20 quarts

              1 gallon = 4 quarts

Answer:

94 degrees

Step-by-step explanation:

Measure of arc BCD = 53+135 = 188 degrees.

Measure of angle A = 188/2 = 94 degrees

Answer:

50

Step-by-step explanation:

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3

Answer:

12.198

Step-by-step explanation:

the thousandth is the third digit after the decimal point, so you round the next number after it, which is 5. so you round it up, ends with 12.198

We get 12.198 after rounding it to the nearest thousandth.

The rounding off decimal places is similar to the basic round-off. We check the previous number. If it is greater than or equal to 5, we increase the value up to which we are rounding by 1, or else keep it the same when the previous digit is less than 5.

The order of digits for decimal places is opposite to the normal number system.

In the number system we have units place, then tens place, then hundreds place, then thousands place, and like that.

In the decimal number system, we start from the highest and go on decreasing.

The first decimal place is the tenth place.

The second decimal place is the hundredth place.

The third decimal place is the thousandth place.

And so on.

In the question, we are asked to round 12.1975 to the nearest thousandth.

As discussed above, the nearest thousandth means rounding off up to the third decimal place.

So we round off 12.1975 up to the third decimal place, that is, we round off up to 7.

The next digit is 5, so we increase 7 by 1 to 8.

Thus, we get 12.198 after rounding it to the nearest thousandth.

Learn more about rounding off decimal places at

https://brainly.com/question/21583892

#SPJ2

Answer:

17

Step-by-step explanation:

b(1) = 16

b(2) = b(2-1) +1

      = b(1) +1

     = 16+1

    = 17

Answer:

x=5

Step-by-step explanation:

-5(-x - 1) + 4x – 1= 49

Distribute

5x +5 +4x -1 = 49

Combine like terms

9x +4 = 49

Subtract 4 from each side

9x+4-4 = 49-4

9x = 45

Divide by 9

9x/9 =45/9

x = 5

Answer:

[tex]\huge \boxed{x=5}[/tex]

Step-by-step explanation:

[tex]{\Large -5(-x - 1) + 4x -1= 49}[/tex]

Expand brackets.

[tex]5x+5+ 4x -1= 49[/tex]

Combine like terms.

[tex]9x+4=49[/tex]

Subtract 4 from both sides.

[tex]9x+4-4=49-4[/tex]

[tex]9x=45[/tex]

Divide both sides by 9.

[tex]\displaystyle \frac{9x}{9} =\frac{45}{9}[/tex]

[tex]x=5[/tex]