Water is drained at constant rate of 2 gallons per minute from a fish tank containing 28 gallons of water which equation represent the number of gallons of water remaining in the tank y based on the number of minutes t since water started draining from the fish tank where 0<_t_<14?

Answer:

x: (40,0)

y:(0,30)

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.

a³/b³=1001/1024+45*sqrt(23)/1024*i

b³/a³=1001/1024-45*sqrt(23)/1024*i

Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!

If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.

It is -2c=-2*1001/1024=-1001/512, and

c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.

If the number were written in scientific notation, the exponent will be -2.

Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.

The number of times a number is multiplied by itself is referred to as its exponent.

In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.

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Answer: 89%

[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]

Answer:

92 public transit

23 bike

Step-by-step explanation:

460 / 5 = 92

460 / 20 = 23

The answer after its estimation will be 3,00,00,000.

Here, the 53,320 will be estimated to 50,000 and 599 will be estimated to 600.

So, on multiplying, we get;

50,000×600 = 3,00,00,000

To offer an estimated, projected result rather than an exact result, we employ approximations in our calculations. Calculations are easier to handle when they are estimated using round numbers.

The result of rounding 109 to the closest ten is 110. and 100 is the nearest hundred. 2) Round the number downward if it is followed by the digits 0, 1, 2, 3, or 4. 102, for instance, is 100 when rounded to the closest ten.

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Answer: b=116, c=64

Step-by-step explanation:

Answer: 3a

Step-by-step explanation: 4a - 1a = 3a

Answer: The answer is the $42 T-Shirts

Step-by-step explanation: 42 divided by 4 is 10.5 dollars per t-shirt.

25 divided by 2 would mean 12.5 dollars per t shirt. There is only a 2 dollar difference, but it is clear that the 4 t-shirt deal is the best.

We can represent the length in Zach's car model by x

Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow

Therefore,

Ginny's model will be 2 + 3x

Next, we are told that the sum of the lengths of both cars is 30 inches

Then

Therefore,

The answer is

Thus, the answer is Option B

Answer:d

Step-by-step explanation:

Answer:

y = 14

Step-by-step explanation:

2y - 16 = 12

add 16 to both sides:

2y - 16 + 16 = 12 + 16

2y = 28

divide both sides by 2:

2y/2 = 28/2

y = 14

Answer: y = 14 is the solution.

Answer:

13 cm

Step-by-step explanation:

You can use the pythagorean theorem to solve this problem. The pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where and b are the legs of a right triangle and c is the hypotenuse.

In the problem, we are given two legs, 12 and 5, so we can substitute them in for a and b and solve from there:

[tex]5^2+12^2=c^2[/tex]

[tex]25+144=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

The missing side is 13 cm long

The distance between the two points is 10 units and the slope of the line is -78/25

To find the distance between two points, we can simply use the formula of distance between two which is given as

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}[/tex]

Let's substitute the values and solve for the distance.

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}\\d = \sqrt{(1-7)^2 + (-3 - 5)^2} \\d = 10[/tex]

2)

The slope of the line can be found using the two points given.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]

let's substitute the values and solve.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = -\frac{78}{25}[/tex]

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The next correct step of the following elimination method is (C) subtract to eliminate 'x'

So, the next correct step of the elimination method:

Then, option (A) and option (D) is incorrect.

Thus, the correct option will be an option (C).

Therefore, the next correct step of the following elimination method is (C) subtract to eliminate 'x'

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The cost of each ticket is 8.9 dollars.

What is cost price?

In mathematics, the term cost price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the Jason bought 4 tickets for basket ball game. He paid a total cost of $42.10 for the tickets and for parking as $6.50

The paid amount for the 4 tickets is: $42.10.

And the parking cost is: $6.50

Total cost price without parking is: $42.10 - $6.50 = $35.60

Therefore, to calculate the cost of each ticket is: 35.60/4 = 8.9 dollars

Hence, the cost of each ticket is 8.9 dollars.

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if the two trains are miles apart after hours, then  the rate of the westbound train is 79 miles per hour

two trains leave the station at the same time, one heading west and the other east.

the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,

what is the rate of the westbound train?

Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:

4 (e + (e - 12)) = 680

4 (2e + 12) = 680

8e - 48 = 680

8e = 728

e = 91 mph

e - 12 = w

91 - 12 = w

79 = w

Therefore, the westbound train travels at 79 miles per hour.

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The total pounds of apples that Chris must pick before Pam’s orchard is cheaper that David's is 14.

The first step is to determine the total cost of picking apples from both orchards.

Cost of picking apples from David's Orchard : (10 x $2) + [(x - 10) x $1]

$20 + $x - $10

= $10 + $x

Cost of picking apples from Pam's Orchard : $10 + ($10 x $1.5) + [(x - 10) x 0.75]

$10 + $15 + 0.75x - 7.5

= $17.50 + 0.75x

When  Pam's Orchard is cheaper, the equation becomes :

$10 + $x  > $17.50 + 0.75x

$x - 0.75x > $17.50 - $10

0.25x > $7.50

x > $7.50 / 2.5

x > 3

Total pounds should be greater than 3, so it can be 4.

Total pounds = 10 + 3 = 14

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Answer:

A = 127.251 cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( where r is the radius )

the area (A) of a semicircle is then

A = [tex]\frac{1}{2}[/tex] πr²

given diameter = 18 then r = 18 ÷ 2 = 9 cm , so

A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²

Answer:

800000

Step-by-step explanation:

(1 x 10^1) = 10

(8 x 10^4) = 80000

10 x 80000 = 800000

Answer:

16

Step-by-step explanation:

4/5=0.8

20*0.8=16

The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Given Data

Function

8x-5x+21 = 36-6y

6y = 36 - 21 - 8x +5x

6y = -3x + 15

y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]

The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]

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Answer: Multiply 102 by 8.82 = 899.64x

The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

Given,

Fractions : 3/8 and 5/4

We have to find a division equation for number of 3/8 in 5/4

Number of 3/8 in 5/4 = x

Now,

Number of a in b = b/a

So here,

Number of 3/8 in 5/4, x = 5/4 / 3/8

Number of 3/8 in 5/4, x = 5/ 3/2

Number of 3/8 in 5/4, x = 5 × 2 / 3

Number of 3/8 in 5/4, x = 10/3

That is,

The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

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Answer:

solving the bracket

x×x = x²

x×-4= -4x

3×x= 3x

3×-4= -12

x²-x-12=0

Using an arithmetic sequence, the number of design that the artist should use is:

b. Design 6.

In an arithmetic sequence, the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

The sequence for the number of circles is:

(4, 6, 8, ...)

Hence the common difference is given by:

d = 8 - 6 = 6 - 4 = 2.

Then the rule for the nth term is:

[tex]a_n = 4 + 2(n - 1)[/tex]

As the first term is of 4.

The maximum number is of 15 shaded circles, hence:

4 + 2(n - 1) ≤ 15

4 + 2n - 2 ≤ 15

2 + 2n ≤ 15

2n ≤ 13

x ≤ 6.5.

Hence the maximum number is of 6, meaning that Design 6 is chosen, given by option b.

The complete problem is given by the image at the end of the answer.

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From the given sequence, it is found that:

a) It is a geometric sequence, as the ratio between consecutive terms is the same.

b) Station 5 will be completed in 48 minutes.

c) Station 9 will be completed in 768 minutes.

In a geometric sequence, the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by the following rule:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In the context of this problem, the ratio between consecutive terms is given by:

r = 24/12 = 12/6 = 6/3 = 2.

Hence it is a geometric sequence.

Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:

24 x 2 = 48 minutes.

The first term of the sequence is of 3, hence the explicit formula is given by:

[tex]a_n = 3(2)^{n-1}[/tex]

Hence the time for the 9th station, in minutes, is given as follows:

[tex]a_9 = 3(2)^{8} = 768[/tex]

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Answer:

b -3

Step-by-step explanation:

t-3(4-t)=-24 multiply

t-12+3t=-24 simplify

4t-12=-24 plus 12 on both side

4t=-12 divide 4 on both side

t=-3