at the water treatment plant, a half empty tank is being filled with waste water at a rate of 850 gallons per minute. After 15 minutes the tank has 35,000 gallons of waste water. Write an equation in standard form that relates the amount of waste water in the tank, y , to the number of minutes, x, that the tank has been filling

Answer:

x = 0.1, y = 0.075

Step-by-step explanation:

Given the 2 equations

27x + 24y = 4.5 → (1)

1.5x + y = 0.225 → (2)

Multiplying (2) by - 24 and adding to (1) will eliminate the y- term

- 36x - 24y = - 5.4 → (3)

Add (1) and (3) term by term to eliminate y

- 9x = - 0.9 ( divide both sides by - 9 )

x = 0.1

Substitute x = 0.1 into either of the 2 equations and solve for y

Substituting into (2)

1.5(0.1) + y = 0.225

0.15 + y = 0.225 ( subtract 0.15 from both sides )

y = 0.075

Answer:

the values for x AND y are 0.1 and 0.075 respectively

Answer:

37.5%

Step-by-step explanation:

150/450 = .375 = 37.5%

The percentage is 150 grams out of 400 grams will be 37.5%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

It is given that the difference between the initial and final value is 15 grams and the initial value is 400 grams.

Then the percentage is 150 grams out of 400 grams will be

P = (150 / 400) x 100

P = 0.375 x 100

P = 37.5%

Thus, the percentage is 150 grams out of 400 grams will be 37.5%.

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Answer:

Area of rectangle = 150 cm

Step-by-step explanation:

Given the following data;

To find the area of the rectangle;

First of all, we would determine the dimensions (length and width) of the rectangle;

For length;

Length, L = 2x

For width;

Width, W = 3x

Mathematically, the perimeter of a rectangle is given by the formula;

P = 2(L + W)

50 = 2(2x + 3x)

50 = 2(5x)

50 = 10x

x = 50/10

x = 5

Length, L = 2x = 2 * 5 = 10 cm

Width, W = 3x = 3 * 5 = 15 cm

Now, we would find the area of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = length * width

Area of rectangle = 10 * 15

Area of rectangle = 150 cm

Answer:

√85

Step-by-step explanation:

We can find the distance between two points by using this formula

d = √(x2 - x1)² + (y2 - y1)²

Where the x and y values are derived from the two given points

The two given points are (-2,5) and (4,-2)

Remember that coordinates are written as (x,y)

Next we want to define our variables ( x2, x1, y2 and y1 are the variables)

x2 = 4

x1 = -2

y2 = -2

y1 = 5

Now to find the distance between the two points we simply substitute the values of the variables into the formula

Formula: d = √(x2 - x1)² + (y2 - y1)²

x2 = 4, x1 = -2, y2 = -2 and y1 = 5

d = √(4 - (-2))² + (-2 - 5)²

The two negative signs before the 2 cancel out and it changes to + 2

d = √(4 + 2)² + (-2 - 5)²

Add 4 and 2

d = √6² + (-2 - 5)²

Subtract -2 and -5

d = √6² + -7²

Apply the exponents

d = √36 + 49

Add 36 and 49

d = √85

We can conclude that the distance between the two points is √85

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

[tex]\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

[tex]\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta[/tex]

Simplify. The denominator uses the difference of two squares pattern:

[tex]\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

[tex]\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta[/tex]

Split into two separate fractions:

[tex]\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta[/tex]

Rewrite the two fractions:

[tex]\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta[/tex]

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

[tex]\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta[/tex]

Hence verified.

Answer:

No

Step-by-step explanation:

irrational numbers have nonrepeating and non terminating decimals

This decimal stops at one digit so this is a rational number

Answer:

I would say no

Step-by-step explanation:

An irrational number can't be written as a simple fraction.  

Answer:

its 196

Step-by-step explanation:

Answer:

(x-1)(x+7)

Step-by-step explanation:

did it on a test and got it right :))

Answer:

114 pi or 359

Step-by-step explanation:

Answer:

the log function is the "inverse" function of an exponential function

by definition  [tex]log_{a} b = c[/tex]  then [tex]a^{c} = b[/tex]

in this problem you have [tex]log_{10} 100[/tex]

thus what x solves this ?  [tex]10^{x} = 100[/tex]  the answer is [tex]10^{2}[/tex]

thus (100,2)

B) the x intercept is when y = 0

   [tex]10^{0} = 1[/tex]

   x intercept at (1,0)

C) at 100, the curve will hit y = 5000

Step-by-step explanation:

Answer:

[tex]\boxed{x=13.89\:km}[/tex]

Step-by-step explanation:

Pythagorean theorem

[tex]x^2=(12^2)+(7^2)[/tex]

[tex]x^2=144+49[/tex]

[tex]x^2=193[/tex]

[tex]x=\sqrt{193}[/tex]

[tex]\boxed{x=13.89\:km}[/tex]

Answer:

y= -6

x = 2

(2,-6)

Step-by-step explanation:

Indepedent variable = x = 2

Plug 2 in for x

f(2) = -5(2) + 4

-10 + 4 = -6

y = -6

Answer:

45

Step-by-step explanation:

Answer:

-26 sqrt(3)

Step-by-step explanation:

-12 sqrt(12) - 2 sqrt(3)

Rewriting

-12 sqrt(4*3) - 2 sqrt(3)

We know sqrt(ab) = sqrt(a)sqrt(b)

-12 sqrt(4)sqrt(3) - 2 sqrt(3)

-12 (2) sqrt(3) - 2 sqrt(3)

-24 sqrt(3) - 2 sqrt(3)

-26 sqrt(3)

Answer:

x = 2 ±sqrt( 97)

Step-by-step explanation:

log10(x^2 -4x+7) =2

Raise each side to the base 10

10 ^ log10(x^2 -4x+7) =10^2

x^2 -4x +7 = 100

Subtract 7 from each side

x^2 -4x+7-7 = 100-7

x^2 -4x = 93

Complete the square

-4/2 = -2  (-2)^2 = 4

Add 4 to each side

x^2 -4x+4 = 93+4

(x-2)^2 = 97

Take the square root of each side

sqrt((x-2)^2 )=±sqrt( 97)

x-2 = ±sqrt( 97)

Add 2 to each side

x = 2 ±sqrt( 97)

Answer:

w+5/w - w+1/2w

w+9/2w

Step-by-step explanation:

Answer:

A&D are corect

Step-by-step explanation:

combine like terms

Answer:

a) the angle ABC is approximately 106 degrees b) 24

Step-by-step explanation:

1) Using the law of cos

AC*AC= AB*AB+BC*BC-2*AB*BC*cosB

8*8= 5*5+5*5-2*5*5*cosB

64= 50- 50c0sB

cosB= 14/(-50)= -7/25.

B= arccosB= arccos(-7/25)= 106degrees.

2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625

sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)

3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)

Answer:

a is the perimeter which is given as 820 mm.

Step-by-step explanation:

Perimeter, P = 820 mm

Length is 100 m less than twice of width

let the length is x and the width is y.

So,

x = 2 y - 100

P = 2 (x + y)

820 = 2 (2y - 100 + y)

410 = 3 y - 100

3 y = 510

y = 170 mm

x = 2 x 170 - 100 = 240 mm

The equation is

2 x = 2 y = a

where, a is the perimeter which is given as 820 mm.

Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.

Answer:

Kazan also SOS jz zks zj sj aka always zks. aiwow

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

Explanation:

Let x be the unknown angle we want to find. This angle is in degrees.

The diagram shows 19 is the opposite of this angle, and the side 35 is adjacent to the angle.

We use the tangent ratio to tie the two sides together

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(x) = \frac{19}{35}\\\\x = \tan^{-1}\left(\frac{19}{35}\right)\\\\x \approx 28.4956386\\\\x \approx 28\\\\[/tex]

Note: The notation [tex]\tan^{-1}[/tex] refers to the inverse tangent, or arctangent.

Answer:

(a,a)

Step-by-step explanation:

Keep in mind that the vertical line represents the y axis and the horizontal line represents the x axis

We want to find the coordinates of C

We can do this by looking at the given coordinates and the axis..

We are given that B is at (0,a) and we are given that D is at (a,0)

Now looking at C, we can tell that C shares the same y value as B and the same x value as D

If B has a y value of a and D has an x value of a then C would have an x and y value of a

Hence C would be at (a,a)

Answer:

6.38548 years

Step-by-step explanation:

1 = 2 [tex]e^{42k}[/tex]

1/2 =   [tex]e^{42k}[/tex]

ln(1/2) = 42k ln(e)

ln(1/2)/42 = k

k = -0.01650

~~~~~~~~~~~~~~

45 = 50 [tex]e^{-0.01650t}[/tex]

45/50 =   [tex]e^{-0.01650t}[/tex]

ln(45/50) =  -0.01650 t ln(e)

ln(45/50)/ -0.01650 = t

t = 6.38548 years

The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value

The decay constant λ is = 0.693/t½

where t½ is the half-life of the element

Given data ,

Let the number of years be t

Let the initial mass of the element be a = 50 grams

The final mass of the element be ( a - x ) = 45 grams

Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half

And , half life t½ = 42 years

So , the decay constant k = 0.693/t½

k = 0.693 / ( 42 )

k = 0.0165

And , k= 2.303/t {log (a/a-x)}

So , t = 2.303 / ( 0.0165 ) log ( 50/45 )

On simplifying , we get

t = 6.384129 years

Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years

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Answer:

Corresponding angles postulate

Step-by-step explanation:

<3 and <7 are corresponding angles and if corresponding angles are equal, the lines are parallel.

If you're trying to establish an identity, the given equation is not an identity. The proper identity would be as follows:

(1 - sin(x) + cos(x))² = (1 - sin(x))² + 2 (1 - sin(x)) cos(x) + cos²(x)

… = (1 - 2 sin(x) + sin²(x)) + 2 (1 - sin(x)) cos(x) + cos²(x)

… = 2 - 2 sin(x) + 2 (1 - sin(x)) cos(x)

… = 2 - 2 sin(x) + 2 cos(x) - 2 sin(x) cos(x)

… = 2 (1 - sin(x) + cos(x) - sin(x) cos(x))

… = 2 (1 - sin(x) + cos(x) (1 - sin(x)))

… = 2 (1 - sin(x)) (1 + cos(x))

But if you're trying to solve an equation:

(1 - sin(x) + cos(x))² = 2 (1 + sin(x)) (1 + cos(x))

2 (1 - sin(x)) (1 + cos(x)) = 2 (1 + sin(x)) (1 + cos(x))

(1 - sin(x)) (1 + cos(x)) - (1 + sin(x)) (1 + cos(x)) = 0

(1 + cos(x)) (1 - sin(x) - 1 - sin(x)) = 0

-2 sin(x) (1 + cos(x)) = 0

sin(x) = 0   or   1 + cos(x) = 0

sin(x) = 0   or   cos(x) = -1

[x = arcsin(0) + 2nπ   or   x = arcsin(0) + π + 2nπ]   or

… [x = arccos(-1) + 2nπ]

We have arcsin(0) = 0 and arccos(-1) = π, so the solution set reduces to

x = 2nπ   or   x = (2n + 1)π

(where n is any integer)

9514 1404 393

Answer:

  A, C, D, E

Step-by-step explanation:

Any relation that is different from a straight line with a defined constant slope will be a relation that is either or both of ...

__

a) degree 3, not linear

b) a linear function

c) a vertical line with undefined slope, not a function

d) a curve opening downward, not linear

e) a line with a bend in the middle, not linear

f) a linear function

Answer:

24.68 gram

Step-by-step explanation:

Given that :

Volume = 182.8 ml

Density of liquid = 0.135 gram/ml

Recall :

Density = mass (g/ml) / volume (ml)

Substitute the value into the equation :

0.135 = mass / 182.8

Mass = 0.135 * 182.8

Mass = 24.678 gram

Hence, weight = 24.678 grams

Answer:

(x + 74) - 318 = 200

x + 74 = 200 + 318

x +74 = 518

x = 518 - 74

x = 444