an oil tank is being filled at a constant rate of .2 feet per minute. After 15 minutes the tank is 6 feet deep. Write an equation that can be used to determine the amount of oil in the tank at any time.

Answer:

[tex] \sf \fbox{Age of pamela is 8 year}[/tex]

Step-by-step explanation:

let the age of Debra is x and Pamela is x+7 year old,

Given condition- In 6 years Pamela will be twice as old as debra, so the algebraic expression will look like,

[tex]x+7+6 = 2(x+6)[/tex]

[tex]x+13 = 2x + 12[/tex]

[tex]2x-x = 13-12[/tex]

[tex]x = 1[/tex]

Age of debra is 1 years,

now we can calculate the age of pamela by substituting value of x,

x + 7 = 1 + 7 = 8 years

━━━━━━━━━━━━━━━━━━━━━━━

Verification-

after 6 years the age of debra & pamela will be 7 & 14. 14 is twice of 7 which satisfies the given condition.

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Answer:

(-4, 0) U (1, ∞)

Step-by-step explanation:

Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).

x = 0           x-1 = 0             x + 4 = 0

                  x = 1                x = -4

Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.

far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0   →  (-)(-)(-) > 0  →   negative > 0  FALSE

- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0   →  (-)(-)(+) > 0  →   positive > 0  TRUE

0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0   →  (+)(-)(+) > 0  →   negative > 0  FALSE

far right (I choose 2): 2(2 - 1)(2 + 4) > 0   →  (+)(+)(+) > 0  →   positive > 0  TRUE

According to the question, to express the rational function for the vertical asymptote whose equation is [tex]x=8[/tex] and horizontal asymptote whose equation is at [tex]y=0.[/tex]

As per the question, the function 'f(x)' is vertical at [tex]x=8[/tex]. Therefore, the denominator be [tex](x-8)[/tex]

[tex]f(x)=\frac{g(x)}{(x-8)}[/tex]

The function 'g(x)' should have same degree as the denominator function has and it is defined as[tex]y=0[/tex]

The rational function can be written as:

Rational function = [tex]\frac{y}{(X-8)}[/tex]

What is rational function?

Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.

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The domain of the function is (2,∞),{x|x>2}

and the range of function is  (−∞,∞),{y|y∈R}

The domain is all values of xx that make the expression defined.

Set the argument in log(x−2)greater than 0 to find where the expression is defined.x−2>0

Add 2 to both sides of the inequality.x>2

Interval Notation:(2,∞)

Set-Builder Notation:{x|x>2}{x|x>2}

The range is the set of all valid y values.

We can find out the range by using the graph.

Interval Notation:(−∞,∞)

Set-Builder Notation:{y|y∈R}

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Answer:

the answer is the 10⁰ ok that

Answer: 2.2

Step-by-step explanation: twenty percent of 11 is 2.2

Using the midpoint formula, the coordinates of the midpoint M is: (-1/2, 1).

Using the distance formula, the length of YZ is: 14.3.

The midpoint formula is: M[(x1 + x2)/2, (y1 + y2)/2].

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

Given the following:

Y(1,-6) = (x1, y1)

Z(-2,8) = (x2, y2)

Apply the midpoint formula to find the midpoint of YZ:

M(x, y) = [(1 + (-2))/2, (-6 + 8)/2].

M(x, y) = (-1/2, 2/2)

M(x, y) = (-1/2, 1)

M(-1/2, 1)

Apply the distance formula to find YZ:

YZ = √[(−2−1)² + (8−(−6))²]

YZ = √[(−3)² + (14)²]

YZ = √205

YZ ≈ 14.3 (nearest tenth)

In conclusion:

Using the midpoint formula, the coordinates of the midpoint M is: (-1/2, 1).

Using the distance formula, the length of YZ is: 14.3.

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Answer:

Here's b > 4 on the number line. When greater than, the arrow always starts with an open circle. If less than, then it will start with a closed circle.

The equation that shows proportionality is in the form y = kx; Where k is the constant of proportionality.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two variables are said to be proportional if an increase or decrease in one variable leads to a corresponding increase or decrease in the other variable.

The equation that shows proportionality is in the form:

y = kx

Where k is the constant of proportionality.

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Answer:

.9

85%

5/6

4/5

Step-by-step explanation:

In percentages .9 is 90%

which is larger than 85%

5/6 as a percentage is 83.33r%

4/5 as a percentage is 80%

After solving the given equation 25²x=144, the value of x = 144/625.

So,

Then,

Therefore, after solving the given equation 25²x=144, the value of x = 144/625.

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[tex]f(x) = \alpha (x - 4) {}^{2} (x - 2) {}^{2} \\ f(x) = \alpha (x {}^{2} - 8x +16 )(x - 4x - 4) \\ f(x) = \alpha (x {}^{4} - 12x {}^{3} + 52x {}^{2} - 96 x + 64) \\ where \: \alpha ∈ \: \real[/tex]

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{x^{2} -7x+10}{x^{2} -8x+15}/\frac{4-x^{2} }{x^{2} +3x-18}[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{(x-5)(x-2)}{(x-3)(x-5)}/\frac{(2-x)(2+x)}{(x+6)(x-3)}=\frac{-(x+2)}{(x+6)}[/tex]

The final expression of the given equation is [tex]\frac{-(x+2)}{(x+6)}[/tex] .

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Using a linear function, it is found that the least possible number of matches played when four players are left is of 339.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For the situation modeled in this problem, we have that:

Thus the average number of players after n matches is given by:

P(n) = 117 - 1/3m.

The least number of matches for there to be 4 players is found when P(n) = 4, hence:

4 = 117 - 1/3m.

1/3m = 113.

m = 113 x 3

m = 339.

Hence at least 339 matches must be played.

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Answer:

Huh?

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19 (?)

Answer:

154

Step-by-step explanation:

Use the correct order of operations.

(120 - 14) + 4² × 3 =

First, do the parentheses and the exponent.

= 106 + 16 × 3

Now do the multiplication.

= 106 + 48

Finally, add.

= 154

Answer:

1920 rings

Step-by-step explanation:

Our equation: 16 x 10 x 12

16 x 10= 160

160 x 12= 1920

14x+70+20x+8=180

34x+78=180

34x=102

x=3

XBC= 20(3) +8

60+8

68

XBA= 14(3)+70

42+70

112

Angle XBC= 68 degrees

Angle XBA= 112 degrees

The correct answer is ( -2.2, -3).

We occasionally discover the value of an unknown variable while solving the system of equations. We can display the graph using the equation, but if the graph and the equation are parallel, we will not be able to solve the system of equations.

We have a condition that, if applied, allows us to determine how many solutions this equation has: if it has one solution, no solutions, or infinitely many solutions.

y = -3 _____(1)

y = x-0.8 _____(2)

to substitute the value of y in the equation in 2

-3 = x - 0.8

-3 + 0.8 =x

-2.2 = x

Thus the correct answer is  ( -2.2, -3).

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The simplified form of 1 and 3 over 4 times, 2 and 2 over 3 is 4/3.

Given,

1 and 3 over 4 times

2 and 2 over 3 times

We can convert this to mathematical form:

That is,

1 and 3 over 4 times = (1 + 3) / 4

2 and 2 over 3 times = (2 + 2) / 3

Now, equate the above terms:

We get,

(1 + 3) / 4 x (2 + 2) / 3

= (4 / 4) x (4 / 3)

= 1 x (4 / 3)

= 4 / 3

That is, the simplified form of 1 and 3 over 4 times and 2 and 2 over 3 times is 4/3.

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The total amount that Amy will spend is $17.98

Amy goes out to eat at El Parral. She orders a Burritos Deluxe dinner for $8.75, fried ice cream for $4, and a Coke for $2.

Amy's gross total is $8.75 + $4 + $ 2  = $14.75

Now, sales tax of 6 percent

Her net bill is $14.75 + 6% of $14.75

$ 14.75 + 0.885

= $15.635

Here, Amy also gives a tip of 15 percent

Her total spending becomes

$15.635 + 15% of $ 15.635

$15.635+ 2.345

$17.980

or $ 17.98

Hence, the total amount that Amy will spend is $17.98

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The answer to the question is c 47,625

The concept used is geometric progression.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

Here we can see that shares are being halved per week

we can say that the value of r is 1/2

so we can use the formula of sum of geometric progression to calculate the total number of shares.

sum of geometric progression formula =a(1-r∧n)/1-r

Here we can see that the value of n is 7

On putting the values in the formula we get

sum=24,000(1-1/128)/(1/2)

On further solving we get-

24000×127×2/128 which is equal to 47,625

Hence the total no of shares  of the company he bought are 47,625

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Answer:

83°

Step-by-step explanation:

Supplementary angles are angles that add up to 180°.
Za + Zy = 180
Za + 97 = 180
Za + 97 - 97 = 180 - 97
Za = 83

The solutions to the proportional equation are given as follows:

x = -4 and x = 5.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using operations such as multiplication or division.

One example of application of proportions is for the solution of equations when two sides are proportional, meaning that multiplication operations are applied between the opposite sides to find the unknown variable.

For this problem, we already are given the following proportional equation:

3x/5 = 12/(x + 1).

Due to the equality sign, we can apply cross multiplication, hence:

3x(x + 1) = 60

3x² + 3x = 60

3x² - 3x - 60 = 0

x² - x - 20 = 0

(x - 5)(x + 4) = 0.

Hence the solutions are found as follows:

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Answer:

-8

Step-by-step explanation:

[tex]-2\left(-4\right)\left(-1\right)\\\left(-4\right)\left(-1\right)\\\left(-a\right) \times \left(-b\right)=(+c)\\= 4\\=-2 \times 4\\(-a) \times (+b) = -c\\=-8[/tex]

The equation is,

→ -2 (-4) (-1)

Let's solve the problem,

→ -2 (-4) (-1)

→ (-2 × -4) × (-1)

→ 8 × -1 = -8

Thus, the answer is -8.

Making t the subject of formula gives the following expression: t = (2 - 3q)/(q + 4).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to describe the steps that should be taken to make t the subject of formula. Therefore, the appropriate and required steps are listed as follows:

q = (2 - 4t)/(t + 3)

Cross-multiplying, we have:

q(t + 3) = (2 - 4t)

qt + 3q = 2 - 4t

Collecting like terms, we have:

qt + 4t = 2 - 3q

Factorizing t, we have:

t(q + 4) = 2 - 3q

Dividing by (q + 4), we have:

t = (2 - 3q)/(q + 4)

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The simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.

It follows from the task content that the expression which is to be simplified, or perhaps written in a different form is; −(−8q−8.7).

Therefore, it follows from the distributive property that we have;

-(-8q) -(-8.7)

Also, since the product of two negative signs yields a positive sign.

Hence, we have; 8q + 8.7 as the equivalent of the expression given.

Ultimately, the simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.

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Point A' after the dilation of the scale factor by 1/3 is (-1,2) is the correct option.

The given point is;

Point A = (3, -6), scale factor = 1/3

Fortunately, because the dilation is centered at the origin (0,0), we can multiply the scale factor by the x and y-coordinates to acquire the image point coordinates.

Point A' = (3×1/3, -6×1/3)

Point A' = (1, - 2)

As a result, if it grows larger, it should start moving away from the origin, while if it grows smaller (as it does here), this should move closer to a origin.

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It will take 5.689 yrs . for the account to contain $2500 .

Simple Interest = ( P * R * T ) / 100

P ( principal amount ) = 2000

R ( rate of interest ) = 4

T ( no . of yrs . for which amount is deposited ) = unknown

According to question

Account Balance = $ 2500 = A( t ) = a [tex]( 1 + r ) ^{t}[/tex]

2500 = 2000 [tex]( 1 + 0.04 )^{t}[/tex]

1.25 =  [tex]( 1 + 0.04 )^{t}[/tex]

t = [log ( 1.25 ) ] / [ log ( 1.04 ) ]

t = 5.689

Hence , it will take 5.689 yrs . for the account to contain $2500 .

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