Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains
x(t) pounds of salt in 200 gallons of brine, and tank B contains
y(t) pounds of salt in 300 gallons of brine. The mixture in each tank is kept uniform by constant stirring. When t = 0, brine is pumped from tank A to tank B at 20 gallons/minute and from tank B to tank A at 20 gallons/minute. Find the amount of salt in each tank at time t if x(0) = 10 and y(0) = 40.

Answer:

only one solution

Step-by-step explanation:

The given equation is

17x- 8 = 3x + 16

Add 8 to both sides

17x = 3x + 24

Subtract 3x to both sides

14x = 24

Divide both sides by 14

x = 24/14

x = 12/7

Since, we got only one value of x.

Therefore, the equation has only one solution.

A is correct option.

Two lines that intersect and form four right angles are perpendicular to each other. This is because they cross at a single point creating four 90 degree angles. Therefore, the lines are not parallel, the angles are not complementary, and their coplanar status is irrelevant.

If two lines intersect and form four right angles, it means that the lines are perpendicular to each other. In geometry, when two lines are perpendicular, they intersect at one point forming four right angles. A right angle is an angle of 90 degrees, which is the total division of a straight angle. Therefore, the two lines are not parallel because parallel lines do not intersect. The angles would not be complementary because complementary angles are two angles that add up to 90 degrees. Lastly, the lines being coplanar or not has no bearing on the angles they form when they intersect.

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Two lines intersecting to form four right angles are perpendicular, which is reflected in B. the lines are perpendicular. Parallel lines don't intersect, complementary angles are about their sum, and not coplanar doesn't relate to angles formed by intersection.

When two lines intersect and form 4 right angles, they possess a special relationship known as perpendicularity. These perpendicular lines meet to form 90-degree angles, also referred to as right angles. This fact is grounded in basic geometric principles.

The correct answer to the question is B. the lines are perpendicular. Choosing any of the other options would not accurately describe the relationship between the lines. Parallel lines do not intersect, complementary angles sum up to 90 degrees but do not describe the relationship between lines, and being not coplanar implies the lines do not lie in the same plane which is irrelevant to the intersection forming right angles.

It is important to recognize that according to Theorem 1, two straight lines cannot intersect in more than one point and Theorem 2 states that vertical angles, which are the angles opposite each other when two lines intersect, are equal. All this supports the fact that if the lines intersect in such a way to form 4 right angles, they are indeed perpendicular.

The value that shows the extraneous solution to the logarithmic equation below is x = -4

Given the logarithmic function expressed as:

log3(18x^3)-log3(2x)=log3(144)

This can also be written as:

log3(18x^3/2x)  = log3(144)
log3 (9x^2) -= log3 (144)

Cancel out the log function to have:

9x^2 = 144

Divide both sides by 9

x^2 = 144/9
x^2 = 16

x = ±4

Hence the value that shows the extraneous solution to the logarithmic equation below is x = -4

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The measure of the exterior angle of the circle ∠ABC = 55°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

Let the measure of the arc be represented as A = 235°

So , the difference of the measures of arc = 235 - 125°

Now , the measure of the external angle ∠ABC = ( 235 - 125 ) / 2

So , the external angle ∠ABC = 55°

Hence , the measure of angle ∠ABC = 55°

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its b i done the test

in mathematics, the common difference or we can call it the rate of change is the amount that we are constantly changing by either adding or subtracting to get to our next term. In other words, it’s consecutive terms increasing or decreasing.

Answer:

D

Step-by-step explanation:

Edge 2022

To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division.

To rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x) + r(x)/b(x), we can use polynomial division. Here are the steps:

Therefore, the rational expression x^3+5x^2+3x-10/x+4 can be rewritten as q(x) + r(x)/b(x), where:

Answer:

Option B.

Step-by-step explanation:

Consider the below figure attached with this question.

The given function is

[tex]y=3(\frac{1}{2})^x[/tex]            .... (1)

We need to find the graph of given function.

The general form of an exponential function is

[tex]y=ab^x[/tex]               .... (2)

where, a is initial value and b is growth or decay factor.

If 0<b<1, then it is a decreasing function.

If b>1, then it is an increasing function.

On comparing (1) and (2) we get

[tex]a=3, b=\frac{1}{2}[/tex]

a=3, it means y-intercept of the function is 3.

[tex]b=\frac{1}{2}[/tex], it means it is a decreasing function.

The table of values is

x          y

-2       12

-1        6

0        3

1       1.5

2       0.75

Plot these ordered pairs on a coordinate plane and connect then by a hand curve. Graph B represents the given function.

Therefore, the correct option is B.

Final answer:

A rational number is a number that can be written as a ratio of two integers, with the denominator not equal to zero.

Explanation:

The definition of a rational number is a number that can be written as a ratio of two integers, where the numerator and the denominator are both integers and the denominator is not zero. For example, fractions such as 2/3, where both 2 and 3 are integers, represent rational numbers. This is different from irrational numbers like √2 or transcendental numbers like π, which cannot be expressed as a ratio of two integers.

Furthermore, while all integers are themselves rational numbers (since any integer 'a' can be written as 'a/1'), not all rational numbers are integers, particularly when the numerator is not a multiple of the denominator.

The average rate of change from x = 0 to x = 2 for the parabola described in the question is -4. Hence the correct option is 1.

The average rate of change of a function between two points is calculated by subtracting the y-values (function outputs) and dividing by the difference in x-values (inputs). In this case, to find the average rate of change of the parabola from x = 0 to x = 2, we use the points (0, 3) and (2, -5).

The average rate of change = (y2 - y1) / (x2 - x1)

Substitute in the given points: ( -5 - 3 ) / ( 2 - 0 )

Simplify the expression: -8 / 2 = -4

Hello, I hope this will help you out!

The ratio of oranges to apples is 10/3! Hope that helped!

Answer:

Given condition: A grocery store display has 60 oranges and 18 apples.

Then,

Number of oranges = 60 and

Number of apples = 18.

Then, we use ratios to make comparisons between two things.

When we express a ratios in words we use the word ''to'' then we say that the ratio of something to something else.

Ratio of oranges to apples = [tex]\frac{Number of oranges}{Number of apples}[/tex]

then,

Ratio of oranges to apples =[tex]\frac{60}{18}[/tex]

Divide numerator and denominator by 6, we get

Ratio of oranges to apples =[tex]\frac{10}{3}[/tex] which is in the simplest fractional form.

The sum of the first ten non-zero multiples of twenty is 1100. This is calculated using the arithmetic series sum formula where n=10, the first term is 20 and the last term is 200.

The sum of the first ten non-zero multiples of twenty can be calculated using the formula for the sum of an arithmetic series. The first ten non-zero multiples of twenty are 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200.

To calculate their sum, you detect a common difference which is the number 20 itself and use the sum formula for an arithmetic series where Sn = n/2 * (a1 + an), where Sn is the sum of n terms, a1 is the first term, and an is the last term.

In this case, n=10, a1=20, and an=200. So, the sum Sn = 10/2 * (20 + 200) = 5 * 220 = 1100. Therefore, the sum of the first ten non-zero multiples of twenty is 1100.

The number 52 is 65% of the number 80.

Chance formula is used to find the quantum or share of commodity in terms of 100. In its simplest form, percent means per hundred. To express a number between zero and one, chance formula is used. It's defined as a number represented as a bit of 100. It's denoted by the symbol, and is majorly used to compare and find out rates.

We have to find 65% of what number is 52.

let the number be x.

So, 65% of x =52

65/100 x = 52

0.65 x = 52

x= 52/ 0.65

x= 80.

Thus, 65% of 80 is 52.

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The answer is: [tex]\( 28x^2 - 23x - 15 \)[/tex]

To multiply the expression  (7x+3)(4x-5)  we apply the distributive property, also known as the FOIL method for binomials.

This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

Here's the step-by-step process:

 1. Multiply the first terms: [tex]\( (7x) \cdot (4x) = 28x^2 \)[/tex]

2. Multiply the outer terms: [tex]\( (7x) \cdot (-5) = -35x \)[/tex]

3. Multiply the inner terms: [tex]\( (3) \cdot (4x) = 12x \)[/tex]

4. Multiply the last terms: [tex]\( (3) \cdot (-5) = -15 \)[/tex]

Now, combine the like terms:

[tex]\( 28x^2 - 35x + 12x - 15 \)[/tex]

Therefore, the correct final expanded form of the expression is:

[tex]\( 28x^2 - 23x - 15 \)[/tex]