If the number of bacteria in a colony doubles every 203 minutes and there is currently a population of 40 bacteria, what will the population be 812 minutes from now?

Answer:

f = 5

g = -3

Step-by-step explanation:

11f + 14g = 13        Q1

11f + 10g = 25       Q2

Q1 - Q2  =

4g = -12

g = -3

put it back in the equation

11f + 10g = 25

11f + 10 (-3) = 25

11f + -30 = 25

11f = 55

f = 5

Answer:

f = 5 , g = - 3

Step-by-step explanation:

11f + 14g = 13 → (1)

11f + 10g = 25 → (2)

subtract (2) from (1) term by term to eliminate f

(11f - 11f) + (14g - 10g) = 13 - 25

0 + 4g = - 12

4g = - 12 ( divide both sides by 4 )

g = - 3

substitute g = - 3 into either of the 2 equations and solve for f

substituting into (1)

11f + 14(- 3) = 13

11f - 42 = 13 ( add 42 to both sides )

11f = 55 ( divide both sides by 11 )

f = 5

solution is f = 5 , g = - 3

Answer: 6 are not enrolled.

Step-by-step explanation:

78 in total so you add 41+22+9 and you get 72 so you do 78-72 and you get 6.

If we plot the inverse function on a graph, then we get a parabola. This parabola has the following conditions: If a>0 , then the equation defines a parabola whose ends point upwards. If a<0 , then the equation defines a parabola whose ends point downwards.

Now, According to the question:

What type of graph is a parabola?

A parabola is the shape of a quadratic function graph. There are two types of parabolas, positive (opening up) or negative (opening down). A parabola has many key features including a vertex, x-intercept(s) and y-intercept.

How do you know if a graph is a parabola?

A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax^2 + bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.

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Answer: a) The amount of interest that would be added to the loan after one year at a 10% annual compound interest rate is 15000010/100 = 15000. Therefore, the total amount of the loan after one year would be 150000+15000 = 165000. After the person paid Rs 85000 at the end of the first year, the remaining amount of the loan would be 165000-85000 = 80000.

To clear the debt at the end of the second year, the person would have to pay 80000+8000010/100 = 80000+8000 = 88000 rupees.

b) If the person had only paid the loan at the end of the second year, the interest on the loan would be 15000010/1002 = 30000 rupees.

The total amount of the loan would be 150000+30000 = 180000 rupees.

Therefore, the difference in interest paid would be 30000-8000 = 22000 rupees more.

He would have to pay 22000 rupees more than what he paid in the first case.

Answer:

5

Step-by-step explanation:

(3-8)²+(0+0)²

25+0

25----> The square root of 25 is 5

Figure shows right angle, angles are 30-60-90 degrees, and side ratio 1:√3: 2.

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The absolute value of the inequality |2x -1| >3  will have a union type of solution set.

By using the absolute rule that states:

An inequality equation's absolute value can be solved.

where the "or" functionality symbolizes the union between the solution sets.

Given that:

|2x - 1| > 3

Applying the absolute rule, we have:

2x - 1 < - 3 or 2x - 1 > 3

2x < -4 or 2x > 4

x < -4/2 or x > 4/2

x< -1 or x > 2    

This denotes the union of between the solution sets.

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A pair of alternate interior angles is - ∠3 and ∠5

A pair of corresponding angles is - ∠1 and ∠5

A pair of alternate exterior angles is - ∠1 and ∠7

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles.

So, ∠3 and ∠5, and ∠4 and ∠6, are alternate interior angles.

According to the definition of corresponding angles, when two parallel lines are intersected by a transversal, the angles that are in the same relative position at each intersection are referred to as being corresponding angles to one another.

So, ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, and ∠4 and ∠8  are corresponding angles.

Alternate exterior angles are created when two or more lines are intersected by a transversal. These angles are formed on the outer side of the transversal on the different sides.

So, ∠1 and ∠7, ∠2 and ∠8 are alternate exterior angles.

Therefore, the alternate interior angles, corresponding angles and alternate exterior angles are ∠3 and ∠5, ∠1 and ∠5, and ∠1 and ∠7 respectively.

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Answer:

24

Step-by-step explanation:

12/2=6 6*4=4

The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.

Angle measurements and side lengths are identical for congruent triangles. These are the criteria for triangle congruence: "Side-Side-Side" SAS (Side-Angle-Side)

If the five conditions for congruence are met, two triangles are congruent. These are right angle-hypotenuse-side (RAHS), side-side-side (SSS), angle-side-angle (ASA), angle-angle-side (AAS), and side-angle-side (SSS) (RHS).

Triangles are said to be congruent if two sets of corresponding angles and the pair of included sides are also so. The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.

You would need at least one pair of comparable sides that are likewise congruent to demonstrate the congruence of two triangles with three congruent, corresponding angles. Then, you might demonstrate congruence using the ASA or AAS congruence theorems or rigid transformations.

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The another word for logarithmic function is log.

A logarithmic equation is one that uses the logarithm of an expression involving a variable. Before attempting to answer an exponential equation, make sure you can write both sides of the problem as powers of the same number.

To generate a given number, a base must be raised to a particular exponent, power, or logarithm. If bx = n, then mathematically, x is the logarithm of n to the base b, denoted as x = logb n. For instance, since 8 has a base-2 logarithm of 3, 3 = log2 8 since 8 = 23

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A function is a relation in which each element of the domain is paired with exactly one element of the range.

Determine whether each relation is a function. Find the domain and range?

(-2,2) (0,0) (2,-2)

This is a function because it is a many to one relation(-2 map to 2,0 map to 0,2 map to -2

Domain( -2,0,2)

Range(-2,2)

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Hope it helps.

If you have any query, feel free to ask.

The entire area bounded by any triangle's three sides is referred to as the triangle's area.

In essence, it is equivalent to 1/2 of base times height, or A = 1/2 b times h. A triangular polygon's base (b) and height (h) must be known in order to calculate its area.

Whether a triangle is scalene, isosceles, or equilateral, it can be used to solve any kind of triangle.

Be aware that the triangle's base and height are at right angles to one another. In square units, the area unit is measured (m2, cm2).

Example :

Consider this triangle with a base of 3 cm and a height of 4 cm. What is its area?

Employing the formula,

Triangle's area is equal to half of b times h.

= 1/2 × 4 (cm) × 3 (cm) (cm)

= 2 (cm) × 3 (cm) (cm)

= 6 cm2

In addition to the method mentioned above, Heron's formula can be used to determine a triangle's area when we know the lengths of its three sides.

In addition, when two sides of a triangle are known as well as the angle that forms between them, the area can be calculated using trigonometric functions.

For each of these circumstances, we shall calculate the area.

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The angle at which the ladder is leaning according to the base and length of the ladder is 62°.

The angle formed between ladder and house is right angled triangle. Thus, the trigonometric formula to be used for calculation is -

cos theta = base ÷ hypotenuse

Keeping the values in formula to find the value of theta which represents angle of leaning of ladder

cos theta = 7/15

Performing division on Right Hand Side of the equation to find the value of theta

cos theta = 0.47

theta = [tex] { \cos }^{ - 1} [/tex] 0.47

theta = 61.97

Thus, the angle is 61.97 or 62°.

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Both "negative 1" and "minus 1" refer to the same value, which is -1. They both indicate that a value is less than zero.

"Negative 1" and "minus 1" are ways to represent the value of -1 in mathematics. In general, a negative number is any number that is less than zero. For example, -1, -2, -3, etc. are all negative numbers.

When we use the word "minus" in front of a number, it indicates that we want to subtract that number from a given value. For example, if we say "5 minus 2," we mean 5 - 2 = 3. Similarly, when we say "minus 1," it means we want to subtract 1 from a given value.

So, "negative 1" and "minus 1" are both ways to indicate the value of -1, which is less than zero.

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The ratio of the edge lengths of the large and small cubes is 6:1

The ratio that compares the edge lengths of the large and small cubes is the ratio of the length of the edge of the large cube to the length of the edge of the small cube.

The edge length of the large cube is 12 cm and the edge length of the small cube is 2 cm. To find the ratio, we divide the length of the large cube by the length of the small cube.

So the ratio of the edge length of the large cube to the small cube is:

12cm/2cm = 6

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To determine if an ordered pair (X,Y) is a solution to a linear inequality in two variables, substitute the values for X and Y into the inequality and check if the inequality holds true.

To determine whether an ordered pair (X,Y) is a solution of a linear inequality in two variables, we must first understand what a linear inequality is. A linear inequality is an equation with two variables (X and Y) that is either greater than or less than an expression. To determine if an ordered pair is a solution to a linear inequality, we must substitute the values for X and Y into the inequality and check if the inequality holds true. If the inequality is true, then the ordered pair is a solution. If the inequality is false, then the ordered pair is not a solution. For example, if we have an inequality of 2X + Y > 5 and the ordered pair (3,1), we can substitute the values for X and Y into the inequality (2(3) + 1 > 5). Since this inequality holds true, the ordered pair (3,1) is a solution

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Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

A) f (0)

Substituting the value of x = 0

f (0) = 6(0) -3

      = 0 - 3

      = -3

B) f (2)

Substituting the value of x =2

f (2) = 6(2) -3

      = 12 - 3

      = 9

C) f (-2)

Substituting the value of x = -2

f (2) = 6(-2) -3

      = -12 - 3

      = -15

D) f (1)

Substituting the value of x =1

f (1) = 6(1) -3

      = 6 - 3

      = 3

E ) f (-3)

Substituting the value of x =2

f (2) = 6(-3) -3

      = -18 - 3

      = -21

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The value of m and n of the parallelogram is given by the equations ,

The value of m = 5

The value of n = 12

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

The measure of side AB = m + 1

The measure of side BC = 12

The measure of side CD = 6

The measure of side CA = n

And , for a parallelogram opposite sides are parallel and opposite sides are congruent

Now , the measure of side AB = measure of CD

The measure of side BC = measure of CA

Substituting the values in the equation , we get

m + 1 = 6

And , n = 12

Subtracting 1 on both sides of the equation , we get

m = 5

Hence , the value of m and n of parallelogram are 5 and 12 respectively

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18  bottles of lemonade did the shop fill

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Answer:

14

Step-by-step explanation:

Answer:

a = 14

Step-by-step explanation:

-a = 14 + (-28)

-a = 14 - 28

-a = -14 / × (-1)

a = 14

A customer earns 1 free night per 10 nights stayed.

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

f(x)=x/10

When we put x=10, we get f(1)=10/10=1

Here f(1)  represents the number of free nights earned by the customer is 1 per 10 nights stayed.

When we put x=20, we get f(2)=20/10=2

Here f(2)  represents the number of free nights earned by the customer is 2 per 20 nights stayed.

When we put x=30, we get f(3)=30/10=3

Here f(3)  represents the number of free nights earned by the customer is 3 per 30 nights stayed.

When we put x=40, we get f(4)=40/10=4

Here f(4)  represents the number of free nights earned by the customer is 4 per 40 nights stayed.

Then, the pattern permits you to conclude that a customer earns 1 free night for every 10 nights stayed.

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Answer:

3 (x + 4)

Step-by-step explanation:

3x = 3 × x

12 = 3 × 4

3x + 12

Take 3 common,

3 (x + 4)

Hence, factorised.

Answer: Hi

We can use the information given to set up the inequality:

Weight of refrigerators + weight of pianos <= 6900 (since the truck can carry no more than 6900 lb)

We can use the weight of each item to write the inequality in terms of x (number of refrigerators) and y (number of pianos):

300x + 525y <= 6900

To graph the inequality, we can use the x and y values as coordinates and plot them on a coordinate plane. The line representing the inequality would be a boundary line, with all the points that satisfy the inequality on one side of the line, and all the points that do not satisfy the inequality on the other side of the line.

To check if 12 refrigerators and 9 pianos will overload the truck, we can substitute these values into the inequality:

300(12) + 525(9) = 3900 + 4725 = 8625

Step-by-step explanation:

To sum up, the inequality 300x + 525y <= 6900 represents the weight that the truck can carry. The points that satisfy the inequality (such as (4, 6) or (10, 3)) would represent a combination of refrigerators and pianos that the truck can carry, while the points that do not satisfy the inequality (such as (12, 9)) would represent a combination that overloads the truck.

20 times we can expect to spin a 5.

Option(B) is correct.

What is probability?

Probability is the branch of mathematics that deals with the likelihood of certain events happening.

A spinner is divided into equal sections, labeled 4 through 8, so there are 5 sections in total (4, 5, 6, 7, 8). If you spin the spinner 100 times, you would expect to spin a 5 on 1/5 of those spins, since there is one 5 section out of five total sections. Therefore, you would expect to spin a 5 100 times / 5 sections = 20 times.

Hence, 20 times we can expect to spin a 5.

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X=-y--y-3 vertical line, there is no y-intercept and the slope is undefined.

X+y= −3

(x + y) + (−y) = −3+ ( − y)

X+y-y=-3-y

X=-y-3

Using the slope formula, calculate the slope.

To find the y-intercept (b), use the slope and one of the points.

Once you have the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line’s equation.

No, so its slope can't be negative. What number is neither positive nor negative? Zero! This relationship always holds: a slope of zero means that the line is horizontal, and a horizontal line means you'll get a slope of zero.

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The value of the composite function are as follows:

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

A composite function is a function that depends on another function. In other words, a composite function is a function that is within another function.

Therefore, let's solve the function as follows:

f(x) = 2x²

g(x) = x + 1

Therefore,

(f - g)(x) = f(x) - g(x) = 2x² - (x + 1) = 2x² - x - 1

(f + g) =  f(x) + g(x) = 2x² + (x + 1) = 2x² + x + 1

(f .g)(-2) = f(g(-2))

g(-2) = -2 + 1 = -1

Hence,

(f .g)(-2) = 2(-1)² = 2

Therefore,

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

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The value of 55 divided by 7 will be 7 remainder 6. The correct option is A.

The expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It should be noted that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, the value of 55 divided by 7 will be:

= 55 / 7

= 7 6 / 7

This is 7 remainder 6.

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Complete question

What is 55/7?

A. 7 Remainder 6

B : 7 Remainder 5

C : 6 Remainder 5

D : 6 Remainder 6

When multiplying a number by a sum, you can apply the distributive property of multiplication over addition. Say you want to multiply 3 by the sum of 10 plus 2, for instance: 3(10 + 2) =? This attribute allows you to add the integers and then multiply the result by three.

The distributive property of multiplication is used when multiplying each integer by the sum of two or more addends. The subtraction and addition of two or more numbers are both subject to the distributive property of multiplication.

Boost the equation's size. Divide (multiply) the initial number in each set, the outer number in each set, the inner number in each set, and the last number in each set. Join similar phrases. If necessary, simplify the equation after solving it.

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