Suppose your parents are traveling on a work-related trip for a whole week. After providing the budget for all other expenses such as food, bills, emergencies. Etc. , they left you p10,000 as allowance for the week to be divided fairly among you and your two other siblings. How would you divide the money, assuming that the amounts should be in whole pesos and with no spare change? explain how you came up with your division in one sentence.

The correct response to Hannah's method is: No, she incorrectly calculated the area of the parallelogram.

Area of a composite shape.

A composite shape is one formed by more than one plane shape.

A given shape that has its two opposite sides to be equal and parallel is called a parallelogram. The area of a parallelogram can be determined by;

Area of a parallelogram = base x height

Also, a square has the measure of its sides to be equal. The area of a square can be determined by:

Area of a square = length x length

Considering the given question, we have;

i. Area of the parallelogram = base x height

                                           = 5 x 12

Area of the parallelogram = 60 cm^2

ii. Area of the square = length x length

                                   = 5 x 5

Area of the square = 25 cm^2

Total area of the given shape = 60 + 25

                                                  = 85 cm^2

Hannah's answer is incorrect. Thus the correct response is No, she incorrectly calculated the area of the parallelogram.

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Answer:

[tex](x, y)=\{(-2,-1), (3,14)\}[/tex]

Step-by-step explanation:

[tex]y=x^2+2x-1, y=3x+5 \\ \\ \implies x^2+2x-1=3x+5 \\ \\ x^2-x-6=0 \\ \\ (x-3)(x+2)=0 \\ \\ x=-2, 3 \\ \\ x=-2 \implies y=-1 \\ \\ x=3 \implies y=14 \\ \\ \therefore (x, y)=\{(-2,-1), (3,14)\}[/tex]

Correct Option: Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.

The conditional relative frequency presents the result of the survey that conveys information about the programming and the audience. A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest. The differences in conditional relative frequencies are used to assess whether or not there is an association between two categorical variables.

Based on the given table (attached below), we have that the programs are categorized based on the intended audience.

Therefore, the 0.375, indicates that 37.5% of the program targeted at adults are recorded.

Therefore, the correct option is:

Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.

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Answer:

Step-by-step explanation:

5.7 pounds use division.

The perimeter of a square is equal to the sum of all of its sides. Since all sides of a square are equal, to find the perimeter you just need to multiply the length of one side by 4. In this case, the perimeter would be 15 inches * 4 = 60 inches.

The circumference of a square is not defined, as it is a two-dimensional shape and does not have a circumference (which is a measure of distance around the edge of a circular shape).

The area of a square is equal to the length of one side squared. To find the area of a square with sides 15 inches long, you would calculate 15 inches * 15 inches = 225 square inches.

The number of miles that miles must be driven in one day for option A to be cheaper is 41 miles or lesser

The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Option A charges $35 per day plus $0.15 per mile. This will be:

35 + 0.15m

Option B charges $0 per day, but $1.00 per mile. This will be m.

Equating them will be:

35 + 0.15m < m

Collect the like terms

m - 0.15m < 35

0.85m < 35

Divide

m < 41

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In most geometry issues, the most popular approach is to utilize a compass and a ruler.

Simply lock that length into the compass by setting it to a setting that is greater than 1/2 but less than the length of the line segment.

The next step is to draw an arc using the compass on the first and second points so that the first and second arcs cross above and below the line segment. Mark the intersections of the two arcs with "up" and "down," "right" or "left," or any other designation.

When a line is drawn between the two arc intersections, it not only bisects the original line segment but also forms a perpendicular line segment to it.

The line segment has now been split into two identical parts. You will have separated the line segment into 4 equal sub-segments if you repeat this process on the first and second sub-segments.

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All numbers with an absolute value greater than 3 but less than 7 is {4, 5, 6}.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We need to write all numbers with an absolute value greater than 3 but less than 7.

Absolute value greater than 3, that is

|x|>3

Absolute value less than 7, that is

|x|<7

Now, 3<|x|<7

3<x<7

Solution set ={4, 5, 6}

Therefore, all numbers with an absolute value greater than 3 but less than 7 is {4, 5, 6}.

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Answer: men: 120 men, 310 women, and 170 children

600*0.2=120

600*0.35=310

600-120-310=170

Answer:

1,160

Step-by-step explanation:

The equation for a homogeneous differential in its general solution.

= (x² + 4y²)³x² = c.

When both f(x,y) and g(x,y) have the same degree, a differential equation of the form f(x,y)dy = g(x,y)dx is referred to as a homogeneous differential equation. For k 0, a function of the type F(x,y) that can be expressed in the form kn F(x,y) is referred to as a homogeneous function with degree n.

If M(x,y) and N(x,y) are both homogeneous functions that have the same degree, then a first-order differential equation is said to be homogeneous. is homogeneous since it contains homogeneous functions that have the same degree, M(x,y) = x 2 - y 2, and N(x,y) = xy (namely, 2).

[tex]$\mathrm{v}+\mathrm{x} \frac{\mathrm{dv}}{\mathrm{dx}}=-\left(\frac{\mathrm{x}^2+\mathrm{v}^2 \mathrm{x}^2}{3 \mathrm{xv} \mathrm{x}}\right)=-\left(\frac{\mathrm{x}^2\left(1+\mathrm{v}^2\right)}{3 \mathrm{x}^2 \mathrm{v}}\right)$[/tex]

[tex]$v+x \frac{d v}{d x}=-\left(\frac{1+v^2}{3 v}\right)$[/tex]

[tex]$x \frac{d v}{d x}=\frac{-1-v^2}{3 v}-v=\frac{-1-v^2-3 v^2}{3 v}=\frac{-1-4 v^2}{3 v}$[/tex]

[tex]$\frac{3}{8} \int \frac{8 v}{1+4 v^2} d v=-\int \frac{d x}{x}$[/tex]

Integrating we have [tex]$\frac{3}{8} \log \left(1+4 v^2\right)=-\log x+\log c$[/tex]

= 3log(1 + 4v²) + 8 log x = log c

= (1 + 4v²)³.x⁸ = c

= [tex]$\left(1+4 \frac{y^2}{x^2}\right)^3 \cdot x^8=c$[/tex]

= (x² + 4y²)³x² = c.

the general solution of the homogeneous differential equation.

=  (x² + 4y²)³x² = c.

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The equation that has the same solution as the given equation include the following: C. 3/2p − 5 + 9/4p = 7 − 5/4p.

From the information provided, we have the following equation:

-16p + 37 = 49 - 21p

Next, we would rearrange the equation by collecting like terms as follows;

-16p + 21p = 49 - 37

5p = 12

p = 12/5

Furthermore, we would evaluate and determine the solution for each of the given equation as follows;

-14 + 6p = -9 - 6p

Collecting like terms, we have:

6p + 6p = -9 + 14

12p = 5

p = 5/12 (Different solution).

2 + 1.25p = -3.75p + 10

Collecting like terms, we have:

1.25p + 3.75p = 10 - 2

5p = 8

p = 8/5 (Different solution).

3/2p − 5 + 9/4p = 7 − 5/4p

Collecting like terms, we have:

3/2p + 9/4p + 5/4p = 7 + 5

5p = 12

p = 12/5 (Same solution).

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Using the the law of syllogism to write a true conditional statement we have that

If points A, B, and C are collinear and A is between B and C then AB + AC = BC

The law of syllogism, also known as transitivity reasoning, is a valid kind of deductive reasoning that adheres to a predetermined pattern.

It is a logical structure for a formal argument that includes a major/minor premise, and conclusion

For a true conditional statement, the conclusion will always be true when the conditions of the hypothesis are reached.

The given conditional statement is "If points A, B, and C are collinear and A is between B and C then AB + AC = BC"

This condition did not see AB and AC as rays that has direction it accounts for just magnitude

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Answer: 1450 Largest, 1045 Smallest

Answer:      1,450 is the largest.

                     1,045 is the smallest.

Please mark on it..

The equation 8x = 60 represents the situation and x represent each friend’s share of the food bill.

The equation x = 76/8 represents the situation and x represent each friend’s share of the food bill and tip.

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

Let x each friend’s share of the food bill.

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. Hence:

8x + 16 = 76

subtracting 16 from both sides of the equation:

8x = 60

Also, let x represent each friend’s share of the food bill and tip.

8x = 76

x = 76/8

The contribution of each friend for food bill is given by 8x = 60

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Answer:

81 cm3

Step-by-step explanation:

The volume of a cylinder is three times that of a cone, as long as it has the same radius and height. Their formulas prove it.

Hope this helps

Answer:

81 cm³

Step-by-step explanation:

V-cylinder = πr²h

V-cone = πr²h/3

You can see from the formulas that the volume of a cone is 1/3 the volume of a cylinder with the same radius (r) and height (h).

Therefore:

πr²h/3 = 27

πr²h = 27(3) = 81 = volume of the cylinder

Independent variable and dependent variable

What occurs as a result of the independent variable is referred to as a dependent variable.

We anticipate that independent variables will have an impact on dependent variables.

Eg. You plan a study to see if variations in the room's temperature have an impact on students' math test results.

The inside temperature of the space is your independent variable. By making the room cooler for half the participants and warmer for the other half, you can change the temperature.

Test results in mathematics are your dependent variable. Using a standardised test, you measure each participant's math prowess to see if there are any temperature-related differences.

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The correct statement is: 'In any experiment, the cause is called the dependent variable, while the effect or result is called the independent variable.'

We know that an independent variable is a variable which is not changed by the other variables you are trying to measure.

An independent variable is also known as input variable.

Or in any experiment, the cause is represented by the independent variable.

Whereas a dependent variable is nothing but the variable that changes as a result of the independent variable. It depends on the independent variable of an experimetent.

It is also called as output variable.

Therefore,   In any experiment, the cause is called the dependent variable, while the effect or result is called the independent variable.

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The linear function that models the balance after t months is given as follows:

y = -75t + 1500.

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

In which the coefficients of the function are given as follows:

Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975, hence two points of the function are given as follows:

(4, 1200) and (7, 975).

Given two points, the slope is calculated as the change in the output divided by the change in the input, hence:

m = (975 - 1200)/(7 - 4)

m = -75.

Hence:

y = -75t + b.

When t = 4, y = 1200, hence the intercept b is calculated as follows:

1200 = -75(4) + b

b = 1200 + 75 x 4

b = 1500.

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The degree of 6 in polynomials is 0. The degree of a polynomial is defined as the highest power of the variable that appears in the equation.

When a numerical coefficient is present, as in example 6, the power is considered to be 0. This means that the degree of the polynomial is 0. To find the degree of a polynomial, we need to first identify the variables and their corresponding powers.

For example, if the polynomial is 4x^3 + 6x^2 - 3x + 6, we can identify that the variable is x and the powers are 3, 2, and 1 respectively. The highest power among the three is 3, so the degree of the polynomial is 3.

In example 6, there is no variable present, only a numerical coefficient. Therefore, the power of the coefficient is 0 and the degree of the polynomial is 0.

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The value of m in the given triangle will be 10.39.

According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle. In other words, a² + b² = c² for the triangle depicted below. The right triangle's legs, a, and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.

where a, b, and c are the base, height, and hypotenuse of the triangle.

Given in the figure there is one big triangle whose height is m and whose hypotenuse is 24 or (18 + 6). let x be the base of the triangle.

From the Pythagorean theorem

x² + m² = 24²

x² = 576 - m²

For another triangle whose base is n and height is 18.

From the Pythagorean theorem

n² + 18² = x².......(1)

from equation (1)

n² + 18² = 576 - m²

n² + m² = 576 - 324

n² + m² = 252........(2)

For another triangle whose base is 5 and height is n.

From the Pythagorean theorem

n² + 6² = m²

n² - m² = 36.....(3)

From comparing equations 2 and 3

n² + m² - (n² - m²) = 252-36

2m² = 216

m² = 108

m = ± 10.39

since the length can not be n negative.

m = 10.39

therefore the value of m in the given triangle is 10.39.

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The equation in slope intercept form is an = 5n - 9

From the question, we have the following parameters that can be used in our computation:

an = -4 + 5(n - 1)

A linear equation in slope-intercept form can be represented as

an = mn + c

Where

slope = m

y-intercept = c

This means that we start by opening the bracket in an = -4 + 5(n - 1)

an = -4 + 5n - 5

Evaluate the like terms

an = 5n - 9

Hence, the equation is an = 5n - 9

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Answer: D

Step-by-step explanation:

-3x + 4 - (5x - 2)

= -3x + 4 - 5x + 2

= -8x + 6

= D

The graph that shows the solution to the inequality, would be Graph A.

The inequality is :

x - 4 ≤ - 1

What this means is that all values of x should be able to deduct 4 such that the result would be less than or equal to - 1.

This means that the largest number that x can take is :
x - 4 = - 1

x = -1 + 4

x = 3

x can be a maximum of 3 and then all other x values have to be less than 3. This is shown as a solution in the first graph.

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Jacob has ran 1154 yards because you divide it by yards

Answer: Jacob ran 1154 yards during the relay race.

Step-by-step explanation:  3462 feet equals 1154 yards.

The formula for a line segment is:

segment = √((x2 - x1)^2 + (y2 - y1)^2)

1. Calculate the difference between the x-coordinates: x2 - x1

2. Square the result of step 1: (x2 - x1)^2

3. Calculate the difference between the y-coordinates: y2 - y1

4. Square the result of step 3: (y2 - y1)^2

5. Add the results of step 2 and step 4: (x2 - x1)^2 + (y2 - y1)^2

6. Calculate the square root of the result of step 5: √((x2 - x1)^2 + (y2 - y1)^2)

This final result is the length of the line segment.

The formula for a line segment is relatively straightforward. Begin by calculating the difference between the x-coordinates (x2 - x1) and square the result. Then find the difference between the y-coordinates (y2 - y1) and square the result. Add the two results together and take the square root of the sum. This final result is the length of the line segment. This formula can be used to calculate the length of any line segment, regardless of its size or shape.

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On solving the provided question we can say that by linear equation x = 12 and y = 35

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

as here we have,

There are =  63 days left in the marking period.

so, Marking Period 3rd Grading Period 21 - 22 January 3, 2022 March 11, 2022 =

63x + 21y = 100

22x + 3y = 64

and, x = 12 and y = 35

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Triangle 1 and triangle 2 are concurrent if, Triangle 1 has vertices at (A, B), (C, D), and (E, F), Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F) and are reflected so, option D is correct.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Given:

Triangle 1 has vertices at (A, B), (C, D), and (E, F),

Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F).

Triangle 1 is reflected on the y-axis and we get triangle 2,

Both, triangle 1 have the same magnitude of dimension as triangle 2,

Thus, both are concurrent also.

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Answer: D is the correct answer

Step-by-step explanation:

imagine math

The algebraic expression for the payment of the plan with y dollar surge is A = x/2 + y.

The concept of algebraic expressions is the use of letters or alphabets to represent numerical values without stating their exact meanings. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given that the annual premium plan is x dollars.

The payment is made semi-annually this is represented as follows:

x/2

There is a surplus charge of y, this is written as:

A = x/2 + y

Hence, the algebraic expression for the payment is A = x/2 + y.

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The terms 3xy and 5yx are like terms because they contain the same variable and also have the same degree .

The Like terms are defined as the terms that contain the same variable and also the variables are raised to the same power .

For Example : the terms 3x² and 7x² are like terms as they have the same variable and that variable has same power "2" .

The terms are given as 3xy and 5yx ,

both the terms have variables x and y ,

the power of x and y in first term "3xy" is "1" , and

the power of x and y in the second term "5yx" is also "1" .

So , we can conclude that the terms 3xy and 5yx are like terms .

Therefore , 3xy and 5yx are like terms .

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The expression 3x + 2y - 5z can be expanded as 3x + 2y - 5z = 3x + 2y - 5z + 0 = 3x + 2y - 5z + 0 + 0 = 3x + 2y - 5z + 0 + 0 + 0.

The expression 3x + 2y - 5z can be calculated as follows:

3x + 2y - 5z = 3x + 2y - 5z

= 3x + 2y - (5z + 0)

= 3x + 2y - (5z + 0 + 0)

= 3x + 2y - (5z + 0 + 0 + 0)

= 3x + 2y - 5z - 0 - 0 - 0

= (3x + 0) + (2y - 0) - (5z - 0 - 0 - 0)

= 3x + 2y - 5z

The expression 3x + 2y - 5z can be expanded by first adding 0 to each side: 3x + 2y - 5z + 0 = 3x + 2y - 5z + 0. Then, we can add 0 to each side again: 3x + 2y - 5z + 0 + 0 = 3x + 2y - 5z + 0 + 0. This can be done for a third time: 3x + 2y - 5z + 0 + 0 + 0 = 3x + 2y - 5z + 0 + 0 + 0. This expansion can be simplified by replacing the like terms: 3x + 0 + 2y - 0 - 5z - 0 - 0 - 0 = 3x + 2y - 5z. This simplification shows that the expression 3x + 2y - 5z is equal to itself and can be used to calculate the value of the expression.

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