Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.

The solution to this system of linear equations is x = 3, y = 2.

2x - 3y = 3

2x = 3 + 3y

2x = 3y + 3

x = (3y + 3) / 2

x = 3/2 + 3/2y

x = 3, y = 2

This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.

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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.

1. Rewrite the equation in standard form is

2x + 3y = 3

2. Subtract 2x from both sides of the equation:

3y = 3 - 2x

3. Divide both sides by 3:

y = (3 - 2x)/3

4. Solve for x by substituting y in the original equation:

2x + 3(3 - 2x)/3 = 3

5. Simplify and solve for x:

2x + 3 - 2x = 3

x = 1

6. Substitute x into the equation y = (3 - 2x)/3

y = (3 - 2(1))/3

y = -1/3

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The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.

The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.

So, if we square the length of the ladder (6^2 = 36)

The length of the base (3^2 = 9),

and add them together, then take the square root of that, we get the height of the wall.

sqrt(36+9) = sqrt(45) = 3*sqrt(5)

so the ladder is 3√5 feet high up the wall.

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Answer:

37,349

Step-by-step explanation:

month 1

27870 x .05 = 1394

27870 + 1394 = 29264

month 2

29264 x .05 = 1463

29264 + 1463 = 30727

month 3

30727 × .05 = 1536

30727 + 1536 = 32263

month 4

32263 x .05 = 1613

32263 + 1613 = 33876

month 5

33876 x .05 = 1694

33876 + 1694 = 35570

month 6

35570 x .05 = 1779

35570 + 1779 = 37349

Answer:

35,570

Step-by-step explanation:

solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.

1. 27870*1.05= 29,263.5

2. 29263.5*1.05=30726.675

3.repeat

4.repeat

5.repeat

6.repeat

if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)

1. 27870÷10= 2,787

2. 2787÷2= 1393.5

3. 27870+1393.5 = 29263.5

solution 2 -Fast but probably needs a calculator

1. 27870*1.05^(5)= 35570

1.05 = monthly increase

power of 5 = ^(5) = 6 months - 1 = 5

The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.

The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given series is 15,20,25,30,...,

The common difference is d = 20 - 15 = 5

First term is, 15

The formula can be written as,

an = a₁ + d(n-1)

an = 15 + 5 ( n - 1 )

an = 15 + 5n - 5

an = 10 + 5n

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Answer:

You need to combine like terms

The volume of the can based on mentioned radius and height of can is 471 inches³.

Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.

Use the below mentioned formula to calculate the volume -

V = πr²h, where V is volume, r is radius and h is height.

Keep the values in formula to find the value of volume of cylinder

V = 3.14×5²×6

Next step is to perform multiplication on Right Hand Side of the equation

V = 471 inches³

The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.

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Answer:

Step-by-step explanation:

fter solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.

What is algebra?

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x

$3.00 when converted to cents is 300 cents.

The value of nickels is 5 x 4x=20x.

The value of dimes is 10 x 3x=30x.

The value of quarters is 25x.

As the total value of money Miguel has is 300 cents, then the algebraic equation will be -

20x + 30x + 25x = 300

Solve to get the value of x -

75x = 300

x = 4

Therefore, the amount of quarters is x = 4 quarters.

The amount of dimes is x = 3x = 3 x 4 = 12 dimes.

The amount of nickels is 4x = 4 x 4 = 16 nickels.

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Answer:

2.46

Step-by-step explanation:

Answer:

[tex]A=283.528736986[/tex]

Step-by-step explanation:

The formula for the area of a circle is:

[tex]A=\pi \times r^2[/tex]

Remember that the radius is half the diameter, we are given the diameter which is 19, which means we need to find the radius:

[tex]d=19[/tex]
[tex]19\times\frac{1}{2} =9.5[/tex]
[tex]r=9.5[/tex]

Substitute and solve:

[tex]A=\pi \times9.5^2[/tex]
[tex]9.5^2=9.5\times9.5=90.25[/tex]
[tex]\pi \times90.25=283.528736986[/tex]
[tex]A=283.528736986[/tex]

Since the question doesn't say to round the area is "283.528736986."

Hope this helps.

The explicit rule for the sequence -2, 5, 12, 19 is

-2 + (n - 1) 7.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

-2, 5, 12, 19

This is an arithmetic sequence.

The first term.

a = -2.

The common difference.

d = 5 - (-2) = 7

= 12 - 5 = 7

= 19 - 12 = 7

Now,

The nth term of an arithmetic sequence.

= a + (n -1)d

= -2 + (n - 1)7

Thus,

The explicit rule is -2 + (n -1) 7.

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Answer:

54 is the correct answer

Isosceles Triangle has 50°, 65°, 65°

An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.

Properties of Isosceles Triangle:

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Answer:

Step-by-step explanation:

The four options just swap the order, and you should choose them all

In accordance with comparative comparative, the x-intercept of function g(x) = ㏒ (x + 4) is equal to x = - 4.

According to function theory, a function f(x) has an x-intercept when f(x) exists for x = 0. Besides, logarithms of 1 for any base is equal to zero, that is:

Logarithm of 1 at any base.

㏒ₐ 1 = 0

If ㏒ x = 0, then x = 1. And if ㏒ (x + 4) = 0, then x + 4 = 0, that is, x = - 4.

Then, by direct comparison between the two logarithmic expression, the logarithmic function g(x) = ㏒ (x + 4) has x = - 4 as its x-intercept.

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The likelihood event:

Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

The correct option is A.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Three softball players discussed their batting averages after a game.

Probability:

Player 1 = six tenths = 6/10

Player 2 = five ninths = 5/9

Player 3 = four sevenths = 4/7

To find better batting averages:

LCM of 10, 9 and 7.

10 = 2 x 5. 9 = 3 x 3, 7 = 7

So, the LCM (10, 9, 7) = 630

Now we have the number of chances are equal for each of the three players.

So, the P(Player 1) = 6/10 = 378/630

P(Player 2)= 5/9 = 350/630

P(Player 3)= 4/7 = 360/630

The Player 1 has better batting average than Player 2 and Player 3.

Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6 8 = 20x x = 8/20, simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The value of x of point C is 4. The coordinate of C is (4,-1).

What is the coordinate of a point?

The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.

The distance between points A and B is 4 units.

The opposite sides of a parallelogram are equal and parallel.

To make parallelogram, the point C lies on the left side of point D.

The distance between point C and D must be 4 unit.

The coordinates of C is (4,-1).

The x value of point C is 4.

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1) The best approximation for the area of this figure is 21+14. 5π units².

2) The total area of the closed figure is 10.5 + 19.63 = 30.13 square units.

3) This is a hexagon with vertices at the specified coordinates on a coordinate plane.

1) The best approximation for the area of this figure is 21 + 14.5π units². The area of a semicircle with a radius of 7 is 14.5π units², and the two segments form a rectangle with an area of 21 units². Adding these two values together gives 21 + 14.5π units².

2) This closed figure can be divided into two parts: a triangle and a quarter of a circle. The area of the triangle can be found using the formula for the area of a triangle (base times height divided by 2). The base of the triangle is the length of the segment from negative 5 comma negative 2 to negative 5 comma 1, which is 3 units. The height of the triangle is the length of the segment from negative 5 comma negative 2 to 2 comma 1, which is 7 units. So the area of the triangle is (3*7)/2 = 10.5 square units.

The area of the quarter of a circle can be found using the formula for the area of a circle (pi times the radius squared). The radius of the semicircle is the length of the segment from 2 comma 1 to negative 5 comma negative 2, which is 5 units. So the area of the quarter of the circle is (pi*5²)/4 = 19.63 square units.

So the total area of the closed figure is 10.5 + 19.63 = 30.13 square units.

3) A hexagon is a polygon with six sides and six angles. In this case, the hexagon is placed on a coordinate plane, with each of its vertices (or corners) located at specific x and y coordinates.

The coordinates provided are: (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2). These coordinates correspond to six points on the plane, and the hexagon is formed by connecting these points in the specified order.

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To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.

To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.

The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.

For example reduce the ratio 225: 125: 25

The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.

If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.

Now divide each number by 5 and see what we get.

225/5: 125/5: 25/5

45: 25: 5

When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.

Now divide each number by 5 again and get a final ratio of 9: 5: 5.

45/5: 25/5: 5/5

9: 5: 1

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Yes, angle 1 is vertically opposite to angle 4 because they are formed due to the intersection of straight lines.

When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.

For example, if two lines intersect and make an angle, say X=55°, then its opposite angle is also equal to 55°. And the adjacent angle to angle X will be equal to 180 – 55 = 125°

In the given figure, ∠AOC and ∠BOD form a pair of vertically opposite angles and similarly ∠AOD and ∠BOC form such a pair. Therefore,

∠AOC = ∠BOD

∠AOD = ∠BOC

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The test score representing the 3rd decile is 67. So the option a is correct.

In the given question, an achievement exam was given to a population of 1,000 students.

However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.

TEST SCORE      42        57        67        72        77        87        97

z score              -1.50     -0.75    -0.25     0        0.25     0.75     1.25

percentile rank  10         25        30       45        50       75        95

Using the table information, we have to find the test score representing the 3rd decile.

As we know that the 3rd decile is equal to the 30th percentile.

So that the 3rd decile have the percentile rank = 30

The test score equivalent to percentile rank 30 is 67.

So, the test score representing the 3rd decile is 67. So the option a is correct.

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Log () helps to determine the single number to be multiplied.

Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.

Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.

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Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.

Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

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The Sutton family's condo's worth in 8 years will be $216000.

An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.

Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.

We can write the function to calculate the worth after {T} years as follows.

A{T, R} = A{i} {1 + RT}

A{T, R} = {120000} {1 + (10/100) x 8}

A{T, R} = {120000} {1 + 0.1 x 8}

A{T, R} = {120000} {1 + 0.8}

A{T, R} = {120000 x 1.8}

A{T, R} = 216000

Therefore, the Sutton family's condo's worth in 8 years will be $216000.

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The total amount of money that Marco has that week would be = $ d + 14.55.

An allowance income is defined as the amount of money an individual earns that can be used to solve their personal needs.

Marco received double payment, an allowance from the mother and from newspaper route.

The total amount of money received from his mother for allowance for that same week = $ d

The amount of money he earned from his newspaper = $14.55

Therefore the total amount of money Marco has that week =$ d + 14.55

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Complete question:

Marco's mom gave him d dollars for his allowance one week. He also earned \$14.55$14.55dollar sign, 14, point, 55 for his newspaper route that week.

How much money does Marco have?

Write your answer as an expression.

Step-by-step explanation:

since the height from M (line MB) to the baseline is splitting the baseline into 2 identical halves, the triangle must be an isoceles triangle (both legs are identical long).

and therefore,

5x - 5 = 3x + 1

2x - 5 = 1

2x = 6

x = 6/2 = 3

Answer:

Step-by-step explanation:

The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:

2l + 2b = 84

Where l is the length of the rectangle and b is the breadth.

We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:

l = b + 6

Substituting the second equation into the first equation, we get:

2(b + 6) + 2b = 84

Expanding the left side of the equation gives:

2b + 12 + 2b = 84

Combining as terms gives:

4b + 12 = 84

Subtracting 12 from both sides gives:

4b = 72

Dividing both sides by 4 gives:

b = 18

Substituting this value back into the equation l = b + 6 gives us:

l = 18 + 6

l = 24

Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.

Based on the provided information, the APR is 71.4%.

Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by

APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100

The finance terms in the given case is $29.99 per week for 73week. Hence,

Total amount paid = 29.99*73 = $2,189.27

Loan principal = $1,095

Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27

Fees = 0 (as it not mentioned in the question)

Number of days in loan terms = 73*7 = 511 days

Substituting the values in the formula,

APR = ((1094.27/1095)/511) * 365 * 100

APR = 71.4%

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Answer:

x=6

Step-by-step explanation:

then x=6 because replacing x 6+3=9

Answer:

59

Step-by-step explanation: