In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0,-1) and T(4,6). Write an equation of the line that contains diagonal AH. [Use of the set of axes below is optional.] Using the given information, explain how you know that your line contains diagonal AH.

Answer: (a) -6x²y

Step-by-step explanation:

[tex]\frac{-18x^{3}y^{2} }{3x^{2} y}[/tex]
X to the power of 2 should be cancelled from the top and bottom, which leads to:
[tex]\frac{-18xy^{2} }{3y}[/tex]
Then Y to the power of 1 should be cancelled from top and bottom (since it can go into both), which leads to:

[tex]\frac{-18xy}{3}[/tex]
Then find the highest common factor (which is 3), and cancel it out from the top and bottom, which leads to:
[tex]\frac{-6xy}{1}[/tex]
which equals to
-6x²y (a)

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

here, we have,

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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Answer:

100π - 192 or 122.159....

Step-by-step explanation:

In order to find the diameter we much first split the rectangle diagonally and find the hypotenuse using Pythagorean theorem.

a^2 + b^2 = c^2

16^2 + 12^2 = c^2

400 = c^2

c = 20

If the diameter of the rectangle is 20, the radius is just half of that which is 10. Then you just need to a do a basic calculation for area of a circle and then subtract out the area of the rectangle.

Area of circle = πr^2 = π(10^2) = 100π (keeping it in exact value since π is infinite)

Area of rectangle = lw = (16)(12) = 192

Area of shaded area = 100π - 192 (exact) = 122.159 (estimate)

Answer:

  3 : 4

Step-by-step explanation:

You want to know the ratio of areas of a rectangle and square such that the rectangle is 50% longer and 50% narrower than the square.

A square that is 2 units on a side will be transformed to a rectangle that is 1.5×2 = 3 units long, and 0.5×2 = 1 unit wide.

The rectangle area is 3×1 = 3. The square area is 2×2 = 4.

The ratio of areas is ...

  rectangle area : square area = 3 : 4

All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.

The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.

An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.

A line segment serves as the foundation for the following angles and lines in geometry:

The process of creating a line perpendicular to a point on a line.

The creation of a 45-degree angle (45°).

The creation of a 30-degree (30-degree) angle.

Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.

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Answer:

Step-by-step explanation:

In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:

The length of one pair of opposite sides is equal.

The two pairs of opposite sides are parallel.

To show these two conditions, you may need additional segments or points such as:

Perpendicular lines or segments to the sides to help show the sides are parallel.

Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.

By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.

Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.

In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:

x₁ + x₂ = b

x₁ · x₂ = c

Whose solution can be found by numerical methods.

Now we proceed to determine the values for each cases:

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Step-by-step explanation:

Since the original volume is 29 and they are looking for 1/7th of that, we can multiply these two numbers

[tex](29)( \frac{1}{7} ) = 4 \frac{1}{7} psi[/tex]

Answer:

x=2

y=0

Step-by-step explanation:

2x=4

x=4/2

x=2

again,

y-1 =2y -1

1-1 =2y -y

0=y

Answer:

the answer is 24 sides

explanation

The solution is, the value is, x = 49.6.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

There is a pair of vertical angles where ∠1=106° and ∠2=3x−75

so, 1 + 2 = 180

or, 106 + 3x - 75 = 180

or, 3x = 149

or, x = 49.6

Hence, The solution is, the value is, x = 49.6.

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The two sequences have the same number (4) in the same position (third)

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

Using the above as a guide, we have

Sequence 1: 16, 8, 4, 2, 1.....

Sequence 2: 1, 2, 4, 8, 16.....

The number 4 is in the same position for the two sequences

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Step-by-step explanation:

Hope it helps :) #CarryOnLearning

The product of a, b, and c is 27/8.

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.

The given expression is

                                      [tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]

To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:

Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]

Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]

Putting the simplified numerator and denominator together, we have:

[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]

Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:

a * b * c = 3 * (-3/4) * (-3/2) = 27/8.

Hence, the product of a, b, and c is 27/8.

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The level of confidence Evelyn used is 92%. Therefore, option B is the correct answer.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

Given that, one sample z interval for proportions and gets a margin of error of 0.0758.

If her sample proportion was 0.75 and her sample size was 100.

We know that, p±z×√p(1-p)/n

Where, P is sample proportion, n is the sample size and z is the standardized normal distribution

Here, 0.75±0.0758×√0.75(1-0.75)/100

= 0.75±0.0758×√0.1875/100

= 0.92

=92%

Therefore, option B is the correct answer.

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To convert 31,750 feet to miles, divide the number of feet by the number of feet per mile:

31,750 feet / 5,280 feet/mile = 6 miles

The base-nine system of 76 base 10 is 84

We will divide 76 by 9 and write down the remainder

9 | 76 R

9 | 8 | 4

9 |8 | 8

The remainder is then written from the bottom value giving us 84

Consequently, base 10 numbers can be converted to base 9 by dividing by 9 and writing the remainder in the reverse order of bottom to top.

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The total value of $6800 compounded quarterly at 6% for 3 years is $8,123

From the question, we have

A = final amount

P = principal amount (initial investment) = $6800

r = annual interest rate = 0.06 ie. 6%

n = number of times interest is compounded per year = 4

t = time (in years) = 3

The total value is calculated as:

A = P(1 + r/n)^(nt)

substitute the known values in the above equation, so, we have the following representation

A = 6800(1 + 0.06/4)^(4*3)

Evaluate

A = 8130.2

Hence,, the value is $8130.2

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Answer:

The original number is 86.

Step-by-step explanation:

The only two-digit numbers whose digits sum to 14 are:

If we reverse and double the original number:

If we add the result of reversing and doubling the original number to the original number:

As the sum of adding the result of reversing and doubling the original number to the original number is 222, the original number must be 86.

Answer:

When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.

You want to subtract 9 and 24 to get the x value:

24 - 9 = 15

x = 15

Step-by-step explanation:

Hope it helps! =D

Hi there, here's your answer:

Given a right angled triangle

With the hypotenuse as 24 units and one of the legs as 9 units
To find:

The 3rd side denoted as 'x'

Solution:

We use Pythagoras Theorem:

[tex]a^2 + b^2 = c^2[/tex]

Where a and b are the legs and c is the hypotenuse.

We know the value of c and b

And a = x
Thus,

[tex]x^2 = c^2 - b^2[/tex]

[tex]x^2 = 576 - 81\\[/tex]

[tex]== > x^2 = 495\\[/tex]

Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units

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Correct me if im wrong :)

The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.

Relative frequency is found by dividing the frequency with the total number of values.

Cumulative frequency is calculated by adding the previous frequencies together.

(a) From the table,

Total number of people = 210

So, Total frequency = 210

Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40

Relative frequency = Frequency / Total frequency

Relative frequency of number of siblings as 2 = 0.1952

Cumulative frequency of number of siblings as 3 = 127 + 43 = 170

(b) Percent of people having exactly 1 sibling = (43 / 210) × 100

                                                                           = 20.48%

Hence the percent of people having exactly 1 sibling is 20.48%.

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rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.

Let's say that the Persian rug is rectangular, with length "l" and width "w".

The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:

Perimeter = 2l + 2w

Given that the distance around it is 22 feet, we can write:

2l + 2w = 22

When we simplify this equation, we obtain:

l + w = 11

A rectangle's area is determined by the product of its length and breadth, which may be written as follows:

l x w = area

Given that the space is 10 square feet, we can write:

l x w = 10

Two equations with two variables are now available:

L+W = 11, and L x W = 10.

To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:

w = 11 - l

Using this expression as w's replacement in the second equation, we obtain:

l x (11 - l) = 10

The result of expanding and rearrangement is a quadratic equation:

l² - 11l + 10 = 0

Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:

(l - 10)(l - 1) = 0

so either l = 10 or l = 1 is true.

w = 1 if l = 10, otherwise. w equals 10 if l = 1.

As w is always smaller than l, we have

The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.

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Answer:

P=10x^2+38y

Step-by-step explanation:

its the answer

Answer:

5

_ y - 7

3

the five is floating for some reason its supposed to be under the line

The slope of a line parallel to another line will have the same slope as the original line. To find the slope of the line 25x - 5y = -10, we need to rearrange the equation into the slope-intercept form y = mx + b, where m is the slope.

First, we'll isolate y:

25x - 5y = -10

5y = 25x + 10

y = (25/5)x + 2

So the slope of the line 25x - 5y = -10 is m = 25/5 = 5.

Therefore, a line parallel to 25x - 5y = -10 will have a slope of m = 5.

The given amounts of money will be written as £5.37, £2.04 and £15.70 respectively. The solution has been obtained by using denominations of money.

What is denomination?

The term "denomination" refers to the units of measure that are used to categorize various financial products such as coins and paper money. Every country has different denomination.

We are given three different amounts of money in words which are to be written in denominations.

So,

a. Five pounds and thirty seven pence = £5.37

b. Two pounds and four pence = £2.04

c. Fifteen pounds and seventy pence = £15.70

Hence, the amounts in their denominations have been obtained.

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There are 47 polar bears and penguins in the water.

The number of snowballs made altogether is 130 snowballs.

The number of snow globes your mother has left is 47 snow globes.

The number of penguins left playing is 97 penguins.

Number of polar bears= 24

Number of penguins = 38

No. of polar bears that got out of the water= 15

Total polar bears and penguins in the water = (24 + 38) - 15

= 47

Number of snowballs made by your brother = 46

Number of snowballs made by you = 59

Number of snowballs made by your sister, brother and you = 25

Total snowballs made= 46 + 59 + 25

= 130 snowballs

Number of snow globes mother has = 51

Number of additional snow globes received = 8

Number of snow globes broken = 12

The number of snow globes your mother has left= (51 + 8) - 12

= 59 - 12

= 47 snow globes

Number of adult penguins(mother and father) = 83

Number of baby penguins = 69

Number of mother penguins that went home = 55

Number of penguins left playing = (83 + 69) - 55

= 97 penguins.

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I think this is it

252-(193×n) =131