a equation of a line that passes through point. (-3, 1) and point (4, 8).

The prove is as follows

Statement             Reason

line BC || line DA  Definition of parallelogram

Draw line AC        Unique line postulate

AC = CA                Reflexive property (common sides)

∠BAC = ∠DCA      Alternate interior angles

∠BCA = ∠DAC      Alternate interior angles

Δ ABC ≅ Δ CDA   ASA triangle postulate

AB ≅ CD               CPCTC theorem

BC ≅ DA               CPCTC theorem

The ASA (Angle-Side-Angle) postulate is a statement about the relationship between the angles and sides of triangles. It states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. In other words, if two triangles have the same shape and size, then they are congruent.

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." This theorem states that if two triangles are congruent, then all their corresponding parts are congruent. In other words, if two triangles have the same shape and size, then all their angles and sides are congruent.

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Answer:

[tex]\dfrac{9}{12} - \dfrac{11}{18} = \dfrac{5}{36}[/tex]

Step-by-step explanation:

We can solve this subtraction of fractions by converting both fractions to forms where they have a common denominator.

To do this, we first have to find the least common multiple (LCM) of their denominators.

    1. Write out the denominators' prime factorizations.

    12           18

    2, 2, 3     2, 3, 3

    2. Multiply the greatest multiple of each prime number.

    2² × 3² = 4 × 9 = 36

So, the LCM of the denominators is 36.

Next, we need to get both fractions' denominators to 36 by multiplying each one by {36 divided by them} over {36 divided by them}.

Remember, this is just multiplying by 1.

[tex]\left(\dfrac{9}{12} \times \dfrac{36/12}{36/12}\right) - \left(\dfrac{11}{18} \times \dfrac{36/18}{36/18}\right)[/tex]

↓ simplifying the fractions being multiplied

[tex]\left(\dfrac{9}{12} \times \dfrac{3}{3}\right) - \left(\dfrac{11}{18} \times \dfrac{2}{2}\right)[/tex]

↓ executing the multiplication

[tex]\dfrac{27}{36} - \dfrac{22}{36}[/tex]

Finally, we can subtract the fractions' numerators.

[tex]\dfrac{27}{36} - \dfrac{22}{36} = \boxed{\dfrac{5}{36}}[/tex]

The weight gained by the spot dog during his time is 57/2 ounces.

An operation is a function in mathematics that converts zero or more input values, also known as "operands" or "arguments," into a clearly defined output value. The operation's complexity is determined by its operand count.

The most frequently studied operations are unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication. The nullary operation, also known as an operation of arity zero, is a constant. A ternary operation, also known as an operation of arity 3, is an example of the mixed product.

Given that, spot the Dog gained 4 3/4 ounces each week for the first 6 weeks of his life.

Convert the mixed fraction into improper fraction:

4 3/4 = 19/4 ounces

The weight gained for 6 weeks is:

19/4 (6) = 114/4 = 57/2

Hence, the weight gained by the spot dog during his time is 57/2 ounces.

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Answer:

688cm^2

Step-by-step explanation:

5*16= 80

16*12= 192

6*12= 72

80+80+192+192+72+72= 688cm^2

Answer:

The exponential growth function for the population can be written as:

P(t) = P0 * e^(rt)

Where:

P0 = initial population = 8,000

r = annual growth rate = 4.3% = 0.043

To find the monthly rate, we need to divide the annual rate by 12 (since there are 12 months in a year):

r_monthly = r/12 = 0.043/12 = 0.00358

So the exponential growth function with monthly growth rate becomes:

P(t) = 8000 * e^(0.00358t)

To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):

r_quarterly = r/4 = 0.043/4 = 0.01075

So the exponential growth function with quarterly growth rate becomes:

P(t) = 8000 * e^(0.01075t)

The given numerical value  is a Statistic.

Parameters are numeric values ​​that characterize the population as a whole. A statistic is a number that describes the characteristics of a sample.

For example, median income in the United States is a demographic parameter. Conversely, the median income for the US sample is a sample statistic. Both values ​​represent median income, but one is a parameter to the statistic. Easy to remember parameters and stats! Both are summary values ​​that describe the group, and have a convenient mnemonic device to remind you which group is being described. Notice their initials.

Parameter = Population

Statistics = Sample

A population is the entire group of people, things, animals, trades, etc. that are being studied. A sample is part of a population.

Following the election, 18 % of the governors of all 50 areas of a country were female.

Given that, 18% of the 50areas of a country  were females.

Now,

18*50/100 = 9

Since it is  a perfect number

The given numerical value  is a statistic.

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To answer this correctly, you could provide me with more information or details, I would be happy to try and help you approximate the height of the sculpture.

What is DNA?

DNA (Deoxyribonucleic acid) is a patch that contains the inheritable instructions used in the development and functioning of all living organisms. It's a long, double-stranded, spiral structure made up of four different structure blocks called nucleotides, which are represented by the letters A, T, C, and G. The specific sequence of these nucleotides along the length of the DNA patch determines the inheritable law of an individual organism and is responsible for its unique characteristics and traits. DNA is located in the nexus of cells and is organized into structures called chromosomes. It's essential for the replication of cells and the transmission of inheritable information from one generation to the coming.

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Using the metric system, a Deka is 10 of a unit. In the metric system, the prefix "deka" (also written as "deca") represents 10 of a unit. So, the correct option is C.

The metric system is an internationally recognized system of measurement that is used in many countries around the world. It is also known as the International System of Units (SI), and it is based on a decimal system, meaning that units are related to each other by powers of 10.

The metric system has a set of base units that are used to measure different types of quantities. The base units are:

Meter (m): used to measure length or distance

Kilogram (kg): used to measure mass or weight

Second (s): used to measure time

Each base unit has a set of prefixes that can be used to create larger or smaller units. These prefixes are based on powers of 10, and they are added to the base unit to indicate the size of the unit. Here are the most common prefixes and their meanings:

Kilo- (k): 1000 times the base unit (e.g., 1 kilogram = 1000 grams)

Hecto- (h): 100 times the base unit (e.g., 1 hectometer = 100 meters)

Deka- (da): 10 times the base unit (e.g., 1 dekagram = 10 grams)

Using these prefixes, you can create units that are appropriate for the quantity you are measuring.

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Answer:

x = 15.25

y = 71/6

Step-by-step explanation:

10x -9y = 46

-2x + 3y = 5

Time the second equation by 5

10x - 9y = 46

-10x + 15y = 25

6y = 71

y = 71/6

Now put 71/6 back in for y and solve for x

10x -9(71/6) = 46

10x -106.5 = 46

10x = 152.5

x = 15.25

Let's check

-2(15.25) +3(71/6) = 5

-30.5 + 35.5 = 5

5 = 5

So, x = 15.25 and y = 71/6 is the correct answer.

The area of the parallelogram is 27 square centimeters.

A region's size on a surface is determined by its area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area might be thought of as how much material of a certain thickness would be required to create a model of the shape, or as how much paint would be required to completely cover the surface in a single application.

The area of the parallelogram is given as:

A = (b)(h)

Here, the base is 4.5cm and the height is 6 cm.

Thus,

A = (4.5)(6)

A = 27 square centimeters.

Hence, the area of the parallelogram is 27 square centimeters.

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Answer:

41

Step-by-step explanation:

You got to first divide 45 by 32. Which is 1.40625 so 1.40625 - 1 = 0.40625 x 100 = 40.625. Round to the nearest whole percent ... 41

The congruent postulates for each triangle pair is given above.

Congruent triangles have both the same shape and the same size.

Given are the triangles as shown in the image.

We can write the congruent postulates for each pair of triangles as -

{ 1 } - AAS {Angle - Angle - Side}

{ 2 } - SSS {Side - Side - Side}

{ 3 } - SAS {Side - Angle - Side}

{ 4 } - SAS {Side - Angle - Side}

{ 5 } - SAS {Side - Angle - Side}

{ 6 } - SAS {Angle - Side - Angle}

Therefore, the congruent postulates for each triangle pair is given above.

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Answer:

B

Step-by-step explanation:

Bus A and B leave at 6:00 am (First bus of the day).

The schedule for Bus A and B are as follows:

Bus A: 6:00 am --> 7:15 am --> 8:30 am

Bus B: 6:00 am --> 6:15 am --> 6:30 am --> 6:45 am --> 7:00 am --> 7:15 am

As you can see, bus A and B leave the station together again at 7:15 am.

Hence, the answer is B.

Answer:

15 or more times

Step-by-step explanation:

30/2=15. It says that at least so 15 or more

SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit systems.

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The given question is incomplete, complete question is:

What is the SI prefix for each of the following multiples and submultiples of a unit?

[tex]10^-^9[/tex]

An independent variable is a variable that can be changed or manipulated in a scientific experiment.

Independent variables are variables in an experiment or research study that are independent of other variables, meaning they are unaffected by the other variables in the experiment. Independent variables are often manipulated by the researcher and are used to observe the effect on a dependent variable. Examples of independent variables include the type of treatment, the level of education, the amount of money offered, and the type of incentive.

It is used to determine the effect that the change has on the dependent variable, which is the variable being tested and measured in the experiment. By changing the independent variable, researchers can observe how the change affects the dependent variable. Examples of independent variables include the amount of light, temperature, time, type of material, and other factors that could influence the outcome of the experiment.

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Thus, In a rhythmic pattern where the whole note is equal to 4 beats, a dotted whole note (o) receives 6 beats.

A dot to the right of a note lengthens it by half of its original value in music notation.

A whole note that has a dot to the right of it is referred to as a dotted whole note. Whole notes typically receive 4 beats.

The note's overall duration is 4 + 2 = 6 beats after the dot adds the note's original duration by half.

Hence, 06 is the right response since a dotted whole note in a time signature where a whole note is equal to 4 beats receives 6 beats.

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Answer:

Step-by-step explanation:

this is so confusing

The interquartile range is 10 (first option)

The interquartile range is the difference between the third quartile and the first quartile of a dataset. It is a measure of variation. The third quartile represents 75% of the dataset. While the first quartile represents 25% of the dataset.  

Interquartile range = third quartile - first quartile

14 - 4 = 10

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The shapes that describes the polygon are;

Parallelogram

Rectangle

Square

Quadrilateral

The figure has the properties of different shapes;

a. A square

The four sides of a square are equal and congruent

b. A parallelogram

Opposite angles of a parallelogram are congruent

c. A quadrilateral

d. A rectangle

Opposite angles are equal and congruent

Hence, the shape can be described as a square, parallelogram, quadrilateral and rectangle.

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The total mass of the 135 boxes that the woman bought is 2358.7 kg

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Each bottle of water has a mass of 728g. A box of mineral water contains 24 bottles from a given factory, hence:

Mass of each box = 24 bottles * 728 g per bottle = 17472 g

The woman bought 135 boxes, therefore:

Total mass of boxes =  135 boxes * 17472 g per box = 2358720 g

But 1 kg = 1000 g

2358720 g = 2358720 g * 1 kg per 1000 g = 2358.7 kg

The total mass is 2358.7 kg

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Answer:

43°

Step-by-step explanation:

Because it is a parallelogram, there is 2 pairs of parallel lines, therefore, opposite angles are equal.

Using an online finance calculator, the annual percentage rate (APR) of an $800 installment loan with a finance charge of $40.72 for 36 monthly payments is 1.656%.

The annual percentage rate (APR) is the cost of borrowing, including the interest and other fees, expressed as a percentage of the debt.

The APR is always computed as an annual rate to show the cost of borrowing or finance charge over a year.

N (# of periods) = 36 months

PV (Present Value) = $800

PMT (Periodic Payment) = $0

FV (Future Value) = $-840.72

I/Y = 1.656% if interest compounds 12 times per year (APR)

I/Y = 1.669% if interest compounds once per year (APY)

I/period = 0.138% interest per period

Total Interest = $40.72

Thus, for Betty Arca's installment loan of $800, the APR is 1.656%.

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The equation of the ellipsoid is[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]

The equation of an ellipsoid is represented as:

[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]

Given that the ellipsoid passes through the points (±6,0,0),(0,±7,0) and (0,0,±5)

It means that:

(±a,0,0)  = (±6,0,0)

(0,±b,0) = (0,±7,0)

(0,0,±c) = (0,0,±5)

By comparison, we have:

±a=±5

±b=±6

±c=±7

So, the equation of the ellipsoid becomes:

[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]

By substituting the values, the equation of the ellipsoid becomes is

[tex]\frac{x^{2} }{36}+\frac{y^{2} }{49} +\frac{z^{2} }{25} =1[/tex]

.An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. In an ellipse, there are two radius measures, one horizontally along the x-axis, the other vertically along the y-axis.For  a circle both these have the same value.

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The moment of inertia (I) is a measure of an object's resistance to rotational motion around an axis. The moment of inertia of a cylinder can be calculated using the following formula:

I = (1/2) × m × r²

where:

I is the moment of inertia of the cylinder

m is the mass of the cylinder

r is the radius of the cylinder.

Here are the steps to calculate the moment of inertia for a cylinder:

Determine the mass of the cylinder. This can be done by weighing the cylinder on a scale or by using its density and volume. The formula for the mass of a cylinder is:

m = density × volume

Measure the radius of the cylinder. This is the distance from the center of the cylinder to its outer edge.

Substitute the values of m and r into the moment of inertia formula:

I = (1/2) × m × r²

Calculate the moment of inertia using a calculator.

Note that the moment of inertia of a hollow cylinder is different from that of a solid cylinder. To calculate the moment of inertia of a hollow cylinder, you need to subtract the moment of inertia of the hollow space from the moment of inertia of the solid cylinder using the parallel axis theorem.

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The ratio for year 10: year 11: and year 12 will be 1: 40: 36.

The utilization of two or more additional numbers that compares is known as the ratio.

The ratio of Year 10 to Year 11 is 1: 40. Then the ratio is given as,

y₁₁ / y₁₂ = 1/40

y₁₁ / 1 = y₁₂ / 40              ...1

The ratio of Year 11 to Year 12 is 10: 9. Then the ratio is given as,

y₁₂ / y₁₃ = 10 / 9

y₁₂ / y₁₃ = 40 / 36

y₁₂ / 40 = y₁₃ / 36         ...2

From equations 1 and 2, then we have

y₁₁ / 1 = y₁₂ / 40 = y₁₃ / 36

y₁₁: y₁₂: y₁₃ = 1: 40: 36

The ratio for year 10: year 11: and year 12 will be 1: 40: 36.

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The distance covered is. 90 miles

Speed is the distance an object travels in a given time.

This is represented as

Speed = Distance ÷ Time

We can also use the speed formula to calculate the distance or time by substituting the known values in the formula for speed and further evaluating,

Distance = Speed × Time or,

Time = Distance/Speed

To find the distance covered, we find the total speed

= 5 + 10(twice as fast on the trip back)

= 15

Distance = speed x time

= 15mph x 6hours

= 90miles

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The total surface area of the given cylinder is; MA sq. units

The curved surface of a cylinder is also known as its lateral surface. The area of this lateral surface is referred to as the lateral surface area of the cylinder.

Meanwhile, the formula for the total surface area of the cylinder is;

Total surface area = Lateral surface area + base area

We are given;

lateral surface area = M sq. units

Area of base = A sq. units.​

Thus;

Total surface area = M * A

Total surface area = MA sq. units

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As the consumption rate of 1997  estimated 2,000 billion barrels of oil last in 74.34 approx 75 year .

As here the rate of 1997 is not given which will be find in the below link which is 73.7000 millions barrels per day was the consumption of oil. here we have awalible the data of per days and we have to calculate for year so in year 1997 there was 365 days  so comsumption of oil yearly was .

1997 consumption = 73.700 million barrels per day

so for 1 year 73.700 million *365 =26,900.5 million barrels per day

her we find the rate of yearly so by this rate we will calculate the consumption of 2000 billion barrels of oil

2000 billion = 2,000,000 millions

here we are calculation this in million

so for 2,000,000 million will be

2,000,000 million /26,900.5 million =74.34 year

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Answer:

4.0007, 4.5, 4.7569, 4.9675, 47,005, 47.569, 47.965

Step-by-step explanation: