the slope of FG is 4. point F is located at (2,3). which could be the coordinates of point G?

The framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

Explanation :

The statement that best explains that Article III of the constitution gives congress the ability to create lower courts inferior to the supreme court from "time to time" is that the framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.

As there will be more framers of the constitution which gave them as a  congress the power to create lower courts as they wanted that the congress should have authority over the courts and to control them.

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complete question:

Which statement best explains why Article lll of the constitution gives Congress the ability to create lower courts inferior to the Supreme Court “from time to time”?

The solution is,  the tangent of each angle that is not the right angle is:

angle tan A = 1.33

angle tan B = 0.75

Here, we have,

Given:

ABC is a right triangle.

angle ACB = 90

To find:

tan A

tan B

We know that tangent of an angle is given by the ratio

= opposite / adjacent

The opposite side and adjacent side is taken with respect to the angle for which the tangent is to be found.

tan A = BC/ AC

         = 8/6

         = 4/3

         = 1.33

and, tan B = AC/BC

                 = 6/8

                 =0.75

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The correlation coefficient for the data-set in this problem is given as follows:

r = 0.75.

To obtain the correlation coefficient of the data-set in this problem, we must insert the points of the data-set into a correlation coefficient calculator.

From the table, the points of the data-set are given as follows:

(0, 5.9), (0.8, 8.6), (1.3, 15.5), (1.6, 17.3), (13.3, 21.5).

Inserting these points into a calculator, the correlation coefficient is given as follows:

r = 0.75.

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The confidence interval of the given data is (117, 107).

Given that:

Sample mean X = 112

Standard deviation σ = 45

Sample size n = 81

Confidence level = 99.7%

Z Score = (x − μ )/σ

Z score = 0.9944

Confidence interval = X±z (σ/√n)

= 112±0.9944(45/√81)

= 112±0.9944(5)

= 112±4.972

= 112+4.972 or 112-4.972

= 116.972 or 107.028

= (117, 107)

Therefore, the confidence interval of the given data is (117, 107).

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The number of tins that Jane needs to buy is 8.

The area of a given figure is the space that the shape will cover when considered in a 2 dimensional plane. To determine the area of a figure, the type and parts of the figure are to be considered.

Given that the area of the garden fence = 46 m^2

Then, 1 liter of paint will cover 12 m^2. So that;

number of liters required = 46/ 12

                                          = 3.83

Since a tin contains half a liter of paint, then;

the number of tins that Jane needs = 2*3.83

                                                           = 7.66

Jane has to buy 8 tins to paint the garden fence.

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The graph of the inequality y ≥ (x+2)^2 is added as an attachment

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

y is greater than or equal to (x+2)^2

Express the statement properly

So, we have

y ≥ (x+2)^2

The above expression is a an inequality of a quadratic function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the expression in a graphing tool and attach the display

See attachment for the graph

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The angle measures of w and x are given as follows:

In this problem we have an isosceles triangle, meaning that two of the side lengths, along with two of the angle measures, are congruent.

The congruent side lengths are given as follows:

SR and RQ.

Hence the congruent angle measures are given as follows:

Hence angle w is given as follows:

w = 51º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle x is given as follows:

x + 2 x 51 = 180

x = 180 - 102

x = 78º.

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Answer:

Option A is the correct choice that shows a function.

Step-by-step explanation:

What is a function?

A function is when there are no repeating "x" values.

For example:

These set of points: {(1,1), (1,2), (1,3), (1,4)} does not  show a function because there is repeating "x" values.

Option A shows that the points {(4,5), (5,5), (6,1), (8,2) is a function because there is no repeating "x" values.

Answer:

526.32

Step-by-step explanation:

Let's assume that the cost price of the bag is "C".

Selling Price = Cost Price - Loss

We get:

500 = C - 0.05C

500 = 0.95C

C = 500/0.95

C ≈ 526.32

Therefore, the cost price of the bag was approximately Rs 526.32.

"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".

A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.

The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.

In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.

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A website is selling barbecue grills for $94, but mentions that they originally cost $200 the discount, as a percentage, is 53%.

The discount is the difference between the original price and the discounted price.

Discount = $200 - $94 = $106

To find the percentage discount, we need to calculate what percentage of the original price the discount represents:

Percentage discount = (Discount/Original price) x 100%

Percentage discount = ($106/$200) x 100%

Percentage discount = 53%

Therefore, the discount, as a percentage, is 53%.

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Answer:

60 (C)

Step-by-step explanation:

65+55=120

180-120=60

An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 6)/(-6 - 0)

Slope (m) = 0/-6

Slope (m) = 0.

At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = 0(x - 0)

y - 6 = 0

y = 6

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The value of x in the rectangle is,

⇒ x = 6

We have to given that;

Corresponding angles are,

⇒ (8x + 19)° and (21x - 13)°

Hence, We can say that;

⇒ (8x + 19)° + (21x - 13)° = 180°

⇒ 29x + 6 = 180

⇒ 29x = 174

⇒ x = 174/29

⇒ x = 6

Thus, The value of x in the rectangle is,

⇒ x = 6

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Answer:

180 square inches

5 x 6 = 32.5

32.5 x 4 = 130

5 x 5 = 25

25 x 2 = 50

130 + 50 = 180

Step-by-step explanation:

first find the area of all the sides (length times width)

width = 5

length = 6.5

5 x 6.5 = 32.5

32.5 is the area for one side. there are 4 others identical to it

32.5 (one side) x 4 (the amount of sides identical) = 130

then you need to find the area for the bottom/top side

5 = length

5= width

5(L) x 5(W) = 25

25 is the area for the bottom. the top is identical to it

25(bottom side) x 2 (the amount of sides identical)

now add all of the sides up

130 + 50 = 180

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.

[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]

=1+4+25+16

=46

[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]

=1+1+1+100

=103

[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]

Therefore, [tex]A_2B_2=4738[/tex]

The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in  [tex]A_2[/tex]  [tex]B_2[/tex] , where   [tex]A_2[/tex]  is the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] , and  [tex]B_2[/tex]  is the product of  [tex]B_2[/tex]  and   [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of   [tex]A_2[/tex]  and  [tex]B_2[/tex] .

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Check the picture below.

Answer: [tex]\frac{8}{15}[/tex]

Step-by-step explanation: In total, Patty placed 45 slips of paper in a bag(10+9+8+7+6+5). Out of those 45 slips of paper, only 24 had even numbers on them(10+8+6), resulting in the fraction [tex]\frac{24}{45}[/tex]. If you divide both 24 and 45 by 3, the fraction can be simplified to [tex]\frac{8}{15}[/tex].

Answer:

Step-by-step explanation:

The equation given is:

120 + 1814x = 180 - 134x

We can simplify this equation by adding 134x to both sides:

120 + 1948x = 180

Next, we can subtract 120 from both sides:

1948x = 60

Finally, we can solve for x by dividing both sides by 1948:

x = 60/1948

Therefore, the solution is:

x = 0.0308 (rounded to four decimal places)

Answer:

To solve the equation, we need to first convert the mixed numbers to improper fractions:

120 + 18 1/4 x = 180 − 1 3/4 x

120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)

Multiplying both sides by 4 to eliminate the fractions, we get:

480 + 73x = 720 - 7x

Combining like terms, we get:

80x = 240

Dividing both sides by 80, we get:

x = 3

Therefore, the solution for x is 3.

If both Tony and Marcus work on the job and the cost of labor is $48.00 per hour then labor estimate for the job is $576.00.

Marcus: 1 slab / 9 hours = 1/9 slab per hour

Tony: 1 slab / 3 hours = 1/3 slab per hour

The total amount of work they can do in one hour is the sum of their individual rates:

Marcus and Tony: 1/9 + 1/3 = 4/9 slab per hour

So together, Marcus and Tony can lay 4/9 of a slab per hour.

time = work / rate

time = 1 / (4/9) = 2.25 hours

total labor cost = hours worked x cost per hour

The total number of hours worked is the sum of the hours worked by Marcus and Tony:

total hours worked = 9 hours + 3 hours = 12 hours

The cost per hour is $48.00, so the labor estimate for the job is:

total labor cost = 12 hours x $48.00/hour

= $576.00

Therefore, the labor estimate for the job is $576.00.

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Based on an equation, the minimum number of years it will take the population of North Dakota to equal the population of South Dakota given the current rates of growth is 15.3 years.

An equation describes the equality or equivalence of two or more mathematical expressions.

Equations use the equal symbol (=), while mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

The population of North Dakota in 2012 = 0.7 million

The yearly population growth rate = 0.028 million

The population of South Dakota in 2012 = 0.83 million

The annual population growth rate = 0.0195 million

Let the number of years for the populations to equal = x

0.7 + 0.028x = 0.83 + 0.0195x

0.0085x = 0.13

x = 15.3 years

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Janeesa needs to drive about 6.9 mph faster than the speed limit to make it on time.

What is the  speed limit

To find out how fast Janeesa needs to drive to make it on time, one can use the formula:

distance = rate x time

In this case, the distance is 247.5 miles, the time is 4 hours, and the rate is what we're trying to find. Rearranging the formula to solve for rate, we get:

rate = distance / time

Plugging in the values we know, we get:

rate = 247.5 / 4 = 61.875

To know how much faster Janeesa needs to drive, one has to subtract the speed limit from the required speed:

Speed Difference = Required Speed - Speed Limit

= 61.875 mph - 55 mph

 = 6.875 mph

Therefore, Janeesa needs to drive approximately 6.9 mph faster than the speed limit to make it on time.

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The balance on the loan at the end of month 4 is approximately $289,836.23.

We are given that;

Amount borrowed= $290,000

Time 25 years

Payment=  $1, 530.73

Now,

To calculate the balance on the loan at the end of month 4, we can use the following formula2:

Balance = (Loan amount - Debt payment) * (1 + Interest rate / 12) - Debt payment

Where:

Loan amount is the original amount borrowed ($290,000)

Debt payment is the amount of principal paid in each monthly payment ($564.06 for the first month and $565.94 for the second month)

Interest rate is the annual interest rate divided by 100 (0.04)

Plugging in the values, we get:

Balance = ($290,000 - $564.06) * (1 + 0.04 / 12) - $565.94 Balance = $289,435.94 * 1.003333 - $565.94 Balance = $290,402.17 - $565.94 Balance = $289,836.23

Therefore, by the interest the answer will be $289,836.23.

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The similarity statement is completed as below

Triangle MTA ~ triangle HTM ~ triangle HMA

A similarity statement is a statement in mathematics that expresses the affinity between two or more figures.

These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.

The similar triangles are

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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The simplified exponential expression for this problem is given as follows:

xy^7/z^(14).

The first step in simplifying the exponential expression is applying the power of power rule at the numerator, as follows:

(y² x z^-5)² = y^4z^(-10).

(for the power of power rule, we keep the bases and add the exponents).

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the exponents are given as follows:

The negative exponent means that the number appears in the denominator, hence the simplified expression is given as follows:

xy^7/z^(14).

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