Washington DC is the midpoint of Maine and South Carolina. If a town in SC is located at

(-2,-20) and a town in Maine is located at (18,42), what is the distance from the town in SC to Washington DC

The greatest common factor (GCF) of the three monomial, 21x³y⁵, 63x⁵y² and 45x¹y³ is 3xy²

The greatest common factor (GCF) of the three monomials, 21x³y5, 63x5y² and 45x¹y³ can be obtained as follow:

First, we shall determine the factors of each monomials. This is illustrated below:

21x³y⁵ = 3 × 7 × x × x × x × y × y × y × y × y

63x⁵y² = 3 × 3 × 7 × x × x × x × x × x × y × y

45x¹y³ = 3 × 3 × 5 × x × y × y × y

Finally, we shall determine the greatest common factor (GCF) from the factors listed above. This is shown below:

3 × x × y × y = 3xy²

Thus, we can conlude that the greatest common factor (GCF) of the three monomials is 3xy²

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Answer: 23.80

Step-by-step explanation:

[tex]\sqrt{19^2+18^2-2*19*18cos(80)}[/tex]

Answer:

Step-by-step explanation:

Amount in 4.6% acct= 15000*(1/3)= 5000

Amount in bonds = 1/4*15000= 3750

Amount in stock= 15000-(5000+3750)= 6250

Amount in each account at the end of three years

5000*(1.046)^3= 5722.22668

3750*(1.052)^3=4365.94728

6250*1.03*(1-.08)*1.06= 6277.85

total: 5722.22668+4365.94728+6277.85=16366.02396

gain= 16366.02396-15000=1366.02396

or (16366.02396/15000)-1= 9.1068264%

The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.

1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.

2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.

3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.

4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.

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After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1

In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a  polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2   0   -5.6   1
    |    -1    0.8  -0.5
    -------------------
          2   -1   -4.8  0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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with scaling factor = 1/2 ,

the coordinate location of the dilated posit C is ( 2,-3)

Answer:

The exact volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

[tex]\boxed{V = \pi r^2 h}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for V:

[tex]\begin{aligned} \implies V&=\sf \pi \cdot 3^2 \cdot 8\\&=\sf \pi \cdot 9 \cdot 8\\&=\sf 72\pi \;cm^3\\&= \sf 226.19\; cm^3\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the volume of the cylinder is 72π cubic centimeters, or approximately 226.19 cubic centimeters to two decimal places.

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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After considering all the given data we conclude that the the probability of rolling a number less than 7 is 1/2, under the condition that the set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12).

The evaluated probability of rolling a number less than 7 on a 12-sided die is the number of outcomes that are less than 7 divided by the total number of possible outcomes.

The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). There are 6 numbers less than 7 in this set (1,2,3,4,5,6) and 12 possible outcomes.

Hence , the probability of rolling a number less than 7 is:

6/12 = 1/2

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The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

Option D is the correct answer.

We have,

The expression:

2/5 - 15 + 8 - 1/5 + 3

Now,

To make the simplification easier,

We combine the fraction and like terms together.

So,

[2/5 + (-1/5)] + [8 + 3 + (-15)]

This can be seen as applying the properties of commutative and associative.

Thus,

The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].

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Answer:

  $15,200

Step-by-step explanation:

You want to know the amount deposited at 1.5% that will earn the same simple interest in a year as $12,000 deposited at 1.9%.

The interest amount is given by the formula ...

  I = Prt

For the two accounts, the interest and the time are the same, so we have ...

  P1·r1 = P2·r2

  12000·1.9% = P2·1.5% . . . . . . . . . . . equate interest amounts for t=1

  P2 = 1.9/1.5·12000 = 15200 . . . . . . divide by 1.5%

Ruth deposited $15,200.

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Based on the information and the image, we can infer that it does correspond to a polygon.

A polygon is a term used in geometry to refer to a closed plane figure made up of three or more line segments called sides. Polygons are classified according to the number of sides they have. For example:

Based on the above information, we can infer that the image corresponds to an irregular polygon with 20 sides.

Note: This question is incomplete. Here is the complete information:

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The value of the variable is equal to 0

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.

These algebraic expressions are also composed of arithmetic operations, such as;

From the information given, we have that;

4x+4=4x-4

To determine the value of x, take the steps;

collect the like terms, we have;

4x - 4x = -4 - 4

subtract the values, we have;

0 = -8

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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Answer:

Exact form: 2.5185185185185

Simplified form: 2.52

Fraction form: 63/25

Step-by-step explanation:

The measurement is closest to the value of d inches is 14. 28

It is important to note that the Pythagorean theorem is stated as;

The Pythagorean theorem states that the square of the longest leg or hypotenuse side of a triangle is equal to the sum of the squares of the other two sides.

This is represented as;

x²= y²+ z²

Now, substitute the values, we get;

x² = 11. 9² + 7.9²

Find the square values, we have;

x² = 141. 61 + 62. 41

add the values, we have;

x² = 204. 02

Now, find the square root of both sides, we get;

x = √204. 02

x = 14.28

Know that d = x = 14. 28

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Answer:

[tex]\left \{ {{R + L = 27} \atop {1.99*L+1.29*R=43.23}} \right.[/tex]

Step-by-step explanation:

The area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex]

To find the area of a regular decagon, we need to know either the side length or the apothem (the perpendicular distance from the center to a side). In this case, you have provided the radius of the decagon, which is 14 units.

For a regular decagon, the apothem (a) is related to the radius (r) by the formula:

[tex]a = r * cos(\pi/10)[/tex]

Let's calculate the apothem using the given radius:

[tex]a = 14 * cos(\pi/10) =12.149[/tex]

Now, we can calculate the area (A) of the regular decagon using the formula:

[tex]A = (5/2) * a^2 * tan(\pi/10)[/tex]

[tex]A = (5/2) * (12.149)^2 * tan(\pi/10) =195.7[/tex]

Rounding to the nearest tenth, the area of the regular decagon with a radius of 14 units is approximately [tex]195.7 unit^{2}[/tex].

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Median: 212

Mode: 212

The median and mode of the data set are 273 and 212 respectively.

The median is the value that splits the mathematical numbers or expressions in half. The median value is the middle number of data points. To find the median first arrange the data points in ascending order.

To find the median, we need to arrange the numbers in order from least to greatest:

3, 4, 5, 212, 212, 334, 414, 823

There are 8 numbers in total, so the median is the average of the two middle numbers, which are 212 and 334.

Median = (212 + 334)/2 = 273

To find the mode, we need to identify the number(s) that occur most frequently. In this case, 212 appears twice, so it is the mode.

Mode = 212

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The length of BC is determined as  6√31  by applying trigonometry ratio.

The length of BC is calculated by applying the following formulas for trig ratios.

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The hypothenuse side of the right triangle is given as 12√31 and the opposite side is length BC.

The length of BC is calculated as follows;

sin 30 = BC / 12√31

BC = 12√31 x sin (30)

BC = 12√31 x ¹/₂

BC = 6√31

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Answer:

31 years

Step-by-step explanation:

A = P(interest rate)^number of years (n)

if the money is to quadruple, A = 4 X 22,000 = 88,000.

P = investment amount = 22,000.

interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.

n is number of years.

22,000 (1.045)^n = 88, 000

divide both sides by 22, 000:

(1.045)^n = 4

take logs for both sides:

log (1.045)^n = log 4

simplify using log laws (by bringing down the n):

n log (1.045) = log 4

divide both sides by log (1.045):

n = (log 4) / log (1.045)

= 31.49 (31 years to nearest year)

The simplest form of the expression by the use of the distributive property is;

[tex]12x^2 + 24x + 9[/tex]

In mathematics, the distributive property, which explains how multiplication interacts with addition or subtraction, is a fundamental concept. By allocating or multiplying a number or term to each term enclosed by a set of parenthesis, it enables you to simplify expressions.

The distributive property is frequently employed in algebraic expressions, equation simplification, and polynomial operations. By spreading out the multiplication over addition or subtraction, it aids in simplifying complex statements and makes calculations easier to understand.

We know that;

[tex]3(4x^2 + 8x + 3)\\12x^2 + 24x + 9[/tex]

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Answer:

Capital expenditures are typically one-time large purchases of fixed assets that will be used for revenue generation over a longer period. Revenue expenditures are the ongoing operating expenses, which are short-term expenses used to run the daily business operations.

Answer:

The volume of the cylinder is 500 π cubic kilometers.

Step-by-step explanation:

Formula: V = πr²h

r = d/2

r = 20km/2

r = 10 km

h = 5km

Solve for the volume using the formula.

Substitute the given

V = π(10km)²(5km)

V = 500π km³

I hope this helps you

The total area of the composite figure is 17 square centimeters.

Remember that the area of a rectangle is equal to the product between its dimensions.

We can separate the figure into two rectangles, one of these rectangles is of 1cm by 2cm, then its area is:

A = 1cm*2cm = 2cm²

The other rectangle is of 3cm by 5cm, then its area is:

A' = 3cm*5cm = 15cm²

Adding that we get a total of:

total area = 2cm² + 15cm² = 17cm²

That is the area of the figure.

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The ball's height is 11 meters after approximately 6.83 seconds and 0.17 seconds.

The height of the ball after t seconds is given by the equation h = 1 + 30t - 5t^2. To find all values of t for which the ball's height is 11 meters, we need to solve the equation [tex]1 + 30t - 5t^2 = 11[/tex].

[tex]30t - 5t^2 - 10 = 0[/tex]

[tex]t^2 - 6t + 2 = 0\\\\t = (6 \pm \sqrt{6^2 - 4(1)(2)}) / 2\\\\\t = (6 \pm \sqrt{32}) / 2\\\\t = (6 \pm 4\sqrt2 / 2\\\\t = 3 \pm 2\sqrt2[/tex]

Therefore, the values of t for which the ball's height is 11 meters are approximately 6.83 seconds and 0.17 seconds.

Rounding to the nearest hundredth, we get:

t ≈ 6.83 or t ≈ 0.17

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The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm

Given data ,

A pendulum of length 18 cm is swinging from a fixed point

Now ,  it swings through an angle of 87°

So , Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

Now , D = ( θ/360 ) x 2πr

On simplifying , we get

D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )

D = ( 0.241667 ) ( 113.04 )

D = 27.3 cm

Hence , the pendulum travels a distance of 27.3 cm

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The relation is a function because (d) Yes because for each output there is exactly one input.

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

The graph

The graph can be represented as

x  g(x)

-5  1

-2  0

-1   -1

0  2

1  3

5   1

The above table of values is a function

This is so because each output values have different input values.

i.e. it would pass the vertical line test when represented on a graph

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The probability that a randomly selected point within the square falls in the red-shaded square is 0.11

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

The areas of the above shapes are

Red square = 1² = 1

White square = 3² = 9

The probability is then calculated as

P = Red square/White square

So, we have

P = 1/9

Evaluate

P = 0.11

Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11

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The piecewise rule for the pattern is given as follows:

A piece-wise function is a function that has different definitions, depending on the input of the function.

The pattern for this problem is given as follows:

1,6,9,1,6,9.

The period of the pattern is given as follows:

3 units.

The pattern of the function is constant, meaning that all the outputs for an input that is a multiple of 3 are of 1, if the remainder of the division is of 1 the output is of 6, and if the remainder of the division is of 2 the output is of 9.

Hence the pattern is defined as follows:

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