Many years ago, the towns of Franklin and Chester agreed to begin posting their populations on signs just outside of their towns. They also agreed to update their signs once per year at the beginning of the year.
During year 111, Franklin's sign read "\text{Franklin: Population of } 20{,}000Franklin: Population of 20,000start text, F, r, a, n, k, l, i, n, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 20, comma, 000", while Chester's sign read "\text{Chester: Population of } 25{,}000Chester: Population of 25,000start text, C, h, e, s, t, e, r, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 25, comma, 000". Each year, the populations grew. Specifically, Franklin's population grew by 5\%5%5, percent each year, and Chester's population grew by 500500500 people each year.
What is the first year in which Franklin's sign shows a larger number than Chester's sign?

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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Answer:

multiplys 3 each time

Step-by-step explanation:

3 x 1. 3 x 3. 9 x 3

By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

what is inequality ?

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."

So, the inequality would be:

Temperature < 8 degrees Fahrenheit

Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

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Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is \(8\frac{2}{3}\)

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like \(2\frac{x}{y}\) is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : \(8\frac{2}{3}\)

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Answer:

A is the answer.

Step-by-step explanation:

Look at the graph of graph A. It has given the correct distance between 2 and -5.

Hoped this helped.

Answer:

B.

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

1/4 = 0.25

The smallest increment is 1/4 of an inch and the uncertainty is 0.125 inches.

The smallest increment is the smallest segment between two consecutive marks. Here, we can see that it corresponds to 1/4 of an inch.

Then the smallest increment in the ruler is 1/4 of an inch or 0.25 inches, and here the correct option is B.

The uncertainty is half of that, which is.

U = 0.25in/2

U = 0.125in

Then the correct options are.

A) B  1/4 Inch

B) B 0.125 inches.

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Answer:

 6x^2 -2x -6

Step-by-step explanation:

f(x) = 6x^2 -4

g(x) = 2x+2

f(x) - g(x) =  6x^2 -4 - (2x+2)

Distribute the minus sign

                   6x^2 -4 - 2x-2

Combine like terms

                  6x^2 -2x -6

Answer:

b

Step-by-step explanation:

6x^2

2x

-4+2=-2

Answer:

Option (A)

Step-by-step explanation:

Volume of a cylinder is given by the formula,

V = πr²h

Here r = radius of the cylinder

h = height of the cylinder

Therefore, volume of a cylinder given in the question,

V = π(\(\frac{18}{2}\))²(8)

  = 648π

  = 2035.8 km²

Volume of the given cylinder is 2035.8 km².

Option (A) will be the answer.

Answer:

X = 103

Step-by-step explanation:

if a circle is 360

half would be 180

the angle is 77

so 180 - 77 = 103

Answer:

x =  11

Step-by-step explanation:

Lines are parallel.   5x + 10 and 10x + 5 are supplements of each other.

Move  5x+ 10 to the corresponding position on the figure.  It will be next to 10x + 5 and form a linear pair with 10x + 5.  A linear pair form a straight angle or two supplementary angles.  Supplementary angles = 180°

Therefore  5x +10 + 10x + 5 = 180°

                   15x  + 15 = 180°

                      15x = 180 - 15

                         15x = 165

                           x =  11

The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.

Here we want to find the solution set of the inequality below:

x ≤ -4

First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so  we need to have a closed set at that end)

This is written as:

(-∞, -4]

The use of the symbols [ ] means that the element belongs to the set.

Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.

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Answer:

18

Step-by-step explanation:

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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The equation that represents the distance traveled by the second car is 60(t + 1.33).

Let t = travel time of the 2nd car when it overtakes the 1st

:

Find the travel time of the 1st car to go 80 mi; time = dist/speed

time = 80%2F60

time = 1.33 hrs for the 1st car to go 80 mi

therefore

(t+1.33) = travel time of the 1st car when it is overtaken

:

When the 2nd overtakes the 1st, they will have traveled the same distance

Write a distance equation, dist = speed * time

:

2nd car dist = 1st car dist

70t = 60(t+1.33)

70t = 60t + 80

70t - 60t = 80

10t = 80

t = 8 hrs travel time of the 2nd car to overtake the 1st

:

;

Confirm this by finding the actual distances, should be equal

70*8 = 560 mi

60*9.33 ~ 560 mi

Hence , the equation that represents the distance traveled by the second car is 60(t + 1.33).

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Answer:

The value that best approximates the radius of the circle is 13.43 inches.

The arc length of a circle is given by the formula L = rθ where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

Since we are given that the central angle measures 64° and that the arc intercepted by this central angle measures 15 inches, we can convert 64° to radians by multiplying it by π/180.

Therefore, θ = (64π)/180.

We can then solve for r using L = rθ and substituting L = 15 inches and θ = (64π)/180. This gives us r ≈ 13.43 inches.

Therefore, 13.43 in best approximates the radius of the circle.

1. 10 to the 3rd power will look like this: 10 x 10 x 10 (multiplying 10 three times)

10 x 10 x 10 is 1000.

Then you multiply 1000 by 5.24 like a regular problem, which will equal 5,240.

There are 3 zeroes so you shift the decimal 3 times.

2. 10 to the second power is 10 x 10. 10x10 is 100.

524,000 divided by 100 is 5240. It’s similar to LOSING two zeroes because you’re DIVIDING.

In the two expressions, the powers of 10 are used to express the numbers in a more compact and manageable form.

To convert \(5.24 * 10^3\) to standard form:

Multiply 5.24 by 1000 (since \(10^3\) = 1000).

5.24 x 1000 = 5240

Therefore, 5.24 x \(10^3\) = 5240

524,000 divided by\(10^2\) is also using the concept of powers of 10.

To convert 524,000 divided by \(10^2\) to standard form:\(10^2\)

Divide 524,000 by 100 (since  = 100).

524,000 ÷ 100 = 5,240

Therefore, 524,000 divided by\(10^2\) equals 5,240.

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Answer: x=14 y=10

Step-by-step explanation:

Answer:

Ahh I did this about a year ago but try math-way (without -) it gives the correct answers sorry I couldn't help more.

Answer:

WR ≈ 13.862

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

WR² + RT² = WT²

WR² + 12.1² = 18.4²

WR² + 146.41 = 338.56 ( subtract 146.41 from both sides )

WR² = 192.15 ( take the square root of both sides )

WR = \(\sqrt{192.15}\) ≈ 13.862 ( to the nearest thousandth )

Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

6 by 36 is the answer.....

Answer: -1 Is the answer.

Answer:

32.4 divided by 0.2 is 162

Step-by-step explanation:

Answer:

.2/32.4=

Step-by-step explanation:

you can do fraction form or long division

Fraction form: 2/10 * 10/324= 1/1620.0061

Decimal Form: 0.00617283950617284 or 0.0062

The value of the perimeter of the polygon is 36 units

The perimeter of a shape is defined as the sum of the length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Thus, the perimeter of the polygon will be:

perimeter of polygon ABCD = AD + AB + BC + CD

Given: D(0, 0), A(4, 12), B(9, 9) and C(12, 5), we will use this to calculate the distances  AD, AB, BC and CD.

We will also need the formula for calculating the distance between two points:

d=√((x2 – x1)² + (y2 – y1)²)

For AD:

D(0, 0) --> A(4, 12)      x1 = 0, y1 = 0, x2 = 4, y2 = 12

d=√((4 – 0)² + (12 – 0)²)  = √16+144 = √160

For AB:

A(4, 12) --> B(9, 9)       x1 = 4, y1 = 12, x2 = 9, y2 = 9

d=√((9 – 4)² + (9-12)²)  = √25+9 = √34

For BC:

B(9, 9) --> C(12, 5)      x1 = 9, y1 = 9, x2 = 12, y2 = 5,

d=√((12 – 9)² + (5-9)²)  = √9+16 = √25 = 5

For CD:

C(12, 5)  --> D(0,0)        x1 = 12, y1 = 5,  x2 = 0, y1 = 0

d=√((0 – 12)² + (0-5)²)  = √144+25 = √169 = 13

Thus, perimeter of polygon ABCD = √160 + √34 + 5 + 13 = 36.48 units

Therefore, the perimeter of polygon ABCD is 36 units. So option C is the correct answer.

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P=a*b

a=P/b

a=18/b

Pairs of the solution (only integer numbers):

b=9, a=2

b=2, a=9

b=6, a=3

b=3, a=6

b=18, a=1

b=1, a=18

So slope of the line m is 9

We know perpendicular lines have slopes negative reciprocal to each other and their product of slopes is -1

If slope of m is p/q then slope of perpendicular line is -q/p and vice versa

Answer:

\(-\dfrac{q}{p}\)

Step-by-step explanation:

Slope-intercept form of a Linear Equation:

\(y = mx + b\)

where:

If line m has a y-intercept of c and a slope of p/q, then:

\(\textsf{Equation of line m}: \quad y = \dfrac{p}{q}x + c\)

If two lines are perpendicular to each other, the product of their slopes will be -1.

Let a = slope of the line perpendicular to line m.

\(\implies a \times \dfrac{p}{q}=-1\)

\(\implies a=-\dfrac{q}{p}\)

Therefore, the slope of the a line that is perpendicular to line m is:

\(-\dfrac{q}{p}\)