HELLLP!!!!!
two major cities each have a population of 25,000 people. the population of city A increases by about 260 people per year. the population of city B increases by about 1% every year.​

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

x = 54, so the vertical angles are 110°.

Step-by-step explanation:

\(2x + 2 = 3x - 52\)

\(2 = x - 52\)

\(x = 54\)

\(2(54) + 2 = 108 + 2 = 110\)

\(3(54) - 52 = 162 - 52 = 110\)

Answer:

option a: -120

Step-by-step explanation:

7in

this should be correct good luck!

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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The transformation function can be represented as vwxyz \($\rightarrow$\)qrstu = (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u).

This algebraic representation of the transformation of pentagon vwxyz into pentagon qrstu is using the notation of a function. A function takes an input (in this case, the coordinates of pentagon vwxyz) and produces an output (in this case, the coordinates of pentagon qrstu). This transformation can be represented by the notation (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u). This notation means that the coordinates (v,w,x,y,z) are being transformed into the coordinates (q,r,s,t,u). This notation is a concise way of expressing the transformation of pentagon vwxyz into pentagon qrstu. It is important to note that the transformation itself is not specified; the notation is simply used as a way of representing the transformation.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

10,200

Step-by-step explanation:

Answer:

10,200

Step-by-step explanation:

Use a calculator or a piece of paper.

I hope this helps, and have a great day!

Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

Answer:

5

Step-by-step explanation:

+2

By using the coordinates of the labeled point, the point-slope equation of the line include the following: D. y + 5 = -3(x - 3)

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:

0 5 2 -2

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

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 5)/(0 - 3)

Slope (m) = -9/3

Slope (m) = -3

At data point (3, -5) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 3(x - 3)  

y + 5 = -3(x - 3)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Measure of angle B is 29°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle ABC.

We have,

Length of AB = 33

Length of AC = 16

Measure of angle C = 93°

Using the sine law,

AB / sin C = AC / sin B

33 / sin 93° = 16 / sin B

Cross multiplying,

33 × sin B = 16 × sin 93°

sin B = (16 × sin 93°) / 33

sin B = 0.4842

B = sin⁻¹ (0.4842) = 0.505 radians = 28.95° ≈ 29°

Hence the angle B is 29°.

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Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

To determine how many games Jerrica would have to win in a row in order to have an 80% winning record, we need to calculate the number of games she needs to win out of a certain total.

Let's denote the number of games she needs to win in a row as x. If she wins x additional games, her total wins would be 20 + x, and her total games played would be 35 + x.

To have an 80% winning record, she would need to win 80% of the total games played. Mathematically, this can be expressed as:

(20 + x) / (35 + x) = 80 / 100

Cross-multiplying, we get:

100(20 + x) = 80(35 + x)

Expanding and simplifying:

2000 + 100x = 2800 + 80x

Subtracting 80x from both sides:

20x = 800

Dividing by 20:

x = 40

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

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The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Step-by-step explanation:

yx = k, where k is a real constant.

When y = 30, x = 3.

=> k = (30)(3) = 90.

Hence when y = 6, x = k/y = (90)/(6) = 15.

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

GF = 11

DF = 28

HF = 14

DG = 25.75

Step-by-step explanation:

GF: Both pairs of parallel lines are congruent, and all angles are 90°. With that said, since DE is 11, and it is parallel to GF, they are equivalent, so GF is 11.

DF: Since the quadrilateral is a rectangle, the intersecting lines are equivalent. This is because both pairs of parallel lines are congruent, and all angles are 90°. So, since GE is 28, and DF is congruent to GE, DF is 28.

HF: As with DF, both the intersecting lines are congruent, so that means the halves that they create are also congruent to one another. With that said, since GH is 14, that means HD, HE, and HF are all 14 as well.

DG: Since rectangle DEFG is a rectangle with a line diagonally crossing from one corner to another, this creates a right triangle with exactly half of the rectangle. The Pythagorean Theorem works to find an unknown side of a right triangle, so it can be used to find side DG. Since the formula is (a^2 + b^2 = c^2), with c being the hypotenuse (line DF), and a & b are the two sides (a can be side GF, and b is what is being solved for), the formula can be turned into this: (11^2 + b^2 = 28^2). This simplifies to (121 + b^2 = 784). Subtract 121 from both sides to get (b^2 = 663). Square root to get b. b is about 25.75 (rounding). This means, the other side of the triangle, or DG, is 25.75 units. Hope this helps! Have a great day! :)

Answer:

s - t = 3. s/3 + t/2 = 6

Step-by-step explanation:

Answer:

0.55 & 5.45

Step-by-step explanation:

EDGE VERIFIED

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

  (d)  22

Step-by-step explanation:

For numbers of days above 19, the fine is constant. The answer choice that is above 19 is 22. For 22 days overdue, the fine will be the same as for 21 days overdue: $10.

 22 could be the number of days

Answer:

D. 22

Step-by-step explanation:

Answer:

10. x ≈ 15,9

11. x ≈ 17,5

Step-by-step explanation:

10. Use the Pythagorean theorem:

\( {x}^{2} = {17}^{2} - {6}^{2} = 289 - 36 = 253\)

\(x > 0\)

\(x = \sqrt{253} ≈15.9\)

11.

\( {x}^{2} = {9}^{2} + {15}^{2} = 81 + 225 = 306\)

\(x > 0\)

\(x = \sqrt{306} ≈17.5\)

The expected value of the gas grill is 6.50 million dollars if a development cost of $4 million is invested.

The expected value is the sum of all possible outcomes multiplied by their associated probabilities.

The expected value of the gas grill can be calculated as follows:

Expected value = (0.10 × 3) + (0.50 × 6) + (0.40 × 8)

= 0.30 + 3.00 + 3.20

= 6.50 million dollars

Therefore, the expected value of the gas grill is 6.50 million dollar.

This calculation allows investors to decide whether or not to invest in a specific project, as the expected return must be greater than the development cost.

In this case, the expected value of 6.50 million dollars is greater than the development cost of 4 million dollars, making the investment a viable option.

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The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Step-by-step explanation:

try this option; all the details are in the attachment. Change the design according to local requirements.

Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.

It should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:

= ✓(0.35² + 0.65²)

= 0.76 miles.

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