Consider points R, S, and T. Point S is in the middle. Point R is below and to the left of point S. Point T is below and to the right of point S. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points. Mark this and return

Children learning to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable is a true statement.

This involves the regularity or repeated way in which something is done or arranged.

Children are very inquisitive and tend to make logical connections when dealing with patterns due to their reasoning skills thereby aiding their learning process.

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The graph is shown in the attached image.

Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its  area is 469 square miles, the population density of Los Angeles is  8486 people per square miles.

Population density simply the measurement of population per unit area.

It is expressed as;

Population density = Number of people / Area

Given the data in question;

We substitute the given values into the above equation.

Population density = Number of people / Area

Population density = 3,979,576 people / 469 square miles

Population density = 8485.23667 ≈ 8486 people per square miles

Given that, the estimated population of Los Angeles in 2019 was 3,979,576 and its  area is 469 square miles, the population density of Los Angeles is  8486 people per square miles.

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Answer:

B. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6}

D. f(-1) = 6

Step-by-step explanation:

The question gives a table marking the different coordinate pairs for a function, where f(x) is y. The top row represents the x-values and the bottom row represents the y-values.

Domain

The domain of a function is the set of x-values that the graph covers. In this case, the x-values are all integers between -2 and 6. We can see this in the top row of the table. Answer choice B best represents this domain.

Solving for F(x)

F(x) represents a specific y-value, for example, f(-1) represents the y-value when x = -1. So, to test choice D, we need to find what y-value matches -1 on the table. The table shows that when x = -1, f(x) = 6. This means that answer choice D must be correct.

Answer:

slope = 11/2

Step-by-step explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7)                Point 2: (-6, -4)

x₁ = -4                              x₂ = -6

y₁ = 7                               y₂ = -4

y₁ - y₂ = m(x₁ - x₂)                               <----- Point-slope form

7 - (-4) = m(-4 - (-6))                            <----- Insert values

11 = m(2)                                             <----- Simplify

11/2 = m                                             <----- Divide both sides by 2

[tex]\huge\boxed{\frac{11}{2}}[/tex]

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values and simplify to find the answer.

[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]

[tex]\dfrac{-4-7}{-6+4}[/tex]

[tex]\dfrac{-11}{-2}[/tex]

[tex]\boxed{\frac{11}{2}}[/tex]

Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.

assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)

= $1.013809453125

the total increase is:
= (1.013809453125 - 1) / 1

= 1.38%

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Answer: Option (1)

Step-by-step explanation:

[tex]4x^4 -38x^3 -17x^2 -30x=0[/tex]

Dividing both sides by [tex]x-10[/tex] (10 is a root, so x-10 is a factor), yields

[tex]4x^3 +2x^2 +3x=0\\\\x(4x^2 +2x+3)=0\\\\x=0, 4x^2 +2x+3=0[/tex]

Solving the second case by the quadratic formula yields [tex]x=\frac{-1 \pm i\sqrt{11}}{4}[/tex].

So, the answer is Option (1).

Answer:  True

Explanation:  Parallel lines are two lines that lie on the same plane and they never intersect.  

The polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0

From the question, we are to divide the given polynomial P(x) by the divisor d(x)

From the given information,

P(x) = x³ + 8

d(x) = x + 2

The division operation is shown in the attachment below.

The quotient, Q(x) = x² -2x + 4

and the remainder, R(x) = 0

We area to express P(x) in the form

P(x) = d(x).Q(x) + R(x)

Thus, we get

x³ + 8 = (x+2)(x² -2x + 4) + 0

Hence, the polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0

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The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:

(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)

(h, k) = (4, 8)

And the radius is found by Pythagorean theorem:

[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]

d = 5

r = 0.5 · 5

r = 2.5

The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

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Answer:

12 ounces

Step-by-step explanation:

168 divided by 14 = 12

Given that the inequalities and that

x ⇒ pep club donations

y ⇒ represent donations raised by the honor society

The inequality is represented by x + y≥ 500

The solution for this is the shaded area above the solid line.

Given x ≥ 100, this is also indicated by the shaded region to the right

The point (300,100) indicates that the contributions made for the pep club were $300 and the donations raised by the honor society were $100.

The point (300,100) is NOT a feasible solution since it does not conform to the gray area of the system of inequalities solution.

To proof the above,

Let x = 300; and y = 100

Plugin in both values in the inequalities we have:

300 + 100 [tex]\ngeq[/tex] 500

400 [tex]\ngeq[/tex] 500 ; Hence it is NOT true; also

300 [tex]\ngeq[/tex] 500.

The point (500,200) indicates that the contributions raised for the pep club were $500 and the donations raised by the honor society were $200.

The point (500,200) IS A possible solution since it falls inside the darkened area of the system of inequalities solution.

To proof the above,

Let x = 500; and y = 200

Plugin in both values in the inequalities we have:

500 + 200 ≥ 500

700 ≥ 500; hence, this is true and it is safe to indicate that the ordered pair satisfies the inequality A.

Conclusion:
The point (500, 200) is a viable solution.

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Answer:

Step-by-step explanation:

The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.

Let w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.

  A = LW

  54 = (2w +3)(w)

Rewriting this equation to standard form gives ...

  2w² +3w -54 = 0

  (2w -9)(w +6) = 0 . . . . factored

  w = 9/2, -6 . . . . . . . . . values that make the equation true

Only the positive width makes sense in a geometry problem, so we have ...

  w = 9/2

  length = 2w +3 = 12

The length of the rectangle is 12 meters; its width is 4.5 meters.

Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.

Hope that helps...........................

The correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

In the question, we are given that a researcher uses a random number generator to simulate the results of an experiment and are asked for the appropriate assignment of random digits for its experimental design.

For the assignment to be correct, the probability of the random numbers must be equal to the probability of the experiment.

We analyze each option:

Thus, the correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

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Answer:

a = 64°

b = 138.7°

Step-by-step explanation:

First, Let's find the measure a,

______

Now,

______

Now that we found out what x equals, let's find 'b'-

The perimeter of the rectangle based on the factors given is 46.

The area of the rectangle is given as (x² + 13x - 90). This will be:

= (x² + 13x - 90)

= x² + 18x - 5x - 90

= x(x + 18) - 5(x + 18)

= (x - 5)(x + 18)

The sides of the rectangle are 5 and 18. The perimeter will be:

= 2(l + w)

= 2(5 + 18)

= 46

The area of the rectangle is given as (x² + 24x - 81.

= (x² + 24x - 81)

= x² + 27x - 3x - 81

= x(x + 27) - 3(x + 27)

= (x - 3)(x + 27)

The sides are 3 and 27. The perimeter will be:

= 2(l + w)

= 2(27 + 3)

= 60

= (x + 1)² + 3(x + 1) + 2

= (x + 1)(x + 1) + 3x + 3 + 2

= x² + x + x + 1 + 3x + 5

= x² + 5x + 6

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Answer:

1/2×base×height

1/2×8×8

32cm²

A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

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Answer:

14

Step-by-step explanation:

If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.

Answer:33

Step-by-step explanation: The expressions have equivalent values when x + 6

The expressions have equivalent values for any value of x.

When x=10 , both expressions have a value of 33.

A. (1,4)

EXPALINATION :

IF WE WRITE THE VALUE x = -1 AND y = 4

THEN, y= -8x - 4

4= -8×-1-4

4= 8-4

AND SECOND EQUATION IS : y = x+5

y = -1 +5

y = 4

hence, solved and explained

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According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.

By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.

Next, we would approximate two points on the line of best fit and then find the slope as follows:

Slope, m = ΔC/Δx

Slope, m = (C₂ - C₁)/(x₂ - x₁)

Slope, m = (400 - 200)/(4000 - 1500)

Slope, m = 0.08.

Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.

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The constant of proportionality of our given tables is; 5.

We are given that x and y are proportional, and this means that:

y = r*x

where;

r is the constant of proportionality.

We are given the table;

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair: 35 = r*7

r = 35/7 = 5

For the second pair:

60 = r*12

60/12 = r

r = 5

Thus, we can conclude that the constant of proportionality is 5.

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Answer: 3

Step-by-step explanation:

Answer:

[tex]2\sqrt{6} +4[/tex]

Step-by-step explanation:

Let x be that unknown number.

From the information given from the question, we can deduce:

[tex]x^{2} -8=8x[/tex]

From here, we can solve for x to find what is the number.

[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)

From here we can use the Quadratic Formula to solve for x.

[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case,

a = 1, b = -8 , c = -8

We substitute a, b and c to find x.

[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]

(Reject the negative solution)

Answer:

Step-by-step explanation:

Let the age of Abel is x and age of Asare is y.

Three times the age of Abel is four more than the age of Asare:

And

In three years, the sum of their ages will be 30 years:

We got two equations.

Simplify and solve by substitution:

Find y:

Percent of the total was spent on veterinary​ care is 31.3186% .

Applying simple percentage formula,

let x be the percentage

x=[tex]\frac{17.1}{54.6} \ 100[/tex]

x=31.3186 %

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