Which list contains ONLY rational numbers?

Answer:

Your answer would be D.

Step-by-step explanation:

The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.

The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:

Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.

Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.

However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.

Final answer:

The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.

Explanation:

To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:

m = (4 - 2) / (3 - 1) = 2 / 2 = 1.

Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:

2 = (1)(1) + b

Which simplifies to:

b = 2 - 1 = 1

So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:

y = x + 1

For this case we define the following variable:

x: unknown number

We then have the following equation:

[tex]- \sqrt {41} x = 1[/tex]

From here, we clear the value of x.

We have then:

[tex]x = - \frac {1} {\sqrt {41}}[/tex]

Answer:

An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:

[tex]x = - \frac {1} {\sqrt {41}}[/tex]

The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.

Three car seats are designed as follows:

As the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.

Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.

The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

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take 23 and multiply by 3 then divide by 2 and your answer should be x34

Answer:

Step-by-step explanation:

Given that the correlation coefficient between the number of college students in a city and the number of city buses is 0.89.

We find that correlation coefficient is a measure of linear association between two variables.

When the absolute value of correlation coefficient is near 1, there is strong correlation. If correlation has a positive sign, there is a posiitive association between the two variables.

Here the correlation coefficient is positive and also near 1.  Thus there is a strong linear correlation between the two variables.

Or whenever there is an increase in one variable there will be an increase in other variable also.

The answer is an octave and a sestet. A sestet is the title specified to the second split of an Italian sonnet (as contrasting to an English or Spenserian sonnet), which must contain of an octave, of eight lines and must be followed by a sestet, of six lines. The first recognized user of this poetical type was the Italian poet named Petrarch.

A neutral atom contains equal amount of proton and electron.

A negative ion contains extra electrons hence there is additional outer shell so it is expected that the radius is bigger than that of a neutral atom.

While a positive ion contains less electron so there is less outer shell so the radius is smaller than that of a neutral atom.

Arranging the radius in increasing order:

positive ion, neutral atom, negative ion

Answer:

[tex]y=1(x-5)^2 + 3[/tex]

Step-by-step explanation:

Given : from the graph vertex is (5,3)

Also graph passes through point (8,12)

We use vertex form of quadratic equation

General vertex form is

[tex]y=a(x-h)^2 + k[/tex]

vertex is (5,3)

h= 5 and k =3

So equation becomes [tex]y=a(x-5)^2 + 3[/tex]

Now we need to find out 'a'

We use (8,12) to find out 'a'

Plug in x=8 and y = 12

[tex]12=a(8-5)^2 + 3[/tex]

[tex]12=a(3)^2 + 3[/tex]

12= 9a + 3

subtract 3 on both sides

9 = 9a

divide both sides by 9

so a=1

Final equation is

[tex]y=1(x-5)^2 + 3[/tex]

An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]

Given the following data:

The vertex form of a quadratic equation can be used to write an equation of the function of a graph.

Mathematically, the vertex form of a quadratic equation is given by this formula:

[tex]y=a(x-h)^2 + k[/tex]

Substituting the given parameters into the formula, we have;

[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]

a = 1.

For the equation:

[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]

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It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We need to find the unit fractions to convert 15 days into seconds.

1 day = 24 hour

1 hour = 60 minutes.

1 minutes = 60 seconds

Therefore, 24 hours = 24 x 60 x 60  = 86400 seconds

There are 86400 seconds in one day.

Then 15 days = 15 x 86400 = 1,296,000

Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.

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The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.

From one of the angle theorems, we have that vertically opposite angles are equal

That means,

measure of ∠ 6 = measure of ∠ 7

From the question,

we have that, m6 = (11x + 8)° and m7 = (12x – 4)°

Since, the measures of angles 6 and 7 are equal, then we can write that

(11x + 8)° = (12x – 4)°

Now, determine the value of x, we will solve the equation

11x + 8 = 12x – 4  

First, subtract 11x from both sides

11x - 11x + 8 = 12x - 11x - 4

8 = x - 4

Now, add 4 to both sides

8 + 4 = x -4 +4

12 = x

∴ x = 12

Now, we will determine the measure of ∠6

m ∠6 = (11x + 8)°

Put x = 12

∴ m ∠6 = (11(12) + 8)°

m ∠6 = (132 + 8)°

m ∠6 = 140°

To determine the measure of ∠4, m4, we will first determine the measure of ∠8.

From the diagram,

m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)

∴ 140° + m ∠8 = 180°

Then,

m ∠8 = 180° - 140°

m ∠8 = 40°

From the diagram, we can observe that angles 4 and 8 are corresponding angles.

Also, from one of the angle theorems, we have that corresponding angles are equal.

Hence, the measure of ∠ 4 equals the measure of ∠ 8.

From above, m ∠8 = 40°

∴ m ∠4 = 40°

Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°

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The value of f(q+1) is 2(q-1).

A relation or expression involving one or more variables.

Given that, f(x) = 2x - 4

When x = q+1

f(q+1) = 2(q+1) - 4

f(q+1) = 2q + 2 - 4

f(q+1) = 2q - 2

f(q+1) = 2(q-1)

Hence, the value of f(x) when x = (q+1) is 2(q-1)

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y = 8 x cos(20)

y = 7.517

y = 7.5