In how many ways can 15 identical math books be distributed among 6 students?

Answer:

63 and 59 are correct

Step-by-step explanation:

The given values of x, the corresponding values of y are:

1. When x = -2, [tex]\(y = \frac{19}{4}\)[/tex]

2. When x = -1, [tex]\(y = \frac{13}{4}\)[/tex]

3. When x = 0, [tex]\(y = \frac{7}{4}\)[/tex]

Let's solve the equation [tex]\(6x = 7 - 4y\)[/tex] for y:

[tex]\[6x = 7 - 4y\][/tex]

First, isolate the term with y:

[tex]\[4y = 7 - 6x\][/tex]

Next, divide both sides by 4 to solve for y:

[tex]\[y = \frac{7 - 6x}{4}\][/tex]

Now, we can find the values of y for each given value of x:

1. For x = -2:

 [tex]\[y = \frac{7 - 6(-2)}{4} = \frac{7 + 12}{4} = \frac{19}{4}\][/tex]

2. For x = -1:

 [tex]\[y = \frac{7 - 6(-1)}{4} = \frac{7 + 6}{4} = \frac{13}{4}\][/tex]

3. For x = 0:

[tex]\[y = \frac{7 - 6(0)}{4} = \frac{7}{4}\][/tex]

Therefore, for the given values of x, the corresponding values of y are:

1. When x = -2, [tex]\(y = \frac{19}{4}\)[/tex]

2. When x = -1, [tex]\(y = \frac{13}{4}\)[/tex]

3. When x = 0, [tex]\(y = \frac{7}{4}\)[/tex]

Complete question:

Solve equation for y. Then find the value of y for each value of x.

6x = 7 - 4y; x = -2, -1, 0

Final answer:

To solve the equation 6x = 7 - 4y for y, subtract 7 from both sides and divide by -4 to isolate y.

Explanation:

To solve the equation 6x = 7 - 4y for y, we need to isolate y on one side of the equation. First, we can move the 7 to the other side by subtracting it from both sides:

6x - 7 = -4y

Next, we can divide both sides by -4 to solve for y:

y = (6x - 7) / -4

The equation of the tangent line to the function y = 4x⁴ at (1, 4) will be y = 16x - 12.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given as,

y = 4x⁴

The slope of the line is given as,

m = y'

m = 16x³

m = 16 (1)³

m = 16

Then the equation of the tangent line is given as,

y = 16x + c

The equation is passing through (1, 4). Then we have

4 = 16 (1) + c

4 = 16 + c

c = - 12

The equation of the tangent line to the function y = 4x⁴ at (1, 4) will be y = 16x - 12.

More about the function link is given below.

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To determine if the parallelogram is a rectangle, we can use the slopes of its sides. Given the coordinates of the vertices, we can calculate the slopes and compare them. If the opposite sides have equal slopes, then the parallelogram is a rectangle.

To determine if the parallelogram is a rectangle, we can use the slopes of its sides. A rectangle has opposite sides that are parallel and equal in length, so the opposite sides of a rectangle will have equal slopes.

Using the given vertices, we can find the slopes for the sides:

Slope of JK = (4 - 0) / (1 - (-5)) = 4/6 = 2/3

Slope of KL = (1 - 4) / (3 - 1) = -3/2

Slope of LM = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

Slope of MJ = (0 - (-3)) / (-5 - (-3)) = 3/(-2) = -3/2

Since the opposite sides JK and LM have equal slopes of 2/3 and the opposite sides KL and MJ have equal slopes of -3/2, we can conclude that the parallelogram is a rectangle.

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Answer:

x = 5

Step-by-step explanation:

Complementary angles are two angles whose sum is 90º

So, if we have two complementary angles 7x and 11x we know that their sum is 90

We are going to write the equation and solve for x:

[tex]7x+11x=90\\18x=90\\x=90/18\\x= 5[/tex]

Therefore, x would be 5. And the angles would be 7(5) = 35º and 11(5) = 55º

Answer: the correct answer would be 8.8 ft/s

The radius of the circle with the given coordinates is 6.32 units.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Given that, the point (4,-3) lies on the circle center (-2,5).

Using distance formula we can find the radius of a circle

We know that, Distance =√[(x2-x1)²+(y2-y1)²]

Now, radius =√[(-2-4)²+(5-(-3))²]

=√[(-6)²+(2)²]

= √36+4

= √40

= 6.32 units

Therefore, the radius of the circle is 6.32 units.

To learn more about the circle visit:

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Answer:

Bean plant grew faster .

Step-by-step explanation:

As given

Plants A birch tree grew 2.5 inches in five months.

i.e 2.5 inches = 5 months

Now calculate birch tree in one month .

[tex]Birch\ tree\ grew\ in\ one\ month = \frac{2.5}{5}[/tex]

                                                               = 0.5 inches

As given

A bean plant grew 8 inches in 10 months.

i.e 8 inches = 10 months

Now calculate bean plant in one month .

[tex]Bean\ plant\ grew\ in\ one\ month = \frac{8}{10}[/tex]

                                                                = 0.8 inches

As given

It rosebush grew 5 inches in eight months.

i.e 5 inches = 8 months

Now calculate rosebush in one month .

[tex]Bean\ rosebush\ in\ one\ month = \frac{5}{8}[/tex]

                                                                = 0.63 inches (Approx)

Therefore Bean plant grew faster .

The answer is both. Desmos graphing calculator is a great tool if you don't have a calculator on you. Hope this helps!

f(x) = x^2-25

 inverse:

y = x^2-25

x = y^2-25

y = sqrt(5 +25)

 Answer is B

Answer:

3 - 5.5 +1.5

Step-by-step explanation:

LEts analyze the given number line

We always start with 0

Arrow goes 3 units to the right, so we put positive 3

from 3 , the arrow ends at -2.5. Arrow goes to the left so we subtract to find the distance. -2.5-3= -5.5

from -2.5 we add 1.5 to reach -1

So the expressio becoems 3 and then subtract 5.5 and then add 1.5

3 - 5.5 +1.5

Answer:

60

Step-by-step explanation:

Answer:  The hexagon will rotate onto itself at 60°.

Step-by-step explanation:

A hexagon is a regular polygon with six sides) having all its sides and all its angles are equal.

For a regular polygon , Order of rotation of the figure = Number of sides .

i.e.  Order of rotation for hexagon = 6

Let [tex]\theta[/tex] be the angle at which hexagon rotate onto itself, then we have

[tex]\theta=360^{\circ}\ \div6=60^{\circ}[/tex]   [∵One complete rotation= [tex]360^{\circ}[/tex]]

Hence, The hexagon will rotate onto itself at 60°.

the first one because all the other ones are wrong