m ≥ 15 graph the inequality

Answer:

-2\(c^{2}\)

Step-by-step explanation:

-8\(c^{2}\) - - 6\(c^{2}\)  is the same as

-8\(c^{2}\)  +  6\(c^{2}\)

-2\(c^{2}\)

Answer: We have to write two fractions that are equivalent to 1(a) and 1(b):

1(a) Equivalent fraction to 1(b):

Conclusion: The two fractions are Indeed the Equivalent!

answer

\(m = + 5 \div \sqrt{6 \: } \: \: \: or \: - 5 \div \sqrt{6} \)

The value of p in the arithmetic sequence is -1.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The common difference (d) is:

d = (p + 5) - (2p + 5) and d = (2p + 7) - (p + 5)

(p + 5) - (2p + 5) = (2p + 7) - (p + 5)

-p = p + 2

p = -1

The value of p in the arithmetic sequence is -1.

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The value of p in the sequence is 3

Arithmetic sequence is a type of sequence which have a common difference between each term in the sequence.

•First term (T₁) = 2p – 3

•2nd term (T₂) = p + 5

•3rd term (T₃) = 2p + 7

•Value of p =?

Common difference = T₂ – T₁ = T₃ – T₂

Using the above, the value of p can be obtained as follow:

T₂ – T₁ = T₃ – T₂

(p + 5) – (2p – 3) = (2p + 7) – (p + 5)

Clear brackets

p + 5 – 2p + 3 = 2p + 7 – p – 5

Collect like terms

p – 2p – 2p + p = 7 – 5 – 5 – 3

–2p = –6

Divide both side by –2

p = –6 / –2

p = 3

Therefore, the value of p is 3

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Answer:

2/5

Step-by-step explanation:

The slope of the line

y=2/5x-4

is 2/5 since it is in the form y = mx+b where m is the slope

Parallel lines have the same slope so a line that is parallel to  y=2/5x-4 has a slope of 2/5

Answer:

h = 9 yds,       assuming his treehouse is a rectangular shape. 9 yds seems pretty high.

Step-by-step explanation:

area = bh

108 yd³ = 12 yd² x h

h = 108/12 = 9 yds

 The prism is 9 yards tall

What is the Volume of Rectangular Prism?

The area occupied inside a rectangular prism is referred to as the volume of the prism. A polyhedron with two pairs of congruent and parallel bases is referred to as a rectangular prism. It has 12 sides, 6 faces (all of which are rectangles), and 8 vertices. Given that the rectangular prism is a three-dimensional (3D) shape, the units cm3, m3, and so forth are employed to express the volume of the rectangle prism. Any polyhedron that possesses all of these qualities is referred to as a cuboid in mathematics.

Given: base of the treehouse= 12 yards²

volume of the treehouse = 108 yards³

To find : how tall is the prism ( height of the treehouse) = ?

Formula Used : The volume of a rectangular prism is calculated using the formula volume of a rectangular prism (V) = l w h,

where "l" stands for base length

"w" for base width.

"h" refers to the prism's height.

Steps for calculating the height

Step 1: The foundation area of 12 square yards has previously been specified.

Step 2: The prism's volume is 108 cubic yards

Step 3: The given rectangular prism's volume = base area x height

=> 108 cubic yards = 12 x h

=> 108/ 12 = h

=> h = 9 yards

Since , the prism is 9 yards tall

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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The solution to the initial value problem is y(x) = 3x sin x + 2x cos x.

To solve the initial value problem, we can use an integrating factor method. First, we rewrite the given equation as dy/dx + y tan x = 2x sin x. By comparing this form with the standard form of a linear first-order differential equation, we can determine the integrating factor. The integrating factor is given by exp(integral(tan x dx)), which simplifies to cos x.

Multiplying the entire equation by cos x, we get cos x dy/dx + y sin x = 2x sin x cos x. The left-hand side of the equation is now the derivative of (y cos x) with respect to x. Integrating both sides, we have ∫(y cos x) dx = ∫(2x sin x cos x) dx.

Integrating the right-hand side and simplifying, we get y(x) cos x = x sin^2(x) + C, where C is the constant of integration. To find the value of C, we use the initial condition y(0) = 5. Plugging in x = 0 and y = 5 into the equation, we get 5 cos 0 = 0 + C. Simplifying, we find C = 5.

Substituting C back into the equation, we have y(x) cos x = x sin^2(x) + 5. Dividing both sides by cos x, we obtain the final solution y(x) = (x sin^2(x) + 5) / cos x. Simplifying further, we get y(x) = 3x sin x + 2x cos x, which is the solution to the initial value problem.

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A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.

A mean = 10

Standard Deviation = 25

We have to determine the z score for the value of 35. So X = 35.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.

The formula is:

Z = (X - mean)/Standard Deviation

Now putting the values

Z = (35 - 10)/25

Z = 25/25

Z = 1

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The perimeter of half of the basketball court is 194 feet.

The basket ball court is divided into two equal halves. The perimeter of the halve of the basket ball court can be calculated as follows:

Therefore, the perimeter is the sum of the whole sides of half of the basket ball court.

Hence,

perimeter of half of the basket ball court = 94 / 2 + 94 / 2 + 50 + 50

perimeter of half of the basket ball court = 47 + 47 + 100

perimeter of half of the basket ball court = 94 + 100

perimeter of half of the basket ball court = 194 feet

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2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3 fraction.

The expression 2/3 is equivalent to 2 divided by 1/3. This is because 2/3 can be written as 2 multiplied by 3, which is equal to 6. This can be represented in fraction form as 2 divided by 1/3. To calculate this expression, we need to divide 2 by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3, which is equal to 6. 2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3.

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Answer:

work done against friction: (a) if a body is moved horizontally against the frictional force this type of work is work done against friction.

(b) for example sliding a box and rolling a drum

work done against gravity: (a) if a body is moved vertically upwards against the gravity of the earth, this type of work is work done against gravity

(b) for example lifting and throwing of a body upward

Step-by-step explanation:

hope it's helpful

The distance from S to the plane x+y+z=0 is sqrt(105)/7.

To find the distance from the sphere S to the plane x+y+z=0, we need to first find the center of the sphere S. We know that the center of the sphere S is (1, 2, 3) and the radius of the sphere is 1. We can use the equation of the plane x+y+z=0 to find the distance from the center of the sphere to the plane.

We can use Lagrange multipliers to find the distance from the center of the sphere to the plane. We need to minimize the function \(f(x, y, z) = (x-1)^2 + (y-2)^2 + (z-3)^2\) subject to the constraint x+y+z=0. Using Lagrange multipliers, we get the following system of equations:

2(x-1) = λ

2(y-2) = λ

2(z-3) = λ

x+y+z = 0

Solving these equations, we get x = 1-λ/2, y = 2-λ/2, and z = 3-λ/2. Substituting these values into the equation x+y+z=0, we get λ = 12/7. Substituting this value of λ into x, y, and z, we get the coordinates of the point on the plane closest to the center of the sphere: (5/7, 4/7, -9/7).

To find the distance from the center of the sphere to the plane, we can use the distance formula. The distance from the center of the sphere to the plane is given by the length of the vector connecting the center of the sphere to the point on the plane closest to the center of the sphere. Therefore, the distance from the sphere S to the plane x+y+z=0 is:

d = sqrt[(5/7 - 1)^2 + (4/7 - 2)^2 + (-9/7 - 3)^2] = sqrt[105/49] = sqrt(105)/7.

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In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.

Speed = Distance/ time

speed =72.4 miles

time=4.62 hours

Distance =speed * time

= 72.4 *4.62

Distance = 334.488 miles

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complete question;

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.

Answer:

x = 62 degrees

Step-by-step explanation:

Since this is a right angle, we can use trig functions

cos theta = adjacent/ hypotenuse

cos x = 3.7/7.9

Taking the inverse cos of each side

cos ^ -1 ( cos x) = cos ^-1 (3.7/7.9)

x =62.07246803

To the nearest degree

x = 62 degrees

A geometry constructions packet is a collection of exercises that require the student to create geometric figures

A Geometry constructions packet is a collection of activities or exercises that focus on the art of creating geometric figures using only a straightedge and a compass. In geometry, construction refers to the process of drawing or creating geometric figures using specific rules and procedures.

Some examples of construction tasks that might be included in a geometry constructions packet are:

Bisecting an angle

Constructing a perpendicular bisector of a line segment

Constructing a triangle given three sides

Constructing a square given one side

Constructing a regular hexagon

Constructing a regular pentagon

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Answer:

here's how I do it .........

Answer:

Step-by-step explanation:

360/2=180

5x+4x=180

9x=180

x=20

5×20:4×20

100:80

\(\\ \sf\longmapsto 3y=z-2x\)

\(\\ \sf\longmapsto -2x=3y-z\)

\(\\ \sf\longmapsto 2x=-3y+z\)

\(\\ \sf\longmapsto 2x=z-3y\)

\(\\ \sf\longmapsto x=\dfrac{z-3y}{2}\)

Answer:

\( x = \frac{z - 3y}{2} \)

Step-by-step explanation:

Question :

\(3y = z - 2x\)

First take 2x to the left to make the 2x as a positive number (So, It's easy to solve)

\(3y + 2x = z\)

Then take 3y to the right side

\(2x = z - 3y\)

Now, divide both sides by 2 to make the x as the Subject

\( \frac{2x}{2} = \frac{z - 3y}{2} \\ x = \frac{z - 3y}{2} \)

hope this helps you.

Please let me know if you have another questions :-)

The graph that results from placing the coordinates on the graph is shown below.

Consequently, the graph's coordinates are (-1,1), (0,3), and (1,5)

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.

There are 3 methods for graphing a linear equation:

1.displaying the graph of a linear equation using two points.

2.Use a linear equation's slope and y-intercept.

3.using a linear equation's x- and y-intercepts.

So we take 3 values to substitute in place of x like

-1,0,1

values of y we get are

1,3,5

Now placing the co ordinates on the graph we get the following graph,

Therefore, the co-ordinates constituting the graph are (-1,1), (0,3), (1,5)

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Answer:

1464

Step-by-step explanation:

Answer:

1104 points

Step-by-step explanation:

50 points for 30 correct moves is 1500 points

2 minutes and 12 seconds is equal to 132 seconds

at 132*-3 for each second is -396

1500-396 =1104 points

The derivative of the function f(x) = 4/(x - 8) is f'(x) = -4/(x - 8)^2.

To find the derivative of the given function f(x) = 4/(x - 8), we can use the quotient rule of differentiation. The quotient rule states that for a function f(x) = g(x)/h(x), where g(x) and h(x) are differentiable functions, the derivative f'(x) is given by (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2.

In our case, g(x) = 4 and h(x) = (x - 8). Taking the derivatives, we have g'(x) = 0 (since 4 is a constant) and h'(x) = 1 (since the derivative of x - 8 is 1).

Applying the quotient rule, we get:

f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2

      = (0 * (x - 8) - 4 * 1) / ((x - 8))^2

      = -4 / (x - 8)^2

Therefore, the derivative of the function f(x) = 4/(x - 8) is f'(x) = -4/(x - 8)^2.

The derivative represents the rate at which the function is changing with respect to x. In this case, the derivative of f(x) gives us the rate of change of the function at any given point. The negative sign in the derivative indicates that as x increases, the function f(x) is decreasing.

The denominator of the derivative, (x - 8)^2, indicates that the function has a vertical asymptote at x = 8. This means that the function approaches infinity as x approaches 8 from either direction.

Understanding the derivative is essential in calculus as it allows us to analyze the behavior of functions, find critical points, determine rates of change, and solve optimization problems. The quotient rule is just one of the differentiation rules that help us find the derivatives of various types of functions.

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9514 1404 393

Answer:

  m∠CAB = 62°

  m∠CBG = 114°

Step-by-step explanation:

Given:

  the above figure

Find:

  What are the measures of angles CAB and CBG

Solution:

The total angle at C is 32°+52° = 84°. We know that "remote interior" angles ECB and EBE have a sum that matches angle CEF.

So, angle CBE = 150° -84° = 66°

Angle CBG is the supplement of this, so is ...

  m∠CBG = 180° -66° = 114°

That angle is the total of "remote interior" angles BCA and CAB. So angle CAB is ...

  m∠CAB = 114° -52° = 62°

The cost of one cookie is 1. This value can be determine from the eliminate methods or substitution methods.

As per data given is a two different formula of pizza and cookie, we can determine it by elimination methods or substitution methods. Let do it by elimination methods. As per formula given are first buy 3 pizza + 2 cookie =  6.50 and the second buy 1 pizza + 1 cookie = 2.50. The calculation will be:

3 pizza + 2 cookie =  6.50

1 pizza + 1 cookie = 2.50     multiply with 3 because we want eliminate pizza

3 pizza + 2 cookie =  6.50

3 pizza + 3 cookie = 7.50       -

0 pizza - 1 cookie = - 1

1 cookie = 1

Hence the price of one cookie will cost you 1.

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Answer:

c. 8

Step-by-step explanation:

Length of an arc

Given

Solving

The best method of variable calculation, whether qualitative or quantitative, depends on the specific context and the type of information being analyzed.

It is not appropriate to definitively label one method as universally better than the other as they serve different purposes and have their own strengths and limitations.

Qualitative methods involve subjective analysis and interpretation of non-numerical data, such as observations, interviews, or surveys. They are valuable when exploring complex phenomena, understanding human behavior, or capturing nuanced information that cannot be easily quantified. Qualitative methods provide rich, in-depth insights and can uncover underlying motivations, attitudes, and perceptions.

Quantitative methods, on the other hand, involve the measurement and analysis of numerical data using statistical techniques. They provide objective and measurable results, allowing for precise comparisons and generalizations. Quantitative methods are particularly useful for testing hypotheses, establishing trends, and making predictions based on large-scale data sets.

Both qualitative and quantitative methods have their merits and should be employed based on the research question, available resources, and the nature of the data. A comprehensive approach that integrates both methods can often provide a more comprehensive and robust understanding of the subject matter.

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When dividing a three-digit number by a one-digit number, the quotient will have either the same number of digits as the dividend or one less digit.

Let's consider an example to illustrate this:

Dividend: 456

Divisor: 6

When we perform the division, we get:

     76

  -------

6 | 456

   - 42

   -----

      16

In this case, the quotient is 76, which has two digits, the same as the dividend.

Now, let's consider another example:

Dividend: 789

Divisor: 9

Performing the division, we get:

     87

  -------

9 | 789

   - 72

   -----

      19

In this case, the quotient is 87, which also has two digits, one less than the three-digit dividend.

So, when dividing a three-digit number by a one-digit number, the quotient will have the same number of digits as the dividend or one less digit.

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The problem requires us to calculate the probability that three of the five even numerical denominations are represented twice, one of the three face cards appears twice, and a second face card appears once.

To solve the problem, we need to determine the number of possible hands that meet the criteria and divide it by the total possible hands that can be dealt from the deck. We will begin by counting the total number of ways nine cards can be dealt from a 52-card deck. We will use the combination formula, which is:

nCr = n! / r! (n - r)!,

where n is the total number of items and r is the number of items chosen.

Here, n = 52 and r = 9. nCr = 52C9 = 52! / 9! (52 - 9)! = 4,104,398,535.

This is the total number of possible hands that can be dealt from the deck. Now, we will count the number of ways to choose the cards that meet the criteria. We will divide this by the total number of hands to get the probability of the event. We will choose the five even numerical denominations first. There are five even numbers, and we need three of them to be repeated twice. Therefore, we need to choose three of the five, which can be done in 5C3 = 10 ways. Once we have selected the three even numbers, we can select two of them to be repeated twice in 3C2 = 3 ways. The remaining four cards can be selected from the deck in 44C4 ways. Next, we will choose the face cards. We need two face cards, one of which is repeated twice. There are three face cards, and we need to choose two of them, which can be done in 3C2 = 3 ways. One of the two chosen cards can be repeated twice in two ways. The last card can be chosen from the remaining 46 cards in 46 ways. The total number of ways to choose the cards that meet the criteria is the product of all the above combinations, i.e., 10 × 3 × 44C4 × 3 × 2 × 46. Therefore, the probability of the event is:

P(event) = (10 × 3 × 44C4 × 3 × 2 × 46) / 52C9= 0.0000532 (rounded to four decimal places)

The formula for the probability that three of the five even numerical denominations are represented twice, one of the three face cards appears twice, and a second face card appears once, is P(event) = (10 × 3 × 44C4 × 3 × 2 × 46) / 52C9 = 0.0000532 (rounded to four decimal places).

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Average speed of a body is the ratio of distance traveled by a body in the given time.

Average speed of a body is the ratio of distance traveled by a body in the given time.

Given information-

The given 2-column table with 3 rows is,

Column 1 is labeled time elapsed (hours) with entries-    2,       4,         7.

Column 2 is labeled Distance Run (miles) with entries- 13.5,   27.5, 48.5.

The distance ran by Larry from hour 2 to hour 4 is,

\(d=27.5-13.5\\d=14\)

Total time taken bay Larry  from hour 2 to hour 4 is,

\(t=4-2\\t=2\rm hr\)

Thus the average speed of Larry from hour 2 to hour 4 is,

\(s=\dfrac{d}{t} \\s=\dfrac{14}{2} \\s=7 \rm m/s\)

Hence,  the average speed of Larry from hour 2 to hour 4 is 7 m/s.

The distance ran by Larry from hour 4 to hour 7 is,

\(d=48.5-27.5\\d=21\)

Total time taken bay Larry  from hour 4 to hour 7 is,

\(t=7-4\\t=3\rm hr\)

Thus the average speed of Larry from hour 4 to hour 7 is,

\(s=\dfrac{d}{t} \\s=\dfrac{21}{3} \\s=7 \rm m/s\)

Hence,  the average speed of Larry from hour 4 to hour 7 is 7 m/s.

Hence

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Larry recorded his time as he ran. What was his  average speed from hour 2 to hour 4?

✔ 7 mph

What was his average speed from hour 4 to hour 7?

✔ 7 mph

Did he speed up or slow down?

✔ stayed the same