This is 9th-grade math

The quadratic equation is y = ax² + bx + c  = y = -2x² + 7x - 1

A quadratic equation is a type of second-degree algebraic expression that deals with a variable multiplied by itself, known as squaring.4 The standard form is ax² + bx + c = 0, with a, b, and c being constants or numerical coefficients, and x being an unknown variable

Substitute each point into this equation in order to find a, b, and c.

(3,2): 2 = 9a + 3b + c     (Eq.#1)

(2,5): 5 = 4a + 2b + c     (Eq.#2)

(1,4): 4 = a + b + c         (Eq#3)2

Subtract Eq.#3 from Eq.#2

  5 = 4a + 2b + c

-(4 = a + b + c)

  1 = 3a + b    (Eq.#4)

Now subtract Eq.#2 from Eq.#1

 2 = 9a + 3b + c

-(5 = 4a + 2b + c)

-3 = 5a + b    (Eq.#5)

Subtract Eq#4 from Eq.#5

 -3 = 5a + b

-(1 = 3a + b)

 -4 = 2a

-2 = a  (Eq.#6)     Substitute a into Eq.#5

-3 = -10 + b

7 = b     Eq.#7     Substitute a and b into Eq.#3

4 = -2 + 7 + c

-1 = c

y = -2x² + 7x - 1  

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Complete question

 Write the equation of the quadratic function that passes through the points (3,2) , (2,5) and (1,4) in vertex form

Write the equation of the quadratic function that passes through the points (3,2) , (2,5) and (1,4) in vertex form

The quadratic function for which -3 is the constant term is option (D) g(x)= -3x² + 3x + 9. is the quadratic function where -3 is the constant term.

A quadratic function is a mathematical function of the form f(x) = a\(x^2\) + bx + c, where "a," "b," and "c" are constants and "x" represents the variable. It represents a parabolic curve.

The quadratic function for which -3 is the constant term is option (D) g(x) = -3x² + 3x + 9. To determine this, we look at the constant term in each function:

(A) In y = (3x+1)(-x-3), the constant term is -3, not -3.

(B) In y = x² - 3x + 3, the constant term is 3, not -3.

(C) In f(x) = (x-3)(x-3), when we expand the expression, we get x² - 6x + 9, so the constant term is 9, not -3.

(D) In g(x) = -3x² + 3x + 9, the constant term is -3.

Therefore, option (D) g(x) = -3x² + 3x + 9 is the quadratic function where -3 is the constant term.

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Answer:

The fact that the notebook.has section dividers

Step-by-step explanation:

The fact that the notebook has section dividers provides a way to separate his financial details into different categories, option A is correct.

An arrangement of objects where the order in which the objects are selected does not matter.

Section dividers allow Wyatt to separate his financial details into different categories, such as income, expenses, savings, investments, etc.

Each section can be used to organize specific information and receipts related to that category.

This system helps him easily access and reference information when needed.

The fact that the section dividers have pockets (option c) is also important as it allows Wyatt to store receipts and other papers related to the records in each section.

However, the key feature that allows him to separate his financial details into different categories is the presence of section dividers.

Hence, the fact that the notebook has section dividers provides a way to separate his financial details into different categories

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The volume of the empty space inside the container -32.60 cubic inches (rounded to the nearest hundredth).

To calculate the volume of the empty space inside the container, we need to determine the volume of the container and subtract the volume occupied by the three tennis balls.

Given data:

Diameter of each tennis ball = 2.5 inches

First, let's calculate the volume of each tennis ball:

Radius of the tennis ball = diameter / 2 = 2.5 inches / 2 = 1.25 inches

Volume of a sphere = (4/3) * π * \(radius^3\)

                  = (4/3) * 3.14 * (1.25 \(inches)^3\)

                  ≈ 14.14 cubic inches (rounded to the nearest hundredth)

Since there are three tennis balls, the total volume occupied by the balls is:

Total volume occupied = 3 * 14.14 cubic inches

                    ≈ 42.42 cubic inches (rounded to the nearest hundredth)

Next, we need to determine the volume of the container. Since the balls touch the container on the sides, top, and bottom, the container forms a cylinder around the balls.

The height of the cylinder is equal to the diameter of the tennis balls, which is 2.5 inches.

Volume of the container = π * \(radius^2\) * height

                      = 3.14 * \((1.25 inches)^2\) * 2.5 inches

                      ≈ 9.82 cubic inches (rounded to the nearest hundredth)

Finally, we can calculate the volume of the empty space inside the container by subtracting the volume occupied by the balls from the volume of the container:

Volume of empty space = Volume of container - Total volume occupied by balls

                    = 9.82 cubic inches - 42.42 cubic inches

                    ≈ -32.60 cubic inches (rounded to the nearest hundredth)

Since the result is negative, it indicates that the balls completely fill the container, leaving no empty space inside.

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Answer: 3 2/4 & 9 13/15

Step-by-step explanation:

4

hope it helps....!!!!

Answer:

The probability of boy in seventh child is 1/2, because the possibility of male child is always 50%.

Step-by-step explanation:

The expressions are:

(r-s)(x) = x + 3

(r+s)(x) = 7x - 3

And the value of (r∘s)(3) is unknown without the expression for r(x).

To find the expressions for (r-s)(x) and (r+s)(x) and evaluate (r∘s)(3), where f(x) = 4x and g(x) = 3x - 3, we can substitute these functions into the given expressions.

1. (r-s)(x):

The expression for (r-s)(x) is obtained by subtracting g(x) from f(x):

(r-s)(x) = f(x) - g(x) = (4x) - (3x - 3) = 4x - 3x + 3 = x + 3

2. (r+s)(x):

The expression for (r+s)(x) is obtained by adding f(x) and g(x):

(r+s)(x) = f(x) + g(x) = (4x) + (3x - 3) = 4x + 3x - 3 = 7x - 3

3. Evaluating (r∘s)(3):

(r∘s)(3) means substituting x = 3 into the function composition (r∘s)(x). First, we evaluate s(3):

s(3) = 3(3) - 3 = 9 - 3 = 6

Then, we substitute s(3) into r(x):

(r∘s)(3) = r(s(3)) = r(6)

Since we don't have the expression for r(x), we cannot determine the specific value of r(6) or simplify it further without additional information.

Therefore, the expressions are:

(r-s)(x) = x + 3

(r+s)(x) = 7x - 3

And the value of (r∘s)(3) is unknown without the expression for r(x).

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Answer:

\(\left\begin{array}{ccccc}&0&0&0&0 \\ \times&&&&9 \\--&--&--&--&--\\& 0 & 0 & 0 & 0 \\--&--&--&--&-- \end{array}\right\)

Step-by-step explanation:

Now,

\(\left\begin{array}{ccccc}&M&A&T&H \\ \times&&&&9 \\--&--&--&--&--\\& H & T & A & M \\--&--&--&--&--\\ ^{a} & ^{b} & ^{c} & ^{d} \end{array}\right\)

where the small letters a,b, c and d refers to carried numbers.

Converting this to equations:

This equation comes from carrying remainders.

We know \(0 \le H \le 9\) because H is a single digit, so by the fourth equation,

9M+b=H

M=0 or 1 since any larger integer value of M will make H a double digit number.

If M=1, we have:

\(\left\begin{array}{ccccc}&1&A&T&H \\ \times&&&&9 \\--&--&--&--&--\\& H & T & A & 1 \\--&--&--&--&--\end{array}\right\)

The only multiple of 9 that will give a remainder of 1 is 9. Therefore:

In this case, H=9

However, even if A and T were to be 0, the least possible number

1009 X 9= 9081

Therefore:

M=0

And sure enough

\(\left\begin{array}{ccccc}&0&0&0&0 \\ \times&&&&9 \\--&--&--&--&--\\& 0 & 0 & 0 & 0 \\--&--&--&--&-- \end{array}\right\)

The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

Answer:

we need the full question

The linear function defined in the table is given as follows:

y = 0.5x + 9.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the table, we get that the slope and the intercept are obtained as follows:

Hence the function is:

y = 0.5x + 9.

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Arguably infinity

The thing is there are an infinite numbers going on forever, an example would be π (pi). If you want to simplify it though it would be most likely infinity.

For your second question, the largest thing in the world is Asia. The largest of the seven continents and outmatched when coming to population. If you are talking about a living creature, undoubtedly the blue whale would come out in first weighing in at 150 tons and 33 meters long.

For the largest number, that's a tricky one. There is no limit to the amount of numbers one could come up with, as you can always add 1 digit anywhere inside of a number and it becomes bigger. This is where infinity comes in.

Infinity is a concept, meaning it isn't a real number, however we do use it in the math world a lot. infinity is the thought that there is no end, for example pi is an infinite number (meaning there is an endless amount of digits.) if you hit 9 on a keyboard and held it forever, you still wouldn't reach the biggest number in existence, because you can always add another 9.

For the largest thing, That moreso depends on what requirements something has to meet for it to be the 'largest' in your eyes. A blue whale is the largest animal, Annapurna is the largest mountain, and so on, but I think the largest thing in the world is the world itself, because the world is a thing. Neither of these questions really have a true "answer," but I hope I could explain the concept of infinity well.

Answer:

x = 12

Step-by-step explanation:

Given a line parallel to a side of the triangle and it intersects the other 2 sides then it divides those sides proportionally, that is

\(\frac{x}{24}\) = \(\frac{5}{10}\) ( cross- multiply )

10x = 120 ( divide both sides by 10 )

x = 12

Answer:

x = 7 √3 km

Step-by-step explanation:

Here, we want to get the value of x

As we can see, we have a right angled triangle with hypotenuse 14 km

we can use the Pythagoras’ theorem to get the value of x

Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

Thus,

14^2 = x^2 + 7^2

x^2 = 196-49

x^2 = 147

x = 7 √3 km

The answer is A. $85.50

The equation of the circle centered at the origin and passing through the point (0, 4) is \($x^2+y^2=16$\).

Let the center of the circle be represented as (h,k) and the radius of the circle be represented as r.

The general equation of a circle is given by \($$(x-h)^2+(y-k)^2=r^2$$\)

where the center of the circle is (h, k), and the radius is r

The equation of the circle with center (5, 9) and radius 11 is \($$(x-5)^2+(y-9)^2=11^2$$\)

To get the equation of the circle centered at the origin and passing through the point (0, 4), the center of the circle is the origin, which means (h, k) = (0, 0), and the radius r is given as the distance from the origin to (0, 4).

That distance is 4 units.

Therefore, the equation of the circle can be given by \($$(x-0)^2+(y-0)^2=4^2$$\)

Simplifying the equation gives:\($$x^2+y^2=16$$\)

Therefore, the equation of the circle centered at the origin and passing through the point (0, 4) is \($x^2+y^2=16$\).

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Answer:

9 scoops

Step-by-step explanation:

3 scoops = 45g

3/45 scoops = 1g

3/45*135 scoops = 135g = 9 scoops

Answer: He bought 7 nachos.

Step-by-step explanation:

Let x= Number of cokes

y = Number of nachos

As per given , we have

x+y=12     (i)

2.50x+3.50y=37    (ii)

Multiply 2.5 on both sides of (i), we get

2.5x+2.5y= 30      (iii)

Subtract (iii) from (ii), we get

y=7      (iv)

Put value of y from (iv) in (i), we get

x+7=12

⇒ x= 12-7

⇒ x=5

Hence, he bought 5 cokes and 7 nachos.

Answer:

perimeter = 7x² + 7y² + 4y - 3x

Step-by-step explanation:

the perimeter (P) is the sum of the 3 sides of the triangle , that is

P = 3x² - y² + 4x² - 7xy + 4y - 3x + 7xy + 8y² ← collect like terms

  = (3x² + 4x²) + (- y² + 8y²) + (- 7xy + 7xy) + 4y - 3x

 = 7x² + 7y² +0 + 4y - 3x

 = 7x² + 7y² + 4y - 3x

9514 1404 393

Answer:

  60/49

Step-by-step explanation:

245% = 245/100, so the ratio is ...

  3/(245/100) = 300/245 = 60/49 . . . as reduced fraction

The ratio 3 : 245% is 60 : 49, or 60/49.

__

As a decimal, it is about 1.2244898. The repeating decimal fraction has a 42-digit repeat.

The fourth step of the risk assessment process is to determine current level of preparedness/mitigation.

The correct option is C.

A risk assessment is a procedure for identifying potential dangers and analyzing what might happen if one happens. A business impact analysis (BIA) is a procedure that determines the probable consequences of interrupting time-sensitive or important business processes. There are various potential hazards to be mindful of.

The ultimate goal of risk assessments is to improve workplace safety and health. However, to order to accomplish this, your risk assessment process must identify occupational hazards and eliminate or reduce the risks they represent.

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Angular velocities: ω_D = v_D/R and ω_AB = v₀/(2R) and  Angular accelerations: α_D = 0 and α_AB = 0

At the instant shown, we can analyze the motion of disk D and bar AB in terms of their angular velocities and angular accelerations.
1. For disk D:
As the disk rolls without slipping, its linear speed at the point of contact with the ring is equal to the product of its radius (R) and its angular velocity (ω_D). Since the inner radius of the fixed ring is 2R, the linear speed of the disk is v_D = ω_D * R.
2. For bar AB:
Since pin B is moving with a constant speed (v₀), we can relate this to the angular velocity of bar AB (ω_AB) as v₀ = ω_AB * 2R.
Now, let's compute the angular accelerations of disk D and bar AB.
1. For disk D:
The disk is rolling without slipping, so its linear acceleration at the point of contact with the ring is equal to the product of its radius (R) and its angular acceleration (α_D). As the disk is at its lowest position and moving with constant speed, its linear acceleration is zero. Therefore, α_D = 0.
2. For bar AB:
Since the pin at B is moving with a constant speed (v₀), the linear acceleration of point B is zero. This implies that the angular acceleration of bar AB (α_AB) is also zero.
In summary, at the given instant:
- Angular velocities: ω_D = v_D/R and ω_AB = v₀/(2R)
- Angular accelerations: α_D = 0 and α_AB = 0

To begin, we can use the fact that the disk is rolling without slipping inside the fixed ring to relate the speed of the disk to the speed of the pin at B. Specifically, we know that the speed of any point on the rim of the disk is equal to the speed of the pin at B, which we'll call vo. Next, we can use the geometry of the system to relate the angular velocities of the disk and bar AB to the speed of the pin at B. Let's start with the disk. The disk is rolling without slipping, so its speed can be related to its angular velocity, which we'll call ωd. Specifically, we know that the speed of any point on the rim of the disk is equal to the product of its radius (R) and its angular velocity (ωd). So, we have:
vo = R * ωd
Solving for ωd, we get:
ωd = vo / R
Next, let's consider bar AB. Since it is pin-connected to the centre of the disk, its angular velocity is equal to the angular velocity of the disk. So, we have:
ωAB = ωd = vo / R
Now, let's compute the angular accelerations of the disk and bar AB. We can do this using the component system given in the problem. Specifically, we can use the fact that the net torque on each component must be equal to its moment of inertia times its angular acceleration.
Let's start with the disk. The only torque acting on the disk is due to the force of gravity, which is trying to rotate the disk clockwise. This torque is equal to the product of the force of gravity (mg) and the distance from the centre of the disk to the point where the force is applied (which is R/2 since the force is applied at the centre of mass of the disk). So, we have:
τd = (mg) * (R/2)

On the other hand, the moment of inertia of the disk can be found using the formula for a solid cylinder rotating about its central axis, which is:
Id = (1/2) * m * R²
Setting these two expressions equal and solving for the angular acceleration of the disk, we get:
τd = Id * αd
(mg) * (R/2) = (1/2) * m * R² * αd
Simplifying, we get:
αd = (2*g) / R
where g is the acceleration due to gravity.
Finally, let's compute the angular acceleration of bar AB. Since it is pin-connected to the centre of the disk, it experiences no net torque. Therefore, its angular acceleration is zero.
In summary, at the instant shown, the angular velocities and angular accelerations of the disk and bar AB are:
ωd = vo / R
ωAB = vo / R
αd = (2*g) / R
αAB = 0

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Answer:

\(\theta=25.84^\circ\)

Step-by-step explanation:

Pendulum

The length of the pendulum is 0.4 m or 40 cm. When swinging, it reaches the top height of 4 cm from the bottom. The geometric construction of this situation is shown in the image below.

The right triangle is formed by the length of the pendulum (40 cm), its horizontal displacement, and the vertical height projected by the pendulum.

This last distance is calculated subtracting the total length of the pendulum and the vertical displacement reached in its higher position.

We need to calculate the angle θ, for which we'll use the cosine since we know the adjacent leg and the hypotenuse:

\(\displaystyle \cos\theta=\frac{36}{40}=0.9\)

The angle is

\(\theta=\cos^{-1}(0.9)=25.84^\circ\)

\(\boxed{\theta=25.84^\circ}\)

Answer:

2/3 can be classified as..

Step-by-step explanation:

It can be classified as a rational number because it can be in the form of p/q as of fraction and is made up of two integers making p the numerator and for q a denominator not involving a zero.

Answer:

real

rational

Step-by-step explanation:

Step-by-step explanation:

Yᴏᴜʀ ᴀɴsᴡᴇʀ ɪs ɪɴ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ...

Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ

Answer:

216

Step-by-step explanation:

l x h x w\

or

length times height times width

The Probability that the student will arranged in order from shortest to tallest is 2.505210.

Probability is a branch of math which deals with the numerical description of certain events is to occur. It is the ratio of the numbers of favorable outcomes to the total number of outcomes. When solving probability problems we need to consider series of random experiments or experiments that involve several different aspects, such as drawing two cards from a deck or rolling several dice. the ability to calculate relative frequencies requires counting the number of possible outcomes of the experiment

If a class has 11 students who are to be randomly assigned seating in the order of shortest to tallest.

The total outcomes= 11! = 39916800

here the total favorable outcome is 1.so,

Probability = 1 / 39916800

                   = 2.505210

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