What is the answer to this question?
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(4a2+2)(6a2-a+2)

Answer:

275 = 25 × 11

The greatest perfect square factor of 275 is 25.

The greatest perfect square that is a factor of 275 is 25.We were able to determine this by breaking down 275 into its prime factors and looking for pairs of factors that were the same.

We can break down 275 into its prime factors to help us determine the greatest perfect square that is a factor of 275.275 = 5 * 5 *11. Since a perfect square is the product of a number multiplied by itself, we need to look for pairs of prime factors that are the same. We can see that 5 is a repeated factor, which means that it is a perfect square. So, we can take out a pair of 5s and get:$$275 = 5 \times 5 \times 11 = 5^2 \times 11$$Therefore, the greatest perfect square that is a factor of 275 is 25.

we have found that the greatest perfect square that is a factor of 275 is 25. Since 5 was a repeated factor, we were able to take out a pair of 5s and get 5 squared, which is 25.

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On solving the provided question we cans say that quadratic equation - x^2-5x-4 = 0 and x = 1 , 3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

quadratic equation -

x^2-5x-4 = 0

x(x-1) -3(x-3) =

(x-1)(x-3) = 0

x = 1 , 3

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Answer:

"2-3 inches of snow":)

Step-by-step explanation:

The Qualitative information is "2–3 inches of snow".

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques.

Here, given that,

A local meteorologist reports the day's weather. "Currently sunny outside, 34°F. Skies will become overcast later this afternoon, as temperatures drop to 25°F, with windy conditions out of the north at 10–15 miles per hour. Radar indicates 2–3 inches of snow expected to fall later tonight."

Now , we know that the qualitative information is "2–3 inches of snow".

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Answer: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

There are 2 purple sections, 2 yellow sections, 3 blue sections, and 1 orange section.

Since there are fewer yellow sections than blue sections, the probability of landing on yellow is less than the probability of landing on blue.

Answer: b

Step-by-step explanation:

the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5) is approximately 24.79 units.

the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6] is approximately 1220.37 square units.

the volume of the solid formed by revolving D about the x-axis is approximately 5.58 cubic units.

the volume of the solid formed by revolving D about the y-axis is approximately 13.89 cubic units.

To find the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5), we need to use the formula for arc length:

L = ∫[a,b] sqrt(1 + [f'(x)]^2) dx

Taking the derivative of f(x), we get:

f'(x) = 8x

Plugging in f'(x) into the formula for arc length, we get:

L = ∫[2,5) sqrt(1 + (8x)^2) dx

Using a substitution of u = 1 + (8x)^2, we get:

du/dx = 16x

dx = du/16x

Substituting these into the integral, we get:

L = ∫[321, 1601) sqrt(u)/16x du

L = (1/128) ∫[321, 1601) u^(-1/2) du

L = (1/64) [u^(1/2)] [321, 1601)

L ≈ 24.79

Therefore, the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5) is approximately 24.79 units.

---

To find the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6], we need to use the formula for surface area of revolution:

A = ∫[a,b] 2πf(x) sqrt(1 + [f'(x)]^2) dx

Taking the derivative of f(x), we get:

f'(x) = 6x^2 - 20/x^2

Plugging in f(x) and f'(x) into the formula for surface area, we get:

A = ∫[1,6] 2π[2x^3 + 20/x] sqrt(1 + (6x^2 - 20/x^2)^2) dx

Using a substitution of u = 6x^2 - 20/x^2 + 1, we get:

du/dx = 12x + 40/x^3

dx = du/(12x + 40/x^3)

Substituting these into the integral, we get:

A = 2π ∫[7,217] (u-1)^(1/2)/6 du

Using a substitution of v = u - 1 and multiplying by 2π/6, we get:

A = π/3 ∫[6,216] v^(1/2) dv

A = π/3 [v^(3/2)/ (3/2)] [6,216]

A ≈ 1220.37

Therefore, the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6] is approximately 1220.37 square units.

---

To find the volume of the solid formed by revolving D about the x-axis, we need to use the formula for volume of solid of revolution:

V = ∫[a,b] π[f(x)]^2 dx

We can see that the region D is formed by the intersection of y

= 5x and y = x, so the bounds of integration are from x = 0 to x = 1.

Plugging in f(x) = (5x - x)^2 = 16x^2 into the formula, we get:

V = ∫[0,1] π(16x^2) dx

V = (16π/3) ∫[0,1] x^2 dx

V = (16π/3) [x^(3)/3] [0,1]

V = (16π/9)

Therefore, the volume of the solid formed by revolving D about the x-axis is approximately 5.58 cubic units.

---

To find the volume of the solid formed by revolving D about the y-axis, we need to use the formula for volume of solid of revolution:

V = ∫[a,b] π[f(x)]^2 dy

Since we have y = 5x and y = x, we can solve for x in terms of y to get the bounds of integration:

x = y/5 and x = y

So the bounds of integration are from y = 0 to y = 5.

Plugging in f(y) = (5y/4)^2 - (y/4)^2 = 24y^2/16 into the formula, we get:

V = ∫[0,5] π(24y^2/16)^2 dy

V = π(36/256) ∫[0,5] y^4 dy

V = (9π/64) [(y^5)/5] [0,5]

V = (1125π/256)

Therefore, the volume of the solid formed by revolving D about the y-axis is approximately 13.89 cubic units.

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Answer:

Here is it graphed. The equation was:

y=-3x+-2/5

Step-by-step explanation:

Answer:

Option 4 .

Step-by-step explanation:

We need to simplify out the given expression . The given expression is ,

\(\rm\implies \dfrac{ 12x^4 ( x -3)(x+5)}{30x(x+3)(x+5)}\)

Now see that the term ( x +5) is common in both numerator and denominator . Therefore we can cancel it out . The expression becomes ,

\(\rm\implies \dfrac{ 12x^4 ( x -3)\cancel{(x+5)}}{30x(x+3)\cancel{(x+5)}} =\dfrac{ 12x^4(x-3)}{30x(x+3)}\)

Now x⁴ and x can again be cancelled out in numerator and denominator . Similarly we can cancel 12 and 30 by 6 . We have ,

\(\rm\implies \dfrac{ 2x^3(x-3)}{5(x+3)}\)

On looking at the provided options , 4th option is correct .

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

Answer:

\(\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}\)

\(\textsf{2.} \quad 2x^2-4x+3\)

\(\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}\)

Step-by-step explanation:

Long Division Method of dividing polynomials

Divide the first term of the dividend by the first term of the divisor and put that in the answer.

Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.

Repeat until no more division is possible.

Write the solution as the quotient plus the remainder divided by the divisor.

\(\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}\)

Solution

\((5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}\)

\(\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}\)

Solution

\((6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3\)

\(\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}\)

Solution

\(\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}\)

The ordered pair of the inequality will be (9,-3).

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that inequality is given as y ≤ 1/3x−6.

The ordered pair can be calculated as:-

y ≤ 1/3x−6

Substitute the value of x equal to 9 and get the value of y,

y ≤ 1/3(9) - 6

y ≤ 3 - 6

y ≤ -3

Hence, the ordered pair will be (9,-3).

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The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

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Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

\(\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}\)

From inspection of the given right triangle RST:

Substitute the values into the formulas:

\(\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}\)

Solve the equation for x:

\(\implies \dfrac{20}{x}=\dfrac{x}{4}\)

\(\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}\)

\(\implies 80=x^2\)

\(\implies \sqrt{x^2}=\sqrt{80}\)

\(\implies x=\sqrt{80}\)

\(\implies x=\sqrt{4^2\cdot 5}\)

\(\implies x=\sqrt{4^2}\sqrt{5}\)

\(\implies x=4\sqrt{5}\)

Solve the equation for y:

\(\implies \dfrac{20}{y}=\dfrac{y}{16}\)

\(\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}\)

\(\implies 320=y^2\)

\(\implies \sqrt{y^2}=\sqrt{320}\)

\(\implies y=\sqrt{320}\)

\(\implies y=\sqrt{8^2\cdot 5}\)

\(\implies y=\sqrt{8^2}\sqrt{5}\)

\(\implies y=8\sqrt{5}\)

Answer:

Step-by-step explanation:

1.

Center: (-2, 3)

Radius: 10/2 = 5

Standard form/ equation: (x + 2)² + (y - 3)² = 25

Standard form:

(x - (-2))² + (y - 3)² = 5²

(x + 2)² + (y - 3)² = 25

2.

Center: (1, 1)

Radius: 6/2 = 3

Standard form/ equation: (x - 1)² + (y - 1)² = 9

Standard form:

(x - 1)² + (y - 1)² = 3²

(x - 1)² + (y - 1)² = 9

Hope this helps!

#1

Equation:-

More simply.

#2

Equation

The inequality to show the weight limit for the elevator is w < 1,800.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, the sign clearly stated that the total weight in the elevator must be less than 1,800 pounds.

The inequality will be:

w < 1800 where w is the weight.

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Answer:

(3,-2)

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex

Answer:

Step-by-step explanation:

100cm/m=260cm/xm

cross multiply and solve:

100x=260

x=2.6

Answer:

0.1,0.5,0.8,0.9

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

36 is the corresponding angle to the angle which is vertically opposite to g.

Corresponding angles are equal.

Vertically opposite angles are equal.

At \(4\) weeks, there is \(7ounce\) more total sap present than after \(2\) weeks.

The apostrophe is utilized prior to the letter "s" if it is one time measurement, as in "week's". Apostrophes are placed after the letter "s" if there are many time units involved, such as weeks.

A week is a span of seven days that was created artificially and without reference to the stars. The biblical narrative of the Creation, which states that God worked for six days before taking a day of rest on the seventh, and the ancient Israelites are widely credited with giving rise to the concept of the week.

Here, \(x=4\) and \(x=2\) is given

When \(x=4\), we get

\(y=3(4)+8\)

\(= 20\)

When \(x=2\), we get

\(y=3(2)+8\)

\(= 14\)

Difference \(=20-14=7\) ounce

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Answer:

y = 2x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (5, 6) into the partial equation

6 = 10 + c ⇒ c = 6 - 10 = - 4

y = 2x - 4 ← equation of line

Following are the mathematical operations for the numerics.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.

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Liliana's next step is to find the area of each of the two trapezoids.

From the question, we have the following parameters that can be used in our computation:

Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid

This is done using

Area = 1/2 * (sum of parallel sides) * height

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Complete question

Area of Trapezoids and Other Figures quick check

Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?

Answer:

$12,150

Step-by-step explanation:

I = Prt

I = (40500)(0.03)(10)

I = 12150

The standard deviation for this Gaussian random variable is approximately 5.09.

Standard deviations are a measure of the spread of data around the mean. The standard deviation is the square root of the variance of a dataset. It is the most commonly used measure of spread and is a measure of how the individual data points deviate from the mean. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

This is calculated by finding the square root of the variance of the random variable, which is the difference between the mean and the probability given:

Variance = (60 - 0.382)2 = 35.22

Standard deviation = √35.22 = 5.09

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Answer:

Your BMI is 14.3 kg/m²

Step-by-step explanation:

<33

The constraint can then be written as: S ≤ 0.07 × T. This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

The constraint can then be written as: S ≤ 0.07 × T, This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.

We are given that the amount of sulfur relative to the total output produced of chemical X may not exceed 7%. To express this constraint in a linear programming model, we can use the following equation:

Sulfur Content ≤ 0.07 × Total Output

Here, the "Sulfur Content" represents the total amount of sulfur present in the chemical blend, while "Total Output" refers to the total amount of chemical X produced. By setting the constraint to be less than or equal to 7% (0.07) of the total output, we are ensuring that the sulfur content does not exceed the given limit.

In a linear programming model, we usually use variables to represent quantities. Let S represent the Sulfur Content and T represent the Total Output. The constraint can then be written as:

S ≤ 0.07 × T

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Step-by-step explanation:

Think of it like a right triangle. Do you have a graph handy?

Ok, graph both of the points. Now connect the points. That's our hypotenuse and the side length we want to find.

Now, bring down a line from (-3,5) to the x axis. Do you see a right triangle?

All we have to do is find the hypotenuse of this right triangle we just drew. We already have the leg lengths which are 3 and 5. Using this, do the pythagorean theorem.

9+25=34

√34 is our hypotenuse & distance between the points

Answer:

\(\displaystyle d = \sqrt{34}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (0, 0)

Point (-3, 5)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

thats cool

Step-by-step explanation: