3u2-2=5u Quadratic Formula

The products that result in a difference of squares or a perfect square trinomial are Quadratic Equations, Perfect Square Binomials, and Difference of Squares. Difference of Cubes is incorrect.

Those apply:

All three of these products can be used to solve a variety of problems involving algebraic equations.

The task:

Which products result in a difference of squares or a perfect square trinomial?

Check all that apply:

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The Intermediate Value Theorem (IVT) states that for any continuous function f(z) and any real number a, if f(a) and f(b) have opposite signs, then there exists a number c in the interval (a,b) such that f(c) = 0.

The IVT states that if a continuous function has different signs (positive or negative) at two points in its domain, then it must have a zero in between those two points. In the case of the function f(z) = 26z^53 + 3, we are asked to find an integer n such that there exists a zero of the function in the interval [n/4, (n + 1)/4].

To find the solution, we can use the IVT by considering two points in the interval with opposite signs. For example, if we take n = 1, then the interval is [1/4, 2/4]. We can evaluate the function at the two endpoints of the interval and look for opposite signs:

f(1/4) = 26 * (1/4)^53 + 3 > 0

f(2/4) = 26 * (2/4)^53 + 3 < 0

Since the function has opposite signs at the endpoints, the IVT guarantees that there exists a zero of the function in the interval [1/4, 2/4]. This means that for n = 1, the IVT is satisfied and the function has a zero in the interval [1/4, 2/4].

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Complete Question:

For which integer n, 0 < n < 3 , does the IVT say that f(z) 26 53 + 3 has & zero in the interval [n/4, (n + 1)/4]?

10 mg of carbon-14 would still be present in the sample after 17,190 years.

The formula: A = A θ * (1/2)(t/t 1/2)

can be used to determine how much carbon-14 is still present in a sample after a specific number of years.

where A is the remaining carbon-14, A 0 is the initial carbon-14 concentration, t is the passing of time, t 1/2 is the carbon-14 half-life (5,730 years), and 1/2 is the decay factor.

By entering the specified values, we obtain:

A = 80 mg * (1/2)^ 5,730 years / 17,190 years

A = 80 mg * (1/2)^3

A = 80 mg * (1/8)

A = 10 mg

Therefore, 10 mg of carbon-14 would still be present in the sample after 17,190 years.

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Answer: Let's call the number of sandals manufactured in a typical month x, and the number of running shoes manufactured in a typical month y. The total cost for sandals and running shoes in a typical month is $2450, so the following equation represents the cost:

2.5x + 4y = 2450

During the month of April, the company doubled the number of sandals manufactured, so x becomes 2x. The total cost during the month of April is $3700, so the following equation represents the cost:

2.5(2x) + 4y = 3700

Expanding the left side:

5x + 4y = 3700

Subtracting the first equation from the second equation:

5x - 2.5x + 4y - 4y = 3700 - 2450

2.5x = 1250

Dividing both sides by 2.5:

x = 500

Substituting x = 500 into the first equation:

2.5 * 500 + 4y = 2450

Expanding and solving for y:

1250 + 4y = 2450

1250 - 1250 + 4y = 2450 - 1250

4y = 1200

Dividing both sides by 4:

y = 300

So the company makes 500 pairs of sandals and 300 pairs of running shoes during a typical month.

Step-by-step explanation:

The solution to the equation are k = 2 or k = -3.5

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

2k^2 - 14 = -3k

Express properly

So, we have the following representation

2k^2 + 3k - 14 = 0

Expand the equation

2k^2 + 7k - 4k - 14 = 0

So, we have

k(2k + 7) - 2(2k + 7) = 0

This gives

k - 2 = 0 or 2k + 7 = 0

Evaluate

k = 2 or k = -3.5

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Using Scalar multiplication, If all the conditions are satisfied, then the set is a subspace of R³

The result of multiplying a real number by a matrix is known as a scalar multiplication. Each entry of the matrix is multiplied by the specified scalar in scalar multiplication.

The following requirements must be met in order to establish whether a set is a subspace of R3 under addition and scalar multiplication:

Closure under addition: If elements u and v are present, then u plus v must also be present.

If u is a member of the set and k is any scalar, then ku must likewise be a member of the set. Closure under scalar multiplication.

The zero vector is contained in: The set must contain the zero vector (0, 0, 0).

includes all negative vectors; if u is in the set, then -u must also be.

These conditions must be checked for each set, and your response must be supported.

The set is a subspace of R³ if all the conditions are met.

The set is not a subspace of R³ if any of the requirements are not met.

Consequently, the set is a subspace of R³ if all of the conditions are met.

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Complete question -

The matrix A of T with transformation T: R²→R² and is reflection of the line y = -x is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

T: IR²→IR² is reflection of the line y = -x.

It is known that e1 = (1,0) and e2 = (0,1) is the standard basis of IR².

So, the transformation is T(e1) = e1' and T(e2) = e2'.

T(e1) = e1' = (0,1)

= 0(1,0) + (-1)(0,1)

= 0 · e1 + (-1) · e2

T(e2) = e2' = (-1,0)

= (-1)(1,0) + 0(0,1)

= (-1) · e1 + 0 · e2

So, now the matrix A becomes [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

Therefore, the new matrix is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

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Find the matrix A of T for the following transformation. T: R²→R² is a reflection in the line y = -x.

As t increases without bound. N(t) approaches:

N(t) is limited by the number of people who started the rumor.

The correct answer is option (A).

The given exponential model is defined as follows:

[tex]N(t)=5501+49e^{-0.7t}[/tex]

For t = 0

Substitute the value of t = 0 in the above equation,

[tex]N(t)=5501+49e^{-0.7\times0}[/tex]

N(t) = 5501 + 49 × 1

N(t) = 5501 + 49

N(t) = 5550

Thus, 5550 people started the rumor.

Since [tex]49e^{-0.7t}[/tex] is greater than zero for all real t.

Then, [tex]5501+49e^{-0.7t} > 5501\\[/tex]

So, as t increases without bound.

N(t) approaches:

N(t) is limited by the number of people who started the rumor.

Therefore, the correct answer is option (A).

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The complete question is as follows:

The equation [tex]N(t)=5501+49e^{-0.7t}[/tex] models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

How many people started the rumor?

N(t) approaches:

A. N(t) is limited by the number of people who started the rumor.

B. N(t) is limited by the carrying capacity of the town.

C. N(t) is limited by the number of days it takes for the entire population to hear the rumor.

D. N(t) is limited by the rate at which the rumor spreads.

E. N(t) is not limited by any value and increases without bounds.

A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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Answer:

16.429

Step-by-step explanation:

x+12.23=28.659

28.659-12.23=16.429

Answer:

Step-by-step explanation:

[tex]\mathrm{x + 12.23 = 28.659}[/tex]

Subtract 12.23 from both sides:-

[tex]\mathrm{x=28.659-12.23}[/tex]

Simplify  :-

[tex]\mathrm{x=16.429}[/tex]

___________________

-Hope this helps!

The volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the given vertices we can write the equation of the base of the triangular region as:

x = 1 - y

The area of the triangular region is given as:

A = 1/2 (b)(h)

A = 1/2 (1-y)(3)

The volume of the region is calculated by taking the integration of the area:

[tex]V = \int\limits^1_0 {\frac{3}{2} [1 - y] } \, dx\\\\V = \frac{3}{2} [y - \frac{y^2}{2} ]_0^1[/tex]

Substituting the values of the limit we have:

V = 3/2 [ 1 - 1/2]

V = 3/2 [1/2]

V = 3/4

Hence, the volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

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Answer: The FOIL method (First, Outer, Inner, Last) is a mnemonic used to help solve and simplify multiplication problems by using the distributive property. To use FOIL, you simply multiply the first term of the first factor with the first term of the second factor, the outer terms of the two factors, the inner terms of the two factors, and the last terms of the two factors. Then, you add the results together to obtain the final answer.

For example, in the first problem, (a + b)(2a - 3b^2), we FOIL by first multiplying "a" and "2a": 2a^2. Next, we multiply "a" and "-3b^2": -3ab^2. Then, we multiply "b" and "2a": 2ab. Finally, we multiply "b" and "-3b^2": -3b^3. Now, we add the four results together to get the final answer: 2a^2 + (-3b^2 + 2b)a - 3b^3.

a. (a + b)(2a - 3b^2) = 2a^2 - 3ab^2 + 2ab - 3b^3 = 2a^2 + (-3b^2 + 2b)a - 3b^3.

b. (k - 8)(4k + b) = 4k^2 + bk - 32k - 8b = 4k^2 + (b - 32)k - 8b.

c. (7x^15)(2x + 2) = 14x^16 + 14x^15 = 14x^15 (x + 1).

d. (3ab - 1)(2ab + 6) = 6a^2 b^2 + 2ab - 3ab + 6 - 2ab = 6a^2 b^2 + 4ab +

Step-by-step explanation:

The solution for the given initial-value is 6ty + t² - 9t + 4y² - y = 12

An initial value problem is a differential equation that is accompanied by an initial condition that specifies the value of one or more variables at a particular time or at a particular point in space. The initial value problem is to find the solution of the differential equation that satisfies the given initial condition. The solution of the initial value problem describes the behavior of the system over time or as a function of space based on the given initial conditions.

The given initial value problem is a non-linear ordinary differential equation and can be solved using numerical methods such as Runge-Kutta methods or numerical integration.

The solution to the initial value problem gives the function y(t) that satisfies the differential equation and the initial condition y(-1) = 2.

Given that

(6y + 2t − 9)dt = (8y 6t − 1)dy = 0

and y = -2

As both = 0 then (6y + 2t − 9)dt = (8y + 6t − 1)dy

that is

(6(-2) + 2t − 9)dt = (8(-2) + 6t − 1)d(-2)

−21dt + 2dt² = 34d−12dt

2dt² − 9dt - 34d

d(2t² −9t−34)

Integration both sides

6ty + t² - 9t + 4y² - y = c

Using y(-1) = 2

-12 + 1 + 9 + 16 - 2 = c

c = 12

Thus, the solution for the given initial-value is 6ty + t² - 9t + 4y² - y -12 = 0

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The angle in the sector formed in radian is 5/4 π

The length of an arc is defined as the part of the circumference of a circle which is bounded by two radii.

The length of an arc = tetha / 360 × 2πr

where( tetha) is the angle

r is the radius

360° = 2π

therefore :

15π/2 = tetha/2π × 2× 6 × π

15π/2 = 6 tetha

tetha = 15π/2 ÷ 6

tetha = 15/12 π

tetha = 5/4 π

therefore the value of the angle in radian Is 5/4 π

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The truth value of a is False and after seeing the result of 1st statement b is true.

A mathematical statement like "3 is bigger than 4," "an infinite set exists," or "7 is prime" is referred to as a proposition.

A statement that is presumptively true is known as an axiom. Although there are several exceptions, mathematical logic can typically classify a claim as true or false given enough information (e.g., "This statement is false").

let p(x):x^2<=4

the domain for x is all positive integers (1, 2, 3, . . .).

(a) p(5)

p(5):25 not equal or less than 4

hence the truth value of a is False

(b)  negation for x;p(x)

after seeing the result of 1st statement b is true.

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Answer:

-1, 6

0, -3

1, -3.9

2, -3.99

f(x) = 5^2x+1

Step-by-step explanation:

for the first question, after plugging in the values of x, we get our answer to be the 2nd table

-1, 6

0, -3

1, -3.9

2, -3.99

for the second question

f(x) = 5^2x+1

after graphing, we can see it never passes x = 2

The area of the billboard is [tex]1,632,400 cm^{2}[/tex], Option (d) is correct.

Since the linear scale factor f=20, then the billboard area:

A = [tex]77.53[/tex]×[tex]20^{2}[/tex]

= [tex]1,632,400 cm^{2}[/tex]

Linear scale Factor:

The size of the enlargement/reduction is represented by the scale factor. For example, a scale factor of 2 means that the new shape is twice the original shape. A scale factor of 3 means that the new shape is three times the size of the original shape.

Therefore, the area of the billboard is [tex]1,632,400 cm^{2}[/tex], and Option (d) is correct.

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Answer:

neither

Step-by-step explanation:

line T: m = -2/3

If line U was parallel to T it would have the same slope (-2/3)

If line U was perpendicular to T it would have a slope that is the negative reciprocal of the slope of line T  (3/2)

Answer:

Cheetah A ran at a faster speed than Cheetah B, as it ran 18 miles in 16 minutes while Cheetah B ran 54 miles in 50 minutes.

Step-by-step explanation:

Answer: its A

Step-by-step explanation:

The completed tiles are placed in the appropriate slots to prove that line j is parallel to k, as follows;

Statements         [tex]{}[/tex] Reasons

1. ∠6 ≅∠3 [tex]{}[/tex]          1. Given

2. ∠3 ≅∠2 [tex]{}[/tex]         2. Vertical ∠s ≅

3. ∠6 ≅ ∠2 [tex]{}[/tex]        3. Transitive Property

4. j ║ k       [tex]{}[/tex]         4. Corresponding ∠s ≅, lines ║

Parallel lines are are two lines that continue indefinitely and do not meet, such that they make the same or congruent corresponding angles with a common transversal.

The details of the reasons used to prove that line j is parallel to line k are as follows;

Vertical ∠s ≅

The vertical angles theorem states that vertical angles, which are angles formed by the intersection of two lines and which are located, opposite to each other are congruent.

Transitive property

The transitive property of congruency states that if a is congruent to b and b is congruent to c, them a is congruent to c

Corresponding ∠s ≅

The corresponding angles formed between parallel lines are congruent.

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The area of a triangle is 43.8178 square centimeters

Let the triangle's third side measure "x" cm.

circumference = x+8+11 = 32;

or x = 32-19 = 13 cm.

If we are aware of all three sides of a triangle, we can use "Heron's Formula" to determine its area.

Triangle's surface area equals the square root of s(s-a) (s-b) (s-c);

where s is the triangle's semi-perimeter; a, b, and c are its three sides.

As a result, s = 32/2 = 16 cm; a= 8 cm; b= 11 cm; and c= 13 cm.

Therefore, the triangle's area is equal to the square root of 16 X (16-8) X (16--11) X (16—13).

= Square root of (1920) = (16 X 8 X 5 X 3).

=43.8178 square centimeters

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The question seems incorrect;

What is the area of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32cm?

The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation dy/dx = y^2 - 4y are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

y² - 4y = 0

y(y - 4) = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation [tex]\frac{dy}{dx} = y^{2} - 4y[/tex] are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

[tex]y^{2} - 4y[/tex]= 0

[tex]y(y-4)[/tex] = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The x-intercept of the function is given by x=±9

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function y=x²-81

To find x-intercepts of the functions we set y=0

Thus y=x²-81

x²-81=0

x=√81

x=±9

Hence, The x-intercept of the function is given by x=±9

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Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability:

P(A|B)=P(A∩B)/P(A)

where:

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening

P(A) is the probability of A happening.

Event A: Positive test.

Event B: Body attempting to reject the kidney.

The percentages associated with a positive test are:

80% of 30%(experience kidney rejection).

9% of 70%(do not experience kidney rejection).

Hence:

P(A)=0.8*0.3+0.09+0.7

P(A)=0.303

The probability of both a positive test and the body attempting to reject the kidney is:

P(A∩B)=0.8*0.3=0.24

Hence, the conditional probability is:

P(B|A)=0.24/0.303

P(B|A)=0.7921.

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

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Answer:

113

Step-by-step explanation:

the formula is: π(d/2)^2

so:

π(12/2)^2=113.09...

Rounded that equals 113.0

Hope that helped! Let me know if you have any other questions.

Answer:

113.0 ft²

Step-by-step explanation:

Solution Given:

diameter(d) :12 ft

radius(r) = d/2= 12/2=6 ft

now

we have

area of the circle= πr²=22/7*6²= 113. 14 ft² =113 ft²

You are right

The coefficient of q in the sum of these two expression is 1/2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are (2/3q −3/4) and (−1/6 q − 2).

We have to add these two expressions.

First arrange in such a way that like terms are together.

(2/3q −3/4) + (−1/6 q − 2) = (2/3q - 1/6q) + (-3/4 - 2)

                                        = (4/6q - 1/6q) + (-3/4 - 8/4)

                                        = 3/6q - 11/4

                                        = 1/2 q - 11/4

Hence the sum of the given expressions is 1/2 q - 11/4. And the coefficient of q is 1/2.

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The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) Rate = k[a]2 - Second Order Rate Law

b) Rate = k[a] - First Order Rate Law

c) Rate = k - No Match

The rate law is an equation that describes the rate of a reaction as a function of the concentrations of the reactants. The rate of a reaction is typically represented as the change in concentration of a reactant or product over time.

a) The rate law equation for a second order reaction is rate = k[a]2, where k is the rate constant and [a] is the concentration of the reactant.

b) The rate law equation for a first order reaction is rate = k[a], where k is the rate constant and [a] is the concentration of the reactant.

c) There is no rate law equation for a reaction with a rate of k.

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The percentage change is 65.38%.

                                [tex]amount of change = \frac{new value - old value }{old value}[/tex]

If the amount of change is positive, it is an increase.

If the amount of change is negative, it is a decrease.

            % of change =amount of change * 100

According to the question,

new quantity = 40

original quantity =23

% change [tex]= \frac{new value - old value}{old value} * 100[/tex]

% change [tex]= \frac{40 - 23}{23} * 100[/tex] = 65.38%

So, the percentage change is 65.38%.

[tex]% change = \frac{new value - old value}{old value} * 100[/tex][tex]% change =\frac{new value - old value }{old value} * 100[/tex]

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Answer:

The expression 2a^2b^2 + 2b^2c^2 + 2a^2c^2 - a^4 - b^4 - c^4 can be factored as:

(2ab^2 + 2bc^2 + 2ac^2)(a^2 - c^2) - (a^2 - b^2)(a^2 - c^2)

= (a^2 + b^2 + c^2)(2ab^2 + 2bc^2 + 2ac^2) - (a^2 - b^2)(a^2 - c^2)