What is the nature of the roots 5x² 3x 2 0?

The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.

The quadratic formula is expressed as;

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

x² + 3x - 28 = 0

Substitute the values of a, b, and c into the formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -3 ±√( 3² -  ( 4 × 1 × -28) )) / (2×1)

x = ( -3 ±√( 9 -  ( -112) )) / (2)

x = ( -3 ±√( 9 + 112 )) / (2)

x = ( -3 ±√( 121 )) / 2

x = ( -3 ± 11 ) / 2

x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2

x = -14/2, x = 8/2

x = -7, x = 4.

Therefore, -7 and 4 are the solutions to the equation.

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The simplification of the given expression is x² - x + 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is √x⁴ = x - 3.  The expression will be simplified as,

√x⁴ = x - 3

Solve the radical term first and simplify the expression further,

x² = x - 3

x² - x + 3 = 0

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My_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .

Now, According to the question:

Create a list containing your 3 variables : my_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .

How do I store multiple values in one variable Python?

append()

We use the append() method for this. You can use this to append single values to the list – value, list, tuple.

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Answer:

y ≈ 95.7°

Step-by-step explanation:

To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.

Inverse of tan(y°) = 4.12:

[tex]tan^{-1}(-0.10) = y[/tex]

Next, I used a scientific calculator to find the angle measure of y. I recommend using the Desmos Scientific Calculator.

[tex]95.7 = y[/tex]

Answer:

True

Step-by-step explanation:

Most of the function f(x) has the domain is (- infinity, positive infinity), So I think this is true!

The relation between area, height and volume is: volume = area * height

In this question we need to find the relation between area height and volume.

the formula for area and volume are based on height:

volume = base area * height

Let v represents the volume, A represents area and h represents the height.

V = A * h

As we know the volume of rectangular prism is:

volume = length * width * height

i.e., V = l * w * h

and the base area is:

area = length * width

i.e., A = l * w

Substitute A =  l * w in V = l * w * h

Then we get, V = A * h

Therefore, the relation between area, height and volume is: V = A * h i.e., volume = area * height

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The three steps for graphing linear inequalities are consists of solving the variables, plotting the points on graph and bound the region.

while solving the inequalities of two variables the inequal sign are changed by equal sign for a certain time. After determining the unknown value, we plot the points on the XY axis.

while graphing the inequal variables the region that satisfy the inequality is bounded by solid line or dashed line depends on the inequal sign.

hence, we need to plot the linear inequalities on XY axis in three steps.

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Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .

the sum of triangle is 180, sum of all the interior angles is equal to 180.

so if you know two angles then apply sum of triangles and find out the value of the third triangle.

isosceles triangle

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.

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The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that the integers lie between the numbers 29 and 39. The numbers will be,

29, { 30,31,32,33,34,35,36,37,38 }, 39

Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.

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Answer:

Sequence:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]

. . . . . . . . . .  ⭐ please take a ruler and measure the distance from AA',    . . .  . . . . . BB', CC', DD', and EE', and then write that distance (it should      . . . . . . . .  be the same for each measurement) in place of 5 in -5. I just     . . . . . . . .  wrote -5 because it was my best approximation for looking at     . . . . . . . .  a laptop screen. ⭐

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]

Step-by-step explanation:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.

The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.

Consider  a cylinder with radius r and height h.

we know that the formula for the volume of cylinder is,

V1 = π * r² * h

Consider a sphere with radius r1.

We know that the formula for the volume of sphere is,

V2 = 4/3 * π * r1³

If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r

V2 = 4/3 * π * r³

And V1 = π * r² * (2r)

V1 = 2 * π * r³

V1 = 2 * 3/4 * V2

V1 = 3/2 * V2

volume of cylinder = 3/2 *  volume of sphere

Therefore, the volume of a sphere = 2/3 * the volume of a cylinder

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The number 1. 8 in the form a / b, using integers, to show that it is a rational number is 9 / 5 .

Note that the number 1.8 consists of two parts 1 and 0.8.

The decimal 0.8 can be written as the fraction is 8 / 10

Add these two numbers :

= 1 + 8 / 10

multiply and divide by 10

= 10 / 10 + 8 / 10

= 10 + 8 / 10

= 18 / 10

simplify the number

= 2 * 3 * 3 / 2 * 5

= 1 * 3 * 3 / 1 * 5

= 9 / 5

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The margin of error is 0.086 and its C.I is (0.575 , 0.785).

What is margin of error?

n = 117 , x =87

Point estimate for the proportion:

P = x/n

= 81/118

= 0.68644

Confidence = 95%, α = 0.05

From z-table area 0.975 close to z=1.96

Margin of error, E = 1.96 √((0.68*0.55)/130)

= 1.96 * 0.05363

= 0.105

= 0.086

Confidence = P ± E

= 0.68 ± 0.105

=(0.68-0.105 , 0.68+0.105)

= (0.575 , 0.785)

Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).

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Answer:

62.5%

Step-by-step explanation:

5/8 × 100

should give you 62.6%

"A binomial is an algebraic expression which has exactly two terms." The examples of binomials are x² + 3, x + y, x³ + 2x, 9 + 7y, xy² + xy, etc.

A polynomial is of various types like monomial, binomial, trinomial, etc.

Monomial contains only single term.

Trinomial contains exactly three terms. All the three are dissimilar.

A binomial is said to have only positive exponents and no negative exponents.

In x³ + 2x, x³ and 2x are two different terms. The variable is only x. The exponent of x³ is 1, the exponent of x is 1. The coefficient of x³ is 1, the coefficient of x is 2.

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Speed of object = 40 feet per second

Given data :

Equation represent speed is s = d/t

Assume;

Speed = S

Time taken = T

Distance cover = D

So,

Speed = Distance / Time

S = D / T

Speed of object = 100 / 2.5

Speed of object = 40 feet per second

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The pigeonhole principle can be used to demonstrate that there must be at least one duplicate in the set nums. Each possible number that can appear in nums is a "pigeonhole" in this context, and each number within nums is a "pigeon."

Method or evidence to confirm that Nums must contain multiple duplicate number: Simple Strategy: Utilizing nested loops, it is intended to determine whether or not each element appears in the array more than once for each element.

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Answer:

A. [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

⭐ What is the multiplicative rate?

To find the multiplicative rate of this exponential function, we need to make an equation to see what each y-value gets multiplied by to get the next y-value.

I am picking the y-values 2 and 2/5, but you can choose any two consecutive y-values.

Equation (let x= the multiplicative rate of change):

[tex]2x = \frac{2}{5}[/tex]

Solve for x:

[tex]\frac{2x}{2} = \frac{2}{5}(2)[/tex]

[tex]x = \frac{2}{10}[/tex]

Simplify:

[tex]x = \frac{1}{5}[/tex]

∴ The multiplicative rate of change of the function is 1/5.

The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔABC

Now , the value of the sides of the triangle is

AB = 54 m

BC = 78 m

AC = 90 m

Now , for the triangle to be right angle triangle , it should satisfy the Pythagoras Theorem

So , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substitute the values in the equation , we get

AC² = AB² + BC²

90² = 54² + 78²

8100 = 2916 + 6084

8100 ≠ 9000

Therefore , the triangle ΔABC is not a right angle triangle

Hence ,

The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle

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The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

The function is an expression or law that defines a relationship between one variable and the independent variable and another variable the dependent variable

The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control

Some examples of a discontinuous function

f(x) = 1 / (x - 2)

f(x) = tan x

f(x) = x2 - 1

For x < 1 and f(x) = x3 - 5 for 1 < x < 2

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A relationship between one variable, the independent variable, and another variable, the dependent variable, is defined by an expression or law known as the function.

The variable being controlled in the problem is the independent variable, and the variable that changes as a result of this control is the dependent variable.

f(x) = 1 / (x - 2)

f(x) = tan x

f(x) = x2 - 1

For x < 1 and f(x) = x3 - 5 for 1 < x < 2

Answer:

see explanation

Step-by-step explanation:

AD = BC = 8 ( opposite sides of a parallelogram are congruent )

DC = AB = 15 ( opposite sides of a parallelogram are congruent )

Consecutive angles in a parallelogram are supplementary , sum to 180° , so

∠ A + ∠ D  = 180° , that is

∠ A + 68° = 180° ( subtract 68° from both sides )

∠ A = 112°

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 68° , and

∠ C = ∠ A = 112°

F=9/5C+32 is the required equation and Greg statement is true

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.

C=5/9(F-32)

We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.

F=9/5C+32

The temperature where John leaves has 77 F.

Let us convert to celsius.

C=5/9(77-32)

C=5/9(45)

C=5(5)

C=25 degrees.

25 degress< 30 degrees.

Hence, F=9/5C+32 is the required equation and Greg statement is true.

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You may use the expression to convert the length of 5 rows of ribbons to inches: length = 5w + (5 - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.

To convert 5 rows of ribbons to inches, you need to know the width of the ribbons and the spacing between the rows.

Let's say the width of the ribbons is w inches, and the spacing between the rows is s inches. In this case, the total length of the ribbons in 5 rows would be 5w + 4s inches, since there are 5 ribbons and 4 spaces between them.

For example, if the width of the ribbons is 0.5 inches and the spacing between the rows is 0.1 inches, the total length of the ribbons in 5 rows would be :5 × 0.5 inches + 4 × 0.1 inches = 2.5 inches + 0.4 inches = 2.9 inches.

In general, to convert the length of n rows of ribbons to inches, you can use the formula: length = nw + (n - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.

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Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.

To find the number of people that need to attend the pancake breakfast, we can set up the following equation:

Number of People x Cost per Person = Total Cost

We know that the total cost is $2,520 and the cost per person is $15, so we can substitute those values into the equation:

Number of People x $15 = $2,520

We can solve for the number of people by dividing both sides of the equation by $15:

Number of People = $2,520 / $15

This gives us the number of people that need to attend the pancake breakfast in order to raise the desired amount of money. In this case, the number of people is 168.

Therefore, Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.

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Answer:

Step-by-step explanation:

If the derivative of g(x) with respect to x (denoted d/dx g(x)) is equal to 0, then the derivative of the product g(x)sin(x) with respect to x can be found using the product rule for derivatives.

The product rule states that if f(x) and g(x) are two functions, then the derivative of the product f(x)g(x) with respect to x is given by:

d/dx (f(x)g(x)) = f(x) * d/dx g(x) + g(x) * d/dx f(x)

In our case, f(x) is g(x) and g(x) is sin(x). Substituting these values into the equation above, we get:

d/dx (g(x)sin(x)) = g(x) * d/dx sin(x) + sin(x) * d/dx g(x)

Since the derivative of sin(x) with respect to x is cos(x) and the derivative of g(x) with respect to x is 0, we can simplify this expression to:

d/dx (g(x)sin(x)) = 0 * cos(x) + sin(x) * 0

Which simplifies to:

d/dx (g(x)sin(x)) = 0

Therefore, if the derivative of g(x) with respect to x is equal to 0, then the derivative of the product g(x)sin(x) with respect to x is also equal to 0.

So basically for the first one do 14.0%x 4.6

Answer:

x = 10

Step-by-step explanation:

7x-22=3x+18

4x -22 = 18

4x = 40

x = 10

Dr. Yung has committed a type l ( false positive) error.

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).

A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),

Therefore, the error is a type 1 error.

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