-x^2+6x-2=0 solve using quadratic formula and explain why you used this method

The least common multiple of 3z² - 75 and z + 5 is 3z² - 45.

The least common multiple of 3z² - 75 and z + 5, we first need to factor each polynomial:

3z² - 75 = 3(z² - 25)

= 3(z - 5)(z + 5)

z + 5 = 1(z + 5)

Next, we identify the common factors between the two polynomials and take the highest power of each:

3(z - 5)(z + 5) has factors of 3, (z - 5), and (z + 5)

1(z + 5) has factors of 1 and (z + 5)

The least common multiple of these two polynomials is the product of the highest powers of each factor.

The least common multiple is:

LCM = 3(z - 5)(z + 5)

= 3z² - 45

We must first factor each polynomial to get the least common multiple of 3z²  - 75 and z + 5.

Z + 5 = 1(z + 5)

= 3z²  - 75

= 3(z² - 25)

= 3(z - 5)(z + 5)

The greatest power of each polynomial is then selected after determining the elements that the two polynomials have in common:

3(z - 5) Factors of (z + 5) include 3, (z - 5), and (z + 5).

The components of 1(z + 5) are 1 and (z + 5).

The sum of the greatest powers of each factor produces the least frequent multiple of these two polynomials.

This is the least frequent multiple:

LCM is equal to 3(z - 5)(z + 5) = 3z² - 45.

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Statement III is not accurate, as the increase in the total number of stuffed toys sold is approximately 0.15%, which is significantly lower than about 2%.

a. I and II

To assess the trends displayed in the given circle graphs for September and October, let's analyze each statement:

I. The market share held by cats increased by about 6.5 percentage points.

In September, the percentage for cats is 199 / 1312 ≈ 15.2%. In October, the percentage for cats is 285 / 1314 ≈ 21.7%.

The difference between these two percentages is approximately 21.7% - 15.2% ≈ 6.5 percentage points.

Therefore, Statement I is accurate, as the market share held by cats increased by about 6.5 percentage points.

II. Roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.

In September, the number of toys in the "other" category is 225. In October, it is 275.

The difference between these two quantities is 275 - 225 = 50.

To assess whether this represents roughly 22.2% more, we calculate 50 / 225 ≈ 0.222, which is approximately 0.222 * 100% ≈ 22.2%.

Therefore, Statement II is accurate, as roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.

III. The total number of stuffed toys sold increased by about 2%.

To calculate the total number of toys sold, we sum the quantities for each category in September (1312) and October (1314).

The difference between these two totals is 1314 - 1312 = 2.

To assess whether this represents an increase of about 2%, we calculate 2 / 1312 ≈ 0.0015, which is approximately 0.0015 * 100% ≈ 0.15%.

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Answer:

Answer is A.) I and II

Without any additional information or measurements, it's difficult to determine any specific properties or characteristics of Trapezoid EFGH. However, some general facts about trapezoids that may be helpful include:

Based on the information you provided, Trapezoid EFGH has a diagonal HF drawn, which is perpendicular to FG. EH is also perpendicular to both EF and HG. The length of side GH is 58 inches.

- Trapezoids have two parallel sides, known as the bases.
- The other two sides of a trapezoid are called the legs.
- The height of a trapezoid is the perpendicular distance between the two bases.
- The length of a diagonal of a trapezoid can be found using the Pythagorean theorem.
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The value of fraction is,

⇒ 19/50

Let numerator be X nd denominator be Y

Hence, WE get;

1st case;

X+6/Y=1/2

X+6 = Y/2

Y = 2X +12

2nd case

X/Y+7=1/3

X/2X +12+7=1/3                        

[putting value of Y from 1st case]

X/2X + 19 =1/3

3 X=2X +19

=19

Now ,Y = 2X + 12

= 2(19) + 12

= 50

Hence, the fraction is,

⇒ 19/50

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If the pattern from the survey was to hold for the larger population then the number of people who would walk 9 - 12 miles per week is 150 people.

To find the number of people who would walk 9 - 12 miles per week from the larger population, the formula is:

= Number of people who walk 9 - 12 miles from sample / Number of people in survey x Population of larger populace

Number of people who walk 9 - 12 miles in sample = 15 people

Number of people in survey :

= 5 + 10 + 15 + 20 + 25

= 75 people

The number of people who walked is:

= 15 / 75 x 750

= 0. 2 x 750

= 150 people

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Triangles ABC and DEF are similar but not congruent, Dilation on △ABC would generate △DEF as described in the statement. The correct option is A.

In a dilation, the shape is scaled up or down uniformly, maintaining the same shape but changing the size.

If triangles ABC and DEF are similar but not congruent, it means that they have the same shape but different sizes.

By performing a dilation on triangle ABC, we can obtain triangle DEF with the same shape but a different size.

This transformation involves multiplying or dividing the coordinates of the vertices by a scale factor, which changes the size of the triangle while preserving its proportions and angles.

Thus, the correct option is A.

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Your question seems incomplete, the probable complete question is:

Triangles ABC and DEF are similar but not congruent.

Which type of transformation on △ABC would generate △DEF as described in the statement?

A

Dilation

B

Translation

C

Reflection

D

Rotation

Step-by-step explanation:

In Mathematics, the circumference of any shape defines the path or the boundary that surrounds the shape. In other words, the circumference is also called the perimeter, which helps to identify the length of the outline of any shape. Recall that the definition of pi (π) is the circumference, c of any circle divided by its diameter, d. Put as an equation, pi is defined as

[tex]\pi = \frac{c}{d} [/tex]

Rearranging this to solve for c we get

[tex]c = \pi \: d[/tex]

The diameter of a circle is twice its radius, so substituting 2r for d

[tex]c = 2\pi \: r[/tex]

Answer:

A .

Step-by-step explanation:

enjoy . because i can't explain right now . ☹️

The discriminant is equal to zero (Δ = 0), the quadratic equation has a real double solution. And when the discriminant is less than zero (Δ < 0), the quadratic equation does not have real solutions, but it does have complex conjugated solutions.

If in a quadratic function the discriminant is greater than zero, it means that the function has two real and distinct roots. The discriminant of a quadratic function is calculated using the formula Δ =  - 4ac, where "a", "b" y "c" are the coefficients of the quadratic function in the standard form [tex]ax^2[/tex]+ bx + c = 0.

When the discriminant is greater than zero (Δ > 0), this indicates that the quadratic equation has different real solutions. That is, the parabola associated with the quadratic function intersects the x-axis at two distinct points. This implies that the function has two different real roots, which can be visualized as points intersecting with the x-edge in the graph of the function.

It is important to note that when the discriminant is equal to zero (Δ = 0), the quadratic equation has a real double solution. And when the discriminant is less than zero (Δ < 0), the quadratic equation does not have real solutions, but it does have complex conjugated solutions. In this last case, the parabola does not intersect the edge x y and has no real points of cut.

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Answer: log(12)

Step-by-step explanation:

log (x) + log (y) = log (xy)

log (3) + log (4) = log (3*4)................substitute

log (12)...................................................simplify

Answer:

[tex] log(12) [/tex]

Step-by-step explanation:

[tex] log(3) + log(4) = log(3 \times 4) [/tex]

[tex] = log12[/tex]

[tex]You \: can \: simplify \: further \: with \: your \: calculator \: if \: you \: wish [/tex]

The inverse of the function y = ln(x - 5) + 3 is:

y =  [tex]e^{(x - 3)} + 5.[/tex]

The inverse of the function y = ln(x - 5) + 3, we need to switch the roles of x and y and solve for the new y.

Let's proceed with the steps:

Swap x and y:

x = ln(y - 5) + 3

Solve for y:

x - 3 = ln(y - 5)

Convert to exponential form:

[tex]e^{(x - 3)[/tex] = y - 5

Solve for y:

y =  [tex]e^{(x - 3)} + 5.[/tex]

In order to find the new value of y for the function y = ln(x - 5) + 3, we must reverse the roles of x and y.

Let's move on to the actions:

Trade x for y:

x = ln(y - 5) + 3

Calculate y:

x - 3 = ln(y - 5)

Make the change to exponential form:

[tex]e^{(x - 3)[/tex] = y - 5

The formula for y is y = [tex]e^{(x - 3)} + 5.[/tex]

The equation y =  [tex]e^{(x - 3)} + 5.[/tex]

The inverse of the function y = ln(x - 5) + 3.

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Option A. The area of the land is approximately 1.54 square kilometers.

To find the area of the trapezoid, we can use the formula:

Area = (1/2) × (a + b) × h

where a and b are the lengths of the parallel sides, and h is the perpendicular distance between them.

Given:

Length of one parallel side (a) = 1.7 kilometers

Length of the other parallel side (b) = 2.4 kilometers

Perpendicular distance (h) = 0.75 kilometers

Plugging in the values into the formula:

Area = (1/2) × (1.7 + 2.4) × 0.75

Calculating the area:

Area = (1/2) × 4.1 × 0.75

Area = 2.05 × 0.75

Area = 1.5375 square kilometers

Rounding to the nearest hundredth:

Area ≈ 1.54 square kilometers

Therefore, the area of the land is approximately 1.54 square kilometers.

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Answer:

Lily will spend 12 hours for watching this season's 24 episodes of Captain's Cove.

Step-by-step explanation:

What is the division means?

For division, we need two values, one get divided by other. let a is divided by b i.e.,  . It means a is divided in b parts.

In our case, given that

30 episodes watching time is 15 hours for Lily.

So we can divide 15 hours in 30 parts to get one episode watching time.

30 episodes watching time ⇔ 15 hours

1 episode watching time ⇔      hours

In the same way, 24 episodes watching time calculated as:

24 episodes watching time  ⇔  24(  )  hours = 12 hours

Hence for 24 episodes of Captain's Cove, Lily will spend 12 hours to watching this season.

To match the pairs , compare each coordinate with the others in the list, looking for the ones with matching x and y values.drag the tiles to the correct boxes to indicate that they represent the same point

I understand that you want to match pairs of coordinates representing the same point. However, I cannot physically interact with tiles or boxes. Nevertheless, I can provide you with some guidance on how to match coordinates.

When matching pairs of coordinates (x, y), you need to find the ones that have the same x and y values. For example, if you have the coordinates (3, 4) and (3, 4), these represent the same point since both the x and y values are the same.

Remember to carefully examine each coordinate, ensuring that both x and y values match before confirming the pairs.

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Answer:

a₇ = 66 , [tex]a_{n}[/tex] = 9n + 3 , a₅₆ = 507

Step-by-step explanation:

(1)

there is a difference of + 9 between consecutive terms, that is

21 - 12 = 30 - 21 = 39 - 30 = 9

add 9 to each term to find the next term in the pattern

a₄ = 39

a₅ = a₄ + 9 = 39 + 9 = 48

a₆ = a₅ + 9 = 48 + 9 = 57

a₇ = a₆ + 9 = 57 + 9 = 66

that is the 7th term a₇ = 66

(2)

since there is a common difference between consecutive terms, then this is an arithmetic sequence with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 12 and d = 9 , then

[tex]a_{n}[/tex] = 12 + 9(n - 1) = 12 + 9n - 9 = 9n + 3

general rule is [tex]a_{n}[/tex] = 9n + 3

(3)

use the general rule with n = 56 to obtain 56th term

a₅₆ = 9(56)  + 3 = 504 + 3 = 507

The required area of the shaded sector is 5π square units.

To find the area of the shaded sector, we need to know the central angle of the sector.

We know that the diameter of the circle is 10, which means the radius is 5 units.

The shaded area is 72°, which means the central angle of the sector is also 72°.

The formula to find the area of a sector is:

Area of sector = (central angle / 360) x πr^2

Substituting the values we have:

Area of sector = (72/360) x π(5)^2

Area of sector = (1/5) x 25π

Area of sector = 5π

Therefore, the area of the shaded sector is 5π square units.

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Using cosine rule, the value of side a in the triangle is 2.63 units

The cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

To determine if the data given is a triangle, we can use cosine theorem and find the missing value.

a² = b² + c² - 2(b)(c) cosA

Substituting the values into the formula;

a² = 4² + 6² - 2(4)(6) cos20

a² = 52 - 45.1

a² = 6.9

a = √6.9

a = 2.63 units

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Answer:

[tex]x=\dfrac{13}{4}[/tex]

Step-by-step explanation:

If the line segment labelled "x" is parallel to the side of the triangle labelled "26", then the two triangles are similar triangles.

Since the corresponding sides lengths are in the same ratio in similar triangles:

[tex]x : 26 = 2 : (14 + 2)[/tex]

Solving for x:

[tex]\begin{aligned}\dfrac{x}{26}&= \dfrac{2}{(14 + 2)}\\\\\dfrac{x}{26}&=\dfrac{2}{16}\\\\\dfrac{x}{26}\cdot 26&=\dfrac{2}{16} \cdot 26\\\\x&=\dfrac{52}{16}\\\\x&=\dfrac{13}{4}\end{aligned}[/tex]

Therefore, the value of x is 13/4.

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[tex]2\sqrt3(cos(-5\pi/12) + i sin(-5\pi/12))[/tex] is the complex number division.

To divide the complex number [tex]\frac{ (32(cos(7\pi/4)+ i sin(7\pi/4)))} {(4\sqrt2 (cos(5\pi/6)+ i sin(5\pi/6)))}[/tex], we can use the formula for dividing complex numbers in polar form.

First, we can convert the complex numbers to polar form by using the identities [tex]cos(\theta) = Re^{(\theta)[/tex] and [tex]sin(\theta) = Re^{(i\theta)[/tex], where R is the magnitude of the complex number and theta is its argument.

For the numerator,

we have [tex]32(cos(7\pi/4)+ i sin(7\pi/4)) = 32(\sqrt2/2 - i \sqrt2/2)[/tex]

= [tex]32(\sqrt2/2(cos(-\pi/4) + i sin(-\pi/4)))[/tex].

Therefore, the magnitude of the numerator is [tex]32(\sqrt2/2) = 16\sqrt2[/tex], and its argument is[tex]-\pi/4[/tex].

For the denominator, we have

[tex]4\sqrt2(cos(5\pi/6)+ i sin(5\pi/6))\\\\ = 4\sqrt2(\sqrt3/2 + i/2)\\\\ = 2\sqrt6+ 2i[/tex].

Therefore, the magnitude of the denominator is 4√6, and its argument is π/6.

To divide the two complex numbers, we can divide their magnitudes and subtract their arguments:

[tex]\frac{(32(cos(7\pi/4)+ i sin(7\pi/4)))} {(4\sqrt2 (cos(5\pi/6)+ i sin(5\pi/6)))}\\\\ = (16\sqrt2 / 4\sqrt6) * (cos(-\pi/4 - \pi/6) + i sin(-\pi/4 - \pi/6))[/tex]

Simplifying the magnitude, we get [tex](16\sqrt2 / 4\sqrt6) = 2\sqrt3[/tex].

Simplifying the argument, we get [tex]-\pi/4 - \pi/6 = -5\pi/12[/tex].

Therefore, the complex number division is equal to [tex]2\sqrt3(cos(-5\pi/12) + i sin(-5\pi/12))[/tex].

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Let purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than the length L of the awning is 38.50 in.

Let L represent the length

Hence, sin 105° / 88 = sin 25° /L

88 × sin 25° / sin 105°

88 × 0.4226 / 0.9659

L= 37.1888/  0.9659

L = 38.50 in

Therefore, the length is 38.50 in.

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The expression of "seven less than four times a number" in algebraic notation is 4x - 7

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

seven less than four times a number

Represent the number with x

So the statement can be rewritten as follows:

four times a number means 4x

So, we have the following

seven less than 4x

seven less than means - 7

So, we have the following

4x - 7

Hence, the expression "seven less than four times a number" in algebraic notation is 4x - 7

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Answer:

  a) {0.63450, 5.63968}

  b) {0.52360 (=π/6), 2.61799 (=5π/6), 3.34395, 6.08183}

  e) {1.23096, 2.09440 (=2π/3), 4.18879 (=4π/3), 5.05223}

Step-by-step explanation:

You want solutions to three quadratic equations involving trig functions.

These identities are useful in the solution process.

  cos²(x) = 1 -sin²(x)

  cos(2x) = 2cos²(x) -1

Using z = cos(x) and putting this in standard form we have ...

  5z² +6z -8 = 0

  (5z +10)(5z -4)/5 = 0 . . . . factor

  (z +2)(5z -4) = 0 . . . . simplify

  z = -2, z = 4/5 . . . . . . -2 is extraneous, as |cos(x)| ≤ 1

  x = {arccos(4/5), 2π-arccos(4/5)} ≈ {0.63450, 5.63968}

Using z = sin(x) and the cos² identity, we have ...

  -10(1 -z²) -3z +9 = 0

  10z² -3z -1 = 0 . . . . . . . . . . . simplify

  (10z -5)(10z +2)/10 = 0 . . . . factor

  (2z -1)(5z +1) = 0 . . . . . . . . simplify

  z = 1/2 or -1/5

  x = arcsin(1/2) or arcsin(-1/5) and π less those values

  x ≈ {π/6, 5π/6, 3.34295, 6.08183}

Using z = cos(x) and the double-angle identity, we have ...

  3(2z² -1) +2 +z = 0

  6z² +z -1 = 0 . . . . . . . . . . . simplify

  (6z +3)(6z -2)/6 = 0 . . . . . factor

  (2z +1)(3z -1) = 0 . . . . . . . simplify

  z = -1/2 or 1/3

  x = arccos(-1/2) or arccos(1/3) and 2π less these values

  x ≈ {1.23096, 2.09440, 4.18879, 5.05223}

__

Additional comment

The first two attachments show the calculator results. (Some of the numbers may not be in the desired interval.)

The remaining three attachments show graphing calculator solutions. The graphing calculator provides a quick and easy solution directly in radians, though maybe not to very many decimal places. (The solutions can be refined to as much numerical precision as you like.)

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Answer:

णततरतज्ञ ररर है कि वह अपने आप

Answer:

1 Question: D

2 Question: C

Just Imo. I did the work tho.

The estimated probability P(more than 4) is approximately 0.9678.

P(more than 4) ≈ 0.9678. A.

To determine whether the normal distribution can be used as an approximation to the binomial distribution, we need to check if both np and nq are greater than or equal to 5.

n = 11 and p = 0.6.

np = 11 × 0.6

= 6.6

nq = 11 × (1 - 0.6)

= 4.4

Since np = 6.6 is greater than 5 and nq = 4.4 is not less than 5, the normal distribution can be used as an approximation.

To estimate P(more than 4) using the normal distribution approximation, we need to find the mean and standard deviation of the binomial distribution, which can be approximated by the normal distribution.

Mean (μ) = np

= 11 × 0.6

= 6.6

Standard Deviation (σ) = √(npq)

= √(11 × 0.6 × 0.4)

≈ 1.397

Now we can use the normal distribution to estimate P(more than 4).

Since we are interested in more than 4, we need to find P(X > 4).

We can standardize the value of 4 using the mean and standard deviation calculated above and then look up the corresponding area under the standard normal distribution curve.

Z = (X - μ) / σ

= (4 - 6.6) / 1.397

≈ -1.860

Looking up the corresponding area in the standard normal distribution table or using a calculator, we find that the area to the left of -1.860 is approximately 0.0322.

P(X > 4) = 1 - P(X ≤ 4)

P(X > 4) ≈ 1 - 0.0322

≈ 0.9678

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The arc angle BCD of in the cyclic quadrilateral is 114 degrees.

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angle in a cyclic quadrilateral is 360 degrees.

The opposite angles of a quadrilateral is supplementary.

Therefore, let's find arc angle BCD as follows:

57 = 1 / 2 (56 + arc CD)

let

arc CD = x

57 = 1 / 2 (56 + x)

57 = 28 + 0.5x

57 - 28 = 0.5x

x = 29 / 0.5

x = 58 degrees

Therefore,

arc angle BCD = 56 + 58

arc angle BCD = 114 degrees

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