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The solution of the equation is x = -2±2i√2. The solution to the equation is found in the Sridharacharya formula.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given equation;

x² + 4x + 12 = 0

The solution to the equation is found as;

x² + 4x + 12 = 0

The solution to the equation is;

\(\rm x=-b \pm \frac{\sqrt{b^2-4ac}}{2a} \\\\ \rm x=-4 \pm \frac{\sqrt{4^2-4\times 4 \times 1}}{2\times 4} \\\\\)

x = -2±2i√2

Hence the solution of the equation is x = -2±2i√2.

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Answer:

Length is 30cm

Width is 13cm

Step-by-step explanation:

Let the width be x cm;

The length will be 2x + 4 cm

Perimeter = 86cm

Perimeter is given by (2 × length) + (2 × width)

2(2x + 4) + 2x = 86cm

4x + 8 + 2x = 86cm

6x = 86 - 8 = 78cm

x = 78/6 = 13cm

Width (x) = 13cm

Length = 2(13) + 4 = 26 + 4 = 30cm

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles was 3:4

Let 3x and 4x are the seeds from the smaller and bigger pile.

= 4x + 2  (greedy hamster placed another 2 pounds of seeds in the bigger pile)

= 3x - 1/4 (ate 1/4 pound from the smaller pile)

4x + 2 = 5x

Because the quantities of seeds in those piles is in the ratio of 5:16

After solving:

x = 2

Smaller pile weight = 3x = 3(2) = 6

Bigger pile wieght = 4x = 4(2) = 8

Thus, the weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

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Answer:

Add maybe

Step-by-step explanation:

add the 500+400+200 try that hope it helps have a great day

Answer: 22

Step-by-step explanation:

Answer:

7.96 × 10⁸ kg

Step-by-step explanation:

Step 1: Given data

Step 2: Determine how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower

To determine this ratio, we need to do the following subtraction.

mG - mE = 8.05 × 10⁸ kg - 9.16 × 10⁶ kg = 7.96 × 10⁸ kg

The Golden Gate Bridge has approximately 7.96 × 10⁸ kg more than the Eiffel Tower.

Step-by-step explanation:

Slope formula:

\( \frac{y2}{x2} - \frac{y1}{x1} = m\)

m = slope

Substitute the points into the formula format:

\( \frac{ - 9}{8} - \frac{ - 3}{ - 4}=m \)

Using Integer rule for subtraction:

\( \frac{ - 9}{8} + \frac{3}{4} = m\)

Solve:

\( \frac{ - 6 \div 6}{12 \div 6} = - \frac{1}{2} = m \)

The slope is -1/2.

Answer:

-1/2 or -0.5

Step-by-step explanation:

You may determine the slope of a line by determining the rise and run of two points on the line. The rise is the vertical change between two places, whereas the run is the horizontal change. The slope is calculated by dividing the increase by the run: Slope equals rise run Slope is short for "raise and ."

Therefore, the slope of the line passing through the points (-4, -3) and (8, -9) is -1/2 or -0.5

~

Hope this helps!

Point A' is at (-2,-2)

Point D' is at (-2,4)

Just multiply each coordinate by 2

After dilation, value of point A' is, (- 2, - 2)

And, Value of Point D' is, (4, - 2)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

In the figure, polygon ABCD is dilated by a factor of 2 to produce A'B'C'D' with the origin as the center of dilation.

Now, We have;

A = (- 1, - 1)

D = (2, - 1)

Hence, After polygon ABCD is dilated by a factor of 2,

Point A' = (-1 ×2, - 1×2)

            = (- 2, - 2)

Point D' = (2×2, - 1×2)

             = (4, - 2)

Thus, After dilation, value of point A' is, (- 2, - 2)

And, Value of Point D' is, (4, - 2)

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A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).

In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;

f(x) = −x² + 2x - 15

f(x) = −2x + 2

0 = −2x + 2

2x = 2

x = 2/2

x = 1

For the maximum value of function 2, we have:

f(1) = −(1)² + 2(1) - 15

f(1) = -14

For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.

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Answer:

I would have to go with B-16

Step-by-step explanation:

A constant is a number value which does not vary (no variable)

Answer:

454%

Step-by-step explanation:

i think this is corrrect hope it helps

Answer:

The answer should be 454%

Step-by-step explanation:

Lmk if this helped

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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The required equation that model the scenario will be |x − 16| = 0.32 and x = 15.68

The modulus of a function can either be positive or negative. This can also be used to determine the minimum and maximum value of a function.

According to the question, we are told that a plant produces sport drinks, which must be within 0.32 fluid ounces of the advertised 16 fluid ounces on the label.

where:

x represents the volume

The equation to model the maximum and minimum volumes and determine the minimum volume in a bottle will be |x − 16| = 0.32

x - 16 = -0.32

x = -0.32 + 16
x = 15.68

The required equation that model the scenario will be |x − 16| = 0.32 and x = 15.68

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Answer:

its lx-16l =0.32: x=15.68

Step-by-step explanation:

Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle

in one hour is c 4

The line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.

If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.

The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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Volume of pyramid with a square base, where the perimeter of the base is 6. 9 cm and the height of the pyramid is 2. 8 cm is 2.6cm^3

To find the volume of a pyramid, we need to use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. Since the base of the pyramid is a square, we can find its area by squaring the length of one of its sides, which we can calculate using the perimeter information provided.

The perimeter of the base is given as 6.9 cm, which means each side of the square has a length of 6.9/4 = 1.725 cm. Therefore, the area of the base is (1.725)^2 = 2.97656 cm^2.

Now that we have both the base area and height of the pyramid, we can plug them into the volume formula:

V = (1/3)(2.97656 cm^2)(2.8 cm)

V = 2.631 cm^3

Rounding to the nearest tenth, we get the final answer as V = 2.6 cm^3.

In summary, to find the volume of a pyramid with a square base, we need to calculate the area of the base using the perimeter information provided, and then use the formula V = (1/3)Bh. Once we have the volume, we can round it to the nearest tenth of a cubic centimeter.

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The complete table is shown in the picture attached. The sale price of the product is $24.

The sale price is the original price minus the discount. It can be expressed as

S = P - D

Where

The discount when an item is on sale can be calculated by

D = d × P

Where d = percent of discount.

Complete the table shown in the picture!

We have

To complete the table, we should find the sale price.

From the information, the discount is

D = d × P

D = 80% × $120

D = $96

The sale price will be

S = P - D

S = $120 - $96

S = $24

The product has a sale price of $24.

The second picture attached shows the complete table.

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Answer:

First Net

Step-by-step explanation:

The first net will be the answer because you can see that the figure has a square base. The first net has a square base as well. Now, the side of the figure has equal triangles, and so does the first net. The first net fits the figure best.

Hope this helps :)

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

Answer:

1331/3375

Step-by-step explanation:

(11/15) ^3 = (11*11*11)/(15*15*15) =1331/3375

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

330 milkshakes

Step-by-step explanation:

240 divided by 8 = 90

90 = number of large milkshakes

240 + 90 = 330