Colorado State Flag (7. 4. A. 1. 4)


Illustrative Mathematics


1. 4: Colorado State Flag


The side lengths of the state flag of Colorado are in the ratio 2:3. If a flag is 12 feet long, what is its height?

Answers

Answer 1

The height of the flag is 18 feets.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Length is equal to 2 (2 + 3) the sum of the side lengths.

The sum of side length divided by (12) equals (2/5)

12 = 0.4(sum of side length) (sum of side length)

divide both sides by 0.4.

The height of the flag is calculated as side lengths plus length.

Height of flag: (30 – 12) = 18 feet

Therefore, the height of the flag is 18 feets.

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Related Questions

How many permutations are there of all the letters in each name?

a) Inverary
b) Beamsville
c) Mattawa
d) Penetanguishene

Answers

Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.

a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.

b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.

c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.

d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.

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11. - a? - 2bc - Icl
if a = -2, b = 3,
and c = -3
problem in the photo
algebra

Answers

Answer:

11

Step-by-step explanation:

remember that the absolute value function always gives a positive value, that is

| - a | = | a | = a

substitute the given values into the expression

- a² - 2bc - | c |

= - (- 2)² - 2(3)(- 3) - | - 3 |

= - (4) - 2(- 9) - | 3 |

= - 4 + 18 - 3

= 14 - 3

= 11

50 points + brainliest PLS HELP ME ASAP. All I need is a right answer and a clear solution. Ty in advance! :)
(anyone who gives absurd answers will be reported right away) ​

Answers

Dimensions of the parallelogram are:

Base is b = 2 ft, Side is a = 5 ft, Height is h = 4 ft.

Its perimeter is:

P = 2(2 + 5) = 2(7) = 14 ft

Its area is:

A = bh = 2*4 = 8 ft²

When the scale factor is 2

Perimeter is 2 times greater:

P = 2*14 = 28 ft

Area is 2*2 = 4 times greater:

A = 4*8 = 32 ft²

When the scale factor is 3

Perimeter is 3 times greater:

P = 3*14 = 42 ft

Area is 3*3 = 9 times greater:

A = 9*8 = 72 ft²

When the scale factor is 1/2

Perimeter is 2 times smaller:

P = 14/2 = 7 ft

Area is 2*2 = 4 times smaller:

A = 8/4 = 2 ft²

solve for x and graph the solution on the number line below 7+x<16

Answers

Step-by-step explanation:

x<16-7x<11

.....................

What is the secret calculator app?

Answers

The secret calculator app is used to protect confidential Photos, Videos, Documents, Passwords, Notes, Contacts and To Dos.

The term calculator is referred as a device that performs arithmetic operations on numbers and it does the basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.

Here we need to find definition and the usage of secret calculator app.

As per the definition of calculator here we know that the app is used to acts like a photo vault to store all password protected files, and can only be viewed inside the app.

As the user who is unaware of this app you will never expect a simple calculator looking app is used to hide files.

Here if you want to access this you will need the password to open the photos from your child.

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how many 1/3 inch cubes does it take to fill a box with width 1 1/3 inches, length 1 1/3 inches, and height 1 2/3 inches?

Answers

The number of 1/3 inch cubes that will fill the box is 26.

Volume of an object.

The volume of an object is the amount or quantity of substance that it would conveniently contain. Different objects has their method of determining their volume depending on their shapes.

Given a cube of length 1/3 inch. The volume of the cube can be determined as;

volume of a cube = length x width x height

The volume of the cube = 1/3 * 1/4 * 1/3

                            = 1/9 cube inches

The volume of the box can be determined as;

Volume of the box = length x width x height

                       = 1 1/3 * 1 1/3 * 1 2/3

                       = 2.963 cubic inches

Volume of the box = 2.963 cubic inches

The number of 1/3 inch cubes that will fill the box = 2.963/ (1/9)

                                                        = 26.667

The number of 1/3 inch cubes that will fill the box is 26.

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Eight packages of paper weigh a total of 38 pounds. What is the weight of 40 packages of the same kind of paper?​

Answers

Answer:

1,520 pounds

Step-by-step explanation:

40x 38 = 1520

What is the answer of 2 by 7 and 3 by 5?

Answers

The answer of 2/7 + 3/5 is a fraction. The answer is 31/ 35.

To add two fractions, the denominators must be the same, in this case, the denominators are different, so we need to find a common denominator to add these two fractions.

A common denominator for 2/7 and 3/5 is 35.

So we can convert both fractions to have 35 as the denominator,

2/7 becomes (2×5)/(7×5) = 10/35

3/5 becomes (3×7)/(5×7) = 21/35

then we can add the numerators:

10/35 + 21/35 = 31/35

so the final answer is 31/35

This is also the simplest form of this fraction which would be 31/35.

--The question is not clear, answering to the question below--

"What is the answer of 2/7 + 3/5?"

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Which cube root function is always decreasing as x increases?
○ f(x) Jm³√x – 8
O
f(x) = 3√√x-5
f(x)=√√-(5-x)
f(x) = -3√x+5

Answers

Option D) f(x) = -3√x+5 is the cube root function is always decreasing as x increases

What is the Formula of Cube Root Function? f(x) = x is the formula for the fundamental (parent) cube root function. After transformations, it can alternatively take the form f(x) = a (bx - h) + k. Here, the transformations are denoted by the real numbers a, b, h, and k.The symbol "" designates the cube root. For instance, 8 Equals (2 + 2 + 2) = 2. Finding the cube root of a number is simple since 8 is a perfect cube number.You need to discover a number that, when multiplied twice by itself, equals the original number in order to get the cube root of a given integer. To get the cube root of 8, then, you need to identify the integer that, when multiplied by itself twice, equals 8. Therefore, since 2 2 2 = 8, the cube root of 8 is 2.

Given data :

y = ³[tex]\sqrt{x}[/tex] is an increasing function as when the value of x increases the value of y increases

And when the value of x decreases , the value of y also decreases.

Now if we have (x+a) or (x-a) instead of x, the function shall have a horizontal shift.

So it shall either move left or right but shall not flip.

So

y = ³[tex]\sqrt{(x - 8)}[/tex] and  y = ³[tex]\sqrt{(x - 5)}[/tex]

are increasing functions.

Only when x becomes -x, that the function shall flip & shall become a decreasing function.

But then it must be - (x-a) or -(x+a) inside.

So

y = ³[tex]\sqrt{-(5 - x)}[/tex] is also increasing

Only

y = ³[tex]-\sqrt{(x + 5)}[/tex] is a decreasing function.

Option D) is the right answer.

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For each linear relationship determine the y intercept write an ordered pair and explain its meaning
A: Ailee has a Gift card to a coffee shop worth $20 each drink she purchases using the gift card costs $4.25

B: Duncan begins to hike a trail that is an elevation of 1000 feet as he hikes his elevation increases 2000 feet each hour he hikes

Please help!!!

Answers

Answer: For the linear relationship in A, the y-intercept is the point where the line crosses the y-axis. This point represents the starting balance on Ailee's gift card before she makes any purchases.

The y-intercept of this linear relationship is the point (0, 20), which represents the fact that Ailee's gift card has a starting balance of $20 before she makes any purchases.

For the linear relationship in B, the y-intercept is the point where the line crosses the y-axis. This point represents Duncan's starting elevation before he begins to hike.

The y-intercept of this linear relationship is the point (0, 1000), which represents the fact that Duncan starts his hike at an elevation of 1000 feet.

Step-by-step explanation:

what is 2.8 repeating as adecimal

Answers

If you mean 2.8888888888...
Let 2.888888888... = X
Then 10X = 28.888888888888....
10X - X = 9X = 28.8888888888... - 2.88888888888... = 26
So X = 26/9
Hope this is what you were asking for.

Please provide an explanation

Answers

If [tex]$\mathrm{x} \neq 3$[/tex], the expression [tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}$[/tex] is equivalent to [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].

What is meant by expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.

A mathematical sentence with variables, numbers, or both is known as an expression. Operation can also be a part of an expression, although an equal sign is never present in an operation. A mathematical expression that demonstrates the equality of two expressions is called an equation. There is a sign of equality in equations.

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

Let the equation be

[tex]$\frac{2 x^3+7 x^2-3 x-25}{x+3}[/tex]

simplifying the equation, we get

[tex]$& \text { Divide } \frac{2 x^3+7 x^2-3 x-25}{x+3}=2 x^2+\frac{x^2-3 x-25}{x+3} \\[/tex]

[tex]$& =2 x^2+\frac{x^2-3 x-25}{x+3}[/tex]

[tex]$& \text { Divide } \frac{x^2-3 x-25}{x+3}=x+\frac{-6 x-25}{x+3} \\[/tex]

[tex]$ =2 x^2+x+\frac{-6 x-25}{x+3}[/tex]

Divide [tex]$\frac{-6 x-25}{x+3}=-6+\frac{-7}{x+3}$[/tex]

[tex]$=2 x^2+x-6+\frac{-7}{x+3}$$[/tex]

Simplifying the equation, we get

[tex]$=2 x^2+x-6-\frac{7}{x+3}$$[/tex]

Therefore, the correct answer is option 1) [tex]$2 x^2+x-6-\frac{7}{x+3}$$[/tex].

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surface area of this triangle

Answers

On solving the provided question we can say that - area of the given triangle will be A = 60 cm sq.

What is triangle?

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

B = 8cm

H = 15 cm

A = 1/2 BH = 1/2 X 8 X 15 = 60cm sq.

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Factor each polynomial completely.
a. 5a²c - 3a²d + 5b²c-3b²d
b. x^2n+ 6x^n +9

Answers

Answers
A = (a^2 + b^2) (5c - 3d)
B = (x^n + 3)^2

Explanation for A:
1. Factor out a^2 from (5a^2c - 3a^2d). This should look like a^2 (5c - 3d).

2. Factor out b^2 from (5b^2c - 3b^d). This should look like b^2 (5c - 3d).

3. Now multiply a^2 (5c - 3d) with b^2 (5c - 3d), by factoring out (5c - 3d) and writing a^2 + b^2 in parentheses like (a^2 + b^2) (5c - 3d)

Explanation for B:
1. Factor out x^n for x^2n + 6x^n, which should look like x^n (x^n + 6).

2. Write 9 as 3^2. The equation should look like x^n (x^n + 6) + 3^2. You can notice that the equation can be factored like (x^n + 3)^2 since you can get 6x^n by
(x^n + 3) multiples by 2, x^2n by squaring if, and 9 by squaring 3.

Sunnyvale School is having their

annual lobster race. A team

consists of five lobsters. The

team score is the average of the five finishing place positions. His sister sally’s team has consistently finished behind his team, however, an unusual pattern has been noticed. For example, Sally’s first lobster finished right behind Peter’s first lobster. Her second lobster finished 2 places behind peter’s second lobster. Her third lobster finished 3 places behind peter’s third, her fourth was 4 places behind his fourth and her fifth was 5 places behind his fifth.

What is Sally's team score?

Answers

Sally's team score is 6.

We can determine Sally's team score by calculating the average of her team's finishing place positions.

From the information given, we know that:

Sally's first lobster finished one place behind Peter's first lobster.Sally's second lobster finished 2 places behind Peter's second lobster.Sally's third lobster finished 3 places behind Peter's third lobster.Sally's fourth lobster finished 4 places behind Peter's fourth lobster.Sally's fifth lobster finished 5 places behind Peter's fifth lobster.

If we assume that Peter's team finished in 1st, 2nd, 3rd, 4th and 5th places, then we can calculate Sally's team score as follows:

Sally's first lobster finished in 2nd placeSally's second lobster finished in 4th placeSally's third lobster finished in 6th placeSally's fourth lobster finished in 8th placeSally's fifth lobster finished in 10th place

To find the average of the five finishing place positions, we add up all the places and divide by 5:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

So, Sally's team score is 6.

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how do i do this qution

Answers

y = -1/2x is the equation of example of the direct variation.

What is polynomia?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

Given four linear equations in them we need to state which equation is an example of direct variation.

The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Or in other words, the direct variation equation always passes through the origin point of a cartesian plane or (0, 0).

Therefore, in the given options y = -12/x is the only equation that is an example of direct variation.

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Which shows that the set of irrational numbers under addition is not closed?
3+3
π + π
π +3
3π + (−3π)

Answers

The option that shows that the set of irrational numbers under addition is not closed is B. π + π.

What is an irrational number?

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.

The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.

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Which statement correctly describes this picture?

Answers

Answer is option D.

Because there, TY is show as a ray with one end point only. And PR is a lone segment.

An investment portfolio is shown below.


Investment Amount Invested ROR
Stock A $1,800 1.5%
Stock B $4,600 3.7%
Stock C $580 11.2%
Stock D $1,122 −2.8%


Using technology, calculate the weighted dollar amount of Stock C.
$27.00
$64.96
$170.20
$184.00

Answers

The required weight of the dollar amount of Stock C is $64.96.

The Correct option is (B).

What is simplification?

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Given:

Investment Amount Invested ROR

Stock A     $1,800     1.5%

Stock B     $4,600     3.7%

Stock C     $580        11.2%

Stock D     $1,122      −2.8%

According to the question,

Weight of dollar amount of Stock C

= 580 × 11.2%

= 580 x 0.112

= $64.96

Hence, the required weight is $64.96.

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(2x + 5) (4x − 3) (5x - 4) can be expanded and fully simplified to give an expression of the form ax³ + bx² + cx + d.
Work out the values of a, b, c and d.

Answers

Answer:

To expand (2x + 5) (4x − 3) (5x - 4), you can use the distributive property and the FOIL method.

The distributive property states that for any two algebraic expressions a and b, and for any two numbers x and y, (a+b)(x+y) = ax + ay + bx + by.

The FOIL method is a way to multiply two binomials. It stands for First, Outside, Inside, Last, and it involves multiplying the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.

Using these methods, you can expand (2x + 5) (4x − 3) (5x - 4) as follows:

(2x + 5) (4x − 3) (5x - 4) = (2x)(4x)(5x) + (2x)(4x)(-4) + (2x)(-3)(5x) + (2x)(-3)(-4) + (5)(4x)(5x) + (5)(4x)(-4) + (5)(-3)(5x) + (5)(-3)(-4)

This can be simplified to:

= 40x³ - 32x² - 60x³ + 48x² - 20x³ + 15x² + 60x - 20x + 100x² - 20x + 12

Combining like terms, we get:

= -12x³ + 143x² + 100x + 12

So, the values of a, b, c, and d are a = -12, b = 143, c = 100, and d = 12.

Step-by-step explanation:

What is an example of an absolute value equation?

Answers

The absolute value of a given number is said to be the positive version of that number. For example, the absolute value of -5 is + 5, which can be written as: − I5 | = 5. Other examples of absolute values ​​of numbers: |−9| = 9, |0| = 0, − |−12| = −12, etc.

Absolute Value Equation:

An absolute value function is an algebraic function whose variables lie within the absolute value bar. This function is also called the modulus function, and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. In general, the absolute value function can be expressed as f(x) = a |x - h| + k, where a represents how much the graph stretches vertically, h represents the horizontal shift, and k represents the vertical shift of the graph for f(x) = |x|. represents If the value of 'a' is negative, the chart opens downwards, if positive, the chart opens upwards.

Now that we understand the meaning of the absolute value function, we understand the meaning of the absolute value equation f(x) = a |x - h|. + k and how the values ​​of a, h, and k affect the value of the function.

'a' value determines how the graph of f(x) is stretched vertically.'h' value specifies horizontal displacement'k' value specifies the vertical displacement

The vertex (x) = a |x - h| + k of the absolute expression f is given by (h, k). You can also use the vertices of f(x) = a |x - h| Find + k using the formula (x - h) = 0 . When determining the value of x, substitute that value into the formula to find the value of k.

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What is the product of 2x 3y )( 2x 3y )? *?

Answers

The product of (2x-3y)(2x+3y) is 4x^2-9y^2.

the solution of the question is as follows,

Product = (2x-3y)(2x+3y)

Product =2x(2x+3y)-3y(2x+3y)

Product = 2x(2x)+2x(3y)-3y(2x)-3y(3y)

{using distributive property of multiplication}

Product = 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0,

Product = 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

distributive property of multiplication

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a - b)(a + b) is equal to a^2 - b^2. This result is used as an identity.

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Find the value of x.
2x-8
6

Answers

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

[tex]6=2x-8 \\ \\ 2x=14 \\ \\ x=7[/tex]

Which expression is equivalent to 7(d - 4)?
Submit
7(-4+ d)
-4(d + 7)
(d + 7).-4
-28d + 7

Answers

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .

what is expression ?

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.

given

The correct response is 4 less than 7, since 4 is less than 7.

Thus, 7-4=3 could be considered.

The first section of 7–4 appears to be answer B.

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).

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what is -2/5 plus 4/3

Answers

The required solution to the given statement is 14/15.

What is the Least Common Multiple(LCM)?

The least common multiple is defined as the least positive integer that is dividable by both given numbers.

A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers. For example, the LCM of 4 and 5 is 20; 20 is the smallest number that is both a multiple of 4 and a multiple of 5

The statement is given in the question below as:

-2/5 plus 4/3

Here "plus" represents the addition sign (+)

So, the algebraic form of the above statement will be as:

⇒ -2/5 + 4/3

Take the LCM between the fractions, we get

⇒ ( -6 + 20)/15

⇒ 14/15

This means 14/15 is obtained from -2/5 plus 4/3.

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Jose has $34 to spend at the Texas State Fair. If the entrance ticket costs $12, then how much money does jose have to spend on food and games?

ONE-STEP EQUATIONS APPLICATION II 6TH MATH
WITH EQUATION!

Answers

Answer:

22

Step-by-step explanation:

34-12=22 you just basically subtract 34 and 12 and it gives you 22 but theres the equation too

34-12=22

Jose has 22$ to spend on food and games

Which table shows a proportional relationship between x and y?

Answers

Answer:

C

Step-by-step explanation:

Put in the form y/x and you should have equivalent fraction

12/4 = 3

15/5 = 3

18/6 = 3

When the fractions are simplified, they all equal 3.

A square has an unknown side length, 2x. Write a simplified expression for its perimeter (distance around the
outside of an object. Remember, side plus side plus...)

Answers

The simplified expression for its perimeter and area are 8x.

What is the perimeter of a square?

The perimeter of a square is the sum of the lengths of all the sides of a square. Thus, by summing the lengths of a square's four sides, we can get its perimeter.

An equal number of sides make up a square. As a result, the side of a square is added four times to determine the square's perimeter.

The formula for finding the Perimeter of square = 4*a

= 4 * 2x

= 8x

Perimeter of square = 8x

Hence, the simplified expression for its perimeter is 8x

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Solve the quadratic by factoring. 3x^{2}+7=-8x+3 3x 2 +7=−8x+3

Answers

The roots of the given quadratic equation are x = -2/3 and x = -2.

What is a quadratic equation?

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is a quadratic equation as follows -

3x² + 7 = - 8x + 3

The given quadratic equations are -

3x² + 7 = - 8x + 3

3x² + 8x = 3 - 7

3x² + 8x + 4 = 0

(x + 2/3)(x + 2) = 0

(x + 2/3) = 0   and   (x + 2) = 0

x = -2/3   and   x = -2    

Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.

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How do you calculate the number of seeds per acre?

Answers

1.  Convert lb./acre to grams/acre

2. Use the TKW to calculate seeds per acre.

What is acre?

The imperial system and US customary systems both use acres as a measure of land area.

According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.

A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.

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