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?

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]

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

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

The Correct option is (B).

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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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:

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.

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

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

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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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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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:

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

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

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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Dimensions of the parallelogram are:

Its perimeter is:

Its area is:

Perimeter is 2 times greater:

Area is 2*2 = 4 times greater:

Perimeter is 3 times greater:

Area is 3*3 = 9 times greater:

Perimeter is 2 times smaller:

Area is 2*2 = 4 times smaller:

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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Step-by-step explanation:

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

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

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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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 .

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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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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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].

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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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.

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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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

1.  Convert lb./acre to grams/acre

2. Use the TKW to calculate seeds per 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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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

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

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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Answer:

1,520 pounds

Step-by-step explanation:

40x 38 = 1520

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:

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:

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

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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