If x2 − 8xy + 12y2 = 8 and x − 6y = 3, then x − 2y =

Proportion is a mathematical concept that describes the relationship between two or more quantities. It is often represented using ratios and can be used to solve for unknown values, scale measurements, and interpret data.

Proportion is a mathematical concept that describes the relationship between two or more numbers or quantities. It is a way of expressing that one quantity is equal to another quantity, or that one quantity is a fraction or multiple of another quantity. Proportions can be represented using ratios, which compare the relative sizes of different quantities.

For example, if we have two ratios, such as 1:2 and 3:6, we can determine if they are proportional by cross-multiplying and checking if the products are equal. In this case, 1 × 6 = 2 × 3, so the ratios are proportional.

Proportions are used in many different areas of mathematics, such as solving for unknown values, scaling up or down, and interpreting data. They are also used in real-world applications, such as finding the missing side length of a similar triangle or calculating the unit price of a product.

The correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.

Let's analyze each statement and determine which one is true:

A. "2/5 of the total tuba and trumpet players are tuba players."

To find out if this statement is true, we need to determine what portion of the total number of players are tuba players. Since the ratio of trumpet players to tuba players is 5:2, for every 5 + 2 = 7 players, 2 are tuba players. So, the proportion of tuba players is 2/7, not 2/5. Therefore, Statement A is false.

B. "The number of trumpet players is 2.5 times the number of tuba players."

According to the given ratio, for every 5 trumpet players, there are 2 tuba players. Thus, the number of trumpet players is indeed 2.5 times the number of tuba players. Therefore, Statement B is true.

C. "There are 2 trumpet players for every 5 tuba players."

This statement matches the given ratio, so it is true. However, it doesn't provide any additional information beyond what's already given in the initial problem.

D. "If there are a total of 100 trumpet and tuba players, 52 of them are tuba players."

To verify this statement, we can calculate the number of tuba players using the given ratio. Since the total ratio parts is 5 (trumpet) + 2 (tuba) = 7, and the total number of players is 100, we can find the number of tuba players as (2/7) * 100 = 28. Thus, Statement D is false.

Therefore, the correct answer is Statement B: "The number of trumpet players is 2.5 times the number of tuba players." This statement accurately reflects the given ratio of trumpet players to tuba players.

Answer:

48√3 sq. in.

Step-by-step explanation:

I know this is correct bc I just had this question and this was the correct answer

Answer:

false

Step-by-step explanation:

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Answer: [tex]x(7y)[/tex]

Step-by-step explanation:

The given expression: [tex]7(xy)[/tex]

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication  :-

[tex]a\times b=b\times a[/tex] for any numbers a and b.

Associative property of multiplication :-

[tex]a\times(b\times c)=(a\times b\times c)[/tex] for any numbers a , band c.

Now, [tex]7(xy)=(7x)y[/tex] [Associative property of multiplication]

[tex]=(x7)y[/tex]  [Commutative property of multiplication]

[tex]=x(7y)[/tex]    [Associative property of multiplication]

Answer:

10.5 days

Step-by-step explanation:

Point slope form

y-5=10(x-1)

Substitute for y

100-5=10(x-1)

Distribute the 10

100-5=10x-10

Combine like terms

95=10x-10

Add ten to both sides

105=10x

Divide by 10

X = 10.5

Answer:

[tex]9\frac{13}{20}\text{ inches}[/tex]

Step-by-step explanation:

Given,

Tucson's average rainfall = [tex]12\frac{1}{4}\text{ inches}=\frac{49}{4}\text{ inches}[/tex]

Also, Yumas's average rainfall = [tex]2\frac{3}{5}\text{ inches}=\frac{13}{5}\text{ inches}[/tex]

Difference between Tucson's average rainfall and Yumas's average rainfall

[tex]=\frac{49}{4}-\frac{13}{5}[/tex]

[tex]=\frac{245-52}{20}[/tex]

[tex]=\frac{193}{20}[/tex]

[tex]=9\frac{13}{20}[/tex]

Hence, Tucson gets [tex]9\frac{13}{20}[/tex]  inches more rainfall.

Answer:

30.27272727272727 and repeating.

Step-by-step explanation:

Answer: [tex]13\sqrt{7}[/tex]

Step-by-step explanation:

In the simple radical form there are no square root is remain to find.

Since, the given expression,

[tex]5\sqrt{28} + \sqrt{63}[/tex]

[tex]5\sqrt{4\times 7} + \sqrt{9\times 7}[/tex]

[tex]5\sqrt{4} \times \sqrt{7} + \sqrt{9}\times \sqrt{7}[/tex]

[tex]5\times 2 \times \sqrt{7} + 3\times \sqrt{7}[/tex]

[tex]10 \sqrt{7} + 3\sqrt{7}[/tex]

[tex](10 + 3)\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

Since, we do not need to find further square root of 7.

Thus, the required radical form of [tex]5\sqrt{28} + \sqrt{63}[/tex] is [tex]13\sqrt{7}[/tex].

Answer:

[tex]13\sqrt{7}[/tex]

Step-by-step explanation:

[tex]5\sqrt{28} +\sqrt{63}[/tex]

To simplify the given expression we simplify each radical

[tex]5\sqrt{28} = 5\sqrt{4*7} = 5*2\sqrt{7} =10\sqrt{7}[/tex]

[tex]\sqrt{63} = \sqrt{9*7} =3\sqrt{7}[/tex]

[tex]5\sqrt{28} +\sqrt{63}[/tex]

[tex]10\sqrt{7}+3\sqrt{7}[/tex]

[tex]13\sqrt{7}[/tex]

The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) is -3/4.

The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) can be found using the concept of implicit differentiation. To find the slope, we need to differentiate the equation with respect to x and then substitute the coordinates (2, -1) into the resulting equation. Let's solve it step by step.

First, we differentiate the equation implicitly with respect to x:

2y * dy/dx + 3(xy + 1)^2 * (y + x * dy/dx) = 0

Next, we substitute the values x = 2 and y = -1 into the equation:

2(-1) * dy/dx + 3(2(-1) + 1)^2 * (-1 + 2 * dy/dx) = 0

Simplifying the equation:

-2dy/dx - 3 * 1 * (-1 + 2dy/dx) = 0

-2dy/dx + 3 + 6dy/dx = 0

Combining like terms:

4dy/dx = -3

Finally, solving for dy/dx, we get:

dy/dx = -3/4

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The slope of the tangent line to the curve at the point \((2, -1)\) is:

[tex]\[\boxed{\frac{3}{4}}\][/tex]

To find the slope of the tangent line to the curve given by the equation [tex]\( y^2 + (xy + 1)^3 = 0 \)[/tex] at the point [tex]\( (2, -1) \)[/tex], we need to use implicit differentiation.

Given the curve:

[tex]\[y^2 + (xy + 1)^3 = 0\][/tex]

We differentiate both sides with respect to x . Using the chain rule and implicit differentiation, we get:

[tex]\[\frac{d}{dx} [y^2] + \frac{d}{dx} [(xy + 1)^3] = 0\][/tex]

First, differentiate [tex]\( y^2 \):[/tex]

[tex]\[\frac{d}{dx} [y^2] = 2y \frac{dy}{dx}\][/tex]

Next, differentiate [tex]\( (xy + 1)^3 \)[/tex] using the chain rule:

[tex]\[\frac{d}{dx} [(xy + 1)^3] = 3(xy + 1)^2 \cdot \frac{d}{dx} [xy + 1]\]\[= 3(xy + 1)^2 \cdot (y + x \frac{dy}{dx})\][/tex]

Putting it all together, we get:

[tex]\[2y \frac{dy}{dx} + 3(xy + 1)^2 (y + x \frac{dy}{dx}) = 0\][/tex]

Now, substitute [tex]\( x = 2 \) and \( y = -1 \)[/tex] into the equation:

[tex]\[2(-1) \frac{dy}{dx} + 3((2)(-1) + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(-2 + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(1) \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1) + 6 \frac{dy}{dx} = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} - 3 + 6 \frac{dy}{dx} = 0\][/tex]

[tex]\[4 \frac{dy}{dx} - 3 = 0\][/tex]

[tex]\[4 \frac{dy}{dx} = 3\][/tex]

[tex]\[\frac{dy}{dx} = \frac{3}{4}\][/tex]

So, the slope of the tangent line to the curve at the point \((2, -1)\) is:

[tex]\[\boxed{\frac{3}{4}}\][/tex]

The probability of getting 5 hearts from the deck of cards is 0.0962.

We need to find the probability of getting 5 hearts.

A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suite contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

P(E)=Number of favourable outcomes/Total number of outcomes.

Now, P(E)=5/52=0.0962

Therefore, the probability of getting 5 hearts from the deck of cards is 0.0962.

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Answer: Second option is correct.

Step-by-step explanation:

The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"

As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.

Hence, Second option is correct.