A rectangle is inscribed in the upper half of the circle x2 y2 = a2 as shown at right. calculate the area of the largest such rectangle.

To solve the given system of linear equations, subtract one equation from the other to eliminate the y-variable, then solve for x and substitute back to find y. The solution is x = 2, y = -1.

To solve the system of equations 6x + 3y = 9 and 2x + 3y = 1, we can use the subtraction method. We want to find the values of x and y that satisfy both equations simultaneously. Observing that both equations have the term 3y, we can subtract the second equation from the first to eliminate the y-terms:

The solution to the system of equations is x = 2, y = -1.

Lines with equations y=−4x−3 and 4x+y=−1 are neither parallel nor perpendicular to the line −x+4y=20. The line y=−14x+6 is also neither parallel nor perpendicular to the given line. The line −x+4y=8 is parallel to the given line.

To determine whether lines are parallel, perpendicular, or neither to the given line −x+4y=20, we'll need to look at their slopes. If the slopes are the same, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular.

First, we should rewrite the given equation in y = mx + b format to identify the slope. The equation becomes y = 1/4x + 5. The slope for the given line is 1/4.

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The correct answer is:

a. all real numbers

When we reflect a function across the y-axis, the x-values change their signs. For the function [tex]\( f(x) = 6(0.25)^x \)[/tex], the domain consists of all real numbers since the function is defined for all real values of x.

When we reflect this function across the y-axis to get g(x), the domain of g(x) remains the same as the original function f(x). This is because reflecting across the y-axis does not affect the x-values for which the function is defined.

So, the correct answer is:

a. all real numbers

Answer:

30

Step-by-step explanation:

To solve for the rectangle's dimensions, the area 525 cm² is divided by the ratio of length to width (7:3), revealing a width of 15 cm and a length of 35 cm.

To find the length and width of a rectangle with an area of 525 square centimeters and a length-to-width ratio of 7:3, we can use proportions. Let's define the width as w centimeters. Then, since the ratio of the length to the width is 7:3, the length can be represented as (7/3)w centimeters.

The area of a rectangle is given by length  imes width. Therefore, we can set up the equation (7/3)w × w = 525 to represent the area. To find w, we solve for w² = (525 × 3) / 7, which gives us w² = 225.

By taking the square root of both sides, we see that w = 15 centimeters. Now to find the length, we use the ratio: length = (7/3) × 15 = 35 centimeters.

Answer:

The mean is 300 and the standard deviation is 8.67.

Step-by-step explanation:

It has been given that the drug has been found to be effective in treating 75% of the people afflicted by a certain disease.

Therefore, probability of success is given by p = 0.75

Now, total number of people affecting from the disease, n = 400

We know the formula for mean, which is given by

[tex]\mu=np\\\mu=400\times 0.75\\\mu=300[/tex]

And the standard deviation is

[tex]\sigma=\sqrt{np(1-p)}\\\sigma=\sqrt{400\cdot0.75(1-0.75)}\\\sigma=8.67[/tex]

Therefore, the mean is 300 and the standard deviation is 8.67.

I hope choice must be given so that we can select which equation can be used to find its value.

I am showing the steps for this problem.

Given that, x represents the width of the rectangle and the perimeter of the rectangle is 28 inches.

Let's assume y represent the length of the rectangle.

Formula to find the perimeter of a rectangle is,

p= 2 * length + 2 * width.

Hence, we can set up an equation as following.

2 y + 2x = 28.

Hope this is your question, if not I think you will, still be able to

find an answer of your question based on this solution.

Hope this helps you!.

Answer: The answer is 2 × (6 + x) + 2 × x = 28.

Step-by-step explanation:  Given that the length of a rectangle is 6 inches longer than its width. the perimeter of the rectangle is 28 inches. if x represents the width of the rectangle, then we are to find the equation that finds the value of 'x'.

Since width of the rectangle is 'x' inches and length is 6 inches longer than the width, so length will be (6 + x) inches.

Also, perimeter is 28 inches, therefore, we have

[tex]2\times(6+x)+2\times x=28\\\\\Rightarrow 6+x+x=14\\\\\Rightarrow 2x=8\\\\\Rightarrow x=4.[/tex]

Thus, the value of x is 4 inches, hence width = 4 inches and length = 4 + 6 = 10 inches.

Final answer:

To factor the expression 4x² − 8x − 60 completely, factor out the greatest common factor of 4, then factor the resulting quadratic expression, which results in C. 4(x − 5)(x + 3).

Explanation:

The question asks you to factor completely the quadratic expression  [tex]4x^2 - 8x - 60[/tex]To factor this expression, first, look for any common factors among the terms. Here, the common factor is 4. Factoring out the 4 gives you [tex]4(x^2 - 2x - 15).[/tex]Next, we factor the quadratic expression within the parentheses.

We look for two numbers that multiply to give − 15 (the constant term) and add to give − 2 (the coefficient of x). These numbers are − 5 and + 3, so the expression factors further into 4(x − 5)(x + 3).

The completely factored form of the quadratic expression  [tex]4x^2 - 8x - 60[/tex] is C. 4(x − 5)(x + 3).

Nadia needs 2 buckets of water to fill the fish tank.

To calculate the volume of water needed to fill the fish tank, we need to find the volume of the tank and subtract the volume of the empty space. The volume of the tank is 2 ft x 1 ft x 1.5 ft = 3 ft³. The volume of the empty space is 2 ft x 1 ft x 0.25 ft = 0.5 ft³. Therefore, the volume of water needed is 3 ft³ - 0.5 ft³ = 2.5 ft³.

Next, we divide the volume of water needed by the volume of water in each bucket to find the number of buckets needed. 2.5 ft³ divided by 1.25 ft³/bucket = 2 buckets. Therefore, Nadia needs 2 buckets of water to fill the fish tank.

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Answer:

X= -24

Step-by-step explanation:

Answer:  The probability of getting 100 % on the quiz is 0.0625.

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Step-by-step explanation:

Since we have given that

Number of true-false questions = 4

Number of chances of answer = 2

1) True,

2) False

Probability of getting correct answer is given by

[tex]\frac{1}{2}[/tex]

Probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions is given by

[tex]\frac{1}{2}^4\\\\=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{16}\\\\=0.0625[/tex]

Hence, The probability of getting 100 % on the quiz is 0.0625.

Final answer:

To solve the inequality 2 > 8 - 43h, subtract 8 from both sides and divide by -43, then flip the inequality sign. The solution is h > 6/43.

Explanation:

To solve the inequality 2 > 8 - 43h, we need to isolate the variable h. Let's start by subtracting 8 from both sides:

2 - 8 > 8 - 8 - 43h

-6 > -43h

Next, we divide both sides of the inequality by -43, but since we are dividing by a negative number, the inequality sign flips:

-6/-43 < -43h/-43

Simplifying the expression:

6/43 < h

The solution to the inequality is h > 6/43.

The decimal number 2.18 can be written as the mixed number 2 9/50, considering that .18 is equivalent to the fraction 18/100, which simplifies to 9/50.

The number 2.18 is not technically a mixed number, but it can be written in a format similar to a mixed number. A mixed number is defined as a number that includes both a whole number and a proper fraction. In this case, the whole number is 2 and the decimal .18 could be viewed as a type of fraction. If we want to express .18 as a fraction, we can convert it to 18/100. This fraction, however, can be further simplified to 9/50 by dividing both the numerator and the denominator by 2. Therefore, we could write 2.18 as the mixed number 2 9/50.

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2x+3+x<30

3x<27

x<9

The answer would be D.