solve on the interval (0,pi)
1+cosθ=((sqrt3)+2)/2

To find the value of X in a rectangle with width X and length 2X, we can use the area formula. By solving the equation, we find X = 9, making the width of the rectangle 9 units.

To find the value of X, we need to use the given information about the length and width of the rectangle. Let's assume the width of the rectangle is X. Since the length is double the width, it is 2X. The area of the rectangle is given as 162, so we can set up the equation:

Width × Length = Area

X × 2X = 162

Simplifying the equation, we get:

2X^2 = 162

Dividing both sides by 2, we have:

X^2 = 81

Taking the square root of both sides, we find:

X = ±9

Since the width cannot be negative, the value of X is 9. Therefore, the width of the rectangle is 9 units.

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The width of the rectangle is 9 units.

To find the width of the rectangle, we can set up the equation for the area. The width of the rectangle is X, and the length is twice the width, meaning the length is 2X. The formula for the area is length times width, so we have X * 2X = 162. Simplifying this equation gives us 2X^2 = 162. Dividing both sides by 2 gives us X^2 = 81. Taking the square root of both sides gives us X = 9. Therefore, the width of the rectangle is 9 units.

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Answer:

  $55

Step-by-step explanation:

Put 8 where n is in the equation and do the arithmetic.

  cost = $6.50·n + 3

  = $6.50·8 + 3 = $52 + 3

  cost = $55

Answer:

The correct option is 4.

Step-by-step explanation:

The given expression is

[tex]25a+5b-13[/tex]

In option (1), the given expression is

[tex]20a+5a+b-13[/tex]

Combine like terms.

[tex]25a+b-13[/tex]

This expression is not equivalent to the given expression.

In option (2), the given expression is

[tex]20(5a+5b)-13[/tex]

Using distributive property.

[tex]100a+100b-13[/tex]

This expression is not equivalent to the given expression.

In option (3), the given expression is

[tex]30ab-13[/tex]

This expression is not equivalent to the given expression.

In option (4), the given expression is

[tex]5(5a+b)-13[/tex]

Using distributive property.

[tex]25a+5b-13[/tex]

This expression is equivalent to the given expression.

Therefore correct option is 4.

Answer:

The answer is "120"

Step-by-step explanation:

I did it myself, and this is the answer i got :) I made sure it was correct but let me know if you have problems!

Consider the difference of polynomials [tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3).[/tex]

The first thing you have to do is take that "minus" sign through the parentheses containing the second polynomial (just change sign + to - and sign - to +):

[tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3)=7x^8+8x^6-2x+9-4x^8-3x^7-3.[/tex]

Then combine terms with the same degree:

[tex]7x^8+8x^6-2x+9-4x^8-3x^7-3=(7x^8-4x^8)-3x^7+8x^6-2x+(9-3).[/tex]

Note that

[tex]7x^8-4x^8=(7-4)x^8=3x^8,\\ \\9-3=6.[/tex]

Thus,

[tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3)=3x^8-3x^7+8x^6-2x+6.[/tex]

Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?

The area of the triangle is half the product of its base and height. The area of the triangle is 137.25 in².

The area of the triangle is half the product of its base and height. It is given by the formula,

[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]

As it is given that the base of the triangle is 15¹/₄ inches, while the height of the triangle is 18 inches. Therefore, the area of the triangle is,

[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]

                         [tex]= \dfrac{1}{2} \times 15(1/4)\times 18\\\\\\ = \dfrac{1}{2} \times \dfrac{(15\times 4)+1}{4} \times 18\\\\\\= \dfrac{1}{2} \times \dfrac{61}{4} \times 18\\\\\\=137.25\rm\ in^2[/tex]

Hence, the area of the triangle is 137.25 in².

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The correct answer is [tex]\frac{1}{2}[/tex].

To find the exact value of [tex]\cos(5\pi/12)[/tex] using a half-angle formula, we can follow these steps:

[tex]\cos(2\theta) = 2\cos^2(\theta/2) - 1[/tex]

Substituting [tex]\theta = 5\pi/6[/tex], we get:

[tex]\cos(5\pi/3) = 2\cos^2(5\pi/12) - 1[/tex]

[tex]\cos^2(5\pi/12) = \frac{\cos(5\pi/3) + 1}{2}[/tex]

[tex]\cos(5\pi/3) = \cos(\pi/3 + \pi) = -\cos(\pi/3)[/tex]

[tex]\cos(\pi/3) = \frac{1}{2}[/tex]

[tex]\cos(5\pi/3) = -\frac{1}{2}[/tex]

[tex]\cos^2(5\pi/12) = \frac{-\frac{1}{2} + 1}{2} = \frac{1}{4}[/tex]

[tex]\cos(5\pi/12) = \pm\sqrt{\frac{1}{4}} = \pm\frac{1}{2}[/tex]

Since cosine is an even function, we take the positive value.

[tex]\cos(5\pi/12) = \frac{1}{2}[/tex]

Therefore, the exact value of [tex]\cos(5\pi/12)$ is $\frac{1}{2}[/tex].

Complete question:

Use a half angle formula to find the exact value of the expression?

[tex]\cos(5\pi/12)[/tex]