David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.

How long will each piece of hose be?

Enter your answers in the boxes.


Shorter piece: ft


Longer piece: ft




25 POINTS PLEASE HELP

Yes, you can evaluate sin(cos^-1(7/11)) without a calculator. The result can be simplified to √(72/121).

Yes, you can evaluate sin(cos-1(7/11)) without a calculator. Let's break it down step by step:

Therefore, sin(cos-1(7/11)) can be evaluated as √(72/121).

Answer: The correct expansion is,

[tex]x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]

Step-by-step explanation:

Since, by the binomial expansion,

[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r}(q)^r[/tex]

Where,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, p = x and q = y and n = 5,

By substituting values,

[tex](x+y)^5=\sum_{r=0}^{5} ^5C_r (x)^{n-r}(y)^r[/tex]

[tex] =^5C_0(x)^{5-0}(y)^0+^5C_1 (x)^{5-1}(y)^1+^5C_2 (x)^{5-2}(y)^2+^5C_3 (x)^{5-3}(y)^3+^5C_4 (x)^{5-4}(y)^4+^5C_5(x)^{5-5}(y)^{5}[/tex]

[tex]=1(x)^5(y)^0+\frac{5!}{4!(5-4)!}x^4y^1+\frac{5!}{3!(5-3)!}x^3y^2+\frac{5!}{2!(5-2)!}x^2y^3+\frac{5!}{1!(5-1)!}xy^4+\frac{5!}{5!(5-5)!}x^0y^5[/tex]

[tex]=x^5+\frac{5!}{4!1!}x^4y^1+\frac{5!}{3!2!}x^3y^2+\frac{5!}{2!3!}x^2y^3+\frac{5!}{1!4!}x^1y^4+\frac{5!}{5!0!}x^0y^5[/tex]

[tex]=x^5+\frac{5\times 4!}{4!}x^4y^1+\frac{5\times 4\times 3!}{3!2!}x^3y^2+\frac{5\times 4\times 3!}{2!3!}x^2y^3+\frac{5\times 4!}{4!}x^1y^4+\frac{5!}{5!}y^5[/tex]

[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]

Which is the required expansion.

To find f(x)/g(x), we factor both f(x) and g(x), and then simplify by canceling common terms. The simplified result is 2x + 3 / x + 2.

To find the quotient of two functions, f(x) and g(x), we divide the first function by the second. In this case, we have f(x) = 2x² - x - 6 and g(x) = x² - 4. The process involves the following steps:

We start by factoring both f(x) and g(x):

f(x) = (2x + 3)(x - 2)
g(x) = (x + 2)(x - 2)

Now we divide f(x) by g(x):

f(x)/g(x) = ((2x + 3)(x - 2)) / ((x + 2)(x - 2))

Notice that the term (x - 2) is common in both the numerator and the denominator, so we can reduce the expression by canceling out the common term, resulting in:

f(x)/g(x) = (2x + 3) / (x + 2)

The correct result is the second option: 2x + 3 / x + 2.

The equation 4y + 12x = 0 in slope-intercept form is y = -3x. The slope (m) is -3, and since there is no constant term, the y-intercept (b) is 0.

The equation provided, 4y + 12x = 0, can be converted into slope-intercept form, which is represented by y = mx + b. The slope, m, indicates the steepness of the line, while the y-intercept, b, denotes the y-value when x equals zero or where the line crosses the y-axis. Let's rearrange the equation step-by-step:

Here, the slope (m) is -3, indicating a decrease in y by 3 units for every increase of 1 unit in x. The equation does not have a b term, thereby indicating that the y-intercept (b) is 0. Hence, the slope-intercept form of the equation is y = -3x + 0, which can be simplified to y = -3x.

The issue was inconsistent units - converting everything to cm squared, the appropriate number of 20 by 30 cm tiles to cover an area of 10.95m squared is 183.

The problem here involves area measurement and conversions. The area of the outdoor space is given in square meters (m²), while the area of the tiles is given in square centimeters (cm²). Therefore, the first step here is to convert all measurements to the same unit.

Since 1 meter is equal to 100 centimeters, we can convert the area of the outdoor space to square centimeters by squaring 100 (which equals to 10,000) and then multiplying it by the area in square meters. That gives us 109,500 cm².

Next, to find the area of a single tile we multiply its length by its width, which is 20 cm by 30 cm, giving us 600 cm². The number of tiles needed will be the total area divided by the area of one tile. So, 109,500 cm² divided by 600 cm² equals to about 182.5.

Since we cannot have a half tile, we round up that number to 183 tiles. Therefore, the correct answer is 183 tiles.

https://brainly.com/question/32024069

#SPJ2

Answer:

4 lbs

Step-by-step explanation:

There are 16 ounces in a pound, so divide 64 by 16 to get the number of pounds.  64 ÷ 16 = 4 lbs

Answer:

The formula that relates circumference and radius is [tex]C=2\pi r[/tex].

Step-by-step explanation:

The circumference of a circle is calculated by the formula

[tex]C=2\pi r[/tex]

Where,

C is circumference of the circle.

r is radius of the circle.

π is 22/7 or 3.14.

In the given options π is not missing. So, all the given options are incorrect.

Therefore the formula that relates circumference and radius is [tex]C=2\pi r[/tex].

As they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.

It is defined as the data representation in visual way, and it makes the appearance of the data simpler.

As we can see in the graph:

Total of 40 compact cars, 4 of 10 each.

Total of 30 mid-size, 3 of 10 each.

And Total of 20 trucks,

However, they all appear to have the same start and end points in the graph, with the mid-sizes being longer than the compacts and the trucks being considerably larger than the others above it, virtually implying that the amounts for all are identical for that period.

Thus, as they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.

Learn more about the graph here:

https://brainly.com/question/16608196

#SPJ2

Answer:

B and E are the answers

Step-by-step explanation:

Enjoy! <3

Answer:

Step-by-step explanation:

I just had the same question and the answer was 5.7. Hope this helps somebody