Calculate 3ab + b for a=2 and b=-3

Find the area of a rectangle having a perimeter of 182 yards and a width 20 yards shorter than twice its length

Studentka2010 [4]

Let the length be $l$ in this equation.

We know that the perimeter of a rectangle is $w2 + l2 = P$

Width is defined in terms of length, so we know $w = l2 - 20$

We can substitute this value of w into the formula for perimeter to find the length.

$(l2 - 20)2 + l2 = 182$

$l4 - 40 + l2 = 182$

$l4 + l2 = 222$

$l6 = 222$

$l = 37$

So the length is 37. Now that we've found the length, we can go back to the Perimeter formula again and find width.

$w2 + (37)2 = 182$

$w2 + 74 = 182$

$w2 = 108$

$w = 54$

Width is 54. Now with both of these values found, we can calculate area with the formula $l * w = A$

$37 * 54 = A$

$1998 = A$

So the area of the rectangle is 1998 yards^2.

3 0

3 years ago

Aubree practices the piano 1197 minutes in 3 weeks. At what rate did she practice, in minutes per day?

Norma-Jean [14]

Answer:

57

Step-by-step explanation:

We need to create a ratio. so Aubree practices the piano for 1197 min: in 3 weeks. So for 1 week, we have to divide 1197 by 3, so 1197/=399. And so we know that 1 week is 7 days, just divide 399 by 7! 399/7=57. The rate that she practiced per day is 57 minutes. So one last final step just to check if this answer is correct is to divide 57 by 60, and that is 0.95. 0.95 out of 1.00 minutes per day is 95/100. Cross multiply with x/60, and you will get your answer, which is 57.

4 0

2 years ago

Read 2 more answers

Convert 28 ounces to pounds. Express your answer in simplest form.

denis23 [38]

It is 1.75 pounds. 16 ounces is equal to 1 pound.

8 0

4 years ago

Which steps should be used to graph the equation y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x

dalvyx [7]

Answer:

The steps are are explained below.

Step-by-step explanation:

Given:

The equation of the line is given as:

$y-4=\frac{1}{3}(x+2)$

The above equation is in point-slope form $y-y_1=m(x-x_1)$ .

Therefore, on comparing, we get

$x_1=-2,y_1=4,m=\frac{1}{3}$

So, the slope is one-third and point is (-2,4).

Now, following are steps for plotting the graph:

i. Plot the point (-2,4).

ii. Since the slope is one-third, it means we need to move 3 units to right from the point (-2,4) and then 1 unit up. So, after translating 3 units right and 1 unit up we mark the second point which is $(-2+3,4+1)\rightarrow )(1,5)$ .

iii. Draw a line passing through the points (-2,4) and (1,5) to get the graph of the line

Thus, the graph is drawn below.

8 0

3 years ago

Read 2 more answers

The least-squares regression line is:

babunello [35]

Answer:

a. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.

Step-by-step explanation:

If we have N points $(x_1, y_1),. ...(x_N, y_N)$ and we want to adjust a model $y = ax+b$

We can define the error associated to this like that:

$E(a,b) = \sum_{n=1}^N [y_n -(ax_n +b)]^2$

So as we can see here we are adding the square distances between the real and the adjusted values in order to minimize the error for this reason the correct answer is:

a. the line that makes the sum of the squares of the vertical distances of the data points from the line (the sum of squared residuals) as small as possible.

For this case we need to calculate the slope with the following formula:

$a=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

7 0

4 years ago