Find the building's average height. 1.667, 1.483, 1.483, 1.451 and 1.381. Buildings in thousands of feet

The area of a rectangle is given by the trinomial y^ 2 +4y-45. If the length of the rectangle is y + 9 , what is the width of th

Tema [17]

Step-by-step explanation:

Area of rectangle =L×W

Width =Area

$w idth= \frac{area \ }{length} \\ \\width = \frac{ {y}^{2} + 4y - 45}{y + 9} \\ \\ = \frac{(y - 5)(y + 9)}{(y + 9)} \\ \\ width = y - 5$

6 0

3 years ago

Cindy has a cylindrical bucket filled with sand; the area of the circular bottom is 10pi inches and the hieght of the bucket is

xz_007 [3.2K]

For the cylindrical bucket filled with sand, the volume of sand in the bucket will be given by the formula:

Volume=Area of the circular bottom x height

We know that the area of the circular bottom is given to be $10\pi$ $in^3$ and the height is 8 inches.

Therefore, Volume of Sand= $10\pi \times 8=80\pi$ $in^3$

Now, for calculating the volume of water, we will employ the formula:

Volume= $\pi$ x $(radius of the circular bottom)^2$ xheight

Thus, from the given data, Volume of water is:

$\pi\times(2)^2 \times 5=20\pi$ $in^3$

As can be clearly seen the volume of sand is more than the volume of water and thus there is more sand than water. The difference in their volumes is $(80\pi-20\pi)$ = $60\pi$ $in^3$ .

6 0

3 years ago

Plz, help ASAP!!!!!!!<br> will mark brainliest

Anarel [89]

Answer:

139

Step-by-step explanation:

first you need to find the x:

180= 8x + 51 + 6x - 25

180 - 51 +25 = 8x + 6x

154 = 14x

154/14 = x = 11

then you have to work out AOB:

8x +51

8(11) +51

88+51 = AOB = 139

to check your work, workout angle BOC and add both. angles together to check if you get 180:

BOC= 6x - 25

6(11) - 25

66 - 25 = 41

To check:

BOC + AOB = 180

41 +139 = 180

180 = 180

Hope this helps!

8 0

4 years ago

Which of the following equations represents a line parallel to 4x - y = -5?

pickupchik [31]

Correct answers are A, C and D.

Parallel lines have equal slopes.

4x - y = -5 ⇒ y = 4x + 5 ⇒ m = 4
8x - 2y = -10 ⇒ 4x - y = -5 ⇒ m = 4
4x + y = -2 ⇒ y = -4x - 2 ⇒ m = -4
4x - y = 2 ⇒ y = 4x - 2 ⇒ m = 4
$2x - \frac{1}{2}y = -\frac{5}{2}\Rightarrow4x-y=-5 \Rightarrow y=4x+5 \Rightarrow m=4$

4 0

3 years ago

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A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two op

shutvik [7]

Answer:

Step-by-step explanation:

Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form

$4p(y-k)=-(x-h)^2$

The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.

Filling in the equation with a vertex of (0, 0) which is our h and k respectively:

$4(3)(y-0)=-(x-0)^2$ which simplifies to

$12y=-x^2$ and multiplying both sides by -1:

$-12y=x^2$ . This is not standard form, but it matches what your equation is in the choices. So to sum up:

The focus is located at (0, -3) and the first choice is true.

The parabola opens upside down and the second choice is not true.

The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.

We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.

So the fifth choice is not true.

6 0

3 years ago

Read 2 more answers