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3 years ago

When adding integers with the same sign, you add andkeep the signchange the sign

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

4 0

Answer:

keep the sign

Step-by-step explanation:

(+) and (+) = +

(+) and (-) = -

(-) and (-) = -

Ex) -6-6=-12

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Which is equivalent to the expression? x2 + 6x + 4 A) (x + 3)2 + 5 B) (x + 3)2 − 5 C) (x − 3)2 + 5 D) (x − 3)2 − 5

elena55 [62]

Answer:

Step-by-step explanation:

(x + 3)² − 5 because :

(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4

6 0

4 years ago

(08.01 LC)

skad [1K]

Answer:

all students on the track-and-field team

Step-by-step explanation:

if the coach wants to find out if they prefer track or field he/she has to ask the people who are experiencing it right now and tell him or her if they prefer this or not

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3 years ago

Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 4x2 + 9y2 = 36. cross-sect

Tasya [4]

$4x^2+9y^2=36\iff\dfrac{x^2}9+\dfrac{y^2}4=1$

defines an ellipse centered at $(0,0)$ with semi-major axis length 3 and semi-minor axis length 2. The semi-major axis lies on the $x$ -axis. So if cross sections are taken perpendicular to the $x$ -axis, any such triangular section will have a base that is determined by the vertical distance between the lower and upper halves of the ellipse. That is, any cross section taken at $x=x_0$ will have a base of length

$\dfrac{x^2}9+\dfrac{y^2}4=1\implies y=\pm\dfrac23\sqrt{9-x^2}$
$\implies \text{base}=\dfrac23\sqrt{9-{x_0}^2}-\left(-\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac43\sqrt{9-{x_0}^2}$

I've attached a graphic of what a sample section would look like.

Any such isosceles triangle will have a hypotenuse that occurs in a $\sqrt2:1$ ratio with either of the remaining legs. So if the hypotenuse is $\dfrac43\sqrt{9-{x_0}^2}$ , then either leg will have length $\dfrac4{3\sqrt2}\sqrt{9-{x_0}^2}$ .

Now the legs form a similar triangle with the height of the triangle, where the legs of the larger triangle section are the hypotenuses and the height is one of the legs. This means the height of the triangular section is $\dfrac4{3(\sqrt2)^2}\sqrt{9-{x_0}^2}=\dfrac23\sqrt{9-{x_0}^2}$ .

Finally, $x_0$ can be chosen from any value in $-3\le x_0\le3$ . We're now ready to set up the integral to find the volume of the solid. The volume is the sum of the infinitely many triangular sections' areas, which are

$\dfrac12\left(\dfrac43\sqrt{9-{x_0}^2}\right)\left(\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac49(9-{x_0}^2)$

and so the volume would be

$\displaystyle\int_{x=-3}^{x=3}\frac49(9-x^2)\,\mathrm dx$
$=\left(4x-\dfrac4{27}x^3\right)\bigg|_{x=-3}^{x=3}$
$=16$

6 0

3 years ago

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the s

Lady bird [3.3K]

Which expression can be used to determine the side length of the rhombus?

The answer is the first option: 10/Cos(30°)

Explanation:

1. As you can see in the figure attached, there is a right triangle and its hypotenuse (which is represented with the letter "x") is the side you want to calculate. So, you have:

Cos(α)=Adjacent leg/Hypotenuse

α=30°
 Adjacent leg=(20 in)/2=10 in
Hypotenuse=x

2. When you substitute these values into the formula, you obtain:

Cos(α)=Adjacent leg/Hypotenuse
 Cos(30°)=10/x

3. Therefore, you obtain the expression to determine the side length of the rhombus by clearing the hypotenuse "x", as below:

x=10/Cos(30°)

7 0

4 years ago

Identify the following fractions as either proper or improper. 8. 14⁄ 15

nalin [4]

Answer:

proper I believe if I'm wrong sorry

4 0

3 years ago