Which figures are polygons? select all that are

anygoal [31]

Wheres the rest of the problem? or is this it?

3 0

3 years ago

In 1995, the moose population in a park was measured to be 4200. By 1998, the population was measured again to be 1600. If the p

Contact [7]

Answer:

P = -2600/3 t + 25600/3

P = -8200/3

Step-by-step explanation:

t is the time in years since 1990, so two points on the line are (5, 4200) and (8, 1600).

Using the points to find the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (1600 − 4200) / (8 − 5)

m = -2600/3

Now writing the equation in point-slope form:

P − 4200 = -2600/3 (t − 5)

Converting to slope-intercept form:

P − 4200 = -2600/3 t + 13000/3

P = -2600/3 t + 25600/3

In 2003, t = 13:

P = -2600/3 (13) + 25600/3

P = -8200/3

6 0

3 years ago

Read 2 more answers

5x +6 (x-2) -8 (x-3) please help

DedPeter [7]

Answer:

3x + 12

Step-by-step explanation:

5x + 6(x - 2) - 8(x - 3) ← distribute parenthesis

= 5x + 6x - 12 - 8x + 24 ← collect like terms

==(5x + 6x - 8x) + (- 12 + 24)

= 3x + 12

8 0

1 year ago

Show that if a and b are positive integers, then ab = gcd (a, b). lcm (a, b) . [Hint: Use prime factorizations of a and b and th

AleksandrR [38]

Answer:

$ab=\gcd(a,b)\cdot \text{lcm}(a,b)$

Step-by-step explanation:

Using the hint, write a and b in the following prime factorization:

$a=p_1^{x_1}p_2^{x_2}\cdots p_t^{x_t}\cdot q,$

$b=p_1^{y_1}p_2^{y_2}\cdots p_t^{y_t}\cdot r,$

where $\gcd(p_i,r)=1,\ \gcd(p_i,q)=1,\ \gcd(r,q)=1,\ \gcd(p_i,p_j)=1,$ for i ≠ j.

Then by the formulae for gcd(a,b) and lcm(a,b) we know that:

$\gcd(a,b)=p_1^{\min(x_1,y_1)}p_2^{\min (x_2,y_2)} \cdots p_t^{\min(x_t,y_t)}$

$\text{lcm}(a,b)= q\cdot r\cdot p_1^{\max(x_1,y_1)}p_2^{\max(x_2,y_2)}\cdots p_t^{\max(x_t,y_t)}$

Note that the expression $\min(x_i,y_i)+\max(x_i,y_i)=x_i+y_i$ for all i, since if the minimum is, <em>without loss of generality</em>, $x_i$ , then the maximum must be $y_i$ , and viceversa. Then, it is straightforward to verify that when we multiply gcd(a, b) and lcm(a, b) its prime factorization matches the prime factorization of ab, and so we can see the equaility holds:

$\gcd(a,b)\cdot \text{lcm}(a,b)=ab.$

7 0

3 years ago

A rectangle with vertices (3,-2),(3,-4), (7, -2), (7, -4) is reflected across the x-axis and then rotated 90° counterclockwise.

BigorU [14]

Answer: A reflection about the y-axis and a clockwise rotation of 90° around the origin.

another example is:

A counterclockwise rotation of 90° around the origin, and then a reflection about the y-axis.

Step-by-step explanation:

Let's do this for a single point because it is essentially the same.

Let's use the point (3, -2)

First, we have a reflection across the x-axis, this only changes the sign of the y-component.

Then the new point will be: (3, -(-2)) = (3, 2)

Notice that this point is on the first quadrant.

Now we do a 90° counterclockwise rotation.

Then we move to the second quadrant, and we change the order of the components in the point (and because we are in the second quadrant, the x-component is negative and the y-component is positive)

Then the new point is (-2, 3)

Now, another transformation that is equivalent to this one is to do first a reflection about the y-axis, so we only change the sign of the y-component

Then the new point is (-3, -2)

And now we are in the third quadrant.

and then we do a rotation of 90° clockwise, which moves our point to the second quadrant, changes the order of the components and leaves the y-component positive and the x-component negative, then the new point is:

(-2, 3)

Same as before.

(notice that we used the same transformations, but applied to different line and direction of rotation)

Another example is if we first start with a counterclockwise rotation of 90° around the origin, the original point (3, -2) is on the fourth quadrant, so this rotation leaves our point in the first quadrant, so we change the order of the components and both of them will have a positive sign.

The new point is: (2, 3)

Now let's do a reflection about the y-axis, which changes the sign of the x-component.

Then the final point is (-2, 3), same as before.

And there are a lot of other transformations that will be equivalent to this ones, these are just two examples.

3 0

2 years ago