Solve for d. 120 - 11d + 2d + 4d

Chris is at the deli and spent $13.65 for 1.75 pounds of turkey. What was the cost per ounce for turkey?

kvasek [131]

Answer:

0.4875 cents per ounce

Step-by-step explanation:

16 ounces per pound

1.75 lbs x 16 = 28 ounces

$13.65/28 ounces = .4875 cents/ounce

Check: 0.4875 cents x 28 ounces = $13.65

5 0

3 years ago

Polygon ABCD is dilated, rotated, and translated to form polygon A′B′C′D′. The endpoints of AB are at (0, -7) and (8, 8), and th

Anton [14]

Rotation and translation are rigid transformations, they don't change figure sizes. Dilation change figure sizes increasing or decreasing them by scale factor.

First, find AB and A'B' by the formula:

$AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}= \sqrt{(8-0)^2+(8-(-7))^2}=\sqrt{8^2+15^2}=\sqrt{64+225}=\sqrt{289}=17,\\ \\A'B'=\sqrt{(x_{B'}-x_{A'})^2+(y_{B'}-y_{A'})^2}= \sqrt{(2-6)^2+(1.5-(-6))^2}=\sqrt{4^2+7.5^2}=\sqrt{16+56.25}=\sqrt{72.25}=8.5.$

As you can see AB=2A'B'. This means that the segment AB was decreased twice to form segment A'B'. Then the scale factor is 1/2.

8 0

3 years ago

What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2

KiRa [710]

Hope this helped. :)

Any point, (x0,y0)(x0,y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate:

Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix

To find the equation of the parabola, equate these two expressions and solve for y0y0 .

Find the equation of the parabola in the example above.

Distance between the point (x0,y0)(x0,y0) and (a,b)(a,b) :

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√(x0−a)2+(y0−b)2

Distance between point (x0,y0)(x0,y0) and the line y=cy=c :

∣∣y0−c∣∣| y0−c |

(Here, the distance between the point and horizontal line is difference of their yy -coordinates.)

Equate the two expressions.

(x0−a)2+(y0−b)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=∣∣y0−c∣∣(x0−a)2+(y0−b)2=| y0−c |

Square both sides.

(x0−a)2+(y0−b)2=(y0−c)2(x0−a)2+(y0−b)2=(y0−c)2

Expand the expression in y0y0 on both sides and simplify.

(x0−a)2+b2−c2=2(b−c)y0(x0−a)2+b2−c2=2(b−c)y0

This equation in (x0,y0)(x0,y0) is true for all other values on the parabola and hence we can rewrite with (x,y)(x,y) .

Therefore, the equation of the parabola with focus (a,b)(a,b) and directrix y=cy=c is

(x−a)2+b2−c2=2(b−c)y

3 0

3 years ago

A polynomial p(x) is divided by a binomial x-a the remainder is 0

schepotkina [342]

If this is the case, then you know by the polynomial remainder theorem that $x-a$ is a factor of $p(x)$ , so there is some polynomial $q(x)$ such that

$p(x)=(x-a)q(x)$