Please answer and show work :)

Mathematics

2 answers:

Rashid [163]3 years ago

5 0

Answer:

2 book cases

Step-by-step explanation:

If she has 1 1/4 gallons of paint then she has two (1/2) gallons and one (1/4) gallon. Each book case takes 1/2 gallon of paint and if you multiply it by 2 it equals 1 gallon. You only have 1/4 gallon left.

1 bookcase (1/2 gallon) + 1 bookcase (1/2 gallon) = 1 gallon. There is only 1/4 gallon left which is less than 1/2.

Zepler [3.9K]3 years ago

5 0

Answer is 2 book cases

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The midpoint of CD is M=(1, 2). One endpoint is C = (6, -2).

Zina [86]

Answer: Endpoint = (-4,6)

Step-by-step explanation:

To find any endpoint use the formula $\frac{x_1+x_2}{2} = Xmp$ $\frac{y_1+y_2}{2} =Ymp$

$\frac{6+x_2}{2} = 1$ $\frac{-2+y_2}{2} =2$

multiply each by 2 to simplify

$\frac{6+x_2}{2*2} = 1*2 = {6+x_2}= 2$ $\frac{-2+y_2}{2*2} =2*2 = -2+y_2=4$ take the equations and simplify

6+ $x_{2}$ = 2 -2+ $y_{2}$ = 4 =

-6 -6 +2 +2

$x_{2}$ = -4 $y_{2}$ = 6

To check use the Midpoint formula

$\frac{-4+6}{2} , \frac{6-2}{2} = \frac{2}{2} , \frac{4}{2} = (1,2)$

8 0

3 years ago

The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0) . The focus of the reflector

Paha777 [63]

Answer:

The depth of the reflector is 0.84 feet

Step-by-step explanation:

<em>(See the figure below)</em>

The equation of a parabola centered at the origin with an axis of symmetry on y-axis is:

$x^{2}=4py$ (1)

With p the distance from the origin to the focus using p=6, the equation (1) of the parabola becomes:

$x^{2}=4(6)y=24y$ (2)

Note that the point B is on the parabola, so this point should satisfy the parabola equation (2) that allow us to use the value x=4.5 to find the y value associated to it, that it is the depth (h) of the reflector:

$(4.5)^{2}=24y$ , solving for y