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2 years ago

A quilt contains cuts of congruent right triangular pieces with a base of

1 answer:

4 0

I’m sorry I’m confused it’s all spaced out can you put it in the comments and I’ll answer in there? Hope you have a nice day!

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What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

4 0

3 years ago

Please answer :'<

sesenic [268]

Answer:

D. 56.3 cubic units

Step-by-step explanation:

To find the volume of a rectangular prism you use the formula <u>v=l*w*h</u> which means you multiply <u>5*3*3.75</u> to find your answer of 56.3 cubic units.

3 0

3 years ago

Read 2 more answers

What is the slope if i only have the two points (9,8) and (3,4)

DIA [1.3K]

The slope should be
m= 2/3 (2 over 3)

3 0

3 years ago

Read 2 more answers

-2(x-2)=-16 answer.

REY [17]

Answer:

-2x+4=-16

-2x = -16-4

-2x = -20

x = -20/-2

x = 10

3 0

3 years ago

Read 2 more answers

Ray and Lilli are designing their own shoes. They have 4 color options for the base and 6 color options for the accent. They can

IrinaVladis [17]

Remark: in the solution, the word Combination is used in the daily usage of the word, not in the combinatorial (mathematical) language.

Let the available 4 base colors be ${b_1, b_2, b_3, b_4}$ ,

the available 6 accent colors be ${a_1, a_2, a_3, a_4, a_5, a_6}$ ,

and the available 2 fonts for the embroidery be ${e_1, e_2}$ ,

so we have 4 b's, 6a's and 2 e's.

The event that Ray and Lilly design identical shoes can happen in the following way:

Ray has in total 4*6*2=48 possible combinations, and in each of these combinations, Lilly makes the same exact combinations of the 3- b's, a's and e's.

The sample space is 48 possible combinations of Ray * 48 possible combinations of Lilly = 48*48
(among these there are 48 matches of the combinations)

Thus P(designing identical shoes)=48/(48*48)=1/48=0.02

Answer:0.02

6 0

3 years ago