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3 years ago

what is the equation of the quadratic graph with a focus of (-1,4) and a directrix of y=2? hint: y=a(x-h)^2+k, a=1/4p

Mathematics

1 answer:

natima [27]3 years ago

3 0

Answer:

y = 1/4(x + 1)^2 + 3.

Step-by-step explanation:

The general form is (x - h)^2 = 4p(y - k) where the focus is (h, k+p) and the directrix is y = k-p

So we have h = -1

k + p = 4

k - p = 2 Adding:

2k = 6 so k = 3 and p = 1.

Therefore:

(x + 1)^2 = 4(y - 3)

4y = (x + 1)^2 + 12

y = 1/4(x + 1)^2 + 3.

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barxatty [35]

Number 1 is C.
Number 2 is C.
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3 years ago

The number 6 is a solution to which of the following inequalities?

Paladinen [302]

Answer:

21 + x < 28

Step-by-step explanation:

27 is in fact greater than 28 if you where to input 6 into the x spot, this is the only one that's a true expression.

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3 years ago

This question is from the similarity chapter. It would be really kind of you if you would answer this question.

katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Angles AYX and ACB are corresponding and they both measure 90 degrees
Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

$\frac{XY}{BC}=\frac{AY}{AC}$

Plug in known values

$\frac{2}{300}=\frac{11}{AC}$

Cross-multiply

$2AC=11*300\\2AC=3300\\AC=1650$

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

$a^2+b^2=c^2$ where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

$300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c$

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0

3 years ago

A __________ contains all the subset of superset. A superset. B proper subset. C null set 2.Positive square root of 1/3 is______

aivan3 [116]

Answer:

i) superset (A)

ii) 0.577 (A)

Step-by-step explanation:

i) A subset is a set which has all its elements contained in another set.

For two sets A and B, if each element of set A is an element of set B, then A is a subset of B.

A superset is a set that houses another set. So if set A is a subset of set B, then B is a superset of A.

Proper subset

For a set (A) to be a proper subset of another (B) every element of A would be in B but there exists at least one element in B that is not in A.

An Empty Set (or Null Set) doesn't have aren't any elements in it. It is empty.

Since every element of the superset is in the superset. Therefore, A superset contains all the subset of superset.

ii) Square root of 1/3 = √⅓

= ± √⅓ = +√⅓ or -√⅓

+√⅓ = +(√1/√3) = +(1/√3)

+√⅓ = +(1/1.7321)

+√⅓ = +0.577

Therefore Positive square root of 1/3 is 0.577 (A)

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3 years ago

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denis-greek [22]

Answer: 28 gallons of paint needed to paint 16 classrooms.

Step-by-step explanation:

As 7 gallons Paint 4 classrooms so if we need to paint 16 classrooms which four times 4 classrooms so 7*4=28 gallons will be needed to paint 16 classrooms

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2 years ago