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4 years ago

Describe a situation with two quantities that have a proportional linear relationship.

Mathematics

1 answer:

posledela4 years ago

5 0

Huffing chin chin cfhjbvuknvghjbgy

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Derive the equation of the parabola with a focus at (-2,4) and a directrix of y=6 . Put the equation in standard form

Maru [420]

Answer:

$y = - \frac{1}{4} {(x + 2)}^{2} + 5$

Step-by-step explanation:

The vertex of this parabola is the midpoint of the focus (-2,4) and where the directrix intersects the axis of symmetry of the parabola (-2,6)

This parabola must open downwards due to the position of the directrix and has equation of the form:

${(x - h)}^{2} = - 4p(y - k)$

where (h,k) is the vertex.

This implies that:

$h = - 2$

and

$k = \frac{4 + 6}{2} = 5$

The value of p is the distance from the vertex to the focus:

$p = |6 - 5| = 1$

We substitute all the values into the formula to get:

$(x - - 2)^{2} = - 4(1){(y - 5)}$

${(x + 2)}^{2} = - 4(y - 5)$

$y = - \frac{1}{4} {(x - 5)}^{2} + 5$

4 0

3 years ago

At a certain college, 28% of the students major in engineering, 18% play club sports, and 8% both major in engineering and play

Alex

Answers: 0.286

Explanation:

Let E → major in Engineering

Let S → Play club sports

P (E) = 28% = 0.28

P (S) = 18% = 0.18

P (E ∩ S ) = 8% = 0.08

Probability of student plays club sports given majoring in engineering,

P ( S | E ) = P (E ∩ S ) ÷ P (E) = 0.08 ÷ 0.28 = 0.286

8 0

3 years ago

A motorcycle can travel 70 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 60 km?

cricket20 [7]

We have the following given
mileage = 70 miles per gallon
distance = 60 km

Required: amount of fuel in gallons

First, we must convert the distance to miles, so
60 km (1 mi/1.6 km) = 37.5 mi

So, the amount of fuel is
37.5 mi / (70 mi/gal) = 0.54 gallons

5 0

3 years ago

Read 2 more answers

What are the missing numbers from 48, 49, 51, 54, 84, 93, 103, 114

TEA [102]

Answer:

50,52,53,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,85,86,87,88,89,90,91,92,94,95,96,97,98,99,100,101,102,103,105,106,107,108,109,110,111,112,113

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Question 1 (Essay Worth 10 points)

Anvisha [2.4K]

Answer:

A. 7n+6

B Three times the quantity of a number plus eight

Step-by-step explanation:

A more than means it comes after

7 times a number

6 more than

7n+6

B 3( n+8)

Three times the quantity of a number plus eight

7 0

3 years ago