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Mumz [18]
2 years ago
9

Johnny is a very picky eater, so he likes to use a lot of condiments. He has ketchup, salt, pepper, and shredded cheese at his d

isposal. His mother tells him he may only make two additions to his meal (i.e., he can add condiments only twice, regardless of whether or not he already used them). How many different ways can Johnny improve his meal?
10
6
12
16
Mathematics
1 answer:
AleksAgata [21]2 years ago
6 0

Answer:

see the attachment photo!

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Find an equation of the parabola with focus (2, −3) and directrix y = 1.
Likurg_2 [28]

Answer:

Step-by-step explanation:

The correct option is option (C).

The required equation of the parabola is

Step-by-step explanation:

Formula:

The distance of a point (x₁,y₁) from a line ax+by+c=0 is

.

The distance between two points (x₁,y₁) and (x₂,y₂) is

Given that, the focus of the parabola is (2,3) and directrix y= - 1.

We know that, a parabola is the locus of points that equidistant from the directrix and the focus.

Let any point on the parabola be  P(x,y)  .

The distance of P from the directrix is

           

=y+1

The distance of the point P from the focus (2,3) is

According to the problem,

 

The required equation of the parabola is

5 0
3 years ago
What is the length of the portion BC of the cloth?
pantera1 [17]
Since this is a right triangle, a triangle with a 90 degree-angle, we can use the trigonometric functions. An example would be the sine function. With respect to the angle, it has the opposite side (o), the adjacent side (a), and the longest side called hypotenuse (h). For the sine function, it would be sine theta = opposite/hypotenuse. Using this relationship,

sin 38 = BC/5
BC = 5*sin38
BC = 3.08 units
7 0
4 years ago
The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 450 dollars per mo
Sphinxa [80]

Answer:

To maximize revenue, the manager should charge $525

Step-by-step explanation:

Given.

Rent = $450.

Unit = 120

Yes assume our function to be F(x).

To maximise F(x), the function will be based how much of the available units (x) is less than the initial 120 units with a corresponding increase in revenue dollars of 5x above the initial revenue.

Initial Revenue = 450 * 120 = $54,000

F(x) = (120 - x)(450 + 5x)

Converting this into standard quadratic form;

F(x) = 54000 + 600x - 450x - 5x²

F(x) = 54000 + 150x - 5x²

F(x) = -5x² + 150x + 54000

Using axis of symmetry formula

(x = -b/2a) for a parabola to determine the x coordinate of the function's vertex (maximum point):

F(x) = -5x² + 150x + 54,000

Where a = -5

b = 150

x = -b/2a

x = -150/2(-5)

x = -150/-10

x = 15 units less than 120

Next is to calculate the corresponding value of F(x) .

By Substitution

F(x) = -5(15)² + 150(15) + 54000

F(x) = -1125 + 2250 + 54000

F(x) = 55,125 --- Maximum Revenue

Calculating the optimum monthly rent based upon the maximum revenue dollars divided by by the previously determined number of units (15) less than the initial 120 units:

Monthly Rent = 55,125/(120 - 15)

Monthly Rent = 55,125/105

Monthly Rent = $525

To maximize revenue, the manager should charge $525

5 0
3 years ago
Enrique leaves his house and starts to run at an average speed of 6 miles per hour. Half an hour later, Enrique’s younger (and f
Sloan [31]

Answer:

t= 0.8 hr  or 48 min.

Step-by-step explanation:

Speed of Enrique= 6 mph

Half and hour late it means that after 1/2 hr.

Speed of Enrique brother = 8 mph

  Lets take Enrique cover x distance in time t hr .

So

x = 6 t                           ------------ 1

Then his brother will cover x/2 distance in time (t-1/2) hr.

So

x/2 = 8 (t-1/2)                   -----------------2

Now from equation 1 and 2

6 t  = 16 (t-1/2)

6 t = 16 t - 8

So t= 0.8 hr  or 48 min.

It means that his brother will take 0.8 hr to cover half of distance cover by  Enrique .

6 0
3 years ago
The measure of ⏜ is 161°, and the measure of ⏜ is 107°.<br><br> What is the measure of ∠ ?
MrRa [10]

Answer:

m<AEB = 46°

Step-by-step explanation:

Given:

Arc AD = 161°

Arc BC = 107°

Required:

m<AEB

Solution:

Vertex angle = ½(sum of intercepted arcs) => Theorem for angle inside a circle and its intercepted arcs)

This:

m<AED = ½(AD + BC)

m<AED = ½(161 + 107) => Substitution

m<AED = ½(268) = 134°

✔️m<AEB = 180° - m<AED => Linear pair theorem

m<AEB = 180° - 134° => substitution

m<AEB = 46°

6 0
3 years ago
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