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Murljashka [212]
3 years ago
10

The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, bu

t it must spend $15 per race entry to cover the cost of the race.
Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000

(I have no idea how to do this. It's just extra credit but I need it)
Mathematics
1 answer:
photoshop1234 [79]3 years ago
6 0
The net amount they raise is the amount they receive minus what they pay in expenses.

They receive:
$10,000 fixed amount in donations
$55 per person

They pay:
$15 per person

If there are x number of entries, they receive 55x from the entries.
Also, they pay 15x for the entries.

The net amount they raise is amount they receive min us amount they pay:

55x + 10,000 - 15x

which simplifies to

40x + 10,0000

They want to raise at least $55,000.
At least $55,000 means $55,000 or more.
They want to raise an amount greater than or equal to $55,000.

Now we write the inequality:

40x + 10,000 >= 55,000

Now we solve the inequality for x, the number of entries.

40x >= 45,000

x >= 1125

They must have 1125 or more race entries to raise $55,000.
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The coefficient of 8 • 2N is _____.
lesantik [10]

Answer:

16 is the coefficient of N.

Step-by-step explanation:

Coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables. The coefficients of an algebraic term can be positive or negative, and this multiplies the unknown term.

For example:

In 2a, 2 is the coefficient of a;

In x, 1 is the coefficient of x but it is not visible;

In 2/3p, 2/3 is the coefficient of p;

In -3f, -3 is the coefficient of f;

In 3 × 6t, 18 is the coefficient of t.

Variable is a symbol, commonly a single letter, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation for the variables that represent them.

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7 0
3 years ago
A N S W E R Q U I C K P L E A S E
chubhunter [2.5K]

Answer:

1. A

2. D

3. D

Step-by-step explanation:

The standard form of a parabola is

y=\frac{1}{4p}(x-h)^2+k            ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .

k-p=-8                   ...(a)

(h,k+p)=(-2,-6)

k+p=-6            .... (b)

h=-2

On solving (a) and (b),  we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

y=\frac{1}{4(1)}(x-(-2))^2+(-7)

y=\frac{1}{4}(x+2)^2-7

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

k-p=5                   ...(c)

(h,k+p)=(2,1)

k+p=1            .... (d)

h=2

On solving (c) and (d),  we get k=3 and p=-2.

Put h=2, k=3 and p=-2 in equation (1).

y=\frac{1}{4(-2)}(x-(2))^2+(3)

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

Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

k-p=-3                   ...(e)

(h,k+p)=(0,-2)

k+p=-2            .... (f)

h=0

On solving (e) and (f),  we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

y=\frac{1}{4(0.5)}(x-(0))^2+(-2.5)

y=\frac{1}{2}(x)^2-2.5

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

Therefore option D is correct.

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