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2 years ago

What two positive numbers whose difference is 7 and whose product is 294

Mathematics

1 answer:

Aloiza [94]2 years ago

7 0

Answer:

Step-by-step explanation:

We will use x and y as our positive numbers. We need to write 2 equations from this information. The first is that the difference between the numbers is 7:

x - y = 7 is the equation for that.

The second is that the product of the 2 numbers is 294:

xy = 294

Let's begin by solving the first equation for x:

x = 7 + y

Now sub that in for x in the second equation:

(7 + y)y = 294 and

$7y+y^2=294$

This is a quadratic, so let's put it into standard form, setting it equal to 0:

$y^2+7y-294=0$

We have to factor this now to find out what values of y satisfy this equation.

Think: "what 2 number multiply to equal -294 and add to equal 7. To find these numbers we find all the factors of 294, which are:

1, 294

2, 147

3, 98

6, 49

7, 42

14, 21

It looks like 14 and 21 will work. If we make the 14 negative, then 21 - 14 = 7. And if the 14 is negative, then -14 * 21 = -294. So the signs are correct. The equation rewritten using those values in place of 7y is:

$y^2+21y-14y-294 = 0$ and we factor by grouping:

$(y^2+21y)-(14y-294)=0$

Out of the first set of parenthesis we can pull out a y, and from the second set we can pull out a 14:

y(y + 21) - 14(y + 21) = 0

What's common now is the factor (y + 21). So factor THAT out, and you're left with:

(y + 21)(y - 14) = 0

Set each of these expression equal to 0 and solve for y:

y + 21 = 0 so

y = -21 and

y - 14 = 0 so

y = 14

Since we were told that both of the numbers are positive, then y has to be 14.

Sub in y = 14 to find x:

x = 7 + 14 so

x = 21

There you go!

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Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.

Ugo [173]

Answer:

The correct answer is

$2\frac{2}{9}$

Step-by-step explanation:

Method 1

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We now add the whole number parts and the fractions separately

$=-2+4-\frac{1}{9} +\frac{1}{3}$

This will give us,

$=2-\frac{1}{9} +\frac{1}{3}$

The least common denominator for the fractional parts is 9.

$=2+\frac{-1+3\times1}{9}$

$=2+\frac{-1+3}{9}$

$=2+\frac{2}{9}$

$=2\frac{2}{9}$

Method 2

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We first convert the mixed numbers to improper fractions to obtain,

$=-\frac{2\times9+1}{9} +\frac{4\times3+1}{3}$

We carry out the multiplication in the numerator to get,

$=-\frac{18+1}{9} +\frac{12+1}{3}$

We add in the numerator to get,

$=-\frac{19}{9} +\frac{13}{3}$

The least common denominator is $9$ .

$=\frac{-19+13\times3}{9}$

$=\frac{-19+39}{9}$

$=\frac{20}{9}$

We convert back to mixed numbers to get,

$=2\frac{2}{9}$

4 0

2 years ago

Janet bought4/5 of a pound of walnuts. Her family ate 1/3 of a pound. How much is left?

Serga [27]

this just wants us to calculate 4/5-1/3

make common denom

4/5 times 3/3=12/15

1/3 times 5/5=5/15

4/5-1/3=12/15-5/15=(12-5)/15=7/15

7/15lb is left

6 0

3 years ago

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HELP PLS ITS DUE IN A FEW MIN

Tanya [424]

Answer:

S = 50w + 75

Step-by-step explanation:

After each week, Mike gains $50.

Letting w = 0 gives us the amount he started with. In this case, that would be $75.

Therefore, the equation is S = 50w + 75.

5 0

3 years ago

Suppose that an airline quotes a flight time of 128 minutes between two cities. Furthermore, suppose that historical flight reco

ANTONII [103]

Answer:

(a) The probability density function of X is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(b) The value of P (129 ≤ X ≤ 146) is 0.3462.

(c) The probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.

Step-by-step explanation:

The random variable X is defined as the flight time between the two cities.

Since the random variable X denotes time interval, the random variable X is continuous.

(a)

The random variable X is Uniformly distributed with parameters a = 10 minutes and b = 154 minutes.

The probability density function of X is:

$f_{X}(x)=\frac{1}{b-a};\ a$

(b)

Compute the value of P (129 ≤ X ≤ 146) as follows:

Apply continuity correction:

P (129 ≤ X ≤ 146) = P (129 - 0.50 < X < 146 + 0.50)

= P (128.50 < X < 146.50)

$=\int\limits^{146.50}_{128.50} {\frac{1}{154-102}} \, dx$

$=\frac{1}{52}\times \int\limits^{146.50}_{128.50} {1} \, dx$

$=\frac{1}{52}\times (146.50-128.50)$

$=0.3462$

Thus, the value of P (129 ≤ X ≤ 146) is 0.3462.

(c)

It is provided that a randomly selected flight between the two cities will be at least 3 minutes late, i.e. X ≥ 128 + 3 = 131.

Compute the value of P (X ≥ 131) as follows:

Apply continuity correction:

P (X ≥ 131) = P (X > 131 + 0.50)

= P (X > 131.50)

$=\int\limits^{154}_{131.50} {\frac{1}{154-102}} \, dx$

$=\frac{1}{52}\times \int\limits^{154}_{131.50} {1} \, dx$

$=\frac{1}{52}\times (154-131.50)$

$=0.4327$

Thus, the probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.

6 0

3 years ago

What are the zeros of the quadratic function y = 6x2 + 3x - 45

klasskru [66]

Answer:

l think

y= x^2

4 0

2 years ago

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