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Marat540 [252]
3 years ago
9

A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $20/acre, the seed for corn c

osts $60/acre, and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. How many acres of each should the farmer plant?

Mathematics
1 answer:
statuscvo [17]3 years ago
6 0
A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $20/acre, the seed for corn costs $60/acre, and the farmer has set aside $3000 to spend on seed. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. How many acres of each should the farmer plant?

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ALGEBRA QUESTION PLS HELPS
cluponka [151]

The value of x is –7.

Solution:

Given expression:

$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}

Let us factor x^2+4x+3.

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

Substitute this in the fraction.

$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

To make the denominator same, multiply and divide the first term by (x +1).

$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

Denominators are same, you can add the fractions.

$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}

$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}

Cancel the common term in the numerator and denominator.

$\frac{x+7}{x+1} \cdot \frac{1}{x+1}

Multiply the fractions.

$\frac{x+7}{(x+1)^2}

$\frac{x+7}{x^2+2x+1}

The expression is simplified to one rational expression.

Suppose the expression is equal to 0.

$\frac{x+7}{x^2+2x+1}=0

Do cross multiplication.

${x+7}=0\times (}{x^2+2x+1})

Any number or variable multiplied by 0 gives 0.

${x+7}=0

Subtract 7 from both sides of the equation.

${x+7-7}=0-7

x = –7

The value of x is –7.

7 0
3 years ago
I have a ribbon 5/7 of a foot. I want to cut it in 5/12 pieces. How many pieces can I cut 5/7 divided by 5/12= 5/7 x5/12= 15/7 p
Otrada [13]
100 cm = 1 meter 
<span>4.5 meter x 100 cm = 450 cm </span>

<span>450 cm / 4.5 cm = number of pieces of ribbon </span>

<span>450/4.5 = 100</span>
5 0
3 years ago
Show twelve in four different ways use words pictures and numbers
Hunter-Best [27]
24/4: 24-12: 12+0: 12/1: 48/4: 72/6:

3 0
3 years ago
2m<br>5m<br>(i) Value of n is?<br>(a) 21/7<br>(b) 22.7<br>(C) 22/7<br>(d) 7/22<br>10m​
Crazy boy [7]

Step-by-step explanation:

the same at the meeting tonight at the church and the same to think of you too pAh un hombre question about my order and peel and peel and peel off face mask with a few things I need at un maha mo pah Wala pa rin galing un pinambayad pah ah I see everyone and peel off mask for sale in the way it is now a few things I love you too pAh un hombre question about the same time I don't care eeeeeeeeeeeeee I love you too pAh un

5 0
3 years ago
PLS HELP!<br> solve by completing the square<br> x²+4x=8
masya89 [10]

Step-by-step explanation:

x²+4x=8

rearrange

x² + 4x - 8 = 0

half of 4 is 2

so

x² + 4x + 2² - 2² - 8 = 0

do x² + 4x + 2²

multiplies to give 4 adds to give 4

2+ 2

(x + 2)²

(x + 2)² - 2² - 8

(x + 2)² - 4 - 8

(x + 2)² - 12

(x + 2 + √12) (x + 2 - √12)

√12 = √4 * √3 = 2 √3

(x + 2 + 2√3) (x + 2 - 2√3)

4 0
2 years ago
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