What are the solutions to the equation x-7/x=6? a. x=-7 and x=1
b. x=-6 and x=-1
c. x=-1 and x=7
d. x=1 and x=6

Answers

Answer 1

Answer: $x - (7)/(x) = 6$
$(x^(2))/(x) - (7)/(x) = 6$
$(x^(2) - 7)/(x) = 6$
$x^(2) - 7 = 6x$
$x^(2) - 6x - 7 = 0$
$x^(2) - 7x + x - 7 = 0$
$x(x) - x(7) + 1(x) - 1(7) = 0$
$x(x - 7) + 1(x - 7) = 0$
$(x + 1)(x - 7) = 0$
$x + 1 = 0$ $or$ $x - 7 = 0$
$x = -1$ $or$ $x = 7$

Answer 2

Answer:

Answer:

Step-by-step explanation:

The equation is $x-(7)/(x)=6$

LCM of the denominator on the left side gives us:

$(x^(2)-7)/(x)=6$

Cross multiplying and arranging gives us:

$x^(2)-7=6x\nx^(2)-6x-7=0$

This is a binomial, to factor this, we have to think of 2 numbers that multiplied gives us $-7$ [the constant term] and added gives us $-6$ [the coefficient of x].

The two numbers are: $-7$ and $1$ .

Now we can write:

$x^(2)-6x-7=0\n(x-7)(x+1)=0$

Hence, either $(x-7)=0$ OR $(x+1)=0$ . This gives us two solutions, $x=7$ and $x=-1$ . Answer choice C is correct.

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A team of three laborers in Mongolia makes rugs by hand for export to the United States. The team works 14 hours a day, six days a week, 50 weeks a year, and is able to make 12 rugs a year. Each laborer is paid a wage that is equivalent to $1.10 per day. The rugs sell for $2,000 each in the United States.

Answers

Given:
3 laborers
works 14 hours a day, 6 days a week, 50 weeks a year
makes 12 rugs a year
material cost 50 per rug
Each laborer is paid a wage of 1.10 per day
rugs sell for 2,000 each in the US
fixed cost 10,000 per year

1.10 per day * # days per year * 3 laborers
50 weeks;/y * 6 days/week = 50 * 6 = 300 days a year
1.10 per day * 300 days a year * 3 laborers = 990 total labor cost

total material cost:
50 per rug * 12 rugs = 600

total revenue:
2,000 x 12 rugs = 24,000

total profit:
total revenue: 24,000
less:
material cost 600
labor cost 990
fixed cost 10,000
profit 12,410

Natalie charges $1490 per month to rent each of her three rental houses. Natalie must pay $5850 in maintenance cots per house per year. If all three houses are occupied, how much money will Natalie earn over seven years?

Answers

3(1490) = 4470 per month for rent she collects...4470(12) = 53640 per yr
3(5850) = 17550 per year she pays in maintenance cost

over 7 yrs...
53640(7) - 17550(7) = 375480 - 122850 = 252630 <== what she earned

Can anyone help me Factor.
81-25x^2

Answers

that is difference of two squares so the answer is (9-5x)(9+5x)

Pls, help Which of the following is true?|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6

Answers

Answer:

Step-by-step explanation:

Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.

Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.

Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.

Are all lines of symmetry also diagonals? explain.

Answers

no not all lines of symmetry are diagonals for example a kite, but most shapes have line of symmetry. sorry if i didnt give enough information buut hope it helps;)

No. Look at a square. The sides are symmetrical, but not diagonal.

Which is f(5) for the function –2x2 + 2x – 3? –107 –63 –43 –37

Answers

If f(x) = - 2x² + 2x - 3, then f(5) will be
$f(x)=- 2x^(2) + 2x - 3\n f(5)=- 2(5)^(2) + 2(5) - 3\n f(5)=- 2(25) + 10 - 3\n f(5)=-50 + 10 - 3\n f(5)=-43$

Thus, your answer is C, -43.

You can just put that value 5 in place of x and then evaluate the output.

The value of f(5) for the given function is given by:

Option C: -43

How to evaluate functions on a given point?

Use the definition of function to evaluate the function on a given point. Most of the time, in general cases, the function will be algebraic and you just need to replace the input variables with the value of the point you want to evaluate the function on.