How do i solve 89 times 69

Answers

Answer 1

Answer: $89\cdot 69\n \n =\left( 90-1 \right) \left( 70-1 \right) \n \n =90\cdot 70-90-70+1$

$\n \n =6,300-160+1\n \n =6,140+1\n \n =6,141$

Answer 2

Answer: 89 x 69 = 6141
hope this helps!!!!!!!!!!

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Express as a single fraction in its simplest form $(3)/(x+2) + (4)/(x-3)$

Answers

$D:x+2\neq0\to x\neq-2\ and\ x-3\neq0\to x\neq3\n\n(3)/(x+2)+(4)/(x-3)=(3(x-3))/((x+2)(x-3))+(4(x+2))/((x+2)(x-3))=(3(x)+3(-3)+4(x)+4(2))/((x)(x)+(x)(-3)+(2)(x)+2(-3))\n\n=(3x-9+4x+8)/(x^2-3x+2x-6)=\boxed{(7x-1)/(x^2-x-6)}$

$(3)/(x + 2) + (4)/(x - 3) = (3(x - 3))/((x + 2)(x - 3)) + (4(x + 2))/((x + 2)(x - 3)) = (3x - 9)/(x^(2) - x - 6) + (4x+ 8)/(x^(2) - x - 6) =(7x -1)/(x^(2) - x - 6)$

Solve for x 3x+2=2x-7

Answers

Answer:

x = - 9

Step-by-step explanation:

Given

3x + 2 = 2x - 7 ( subtract 2x from both sides )

x + 2 = - 7 ( subtract 2 from both sides )

x = - 9

X= -9 is the answer

Prove that 1 - cosx / sinx = sinx / 1 + cosx
how?

Answers

Answer:

see explanation

Step-by-step explanation:

using the identity

cos²x = 1 - sin²x

consider the left side

$(1-cosx)/(sinx)$

multiply numerator/ denominator by (1 + cosx)

= $((1-cosx)(1+cosx))/(sinx(1+cosx))$ ← expand numerator

= $(1-cos^2x)/(sinx(1+cosx))$

= $(sin^2x)/(sinx(1+cosx))$ ← cancel sinx on numerator/ denominator

= $(sinx)/(1+cosx)$

= right side , thus proven

Assume that a student attends a four-year college with tuition costs of $20,000 per year, room and board costs of $5,000 per year, and books/entertainment costs of $1,000 per year. If the student did not go to college, she would work at a job that pays $25,000 per year but still face the same room and board and entertainment expenses. The opportunity cost of attending college for this student for four years is:

Answers

Answer:

$180,000.

Step-by-step explanation:

We have been given that a student attends a four-year college with tuition costs of $20,000 per year, room and board costs of $5,000 per year, and books/entertainment costs of $1,000 per year. If the student did not go to college, she would work at a job that pays $25,000 per year but still face the same room and board and entertainment expenses.

We know that opportunity cost is the profit lost, when one alternative is selected over another.

Opportunity cost of attending college for 4 years would be amount lost from job in 4 years plus amount spent on studies because the student lost $25,000 for four years for not doing the job and spent $20,000 for 4 years on studies.

$4(\$25000+\$20,000)=4(\$45,000)=\$180,000$

Therefore, the opportunity cost of attending college for this student for four years is $180,000.

Final answer:

The opportunity cost of attending college for four years is $100,000.

Explanation:

The opportunity cost of attending college for four years is the value of the best alternative that the student foregoes by choosing to attend college. In this case, the student could have worked and earned $25,000 per year instead of going to college. So, the opportunity cost for four years would be $25,000 * 4 = $100,000.