MATHEMATICS HIGH SCHOOL

The length L of a steel rod is 7.36 correct to 2 decimal place

Answers

Answer 1

Answer:

Answer:

The length of the steel rod, correct to 2 decimal places, is 7.36 units.

Step-by-step explanation:

Since the number already has two decimal places, there is no need to make any changes or rounding in this case.

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If a polynomial P(x) has P(-2)=0, then which of the following can you conclude?P(x) has a factor (x+2)P(x) has a constant term of -2P(x) has an x-intercept of -2Both P(x) has a factor (x+2) and P(x) has an x-intercept of -2

Point-slope form to slope-intercept form

Answers

y=mx+b
y-y1=m(x-x1)

They are different, and the conversion depends on what you need.

What you need:
y-y1=m(x-x1)
y-y1=mx-mx1 (distribute the m)
y=mx-mx1+y1 (move the y1)
y=mx+b (combine mx1 and y1)

I need help solving x^2+3xy-y^2=12 and x^2-y^2=-12

Answers

$substitute:x^2-y^2=-12\ to\ x^2+3xy-y^2=12\n\n3xy-12=12\n3xy=12+12\n3xy=24\ \ \ \ \ /:3\nxy=8\to x=(8)/(y)\n\nsubstitute\ to\ x^2-y^2=-12\n\n\left((8)/(y)\right)^2-y^2=-12\n\n(64)/(y^2)=y^2-12$

$(64)/(y^2)=(y^2-12)/(1)\n\ny^2(y^2-12)=64\n\ny^4-12y^2-64=0\n\nsubstitute:y^2=t > 0\n\nt^2-12t-64=0$

$a=1;\ b=-12;\ c=-64\n\Delta=b^2-4ac\to\Delta=(-12)^2-4\cdot1\cdot(-64)=144+256=400\n\nt_1=(-b-\sqrt\Delta)/(2a);\ t_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(400)=20\n\nt_1=(12-20)/(2\cdot1)=(-8)/(2)=-4 < 0;\ t_2=(12+20)/(2\cdot1)=(32)/(2)=16\n\ny^2=16\Rightarrow y=\pm√(16)\Rightarrow y=-4\ or\ y=4\n\nx=(8)/(-4)=-2\ or\ x=(8)/(4)=2\n\nSolution:x=-2\ and\ y=-4\ or\ x=2\ and\ y=4$

What is the solution to 2x+5>3x+1

Answers

   2x + 5 > 3x + 1
- 2x     - 2x
   5 > x + 1
   - 1 - 1
   4 > x
   x < 4

The solution is 4>x Because you subtract 1 from both sides and you subtract 2x from both sides and you get x<4 or 4>x

what rational number lies in between -14/31 and -17/33? A. -989/3069 B. -123/276 C. -989/2046 D. -4/7

Answers

-14/31 and -17/33

-17/33 - (-14/31) = (-17/33*31/31) - (-14/31*33/33) = -527/1023 + 462/1023

= (-527+462)/1023 = -65/1023

-65/1023 ÷ 2 = -65/1023 * 1/2 = -65/2046

-17/33 - (-65/2046) = (-17/33*62/62) - (-65/2046) = -1054/2046 + 65/2046
= -989/2046 Choice C.

What is the domain of the relation {(2, 8), (0, 8), (–1, 5), (–1, 3), (–2, 3)}?

Answers

The domain is simply all of the x values.

We have a 2, 0, -1, -1, and -2.

Get rid of duplicates, so 2, 0, -1, and -2.

We're going to want to order those, so -2, -1, 0, and 2.

And put some fancy brackets on that. {-2, -1, 0, 2}

Domain Range
    -1 3
   0 5
   2 8
   3

The domain of the relation {(2, 8), (0, 8), (-1, 5), (-1, 3), (-2, 3)} is {-1, 0, 2, 3}.

Two lines are perpendicular. The slope of one line is -2, What is the slope of the other line?A. 1/2

B. -1/2

C. -2

D. 2

Answers

perpendicular lines have negative reciprocal slopes. All that means is " flip " the slope and change the sign.
slope = -2, or -2/1....so flip the slope...-1/2...and change the sign...1/2.
so the perpendicular slope would be 1/2.

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Each sales associate at an electronics store has a choice of the two salary options shown below:-$115 per week plus 9.5% commission on the associate's total sales -$450 per week with no commission The average of the total sales amount for each associate last year was $125,000. Based on this average, what is the difference between the two salary options each year? (52 weeks = 1 year) (10 POINTS)

Math help me ASAP!!!

You are a plumber, and you are repairing a toilet leak. The job should take 0.9 hours. About how many minutes will ittake to complete the job?O 0.015O 5.4O 54O 67O 540

Solve: 3(2x - 5) = 6x - 15 A) 0 B) 1 C) 20 D) infinitely many solutions