MATHEMATICS HIGH SCHOOL

6. The equation of line A is 3x + 6y - 1 = 0. Give the equation of a line that passes through thepoint (5,1) that is

/1 a. Perpendicular to line A

Answer:

/1 b. Parallel to line A

Answer:

Answers

Answer 1
Answer: Step 1: Convert to slope-intercept form to find the slope of the line.

This isn't necessary if you know all the shortcuts, it just makes your life a bit easier.

3x+6y-1=0\n6y=-3x+1\ny=-(3)/(6)x+(1)/(6)\n-(1)/(2)x+(1)/(6)

Now we want to find the equations for our new lines. It's easiest to do this in slope-intercept form, so let's start finding the slope and y-intercept.

So for the perpendicular line, the slope is going to flip and change signs, this is aka its opposite reciprocal.
And for the parallel line, it'll stay the same.

-(1)/(2) ⇒ (2)/(1)=2
-(1)/(2) ⇒ -(1)/(2)

As for the y-intercept, just apply that slope until you get a point where x=0.

(5, 1) with a rise of 2 and a run of 1...let's work backwards to (0, b)
(5, 1), (4, -1), (3, -3), (2, -5), (1, -7), (0, -9).

(5, 1) with a rise of -1 and a run of 2...let's work backwards to (0, b)
(5, 1), (3, 0), (1, -1)...gonna have to take half a step here...(0, -1.5).

Now let's construct our equations in slope-intercept form.

y = 2x-9\ny=-(1)/(2)x-(3)/(2)

And now it's time to convert to general form!

Make sure we have common denominators...check.

Multiply by the denominator...

y=2x-9\n2y=1x-3

...check.

Aaaand bring everything over!

\boxed{-2x+y-9=0}\n\boxed{-x+2y-3=0}

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Hello! I could use some help with this algebra question:)
A businessman buys 1,440 dozen pens at $2.50 a dozen and then sells them at a price of 25¢ apiece. What is his total profit on the lot of pens?

Which polynomial represents the area of the rectangle?a. 3x2+2x−5
b. 3x2−5
c. 3x2−2x−5
d. 3x2−8x−5

Answers

Answer:

Step-by-step explanation:

The correct option is C.

Step-by-step explanation:

The width of the rectangular pen is

The length of the rectangular pen is

The perimeter of a rectangle is

Therefore the correct option is C.

Final answer:

Without specific dimensions for the rectangle, it's impossible to definitively determine which polynomial represents its area. If we knew the length and width in terms of x, we could then form a polynomial by multiplying them.

Explanation:

This question is based on the concept of polynomials and their application in representing areas. From the provided question, we don't have specific dimensions of the rectangle, thus making it impossible to definitively determine which polynomial represents its area.

If the length and width of the rectangle were expressed in terms of x (e.g., 3x and x, or some other terms x and 2x-5), then we could put these expressions in the form of a polynomial by multiplying them together. For example, if we suppose our rectangle has sides of 3x and x, then the area would be represented by the polynomial 3x2, which equals to 3x*x.

However, without specific rectangular dimensions, we can't accurately choose between the provided options: 3x2+2x−5, 3x2−5, 3x2−2x−5, and 3x2−8x−5.

Learn more about Polynomials in Area Calculation here:

brainly.com/question/12723489

#SPJ2

Compute the perimeter of the rectangle using the distance formula. (round to the nearest integer)A) 33
B) 34
C) 38
D) 45

Answers

the answer is D if you count both of the long sides it will give you 21 each and 5 on the short side so that would give you 47 is the preimeter so D is the closest.

Which polynomial is prime? 3x3 + 3x2 – 2x – 2 3x3 – 2x2 + 3x – 4 4x3 + 2x2 + 6x + 3 4x3 + 4x2 – 3x – 3

Answers

Answer:3x^3-2x^2+3x-4


Step-by-step explanation:

We know that a polynomial is said to be prime if it does not factorize into polynomials.

1. 3x^3+3x^2-2x-2\n=3x^2(x+1)-1(x+1)\n=(x+1)(3x^2-1)

This is not prime as it can factorize.

2.3x^3-2x^2+3x-4\n=x^2(3x-2)+1(3x-4)

(3x-2)\ and\ (3x-4) are not same , thus we cannot factorize the above polynomial.

Therefore this polynomial is prime.

3.4x^3+2x^2+6^x+3=2x^2(2x+1)+3(2x+1)\n=(2x+1)(2x^2+3)

This is not prime as it can factorize.

4.4x^3+4x^2-3x-3\n=4x^2(x+1)-3(x+1)\n=(x+1)(4x^2-3)

This is not prime as it can factorize.

The correct answer is B. 3x3 – 2x2 + 3x – 4 :D

have a good day!

74. Seven workers are hired to seed a field by hand. Each is given a plot 7 x 7feet in size. What is the total area of the field?

Answers

Answer:

The total area of the field is 343 square feet

Step-by-step explanation:

Let us solve the question

∵ There are 7 workers hired to seed a field by hand

∵ Each is given a plot 7 x 7  feet in size

→ The plot has shaped a square because its two dimensions equal

∴ The side of the plot =7 feet

∵ The area of the square = side × side

∴ The area of each plot = 7 × 7

∴ The area of each plot = 49 square feet

→ To find the total area multiply the area of 1 plot by the number

   of the workers

∵ The total area = 49 × 7

∴ The total area = 343 square feet

∴ The total area of the field is 343 square feet

2x^4=9x^2 solve by factoring

Answers

Step-by-step explanation:

2x⁴ = 9x²

2x⁴ - 9x² = 0

x²(2x² - 9) = 0

Either x² = 0 or 2x² - 9 = 0.

When x² = 0, x = 0.

When 2x² - 9 = 0, x² = 9/2, x = ± 3/√2.

Hence the solutions are

x = 0, x = 3/√2 and x = -3/√2.

Subtract these polynomials. (3x2 + 3x + 3) - (x2 + 2x + 3) =

A. 2x2 + x
B. 2x2 + 5x
C. 2x2 + 5x + 6
D. 2x2 + x + 6

Answers

Answer:

2x^2+1x

Step-by-step explanation:

Subtract these polynomials.  

(3x^2 + 3x + 3) - (x^2 + 2x + 3)

To subtract, we multiply negative sign inside the second parenthesis

3x^2 + 3x + 3-x^2 - 2x - 3

To subtract the polynomials we combine like terms

3x^2-x^2+ 3x- 2x+3-3

2x^2+1x
3x^2 -x^2= 2x^2
3x-2x=x
3-3=0

The answer is A.
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