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2 years ago

HELP A line passes through two points with coordinates (6,-8) and (-3,7).

Mathematics

1 answer:

FromTheMoon [43]2 years ago

4 0

Answer:

Step-by-step explanation:

<u>Equation of the Line</u>

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the points (6,-8) and (-3,7), thus:

$\displaystyle y+8=\frac{7+8}{-3-6}(x-6)$

$\displaystyle y+8=\frac{15}{-9}(x-6)$

Simplifying:

$\displaystyle y+8=-\frac{5}{3}(x-6)$

Multiplying by 3:

$3(y+8)=-5(x-6)$

$3y+24=-5x+30$

Moving all the variables to the left side:

3y + 5x = 30 - 24

3y + 5x = 6

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15 years

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3 years ago

5. Marie buys 2 pounds of turkey and 1 pounds of ham. She pays a total of $20,

NARA [144]

Answer:Let t = cost per pound of turkey

Let h = cost per pound of ham

4t + 2h = 30

t = h - 1.5

substitute h-1.5 in place of t in 1st equation

4(h-1.5) + 2h = 30

4h - 6 + 2h = 30

6h - 6 = 30

6h = 36

h = 6

t = h-1.5 = 4.5

1 pound of turkey costs $4.50

1 pound of ham costs $6.00

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cost of 1 pound each $10.50

Step-by-step explanation:

8 0

2 years ago

If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Lelechka [254]

Answer:

$\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }$

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

$f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)$

So we can say that

$a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}$

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

$(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab$

and we can notice that

$a^2+b^2=(a+b)^2-2ab$ so

$(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab$

it comes

$x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}$

multiply by 3

$3x^2-20x+2*16+5=3x^2-20x+37$

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