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2 years ago

Write the point-slope form of the equation of the line through the given

Mathematics

1 answer:

Marat540 [252]2 years ago

7 0

Answer:

y+3 = -2(x)

Step-by-step explanation:

The equation of the line that passes through the points

(5,-5) and (-5,-1) is y=-2/5x-3.

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write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

inessss [21]

Answer:

$f(x)=3x^3+x^2+3x+1$

Step-by-step explanation:

If a real number $-\frac{1}{3}$ is a zero of polynomial function, then

$x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}$

is the factor of this function.

If a complex number $-i$ is a xero of the polynomial function, then the complex number $i$ is also a zero of this function and

$x-(-i)=x+i\ \text{ and }\ x-i$

are two factors of this function.

So, the function of least degree is

$f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)$

If the polynomial function must be with integer coefficients, then it has a form

$f(x)=3x^3+x^2+3x+1$

4 0

3 years ago

If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes

anyanavicka [17]

ANSWER

$x = 2 \: \: or \: \: x = 15$

$x = - 2 \: \: or \: \: x = - 15$

EXPLANATION

The given polynomial is

$f(x) = {x}^{2} + kx + 30$

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

$m + n = - \frac{b}{a} = -k$

and the product of roots is

$mn = \frac{c}{a} = 30$

The square difference of the zeroes is given by the expression.

$( {m - n})^{2} = {(m + n)}^{2} - 4mn$

From the question, this difference is 169.

This implies that:

$( { - k)}^{2} - 4(30) = 169$

${ k}^{2} -120= 169$

$k^{2} = 289$

$k= \pm \sqrt{289}$

$k= \pm17$

We substitute the values of k into the equation and solve for x.

$f(x) = {x}^{2} \pm17x + 30$

$f(x) = (x \pm2)(x \pm 15)$

The zeroes are given by;

$(x \pm2)(x \pm 15) = 0$

$x = \pm2 \: \: or \: \: x = \pm 15$

5 0

3 years ago

The distance between City A and City B is 200 miles. A length of 2.1 feet represents this distance on a certain wall map. City C

ratelena [41]

Answer:

300 miles

Step-by-step explanation:

200/2.1= 95.238...

95.238...*3.15=300

Hope this helps :)

3 0

3 years ago

Read 2 more answers

What is 3,242 round to the nearer ten

ale4655 [162]

Answer:

3240

Step-by-step explanation:

Can’t explain

3 0

3 years ago

a book is 6 inches wide and 9 inches tall A publisher want to scale factor of 1.5 to enlarge a book. what will the area of the f

VladimirAG [237]

Answer:

Step-by-step explanation:

6 inches enlarged by 1.5 = 9 inches

9 inches enlarged by 1.5 = 13.5 inches

Area would be 9x13.5=

121.5 inches for the area

Hope this helps you out.

8 0

3 years ago