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3 years ago

(x+4)(2x+3)(-x-9)=f(x) find the zeros

Mathematics

1 answer:

Sonbull [250]3 years ago

6 0

9514 1404 393

Answer:

x = {-9, -4, -3/2}

Step-by-step explanation:

The zeros are the values of x that make the factors zero. (If a factor is zero, the product will be zero.)

x+4 = 0

x = -4 . . . . subtract 4

2x+3 = 0

2x = -3 . . . . subtract 3

x = -3/2 . . . divide by 2

-x-9 = 0

-9 = x . . . . add x

The zeros are ...

x = {-9, -4, -3/2}

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Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.

lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0

3 years ago

A random sample of 18 adults, chosen from the 1500 adults in the town, took a survey asking their opinion on a recent property t

Tamiku [17]

Answer:

C) I & III

Step-by-step explanation:

Given:

Sample size, n = 18

Sample proportion = 25% = 0.25

Here, a random sample of 18 adults were chosen from the 1500 adults in town. This shows that the random condition was satisfied because the sample was drawn randomly from the general population of adults in the town.

For the normal condition to be satisfied, np should be greater than 10, ie np > 10.

In this case, np = 18 * 0.25 = 4.5

Since np is less than 10, the normal condition was not satisfied.

For the 10% condition to be satisfied, sample size should not be more than 10% of the general population.

Here, the sample size is 18 and the population is 1500. Therefore,

$\frac{18}{1500} * 100 = 1.2$

Since the sample size is 1.2% of the population which is less than 10%, the 10% condition was satisfied.

The correct option is C, because only I & III were satisfied.

4 0

3 years ago

Find the volume of a sphere with the diameter of 4

givi [52]

$d=4 \Rightarrow r=2\\V=\dfrac{4}{3}\pi r^3\\
V=\dfrac{4}{3}\pi \cdot2^3\\
V=\dfrac{4}{3}\pi \cdot8\\
V=\dfrac{32}{3} \pi
$

5 0

3 years ago

Can someone please help me.

skelet666 [1.2K]

To find the slope of the line, you need two points.
(-2 , 5) and (3 , -5)

5 - (-5) / -2 - 3
10 / -5 = -2

The slope of the line is -2. So your answer is C.

8 0

3 years ago

What is the distance between (–4, –10) and (–4, –4)?

Gre4nikov [31]

Answer:

6 units

Step-by-step explanation:

(-4 , -10) ; (-4 , -4)

Distance = $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$