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3 years ago

Find all x-intercepts of the function. Express your answer as a list of x-values. f ( x ) = − 45 x 3 + 60 x 2 − 20 x

Mathematics

1 answer:

mr Goodwill [35]3 years ago

6 0

Answer:

x = 0, $\frac{2}{3}$

Step-by-step explanation:

Factorise f(x) and equate to zero for x- intercepts

f(x) = - 5x(9x² - 12x + 4) = 0 ( common factor of - 5x )

To factor the quadratic consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is

product = 9 × 4 = 36 , sum = - 12

The factors are - 6 and - 6

Use these factors to split the middle term

9x² - 6x - 6x + 4 = 0 ( factor the first/second and third/fourth terms )

3x(3x - 2) - 2(3x - 2) ( factor out (3x - 2) )

(3x - 2)(3x - 2), hence

f(x) = - 5x(3x - 2)(3x - 2) = 0

equate each factor to zero and solve for x

- 5x = 0 ⇒ x = 0

(3x - 2)² = 0 ⇒ x = $\frac{2}{3}$ of multiplicity 2, indicating turning point

x - intercepts are x = 0, $\frac{2}{3}$

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Solve this for me (geometry)

VashaNatasha [74]

Given:

A figure of a circle. $KJ=6,KL=x-2,ML=4$ .

To find:

The length of KJ.

Solution:

From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.

Therefore, the length of KJ is 6 units.

Note: In the given question we need to find KL instead of KJ because KJ is already given.

According to the tangent secant theorem:

$a^2=bc$

Where,

a is the length of the tangent.
b is the length of the external segment of the secant.
c is the measure of the secant.

Using the tangent secant theorem, we get

$ML^2=KL\times JL$

$(4)^2=(x-2)\times (6+x-2)$

$16=(x-2)\times (4+x)$

$16=4x+x^2-8-2x$

On further simplification, we get

$16=x^2+2x-8$

$0=x^2+2x-8-16$

$0=x^2+2x-24$

Splitting the middle term, we get

$x^2+6x-4x-24=0$

$x(x+6)-4(x+6)=0$

$(x+6)(x-4)=0$

$x=-6,4$

For $x=-6$ ,

$KJ=-6-2$

$KJ=-8$ , which is not possible because side cannot be negative.

For $x=4$ ,

$KJ=4-2$

$KJ=2$

Therefore, the measure of KL is 2 units.

7 0

3 years ago

So far a total of 48 tickets have been sold for the school play for a total revenue of $220. How many student tickets have been

Advocard [28]

Let x be the number of adult tickets and y be the number of student tickets.

From the first sentence we can set up both equations:

1) x + y = 48
2) 7x + 3y = 220

Rearrange #1 to isolate x:
x = 48 - y

Sub that into #2 and solve for y to get your answer:
7(48 - y) + 3y = 220
336 - 7y + 3y = 220
-4y = -116
y = 29

29 student tickets were sold.

6 0

3 years ago

If one side of a rectangle is three less than the other side and the perimeter is 46 inches, find the area of the rectangle.

BaLLatris [955]

$a-one\ side\ of\ rectangle\\a+3-other\ side\ of\ rectangle\\2a+2(a+3)=2a+2a+6=4a+6-the\ perimeter\\46\ in-the\ perimeter\\\\\text{The equation:}\\\\4a+6=46\qquad\text{subtract 6 from both sides}\\\\4a=40\qquad\text{divide both sides by 4}\\\\a=10\\\\a+3=10+3=13\\\\\text{Dimensions of the rectangle:}\ 10\ in\ \times\ 13\ in.\\\\\text{The area of the rectangle:}\\\\\boxed{A=10\cdot13=130\ in^2}$

7 0

4 years ago

Which value is an output of the function?<br> O-6<br> O-2<br> O 4<br> O7

Black_prince [1.1K]

The answer is the second one

3 0

3 years ago

2. Determine the ratio of 6 feet to 4 yards in lowest terms.

Sladkaya [172]

Answer:

1:2

Step-by-step explanation:

1 yard is 3 feet

6 ft = 2 yd, so the ratio is 2 yd : 4 yd = 2:4 = 1:2

5 0

3 years ago