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3 years ago

Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

Mathematics

1 answer:

Inessa [10]3 years ago

3 0

6x⁴ + 7x² - 10
6x⁴ - 5x² + 12x² - 10
x²(6x²) - x²(5) + 2(6x²) - 2(5)
x²(6x² - 5) + 2(6x² - 5)
(x² + 2)(6x² - 5)

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What is the quotient of the following in simplest form? 5/9 divided by 2/3

Assoli18 [71]

Answer:

5/6

Step-by-step explanation:

You write the question as such: 5/9 divided by 2/3.

After that, you keep the first fraction, flip the sign and the fraction.

You will get: 5/9 multiplied by 3/2.

When you get this, you then cross multiply and simplify as such.

5/3 multiplied by 1/2.

5/6 would be your solution.

4 0

2 years ago

Pleaseeee help ASAP it’s due today :(

Aleksandr [31]

Let, price increased by x times.

New price = 40 + ( 1 × x ) = 40 + x

It is given that for each $1 increase park loses 300 visitors.

Number of visitors = ( 24000 - 300x )

So, revenue is given by :

R = ( 24000 - 300x )( 40 + x ) ....1)

To finding critical point :

R'(x) = 0

-300( 40 + x ) + ( 24000 - 300x ) = 0 .....By product law

-12000 - 300x + 24000 -300x = 0

600x = 12000

x = 20

So, revenue is maximum at x = 20 .

Putting x = 20 in equation 1) , we get :

R = ( 24000 - 300x )( 40 + x )

R = [ 24000 - 300(20)][40 + 20 ]

R = $1080000

Therefore, park should charge $( 40 + 20 ) = $60 for maximising the revenue and maximum revenue is $10,80,000 .

Hence, this is the required solution.

5 0

3 years ago

The edge length of cube A is two times the edge length of cube B. How many times greater isthe volume of the cube A than the vol

allsm [11]

Answer:

<h2>8 times greater</h2>

Step-by-step explanation:

The formula of a volume of a cube:

$V=a^3$

a - edge length

-----------------------------------

The edge length of cube B is a.

The edge length of cube A is 2a.

Calculate the volumes:

$V_A=(2a)^3=2^3a^3=8a^3\\\\V_B=a^3$

How many times greater is the volume of the cube A than the volume of cube B?

Make the quotient:

$\dfrac{V_A}{V_B}=\dfrac{8a^3}{a^3}=8$

4 0

3 years ago

what is the equation, in slope- intercept form, of the line that contains the points (-3,4) and (5,7)

gavmur [86]

Answer:

y = $\frac{3}{8}$ x + $\frac{41}{8}$

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

To calculate the slope use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (5, 7)

m = $\frac{7-4}{5+3}$ = $\frac{3}{8}$ , hence

y = $\frac{3}{8}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (5, 7 ), then

7 = $\frac{15}{8}$ + c ⇒ c = 7 - $\frac{15}{8}$ = $\frac{41}{8}$

y = $\frac{3}{8}$ x + $\frac{41}{8}$ ← equation in slope-intercept form

6 0

3 years ago

When Theresa got her puppy, it weighed 6 ponds less than 2/3 of its weight now. If the puppy weighed 4 pounds when she first rec

sesenic [268]

Answer:

15 lb

Step-by-step explanation:

let the current weight of the puppy be X, the initial weight of the puppy is 4lb or $\frac{2}{3}X-6\ lb$ , (6 lb less 2/3 X) .

#We equate the current weight to the initial weight to determine X:

$4\ lb=\frac{2}{3}X-6\ lb\\\\10 \ lb=\frac{2}{3}X\\\\X=15$

Hence, the current weight of the puppy is 15 lb

5 0

3 years ago