MATHEMATICS HIGH SCHOOL

2x^4=9x^2 solve by factoring

Answers

Answer 1

Answer:

Step-by-step explanation:

2x⁴ = 9x²

2x⁴ - 9x² = 0

x²(2x² - 9) = 0

Either x² = 0 or 2x² - 9 = 0.

When x² = 0, x = 0.

When 2x² - 9 = 0, x² = 9/2, x = ± 3/√2.

Hence the solutions are

x = 0, x = 3/√2 and x = -3/√2.

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Pizza Time has collected data about customer pizza topping preferences. They have calculated that P(pepperoni) = 0.7, P(olives) = 0.6, and P(pepperoni or olives) = 0.8. Determine the P(pepperoni and olives).A.0.5

B.0.6

C. 0.7

Answers

Answer:

Option A is correct that is $.5=P(A\capB)$

Step-by-step explanation:

We have given probabilities

P(pepperoni)=0.7

P(olives)=0.6

P(pepperoni or olives)=0.8

We need to find the probability of pepperoni and olives

We have a formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Here we have say A is the event of peperroni tha is $P(A)=0.7$

B is the event of olives that is $P(B)=0.6$

pepperoni or olives that is is $P(A\cup B)=0.8$

Pepperoni and olives that is $P(A\cap B)$ we have to find

On substituting the values in the formula we will get

$0.8=0.7+0.6-P(A\cap B)$

$0.8=1.3-P(A\cap B)$

$-.5=-P(A\cap B)$

$.5=P(A\cap B)$

On simplifying the equation we will get

$.5=P(A\cap B)$

Therefore, Option A is correct.

The answer would be 0.5. This is because the sum off Olives and Pepperoni is 0.13 and the number of those people who choose Pepperoni or Olives is only 0.8. Thus, the remaining number is now on Pepperoni and olives.

An online store that has been successfully growing on its initial angel investment and revenue wants to invest $5 million to expand the business. The bank is willing to lend the business this money at a 10 percent interest rate over an eight-year term. Calculate the monthly payment and explain what the business must be able to do with this money in order for this to be a smart business decision.

Answers

At simple interest: 10% = 5,000, 000 x 10/100 = 5,000,000 x (1/10) =$500,000 spread over 8 years = 8 x $62,500 monthly interest payment = $62,500/12=$5208.33 Smart decision: has to at least break-even, if not generate more than the total interest repayment.

Answer:

$5208.33

Step-by-step explanation:

5,000,000 x 0.10= $500,000 500,000 / 8= $62500 62500/ 12= $5208.33 total interest repayment

What is the length of a side of a cube with a volume of 2197 ft3?

Answers

Vloume = (Length)^3
so, Length = (2197)^(1/3)
Length = 13 ft

Find the equation of the circle whose center and radius are given.center ( 7, -3), radius = 7

Answers

Answer: The required equation of the circle is $x^2+y^2-14x+6y+9=0.$

Step-by-step explanation: We are given to find the equation of the circle with center at the point (7, -3) and radius of length 7 units.

We know that

the standard equation of a circle with center at the point (h, k) and radius of length r units is given by

$(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

For the given circle,

center, (h, k) = (7, -3) and radius, r = 7 units.

From equation (i), we get

$(x-7)^2+(y-(-3))^2=7^2\n\n\Rightarrow (x-7)^2+(y+3)^2=49\n\n\Rightarrow x^2-14x+49+y^2+6y+9=49\n\n\Rightarrow x^2+y^2-14x+6y+9=0.$

Thus, the required equation of the circle is $x^2+y^2-14x+6y+9=0.$

(x – h)² + (y – k)² = r²

Fill in the numbers

(x – 7)² + (y +3)² = 49

Find the area of the green sector if m∠ A = π 6 and the circle has a radius of 10 inches.

Answers

The area of the sector, when the measure of the central angle is in radians, can be solved using this equation:
A = (n/2) r²

From the given values,
A = (π/6/2) (10²)
A = 25π/6 = 26.18 in²

Therefore, the area of the sector with the central angle measuring π/6 with the radius of the circle 10 inches is 26.18 in²

a bicycle tire is 28 inches in diameter. approximately how far does the bicycle move foward each time the wheel goes around?

Answers

Answer:

Step-by-step explanation:

circumference=2πr=2π×14=28π=28×22/7≈88 inch

it covers a distance of 88 inch in one revolution.

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