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2 years ago

What is the difference between factoring and solving ?

Mathematics

1 answer:

trapecia [35]2 years ago

6 0

Answer:

Factoring is a step taken towards solving a quadratic equation. ... You cannot factor them, the only way to find the roots then, is by using the quadratic formula. Suppose you factor the quadratic polynomial as and . Then set them equal to zero and solve for , you will have

Step-by-step explanation.

Example 1 – Solve: x2 + 16 = 10x

Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order.

Step 2: Use a factoring strategies to factor the problem.

Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero.

Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.

You might be interested in

The following table shows the salary of 7 people in an office last year.

kotegsom [21]

Answer:

a. £24,714.29

b. £16,833.33

Step-by-step explanation:

The calculation of mean income is given below:-

Mean income = Total addition of salaries ÷ Number of workers

= £9,500 + £25,000 + £13,250 + £72,000 + £12,750 + £29,500 + £11,000

= £173,000 ÷ 7

= £24,714.29

Now,

the Mean income excluding Deva's salary:

= Formula of Mean income

= Total addition of salaries excluding Deva salary ÷ Number of workers

= (£9,500 + £25,000 + £13,250 + £12,750 + £29,500 + £11,000) ÷ 6

= £101,000 ÷ 6

= £16,833.33

7 0

2 years ago

Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.

vekshin1

$x^2+y^2+z^2=100z\iff x^2+y^2+(z-50)^2=50^2$

The surface of interest can be parameterized by

$\mathbf r(u,v)=\begin{cases}x(u,v)=50\cos u\sin v\\y(u,v)=50\sin u\sin v\\z(u,v)=50(\cos v+1)\end{cases}$

with $0\le u\le2\pi$ and $0\le v\le\arccos\dfrac{49}{50}$ .

The area of the surface $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm dA=\iint_T\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv$

We have

$\|\mathbf r_u\times\mathbf r_v\|=50^2\sin v$

so the area is given by the double integral

$\displaystyle50^2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\arccos(49/50)}\sin v\,\mathrm dv\,\mathrm du=100\pi$

6 0

2 years ago

It takes 45 minutes to drive to the nearest bowling alley taking city streets going

Savatey [412]

Answer:

21 minutes

Step-by-step explanation:

Given the following :

Taking CITY STREET:

Time taken to drive to nearest bowling alley = 45 minutes = 45/60 = 0.75 hours

Speed of travel = 30 miles per hour

Taking FREEWAY:

speed of travel = 65miles per hour

If the distance to bowling alley is the same along both routes, The time taken along FREEWAY will be :

Distance to bowling alley taking city center :

Speed = distance / time

30 mph = distance / 0.75 hour

Distance = 30 × 0. 75 = 22.5 miles

Since distance is the same :

Time taken along FREEWAY :

Time taken = distance / speed

Time taken = 22.5 / 65 = 0.3461538 hour

Converting to minutes :

0.3461538 × 60 = 20.769 minutes

= 21 minutes ( to the nearest minute)

7 0

2 years ago

32% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find t

Lorico [155]

Answer:

A. 21.06%

B. 66.88%

C. 81.56%

Step-by-step explanation:

There are two possible answer for the question asked, yes(more likely to make purchases) or no. The probability for a random adults answer yes to the question is 32% so the probability that the adults answer no is 68%.

(a) exactly two

There is only one case for this question, 2 people say yes and 8 people say no. The calculation for this problem will be:

2P10 * P(yes)^2 * P(no)^8= 10!/2!8!* 32%^2 * 68%^8 = 0.21066= 21.06%

(b) more than two

There are a lot of case for more than two, its easier to find out the negation of the probability which is "two or less". Case that fulfill "two or less" will be: 2 yes and 8 no

1 yes and 9 no

0 yes and 10 no

The calculation for the negation will be:

~P(X)= 0P10 * P(yes)^0 * P(no)^10 + 1P10 * P(yes)^1 * P(no)^9 + 2P10 * P(yes)^2 * P(no)^8 =

10!/0!10!* 32%^0 * 68%^10 + 10!/1!9!* 32%^1 * 68%^9 + 10!/2!8!* 32%^2 * 68%^8

0.02113 + 0.09947 + 0.21066 = 0.33126= 33.12%

Since its the negation, you need to subtract 1 with the negation

P(X)= 1 - ~P(X)

P(X)= 1 - 33.12%= 66.88%

Same formula as above, but the case is:

2 yes and 8 no

3 yes and 7 no

4 yes and 6 no

5 yes and 5 no

The calculation will be:

2P10 * P(yes)^2 * P(no)^8 + 3P10 * P(yes)^3 * P(no)^7 + 4P10 * P(yes)^4 * P(no)^6 + 5P10 * P(yes)^5 * P(no)^5 =

10!/2!8!* 32%^2 * 68%^8 + 10!/3!7!* 32%^3 * 68%^7 + 10!/4!6!* 32%^4 * 68%^6 + 10!/5!5!* 32%^5 * 68%^5

0.21066 + 0.26435 + 0.21770 + 0.1229= 0.81561= 81.56%

8 0

2 years ago

A grocery store sells a bag of 5 oranges for $3.10. If Levi spent $2.48 on oranges, how many did he buy?

Svetllana [295]

Answer:

Four

Step-by-step explanation:

1. $3.10 divide by 5 = $0.62

2. $0.62 multiply by 4 = $2.48

So Levi bought 4 oranges

7 0

2 years ago