MATHEMATICS HIGH SCHOOL

What is the least common mulitple of 12,48,and 96

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

LCM of 12,48 and 96 is 96

Answer 2

Answer:

Answer:

Step-by-step explanation:

12/2= 6

48/2= 14

96/2=48

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Find dy/dx if y= (1+x)e^x^2

Answers

$y=(1+x)e^(x^2)\ny'=(1+x)'\cdot e^(x^2)+(1+x)\cdot(e^(x^2))'\ny'=1\cdot e^(x^2)+(1+x)\cdot e^(x^2)\cdot (x^2)'\ny'=e^(x^2)+(1+x)e^(x^2)\cdot2x\ny'=e^(x^2)(1+(1+x)\cdot2x)\ny'=e^(x^2)(1+2x+2x^2)\ny'=e^(x^2)(2x^2+2x+1)\n$

You first need to know that:

$If\quad y=u\cdot v\n \n \frac { dy }{ dx } =u\frac { dv }{ dx } +v\frac { du }{ dx } \n \n$

Knowing that u is a function of x and that v is a function of x.

So:

$y=\left( 1+x \right) { e }^{ { x }^( 2 ) }=u\cdot v\n \n u=1+x,\n \n \therefore \quad \frac { du }{ dx } =1$

$\n \n v={ e }^{ { x }^( 2 ) }={ e }^( p )\n \n \therefore \quad \frac { dv }{ dp } ={ e }^( p )={ e }^{ { x }^( 2 ) }\n \n p={ x }^( 2 )\n \n \n \therefore \quad \frac { dp }{ dx } =2x$

$\n \n \therefore \quad \frac { dv }{ dp } \cdot \frac { dp }{ dx } =2x{ e }^{ { x }^( 2 ) }=\frac { dv }{ dx }$

And this means that:

$\frac { dy }{ dx } =\left( 1+x \right) \cdot 2x{ e }^{ { x }^( 2 ) }+{ e }^{ { x }^( 2 ) }\cdot 1\n \n =2x{ e }^{ { x }^( 2 ) }\left( 1+x \right) +{ e }^{ { x }^( 2 ) }$

$\n \n ={ e }^{ { x }^( 2 ) }\left( 2x\left( 1+x \right) +1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2x+2{ x }^( 2 )+1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2{ x }^( 2 )+2x+1 \right)$

Which function is odd? Check all that apply.A. y = sin x
B. y = csc x
C. y = tan x
D. y = cos x

Answers

The odd function is

y = sin x

y = cos x

A function f is deemed weird if f(-x) Equals -f for any value of x. (x). A function is said to be an even function if f(-x) = f for any value of x. (x).

What do odd functions entail?

The meaning of odd function

T function where the absolute value does not change if the independent variable's sign is reversed but the sign of the function itself does.

If f(-x) = -f for any number x, a function f is considered strange (x). When f(-x) = f for any number x, a function is referred to as an even function (x). Even while most functions are neither odd nor even, some of the most significant functions are.

To learn more about odd function refer to:

brainly.com/question/18043852

#SPJ13

Answer:

A. y = sin x

B. y = csc x

C. y = tan x

Step-by-step explanation:

To find average monthly income, multiply the net pay by the number of pay periods per year. Then divide this yearly income by 12 months.true
false

Answers

True. To find average monthly income, multiply the net pay by the number of pay periods per year. Then, divide this yearly income by 12 months.

For example:
Daily wages:
Daily wages * 365 days = Total Wage
Total wage / 12 months = average monthly income

Weekly wages:
Weekly wages * 52 weeks = total wage
total wage / 12 months = average monthly income

Which is equivalent to (4xy – 3z)2, and what type of special product is it?16x2y2 + 9z2, the difference of squares
16x2y2 + 9z2, a perfect square trinomial
16x2y2 – 24xyz + 9z2, the difference of squares
16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answers

(4xy - 3z)²

(4xy - 3z)(4xy - 3z)
4xy(4xy - 3z) - 3z(4xy - 3z)
16x²y² - 12xyz -12xyz + 9z²

16x²y² - 24xyz + 9z², a perfect square trinomial.

The correct option is $\boxed{{\mathbf{Option D}}}$ .

Further explanation:

The binomial algebraic expression is an algebraic expression that consists two terms and it is separated by plus or minus.

Binomial expression can be mathematically expressed as,

$a + b$

The trinomial algebraic expression is an algebraic expression that consists three terms and it is separated by plus or minus.

Trinomial expression can be mathematically expressed as,

$a + b + c$

Here, $a,b{\text{ and }}c$ are the real numbers.

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Given:

The given algebraic expression is ${\left( {4xy - 3z} \right)^2}$ .

Step by step explanation:

Step 1:

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Similarly, the expression ${\left( {4xy - 3z} \right)^2}$ can be written as,

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= \left( {4xy - 3z} \right)\left( {4xy - 3z} \right) \n&= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n\end{aligned}$

Step 2:

The distributive property can be used to solve the square of the binomial.

The distributive property can be expressed as,

$a\left( {b + c} \right) = ab + ac$

Now apply the distributive property to solve the expression ${\left( {4xy - 3z} \right)^2}$ .

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n&= 16{x^2}{y^2} - 12xyz - 12xyz + 9{z^2} \n&= 16{x^2}{y^2} - 24xyz + 9{z^2} \n\end{aligned}$

Therefore, the expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the perfect square of the binomial $\left( {4xy - 3z} \right)$ .

The expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the trinomial.

Thus, option D a perfect square trinomial $16{x^2}{y^2} - 24xyz + 9{z^2}$ is correct.

Learn more:

Learn more about the function is graphed below brainly.com/question/9590016
Learn more about the symmetry for a function brainly.com/question/1286775
Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords: binomial, polynomial, algebraic expression, difference, product, trinomial, distributive property, equivalent, expression, terms, plus, separated, multiply, minus, addition

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.If interest rates stay at 4% APR and I continue to make my monthly $50 deposits into my retirement plan, I should have at least $30 comma 000 saved when I retire in 25 years.

The statement ___________ because I will have $ ___________ nothing in my retirement account when I retire in 25 years.
(Round to the nearest cent as needed.)

Answers

Answer:

False

$25,706.48

Step-by-step explanation:

The annual percentage rate (APR) is 4%, so the monthly rate is 4%/12 = ⅓%.

25 years = 300 months.

The monthly deposit (annuity) is $50.

The future value of the annuities is:

F = A [(1 + i)ⁿ − 1] / i

Given i = 1/300, A = 50, and n = 300:

F = 50 [(1 + 1/300)³⁰⁰ − 1] / (1/300)

F = 25,706.48

The statement is false. The amount after 25 years is less than $30,000.

Final answer:

The statement doesn't make sense because if you make $50 monthly deposits at a 4% APR for 25 years, you will have approximately $41,981.86 in your retirement account, not only $30,000.

Explanation:

The statement does not make sense or is clearly false. Let's add up the total deposits over 25 years and calculate the interest gained using the given annual percentage rate (APR) of 4%.

Total deposits = $50/month * 12 months/year * 25 years = $15,000
Using formula for compound interest, Final Value = P (1 + r/n)^(nt) where P is principal amount (initial investment), r is annual interest rate (decimal), n is number of times that interest applied per time period, t is time the money is invested for. In this case, P=$50, r=4%/12/100%=0.003333, n=1 (monthly), t=12*25=300. After calculations, the final value comes to approximately $41,981.86

Therefore, if you continue to make $50 monthly deposits with a 4% APR for 25 years, you will have just under $41,981.86 in your retirement account, not $30,000 as stated. So, the statement is inaccurate.