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2 years ago

Which is the completely factored form of 12x4 + 39x3 + 9x2?

Mathematics

1 answer:

Troyanec [42]2 years ago

6 0

<h3><u>Explanation</u></h3>

Given expression

${12x}^{4} + {39x}^{3} + {9x}^{2}$

Factor the expression by using common factor.

We csn pull out 3x² out of the expression.

${3x}^{2} (4 {x}^{2} + 13x + 3)$

We simply pull out the x-term with lowest degree and 3 out of the expression. If another expression cannot be factored after first factoring then that's the final answer.

The expression can still be factored. Factor the expression by using two brackets.

${4x}^{2} + 13x + 3 \\ (4x + 1)(x + 3)$

New factored form

$3 {x}^{2} (4x + 1)(x + 3)$

<h3><u>Answer</u></h3>

$\large \boxed { {3x}^{2} (4x + 1)(x + 3)}$

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Three consecutive even numbers add up to 36. Select all of the following equations that will find the lowest number of the three

Misha Larkins [42]

Equation A find the lowest number of the three. Equation A satisfies the given conditions.

<h3>What is even number? </h3>

If the number is divisible by 2 then the number will be an even number. Similarly, the number is not divisible by 2 then the number will be an odd number.

Assume the three consecutive integers are 2x,2x+2,2x+4

The sum of the three consecutive even numbers are 36;

x+x+2+x+4 = 36

3x+6=36

3x=30

x=10

The three integers are found as;

x =10

x+2 = 10+2 = 12

2x+4 =10+4=14

Hence, equation A find the lowest number of the three. Equation A satisfies the given conditions.

To learn more about the even number, refer to the link;

brainly.com/question/2289438

#SPJ1

5 0

2 years ago

How much money has to be invested at 5.9% interest compounded continuously to have $15,000 after 12 years?

scoray [572]

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.

Step-by-step explanation:

The given is,

Future value, F = $15,000

Interest, i = 5.9%

( compounded continuously )

Period, t = 12 years

Step:1

Formula to calculate the present with compounded continuously,

$F=Pe^{(i)(t)}$ ...............(1)

Substitute the values in equation (1) to find the P value,

$15000=Pe^{(0.059)(12)}$ ( ∵ $i = \frac{5.9}{100}=0.059$ )

$15000=Pe^{0.708}$

$15000=P(2.0299)$ ( ∵ $e^{o.708} =2.0299$ )

We change the P (Present value) into the left side,

$P=\frac{15000}{2.0299}$

$=7389.427$

≅ 7389.43

P = $ 7389.43

Result:

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.

8 0

3 years ago

Edward's school is 132 miles away from his home . He goes by car to school and back. The car consumed 4 gallons of gas taking hi

mixer [17]

Total distance is 132 miles x 2 times/day x 5 days = 1320 miles
That used 4 gallons of fuel, so 1320 miles/4 gallons = 330 miles per gallon

5 0

3 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function <em>f</em>, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to <em>x</em> :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

3 years ago

In a company 60% of the workers are men is 880 women work for the company how many workers are there in all

borishaifa [10]

I will do my best to answer this question due to the gramatical errors made making it difficult to read and understand.
assuming that the 880 is the number of women employed that makes up 40% of the company employees
880+ (880*1.5) = 2200 employees total

7 0

2 years ago