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4 years ago

Choose the correct simplification of (4x3 + 3x2 − 6x) − (10x3 + 3x2).

2 answers:

7 0

Answer:
-6x (x + 1)(x - 1)

Explanation:
Before we begin, remember the following:
(-ve) * (-ve) = +ve
(-ve) * (+ve) = -ve
(+ve) * (+ve) = +ve
(+ve) * (-ve) = -ve
a² - b² = (a + b)(a - b)

Now, for the given:
(4x³ + 3x² - 6x) - (10x³ + 3x²)
First, we eill remove the brackets based on the rules mentioned above. This will give us:
4x³ + 3x² - 6x - 10x³ - 3x²
Now, we will combine like terms as follows:
(4-10)x³ + (3-3)x² - 6x
-6x³ - 6x
Taking -6x as a common factor:
-6x (x² - 1)
Factoring the bracket as difference between two squares will give us the final simplest form:
-6x (x + 1)(x - 1)

Hope this helps :)

Nadya [2.5K]4 years ago

5 0

$4x^{3} +3 x^{2} -6x - (10 x^{3}+3 x^{2} )$

First, distribute the negative into the parenthesis

$4x^{3} +3 x^{2} -6x - 10 x^{3}-3 x^{2}$

Next, combine like terms

$-6x^{3} - 6x$ is your final answer

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Find the sum or difference (4y+3)-(y-2) do help me pls i can't remember how to do these

konstantin123 [22]

(4y+3)-(y-2) = 4y+3-y+2 = 3y+5

6 0

3 years ago

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A city park designer is designing a new park. The park will be shaped like a right triangle and there will be two pathways for p

Aloiza [94]

Answer:

VW=36

VT=27

Step-by-step explanation:

VW is the midsegment of the triangle

VW=72/2

=36

VXT is a right angle triangle

a²+b²=c²

a=√c²-b²

a=√45²-36²

a=√(45-36)(45+36)

a=√9×81

a=√9×√81

a=27

therefore

VT=27

8 0

3 years ago

Assignment: Compound Interest Investigation

sukhopar [10]

To help Tyler better understand how his money will increase in an account that uses simple interest and one that uses compound interest, we are going to use two formulas: a simple interest formula for the accounts that use simple interest, and a compound interest formula for the accounts that use compound interest.
- Simple interest formula: $A=P(1+rt)$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is number of years
- Compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is he number of years
$n$ is the number of times the interest is compounded per year

1.
a. This is a compound interest account, so we are going to use our compound interest formula. We now that $P=1500$ , $t=5$ , and since the interest is compounded annually (1 time a year), $n=1$ . To find the interest rate in decimal form, we are going to divide it by 100%: $r= \frac{4}{100} =0.04$ . Now that we have all the values lets replace them in our compound interest formula:
$A=1500(1+ \frac{0.04}{1}) ^{(1)(5)}$
$A=1824.98$
We can conclude that after 5 years he will have $1824.98 in this account.
b. Here we will use our simple interest formula. We know that $P=1500$ , $t=5$ , and $r= \frac{4}{100} =0.04$ . Lets replace those values in our simple interest formula:
$A=1500(1+(0.04)(5))$
$A=1800$
We can conclude that after 5 years he will have $1800 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $1824.98-1800=24.98$

2.
a. Here we are going to use our compound interest formula. We know that $P=2000$ , $t=1$ and $r= \frac{8}{100} =0.08$ . We also know that the interest is compounded Quaternary (4 times per year), so $n=4$ . Now that we have all our values lets replace them into our formula:
$A=2000(1+ \frac{0.08}{4} )^{(4)(1)}$
$A=2164.86$
We can conclude that after 1 year he will have $2164.86 in this account.
b. Here we are going to use our simple interest formula. We know that $P=2000$ , $t=1$ , and $r= \frac{8}{100} =0.08$ . Once again, lets replace those values in our formula:
$A=2000(1+(0.08)(1))$
$A=2160$
We can conclude that after 1 year he will have $2160 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $2164.86-2160=4.86$

3.
a. Since Bank A offers an account with a simple interest, we are going to use our simple interest formula. From the question we know that $P=3200$ , $t=3$ , and $r= \frac{3.5}{100} =0.035$ . Now we can replace those values into our formula to get:
$A=3200(1+(0.035)(3))$
$A=3536$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$
$InterestEarned=3536-3200=336$
We can conclude that the interest earned for Bank A is $336
b. Since Bank B offers an account with a compound interest, we are going to use our compound interest formula. We know that $P=3200$ , $t=3$ , $r= \frac{3.4}{100} =0.034$ , and since the interest is compounded annually (1 time a year), $n=1$ . Now that we have all the values, lets replace them in our formula to get:
$A=3200(1+ \frac{0.034}{1} )^{(1)(3)}$
$A=3537.62$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$ :
$InterestEarned=3537.62-3200=337.62$
We can conclude that the interest earned for Bank B is $337.62
c. Even tough the interest returns between the tow Banks are very similar, Bank B offers a slightly better interest over a period of time, which can make a big difference in the long run. If Tyler wants the earn more money, he definitively should deposit his money in Bank B.
d. The compound interest account from Bank B will yield more money than the simple account one from Bank A The difference between the tow amounts is $3537.62-3536=1.62$

6 0

4 years ago

two technicians regularly make repairs when breakdowns occur on an automated production line. the first technican, who services

xxMikexx [17]

Answer:

52.63% probability that thids intial repair was made by the first technican

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Incomplete repair

Event B: Made by the first technican.

The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.

This means that $P(B) = 0.4, P(A|B) = 0.05$ .

Probability of an incomplete repair:

5% of 40%(first technican) or 3% of 60%(second technican). So

$P(A) = 0.05*0.4 + 0.03*0.6 = 0.038$

Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican

$P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263$

52.63% probability that thids intial repair was made by the first technican

8 0

4 years ago

Express 0.1588 in scientific notation

Aleks [24]

The answer is 158.8 x (10 to the 3rd power)

(couldn't put a exponent for the the number 3)

4 0

4 years ago

Read 2 more answers