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3 years ago

Simplify m - {n + [p - (m + n - p)]}. a. -2m + 2p b. 2m - 2p c. -2m - 2p

Mathematics

2 answers:

zzz [600]3 years ago

6 0

Answer: The correct option is (b) $2m-2p.$

Step-by-step explanation: We are given to simplify the following expression:

$E=m-\{n+[p-(m+n-p)]\}$

We will be using the simple algebraic operations and the rule of BODMAS to simplify the above expression.

The simplification is as follows:

$E\\\\=m-\{n+[p-(m+n-p)]\}\\\\=m-\{n+[p-m-n+p]\}\\\\=m-\{n+[2p-m-n]\}\\\\=m-\{n+2p-m-n\}\\\\=m-\{2p-m\}\\\\=m-2p+m\\\\=2m-2p.$

Therefore, the simplified form is $2m-2p.$

Thus, (b) is the correct option.

Vlad [161]3 years ago

5 0

To simplify the following expression, we first simplify the terms inside the parenthesis from inner going outer. The first one is [p - (m + n - p)] equal to p - m- n + p = 2p - m - n. Then, n +2p - m - n equal to 2p -m. Then, m - 2p + m equal to 2m -2p. Answer is B

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One movie is 120 minutes long. Another is 100 minutes long.

steposvetlana [31]

Answer:

5:20pm

Step-by-step explanation:

120+100=320minutes

320/60=5hrs 20min

12+5:20= 17:20pm or 5:20pm

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3 years ago

The buyer for a chain of stores purchased lawn ornaments in bulk, paying $23 each. The stores will sell each lawn ornament for $

Naya [18.7K]

Answer:

The markup percentage is 61.2

Step-by-step explanation:

Given as :

The cost price of each ornaments = $23

The sell price of each ornament = $37.08

Let The markup percentage = x

<u>Now, According to question</u>

Markup percentage = $\dfrac{s.p - c.p}{c.p}$ × 100

Or, x% = $\dfrac{37.08 - 23}{23}$

Or, x% = $\dfrac{14.08}{23}$

Or, x% = 0.612

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So, The The markup percentage = x = 61.2

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3 years ago

A neighborhood trash pick up comes every 5 days, while the recycling pick up is every 8 days. After how many days will both tras

Ivanshal [37]

Answer:

40 days

Step-by-step explanation:

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3 years ago

Write the polynomial f(x)=x^4-10x^3+25x^2-40x+84. In factored form

Verizon [17]

<h2>Steps:</h2>

So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is $\pm \frac{p}{q}$ , with p = the factors of the constant and q = the factors of the leading coefficient. In this case:

$\textsf{leading coefficient = 1, constant = 84}\\\\p=1,2,3,4,6,7,12,14,21,28,42,84\\q=1\\\\\pm \frac{1,2,3,4,6,7,12,14,21,28,42,84}{1}\\\\\textsf{Potential roots =}\pm 1, \pm 2,\pm 3,\pm 4,\pm 6, \pm 7,\pm 12,\pm 14,\pm 21,\pm 28,\pm 42,\pm 84$

Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:

$f(1)=(1)^4-10(1)^3+25(1)^2-40(1)+84\\f(1)=1-10+25-40+84\\f(1)=60\ \textsf{Not a root}\\\\f(2)=2^4-10(2)^3+25(2)^2-40(2)+84\\f(2)=16-10*8+25*4-80+84\\f(2)=16-80+100-80+84\\f(2)=80\ \textsf{Not a root}\\\\f(3)=3^4-10(3)^3+25(3)^2-40(3)+84\\f(3)=81-10*27+25*9-120+84\\f(3)=81-270+225-120+84\\f(3)=0\ \textsf{Is a root}$

Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:

3 | 1 - 10 + 25 - 40 + 84
_________________

Firstly, drop the 1:

3 | 1 - 10 + 25 - 40 + 84
↓
_________________
1

Next, multiply 3 and 1, then add the product with -10:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3
_________________
1 - 7

Next, multiply 3 and -7, then add the product with 25:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21
_________________
1 - 7 + 4

Next, multiply 3 and 4, then add the product with -40:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21 + 12
_________________
1 - 7 + 4 - 28

Lastly, multiply -28 and 3, then add the product with 84:

3 | 1 - 10 + 25 - 40 + 84
↓ + 3 - 21 + 12 - 84
_________________
1 - 7 + 4 - 28 + 0

Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format $ax^3+bx^2+cx+d$ . In this case, our quotient is $x^3-7x^2+4x-28$ .

So right now, our equation looks like this:

$f(x)=(x-3)(x^3-7x^2+4x-28)$

However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:

$f(x)=(x-3)(x^2(x-7)+4(x-7))$

Now it can be rewritten as:

$f(x)=(x-3)(x^2+4)(x-7)$

<h2>Answer:</h2>

Since the polynomial cannot be further simplified, your answer is:

$f(x)=(x-3)(x^2+4)(x-7)$

6 0

3 years ago

PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!!!!!!!!!!!!!!!PLSSSSSSS HELPPPPPPP I WILL GIVE BRAINLIESTTTTTTTTTT!!!

Arisa [49]

Answer: y^2/x

Step-by-step explanation:

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3 years ago