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3 years ago

If(2p+3)(p+5)=p2 +p+,whatisthevalueof++?

Mathematics

1 answer:

Zarrin [17]3 years ago

5 0

Answer: (p - 1) • (5p + 3)

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2".

STEP

Equation at the end of step 1

(5p2 - 2p) - 3

STEP

Trying to factor by splitting the middle term

2.1 Factoring 5p2-2p-3

The first term is, 5p2 its coefficient is 5 .

The middle term is, -2p its coefficient is -2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 5 • -3 = -15

Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -2 .

-15 + 1 = -14

-5 + 3 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 3

5p2 - 5p + 3p - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

5p • (p-1)

Add up the last 2 terms, pulling out common factors :

3 • (p-1)

Step-5 : Add up the four terms of step 4 :

(5p+3) • (p-1)

Which is the desired factorization

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Describe and correct the error(s) made in each of the problems below.

ladessa [460]

Answer:

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

Step-by-step explanation:

<u>Errors in Algebraic Operations </u>

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
Not to confuse product of fractions with the sum of fractions. Rules are quite different

The first expression is

$1-x / (5-x)(-x)=x-1 / x(x-5)$

Let's arrange into format:

$\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}$

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

$\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}$

Now for the second expression

$5/s+2/5=2/s$

Let's arrange into format

$\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}$

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

$\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}$

6 0

3 years ago

A helicopter leaves bristol and flies due east for 10 miles.Then the helicopter flies 8miles north before landing. What is the d

DedPeter [7]

Answer:

The distance of the helicopter from the bristol is approximately 1<u>2.81 miles</u>

Step-by-step explanation:

Given:

Helicopter flies 10 miles east of bristol.

Then the helicopter flies 8 miles North before landing.

To find the direct distance between the helicopter and bristol.

Solution:

In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter

The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.

On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.

Applying Pythagorean theorem to find the hypotenuse of the triangle.

$Hypotenuse^2=Short\ leg^2+Shortest\ leg^2$

$Hypotenuse^2=10^2+8^2$

$Hypotenuse^2=100+64\\Hypotenuse^2=164$

Taking square root both sides.

$\sqrt{Hyptenuse^2}=\sqrt{164}\\Hypotenuse = 12.81\ miles$

Thus, the distance of the helicopter from the bristol is approximately 12.81 miles

6 0

3 years ago

The mean distance between the data values and the mean of the data set best describe which of the following?

andrezito [222]

Mean Absolute Deviation I'm pretty sure. Hope this helped, have a great day! :D

5 0

3 years ago

a sum of RS 500 is in the form of denominators of RS5 & RS 10..if the total no. of notes is 90 ,find the no. of notes of eac

Katarina [22]

Let rs.5 denominations be x , then rs 10 denominations will be 90-x

then total amount 5x + 10(90-x) which is rs.500

5x + 10(90-x) = 500

900 - 5x = 500
400 = 5x
therefore x = 80
therefore no. of rs.5 is 80
no. of rs.10 is 90-x = 90-80 = 10

8 0

3 years ago

Answer this if you're cool

GalinKa [24]

I’m doing this to in 8th grade I don’t understand it neither

7 0

3 years ago

Read 2 more answers