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3 years ago

Simplify the expression 6 - 2x + 5+ 42. Hint: Your final expression shoul donly have two terms.

Mathematics

1 answer:

il63 [147K]3 years ago

3 0

Answer:

-2x+53

Step-by-step explanation:

42+5+6=53

leave the -2x

(the two is negative because we were previously subtracting)

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Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

3 years ago

HELPPP!!!! What is one solution? Eliminate any extraneous solutions.

olga nikolaevna [1]

Answer:

The correct answer is x= 4/5 because you cannot take the root of a negative number

4 0

3 years ago

Help me pls only 10points

NeX [460]

y=-7x+8

y=-7x-8

-7x+8=-7x-8

8=-8

x∈∅

B. No solutions

3 0

4 years ago

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in ye

sdas [7]

Answer:

$10 + (\frac{2}{3}) a = 50$ is the CORRECT equation.

Step-by-step explanation:

The given question is INCOMPLETE.

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?

Now here:

a: The tree’s age in years.

Also, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”

⇒ 10 + two-thirds of that tree’s age = 50

$\implies 10 + (\frac{2}{3}) a = 50$

But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.

So, the written equation by Javier is Incorrect.

Now, solving the written correct equation for the value of a, we get:

$\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60$

Hence the correct age of the tree = 60 years

5 0

4 years ago

Solve for c: c= 5 5/6 x 2 A. 10 5/6 B. 11 2/3 C. 10 2/3 D. 11 5/6

exis [7]

Answer:

B. 11 2/3

Step-by-step explanation:

c = 5 5/6*2

Change the mixed number to an improper fraction

5 5/6 = (6*5+5)/6 = (30+5)/6 = 35/6

c = 35/6 *2

c = 35/6 *2/1

= 70/6

Now we change it back to a mixed number

6 goes into 70 11 times

11*6 = 66 with 4 left over

11 4/6

We can simplify 4/6 by dividing the top and bottom by 2

11 2/3

6 0

3 years ago