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4 years ago

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There are 17.8 grams of salt in a solution. If 5.9 grams of salt are added to the solution, how many grams of salt will be in th

e

1 answer:

astraxan [27]4 years ago

4 0

Answer:

Step-by-step explanation:

2

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The smaller triangle was dilated to form the larger triangle. What is the value of x? A smaller triangle has side lengths of 5,

Alenkasestr [34]

Answer:

the answer is 7.5

Step-by-step explanation:

took the quiz on edge ;-)

8 0

3 years ago

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What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

4 years ago

The hypotenuse of a right triangle is 13ft long. The longer leg is 7ft longer than the shorter leg. Find the side lengths of the

DochEvi [55]

Answer:

The short side is 5ft and the longer side 12ft

Step-by-step explanation:

I knew that the hypotenuse was 13 so it couldn’t be more than 13. I was guessing at numbers until I got to 5 then added 7. After I use Pythagorean theorem to check and I got 13.

7 0

3 years ago

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Help!!!!!!!!!!!!!!!!!!!!!

laila [671]

15 2/6 or 15 1/3 (simplest form) because 3x6+5=23/6 x 4/1 = 92/6 converted to mixed number is 15 1/3

3 0

3 years ago

Which expressions are equivalent to 2^5 2^4

KIM [24]

Answer with explanation:

The given expression is

$=2^5 \times 2^4$

→As, multiplication of real number follows Commutative property.

Which states that, if a and b are any two real numbers , then

a × b= b × a

The Expression equivalent to ,the above expression are

$1. 2^4 \times 2^5\\\\ 2. 2^5=32 \text{and} 2^4=16, \text{So} 2^5 \times 2^4=32 \times 16=512$

5 0

3 years ago

Read 2 more answers