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2 years ago

For what values of x is the following inequality true? 5/7 + x/7 >(underlined) 10. PLZ HELP!!! 12 points

1 answer:

3 0

Hello! Thank you for your question! I will be most happy to help!

So here what we are going to do is solve for X.

Step 1: Simplify x/7

Equation at the end of step 1: 5/7 + x/7 - 10 > 0

Step 2: Simplify 5/7

Equation at the end of step 2:

5/7 + x/7 - 10 > 0

Step 3: Adding fractions which have a common denominator:

3.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5 + x / 7 = x + 5 / 7

Equation at the end of step 3:

(x + 5) / 7 - 10 > 0

Step 4: Rewriting the whole as an Equivalent Fraction:

4.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 7 as the denominator:

10 = 10 / 1 = 10 * 7 / 7

Equivalent fraction: The fraction thus generated looks different but has the same value as the whole

Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5) - (10 * 7) / 7 = x - 65 / 7

Equation at the end of step 4:

x - 65 / 7 > 0

Step 5: 5.1 Multiply both sides by 7

Solve Basic Inequality:

5.2 Add 65 to both sides

x > 65

Final answer: x > 65

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2 years ago

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

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5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

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But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle).