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3 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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An interior designer wants to decorate a newly constructed house. The function f(x) = 49x^2 - 200 represents the amount of money

Illusion [34]

The given function for the amount of money earned is a function of the

function for the number of rooms decorated.

The correct responses are;

Part A: The amount made as a function hours worked, x, is; f(x) = x² - 200

Part B: The difference quotient f(x) = x² - 200 is 2·x + h

Reasons:

The given parameters are;

f(x) = 49·x² - 200 = Amount of money earned by the designers

Where;

x = The number of rooms decorated

$g(x) = \dfrac{1}{7} \cdot x$ = The number of rooms decorated

Where;

x = The number of hours he works

Part A: To determine the amount of money the interior designer will make

decorating the house as a function of the hours he works.

Solution:

The amount made as a function of the number of hours worked is given by

plugging in the number of rooms decorated, x = g(x) = (1/7)·x, in f(x) as

follows;

$f \left( \dfrac{1}{7} \cdot x \right) = 49 \cdot \left( \dfrac{1}{7} \cdot x \right)^2 - 200 = x^2 - 200$

Therefore, the amount of money the interior designer will make decorating

the house as a function of the hours he works, x, is f(x) = x² - 200.

Part B:

The difference quotient is given as follows;

$Difference \ quotient = \dfrac{f(x + h) - f(x)}{(x + h) - x} = \dfrac{f(x + h) - f(x)}{h}$

$\dfrac{f(x + h) - f(x)}{h} = \dfrac{((x + h)^2 - 200)- (x^2 - 200)}{h} = \dfrac{h^2 + 2 \cdot x \cdot h}{h} = h + 2 \cdot x$

The difference quotient for f(x) = x² - 200 is h + 2·x

Learn more here:

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7 0

3 years ago

Michael is using a drawing program to complete a construction. Which construction is he completing? A circle is drawn with two p

Varvara68 [4.7K]

The drawing shows a circle, with the two lines forming a cross assumed to be perpendicular to each other, so this is most likely to be a square, as the four points at which the perpendicular lines intersect with the circle can be connected to form a square.
We would need 3 points for an equilateral triangle, 5 for a pentagon, and 6 for a hexagon, which do not fit the current steps.

3 0

3 years ago

Read 2 more answers

Two sides of a right triangle are 8’ and 12’ find the area of the triangle if 8 and 12 are a leg hypotenuse

jeka94

so you are tryna find the hypotenuse right?

C = your hypotenuse

C² = A² + B²

C² = 8² + 12²

C² = 64 + 144

C² = 208

C = √208