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3 years ago

How to solve 3/2 = 9/10k (in fraction form). Please show work

2 answers:

8 0

$\frac{3}{2}=\frac{9}{10k}\\\\ 3 \times 10 k=9 \times 2\\\\30 k=18\\\\k=\frac{18}{30}\\\\ \text{Dividing numerator and denominator by 6}\\\\k=\frac{3}{5}$

⇒Used Cross Multiplication Method

antoniya [11.8K]3 years ago

5 0

3/2 and 9/10. Look at the denominators. 2 times what number equals 10. That number would be 5. So if you multiply the first fractions denominator by 5 you get 10. Do the same to the top. you get a new fracrion which is 15/10. Add normally. 15/10 + 9/10 = 24/10. In lowest terms it is 2 2/5 (2 wholes and 2 out of 5)

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Give an example of an odd function and explain algebraically why it is odd.

NARA [144]

F(x) = x^3
f(-x) = (-x)^3 = -x^3
but if u factor out the negative then
f(-x) = -(x)^3
therefore it is an odd function because f(-x) = -f(x)

4 0

3 years ago

What is the quadratic portion in this quadratic equation 7x2-12x+16=0

alexdok [17]

Answer:

x = 6/7 + (2 i sqrt(19))/7 or x = 6/7 - (2 i sqrt(19))/7

Step-by-step explanation:

Solve for x:

7 x^2 - 12 x + 16 = 0

Hint: | Write the quadratic equation in standard form.

Divide both sides by 7:

x^2 - (12 x)/7 + 16/7 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 16/7 from both sides:

x^2 - (12 x)/7 = -16/7

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36/49 to both sides:

x^2 - (12 x)/7 + 36/49 = -76/49

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6/7)^2 = -76/49

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6/7 = (2 i sqrt(19))/7 or x - 6/7 = -(2 i sqrt(19))/7

Hint: | Look at the first equation: Solve for x.

Add 6/7 to both sides:

x = 6/7 + (2 i sqrt(19))/7 or x - 6/7 = -(2 i sqrt(19))/7

Hint: | Look at the second equation: Solve for x.

Add 6/7 to both sides:

Answer: x = 6/7 + (2 i sqrt(19))/7 or x = 6/7 - (2 i sqrt(19))/7

6 0

3 years ago

Can you find the limits of this

Pavel [41]

Answer:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{-3}{8}$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]: $\displaystyle \lim_{x \to c} b = b$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Addition/Subtraction]: $\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$

L'Hopital's Rule

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

We are given the following limit:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16}$

Let's substitute in x = -2 using the limit rule:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{(-2)^3 + 8}{(-2)^4 - 16}$

Evaluating this, we arrive at an indeterminate form:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \frac{0}{0}$

Since we have an indeterminate form, let's use L'Hopital's Rule. Differentiate both the numerator and denominator respectively:

$\displaystyle \lim_{x \to -2} \frac{x^3 + 8}{x^4 - 16} = \lim_{x \to -2} \frac{3x^2}{4x^3}$

Substitute in x = -2 using the limit rule:

$\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{3(-2)^2}{4(-2)^3}$

Evaluating this, we get:

$\displaystyle \lim_{x \to -2} \frac{3x^2}{4x^3} = \frac{-3}{8}$

And we have our answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

6 0

3 years ago

The perimeter of an isosceles triangle is 23 cm. The base is 4 cm less than one of the equal sides. Find the length of each side

creativ13 [48]

Since it is an isos. triangle we know that both sides are equal
Let's let the base=b and the legs =L
We know that B=L-4
And L-4+L+L=23
3L-4=23
3L=27
L=9
Hope this helps! :)
Let me know if you have any questions!

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3 years ago

Help Me! 40 Points!!!!! TY!

Kamila [148]

Answer:

Step-by-step explanation:

The y intercept is is -3 so that eliminates 2 options. Next the king goes up to the top right so it’s a positive slope. So that leaves only one option. The slope goes up one and to the side two. So it’s 1/2

8 0

3 years ago

Read 2 more answers