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3 years ago

How is the parent function y=x2 related to the given function Y=3(x+1)2?

1 answer:

6 0

Parent function: y = f(x) = x^2

given function: y = g(x) = 3 (x+1)^2

=> g(x) = 3 * f(x + 1)^2

So, from the point of view of graphs, the given function, g(x), is the parent function, f(x) = x^2, shifted one unit to the left and amplified by a factor of 3.

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Answer is 5
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2 years ago

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What is the value of the expression (x-y)2 when x=5 and y=-1

rodikova [14]

(5- -1)2
(5+1)2
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3 years ago

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 67°, a

kvasek [131]

Among many other formulas, the area of a triangle is

$S = \frac 1 2 a c \sin B$

where B is the angle between sides a and c.

$S=\frac 1 2(10)(20) \sin 67^\circ \approx 92.05 \textrm{ sq cm}$

Answer: 92.05 sq cm, first choice

Bonus. Here's a formula for the area S of a triangle your teacher doesn't know:

$16S^2 = 4a^2b^2 -(c^2-a^2-b^2)^2=(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)$

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3 years ago

Log2(3x-1) = log2 (x+8)

Keith_Richards [23]

Answer:

X= 9/2

Alternative form

x=4 1/2, x=4.5

Step-by-step explanation:

*= Multiply

1. log (little 10 under) (2)*(3x-1)= log (little 10 under) (2)*(x+8)

2. then divide both side by log (little 10 under (2))

3. 3x-1=x+8

4. move variable to the left side and change its sign

5. 3x-x-1=8

6. then move constant to the right side and change its sign

7. 3x-x=8+1

8. collect like terms

9. 2x=8+1

10. add 8+1

11. 2x=9

12. then divide both sides by 2

13. 2/2 9/2

14. 2/2 cancels out so x=9/2 is the answer

4 0

3 years ago

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D.sqrt(2+x^/2)<br> Solve this question please

lidiya [134]

Answer:

Option a.

Step-by-step explanation:

By looking at the options, we can assume that the function y(x) is something like:

$y = \sqrt{4 + a*x^2}$

$y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }$

such that, y(0) = √4 = 2, as expected.

Now, we want to have:

$y' = \frac{x*y}{2 + x^2}$

replacing y' and y we get:

$\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}$

Now we can try to solve this for "a".

$\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}$

If we multiply both sides by y(x), we get:

$\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}$

$a*x = \frac{x*(4 + a*x^2)}{2 + x^2}$

We can remove the x factor in both numerators if we divide both sides by x, so we get:

$a = \frac{4 + a*x^2}{2 + x^2}$

Now we just need to isolate "a"

$a*(2 + x^2) = 4 + a*x^2$

$2*a + a*x^2 = 4 + a*x^2$

Now we can subtract a*x^2 in both sides to get:

$2*a = 4\\a = 4/2 = 2$

Then the solution is:

$y = \sqrt{4 + 2*x^2}$

The correct option is option a.

7 0

2 years ago