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2 years ago

Write an exponential function y=ab^x whose graph passes through (1,6) and (3,54)

1 answer:

7 0

$y=ab^x\\\\(1;\ 6)\to x=1;\ y=6\\(3;\ 54)\to x=3;\ y=54\\\\\text{substitute the values of x and y to the equation}\\\\ \left\{\begin{array}{ccc}6=ab^1&\to&a=\dfrac{6}{b}^{(*)}\\54=ab^3\end{array}\right\\\\\text{substitute (*) to the second equation}\\\\54=\dfrac{6}{b}\cdot b^3\\\\54=6\cdot b^2\ \ \ \ |:6\\\\b=9\to b=\sqrt9\to b=3 \\\\\text{substitute the value of b to the (*)}\\\\a=\dfrac{6}{3}=2\\\\\text{Answer:}\ y=2\cdot3^x$

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Find the x-intercepts of the parabola with vertex (1,-108) and y-intercept (0,-105). Write your answer in this form: (X1,y1), (x

Stolb23 [73]

Answer:

(7, 0) and (-5, 0)

Step-by-step explanation:

Vertex form

$y=a(x-h)^2+k$

(where (h, k) is the vertex)

Given:

vertex = (1, -108)

$\implies y=a(x-1)^2-108$

Given:

y-intercept = (0, -105)

$\implies a(0-1)^2-108=-105$

$\implies a(-1)^2=-105+108$

$\implies a=3$

Therefore:

$\implies y=3(x-1)^2-108$

The x-intercepts are when y = 0

$\implies 3(x-1)^2-108=0$

$\implies 3(x-1)^2=108$

$\implies (x-1)^2=36$

$\implies x-1=\pm \sqrt{36}$

$\implies x=1\pm 6$

$\implies x=7, x=-5$

Therefore, the x-intercepts are (7, 0) and (-5, 0)

7 0

1 year ago

15 POINTS FOR AN EASY QUESTION!!!

Rainbow [258]

Your answer is C. 6.5!
If you need steps just tell me!
Hope this helped!
:)

7 0

2 years ago

Read 2 more answers

Someone explain this to me

e-lub [12.9K]

Answer: a) y = f(x - 6)

b) y = f(x) - 2

Step-by-step explanation:

For transformations we use the following formula: y = a f(x - h) + k

a = vertical stretch
h = horizontal shift (positive = right, negative = left)
k = vertical stretch (positive = up, negative = down)

a) f(x) has a vertex at (-1, 1)

M has a vertex at (5, 1)

The vertex shifted 6 units to the right → h = +6

Input h = +6 into the equation and disregard "a" and "k" since those didn't change. ⇒ y = f(x - 6)

b) f(x) has a vertex at (-1, 1)

N has a vertex at (-1, -1)

The vertex shifted down 2 units → k = -2

Input k = -2 into the equation and disregard "a" and "h" since those didn't change. ⇒ y = f(x) - 2

7 0

2 years ago

Solve F = C + 32 for C

muminat

To solve an equation for a variable, you must isolate the variable on either side of the equation. To do this, simply subtract 32 from both sides of the original equation:

F ( – 32 ) = C + 32 ( – 32 )
F – 32 = C

We have proven that C is equal to (F – 32). This equation (bold) is the answer to your problem.

I hope this helps!

6 0

2 years ago

Sam has 1000 to distributed among two groups equally. Later ,the first part is divided among five children and second part is di

melisa1 [442]

So basically sam split the 1000 to 2 groups so we have 1000 ÷ 2
now the first group divided the 500 (since 1000÷ 2 is 500) among five children so it would be 500 ÷ 5 which equals 100 per child and the second group divided their 500 between to boys, so you would get 500÷2 which is 250
so for group one it would be: 1000÷2÷5 which equals 100 per child and the second group is 1000÷2÷2 which equals 250 for each brother

3 0

2 years ago