All categories

2 years ago

What is a and b . y=ab^x

Mathematics

1 answer:

VladimirAG [237]2 years ago

4 0

Answer:

a = 4, b = $\frac{1}{2}$

Step-by-step explanation:

Use any ordered pairs of points from the table.

Substitute into the equation and solve for a and b, that is

Using (0, 4), then

4 = a $b^{0}$ = a

Hence a = 4

Using (2, 1), then

1 = 4 $b^{2}$ ( divide both sides by 4 )

b² = $\frac{1}{4}$ ( take the square root of both sides )

b = $\frac{1}{2}$

Equation is

y = 4 $(\frac{1}{2}) ^{x}$

You might be interested in

the coordinates of the vertex of a parabola in the xy-plane are (-4,k). If the y-intercept of the parabola is 12 and the parabol

svp [43]

The value of k is (A) 20/3.

<h3>What is a parabola?</h3>

A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics.
It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
A point and a line are two ways to describe a parabola.

To find the value of k:

y - b = c (x - a)²

Where (a, b) is the vertex and c is the constant.

(a, b) = (-4, k)
y - k = c (x - (- 4))²
y - k = c (x + 4)²

So,

x = 0, y = 12
12 - k = 16c
k = 12 - 16c ...... (1)

Then,

(-3, 7) = (x, y)
7 - k = c (1)²
k = 7 - c ...... (2)

Now,

12 - 16c = 7 - c
12 - 7 = 16c - c
5 = 15c
c = 5/15 = 1/3

So, the value of k:

k = 12 - 16 (1/3) = 12 - 16/3 = 36-16/3 = 20/3

Therefore, the value of k is (A) 20/3.

Know more about a parabola here:

brainly.com/question/4061870

#SPJ4

The complete question is given below:

The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?

(A) 20/3

(B) 16/5

(D) 12/5

5 0

9 months ago

What is the slope of the line?

Talja [164]

Answer:

$\displaystyle m=1$