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2 years ago

PLEASE ANSWER ASAP

Mathematics

1 answer:

mote1985 [20]2 years ago

8 0

Answer:

y = 2 $(3)^{x}$

Step-by-step explanation:

For the exponential function in the form

y = a $b^{x}$

Use ordered pairs from the table to find a and b

Using (0, 2 ), then

2 = a $b^{0}$ ( $b^{0}$ = 1 ) , thus

a = 2, so

y = 2 $b^{x}$

Using (1, 6 ) , then

6 = 2b ( divide both sides by 2 )

b = 3

Thus the exponential function is

y = 2 $(3)^{x}$

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Write an equation in slope-intercept form of the line that passes through the given points.(3,5) and (0,4) please answer with al

alukav5142 [94]

Answer:

Y = (1/3)X + 4

Step-by-step explanation:

You need to know the equation Y = mX + b, for two sets of coordinates

Therefore we need to find the slope and the interception of the given points.

1) The slope of the line

We can use the point slope form, and clear for the slope m

y - y1 = m (x-x1)

m = (y -y1) / (x -x1)

The data given is: A (3, 5) and B (0, 4)

Then substitute in the slope: m = (5 -4)) / (3 -0) = (1/3)

m = 1/3

2) Find the interception

From the general equation slope intercept Y = mX + b, clear b

b = Y - mX

Now substitute any given point to obtain b the interception

b = Y - mX

Lets choose point A (3, 5), remember m = 1/3

b =5 - (1/3)(3)= 4

b = 4

3) Therefore with the values of m and b, the general equation for the slope intercept form is:

Y = mX + b -->

Y = (1/3)X + 4

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2 years ago

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Rudik [331]

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2 years ago

Read 2 more answers

What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

<u>Answer:</u>

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

<u>Solution: </u>

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

6 0

2 years ago