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3 years ago

If y=3x+1 were changed to y=x+1 how would the graph of the new function compare with the original?

1 answer:

5 0

F(x)=3x+1 (preimage)
g(x)=x+1 (image)
it is undergoing a reduction/compression with translation.
In general, a linear transformation is
g(x) = a*f(bx-h)+k
h=horizontal translation (right if h>0, left if h<0, note formula has minus sign)
k=vertical translation (up if k>0, down if k<0)
a=vertical stretching, (stretching if |a|>1, compression if |a|<1, also, if a<0, a reflection across the x-axis is performed)
b=horizontal stretching (|b|>0 compression, |b|<0 stretching, also, if b<0, a reflection across the y-axis is performed)

In this case,
g(x)=f(x/3), so it is a horizontal stretching.
Note that the y-intercept remains unchanged.

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Simplify. final answer should be written in standard form (a+b)(3a-b)(2a+7b)

algol13

we have

(a+b)(3a-b)(2a+7b)

step 1

Solve

apply distributive property

(a+b)(3a-b)=3a^2-ab-3ab-b^2=3a^2-4ab-b^2

step 2

Multiply (3a^2-4ab-b^2) by (2a+7b)

6a^3+21a^2b-8a^2b-28ab^2-2ab^2-7b^3=6a^3+13a^2b-30ab^2-7b^3

answer is

6 0

1 year ago

PLEASE HELP!!

madam [21]

Answer:

k=2/3

Step-by-step explanation:

Step 1:

Step 1 in solving the exponential equations is re-writing the base same as other side of the equation

so,

$25^{3k}=625\\=> 25^{3k}=25^2$

Step 2:

Second step is equating the exponents

The rule used is:

$If\ B^m=B^n\ then\ m=n$

So in this case

$3k=2\\k = \frac{2}{3}$

So the solution is:

k=2/3 ..

3 0

3 years ago

Show that n(n+1)(n+2) is divisible by 6<br>Solution<br>(

vladimir2022 [97]

Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

(n+1)(n+2)(n+3)=

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

6 0

3 years ago

Which CANNOT be used to prove that lines in and n are parallel?

Misha Larkins [42]

C.24 is supplementary to 7

4 0

3 years ago

A. A group of twelve art students are visiting a local art museum for a field trip. The total cost of admission for the students

Shalnov [3]

Answer:

a) $10.42

b) 11 trips

c) 10 cookies

d) 12/125ths of a cheesecake (or 9.6%)

Step-by-step explanation:

Let x = the cost of admission for each student

Let y = the total cost of admission

⇒ y = 12x

⇒ 125 = 12x

⇒ x = 125 ÷ 12

⇒ x = 10.42

So the cost of admission for each student = $10.42

Let x = the number of trips

Let y = the total number of passengers

⇒ y = 12x

⇒ 125 = 12x

⇒ x = 125 ÷ 12

⇒ x = 10.42

Therefore, the van must make 11 trips in order to bring 125 passengers to the same location. (If it took 10 trips, then it would only bring 120 passengers, hence why we have to round make 11 trips to bring the last 5 passengers).

Let x = the number of cookies each neighbor will receive

Let y = the total number of baked cookies

⇒ y = 12x

⇒ 125 = 12x

⇒ x = 125 ÷ 12

⇒ x = 10.42

Therefore, each neighbor will receive 10 cookies (we have to round it down, as if each neighbor received 11 cookies, we would need 132 in total).

Let x = the number of cheesecakes purchased

Let y = the amount of cheescake each guest will receive

⇒ y = 125x

⇒ 12 = 125x

⇒ x = 12 ÷ 125

⇒ x = 12/125 = 0.096 = 9.6%

Therefore, each guest will receive 12/125ths of a cheesecake (or 9.6%).

6 0

2 years ago