Please explain . solve the system by elimi ation -x-18y=-3 7x-9y=21

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?

Andrei [34K]

Answer:

A. right 2, up 3

Step-by-step explanation:

We have that,

The function $f(x) = x^2$ is transformed to $g(x) =(x- 2)^2+3$ .

We see that,

The function f(x) is translated 2 units to the right and 3 units upwards to obtain the function g(x).

So, the correct transformation is 'right 2, up 3'.

Hence, option A is correct.

5 0

4 years ago

Read 2 more answers

Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview

mario62 [17]

Answer: The required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.$

So, the general solution of the given equation is

$y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.$

According to the given conditions, we have

$y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.$

From equation (ii), we get

$B=\dfrac{7}{3}.$

Thus, the required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

7 0

3 years ago

the ratio of goats to sheep at a university research farm is 4: 7. The number of sheep at the arm is 28. what is the number of g

GalinKa [24]

4+7=11 i.e. The whole.
7/11=28

1/11=4
Goats are 4/11 therefore
4 x 4= Ans
All the animals add up to 44 and if you check w/ 7/11 it is correct.

4 0

3 years ago

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a dilation

Talja [164]

Correct answer is B.

4 0

3 years ago

Simplify: 3 . 3^2 + 8 ÷ 2 - (4 + 3) A: 32 B: 24 C: 23 D: 30

yaroslaw [1]

Answer:

its none of these answers ;-;

Step-by-step explanation:

3^2 + 8 ÷ 2 - (4 + 3)

we do what's in parentheses first. (pemdas)

so now we have, 3^2 + 8 ÷ 2 - 7

next exponents, 3^2=9

9 + 8 ÷ 2 - 7

next division, 8÷2=4

9 + 4 - 7

next addition, 9+4=13

13-7

finally subtraction, 13-7=6

final answer: 6

7 0

4 years ago