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ella [17]
2 years ago
15

Which transformations are needed to transform the graph of y = f(x) to g(x) = -f(x - 1) + 3

Mathematics
1 answer:
love history [14]2 years ago
7 0
<h2>Explanation:</h2>

Lets's solve this step by step. Here we have a function:

y=f(x)

So:

Step 1. Reflection across the x-axis:

y=-f(x)

Step 2. Shifting 1 unit to the right

y=-f(x-1)

Step 3. Shifting 3 unit up

y=-f(x-1)+3

Finally:

g(x)=-f(x-1)+3

So <em>the graph of f has been reflected across the x-axis, shifted 1 unit to the right and 3 units up to become the graph of g.</em>

You might be interested in
28 in 21 in., 20 in.<br> Is this a right triangle?
ankoles [38]

Answer:

No, it is not a right triangle.

Step-by-step explanation:

The simplest way to determine is testing out the numbers with Pythagorian theorem.

If it complies with the theorem, it is a right triangle.

let's assume c = 28, b = 21, and a = 20

the longest side is the hypotenuse so side c (28 in) will be the hypotenuse.

According to the Pythagorian theorem, the square of the length of hypotenuse must equal to the sum of squares of other two sides.

check:

c^2 = 28^2 = 784

a^2 + b^2 = 21^2 + 20^2 = 841

because c^2 is not equal to a^2 + b^2, the triangle is not a right triangle.

7 0
2 years ago
The first quartile of the data set below is
Ray Of Light [21]

Answer:

28

Step-by-step explanation:

When you put the numbers in order and then cut into 4 equal parts 28 is the first cut

sorry idk if that made sense or not

3 0
3 years ago
Combined, Teresa and Janey have saved $345 dollars. Teresa has saved twice as much as Janey. How much money do they each have?
Tema [17]

Answer: Janey has $115, and Teresa has $230.

Step-by-step explanation:

Set x be the money that Janey have, then Teresa have 2x.

x + 2x = 345

      3x = 345

         x= $115

2x= 2(115)= $230

6 0
3 years ago
Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296
scoray [572]

Answer:

648(x^{3} + 3x^{2} - 4x + 2)

Step-by-step explanation:

When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.

6 0
2 years ago
A dairy needs 325 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk contai
zubka84 [21]

The amount of milk containing 6% butterfat and 1% butterfat are 260 gallons and 65 gallons respectively.

<u><em>Explanation</em></u>

Suppose, the amount of milk containing 6% butterfat is x gallons

As the amount of mixture of milk should be 325 gallons, so the amount of milk containing 1% butterfat will be: (325-x) gallons

Given that, the mixture of milk is containing 5% butterfat. So, the equation will be....

0.06x+0.01(325-x)=0.05*325\\ \\ 0.06x+3.25-0.01x=16.25\\ \\ 0.05x= 13\\ \\ x= \frac{13}{0.05}=260

So, the amount of milk containing 6% butterfat is 260 gallons and the amount of milk containing 1% butterfat is (325-260) gallons = 65 gallons.

8 0
3 years ago
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