Question

If someone can do these for me that would be awesome! Ill give lots of points

Answer 1

Answer:

3a. horizontal shift to the left 4 units, reflection on the x-axis

3b. vertical shift down 5 units

4. 4$\sqrt{3}$

5. 3x²y²$\sqrt{2x}$

6. $\frac{4\sqrt{35} }{5}$

7. $\frac{45-5\sqrt{7} }{74}$

8. 3√2

9. -2√7 + 5√13

10. 7√2 + 2√14

11. 10 + √15 + 2√35 + √21

12. P = 18√6 + 6√15

Step-by-step explanation:

this is gonna be a bit long but bare with me

3a. y = $-\sqrt{x+4}$ < -- this is a horizontal shift to the left 4 units and a reflection on the x-axis. a horizontal shift is located next to the parent function (in this case f(x) = √x). a reflection on the x-axis is located outside of the parent function.

3b. y = $\sqrt{x}$ - 5 < --- this is a vertical shift down 5 units. a vertical shift is located outside of the parent function

4. $\sqrt{48}$ to solve a radicand, we can break it up into known factors, such as numbers that are a perfect square that are factors of the number. you can create a factor tree for this, or you can do it mentally by thinking of terms.

48 can be divided by divided by 16 and 3

16 is a perfect square of 4, which goes outside of the radicand

the answer to $\sqrt{48}$ is 4$\sqrt{3}$

5. again, to solve $\sqrt{18x^5y^4}$, we break it down into known factors.

lets start with 18: it can be broken down into 9 and 2, 9 is a perfect square of 3

so far the radicand looks like this: 3$\sqrt{2x^5y^4}$

next we will break down $x^5$. looking at the exponent, we can see that we have a perfect square in the exponent, which is 4. the square root of 4 is 2. we would leave the leftover x in the radical as it is not a perfect square, and put x² on the outside as it is a result of the perfect square

3x²$\sqrt{2xy^4}$

finally lets look at $y^4$. we see that the exponent is a perfect square, 4. the square root of 4 is 2, so y² would go on the outside, and no y terms would be left on the inside. the final radical looks like this:

3x²y²$\sqrt{2x}$

6. $\frac{4\sqrt{7} }{\sqrt{5} }$

to solve this, we would need to rationalize the denominator by getting rid of the radical in the denominator. to do this we would multiply the expression by $\sqrt{5}$ and we would get:

$\frac{4\sqrt{35} }{5}$

we cannot simplify this any further, so this would be our answer

7.  $\frac{5}{9 + \sqrt{7} }$ like the last question, we need to get rid of the square root in the denominator by multiplying the entire expression by $9 - \sqrt{7}$. we get:

$\frac{5(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }$

the denominator can be multiplied together to get 81 - 7 = 74, and in the numerator we get 5(9-√7) which can be distributed as 45 - 5√7. in total we get:

$\frac{45-5\sqrt{7} }{74}$ this cannot be simplified any further, so this is the answer

8. 3√50 - 3√32 to solve, we need to get the same radical. to do this, we can break each radical up into known terms. √50 can be simplified as 25 and 2. 25 is a perfect square, and is equal to 5. √50 = 5√2

3(5√2) = 15√2

we can break up √32 as 16 and 2. 16 is a perfect square which is equal to 4. √32 = 4√2

-3(4√2) = -12√2

the expression looks like this: 15√2 - 12√2 < subtract normally and we get 3√2 <-- this is our final answer, and we cannot simplify further

9. 2√7 - 4√13 -4√7 + 9√13 < we can combine like terms by adding/subtracting

2√7 -4√7 = -2√7

-4√13 + 9√13 = 5√13

-2√7 + 5√13 this cannot be simplified further, so this is the answer

10. √7(√14 + 2√2) < distribute √7 into the expression

√7 × √14 = √98 = 7√2

√7 × 2√2 = 2√14

the answer is 7√2 + 2√14

11. (√5 + √7)(√20 + √3) < to solve, we can FOIL this out

(√5 + √7)(√20 + √3) = 10

(√5 + √7)(√20 + √3) = √15

(√5 + √7)(√20 + √3) = 2√35

(√5 + √7)(√20 + √3) = √21

we get the following expression: 10 + √15 + 2√35 + √21, we cannot simplify this further so this is our answer

12. the perimeter of a rectangle is P = 2l + 2w. we are given the width 3√6 + 4√15 and the length 6√6 - √15. plugged into the formula we have:

2(3√6 + 4√15) + 2(6√6 - √15) < distribute 2 into each expression:

(6√6 + 8√15) + (12√6 - 2√15) < combine like terms, as in combine terms with like radicals

6√6 + 12√6 = 18√6

8√15 - 2√15 = 6√15

P = 18√6 + 6√15

we cannot simplify this further, so this is the answer

hope this helped!