If someone can do these for me that would be awesome!Ill give lots of points
Accepted Solution
A:
Answer:3a. horizontal shift to the left 4 units, reflection on the x-axis3b. vertical shift down 5 units4. 4[tex]\sqrt{3}[/tex]5. 3xΒ²yΒ²[tex]\sqrt{2x}[/tex]6. [tex]\frac{4\sqrt{35} }{5}[/tex]7. [tex]\frac{45-5\sqrt{7} }{74}[/tex]8. 3β29. -2β7 + 5β1310. 7β2 + 2β1411. 10 + β15 + 2β35 + β2112. P = 18β6 + 6β15Step-by-step explanation:this is gonna be a bit long but bare with me3a. y = [tex]-\sqrt{x+4}[/tex] < -- 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) = βx). a reflection on the x-axis is located outside of the parent function. 3b. y = [tex]\sqrt{x}[/tex] - 5 < --- this is a vertical shift down 5 units. a vertical shift is located outside of the parent function4. [tex]\sqrt{48}[/tex] 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 316 is a perfect square of 4, which goes outside of the radicandthe answer to [tex]\sqrt{48}[/tex] is 4[tex]\sqrt{3}[/tex]5. again, to solve [tex]\sqrt{18x^5y^4}[/tex], 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 3so far the radicand looks like this: 3[tex]\sqrt{2x^5y^4}[/tex]next we will break down [tex]x^5[/tex]. 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 xΒ² on the outside as it is a result of the perfect square3xΒ²[tex]\sqrt{2xy^4}[/tex]finally lets look at [tex]y^4[/tex]. we see that the exponent is a perfect square, 4. the square root of 4 is 2, so yΒ² would go on the outside, and no y terms would be left on the inside. the final radical looks like this:3xΒ²yΒ²[tex]\sqrt{2x}[/tex]6. [tex]\frac{4\sqrt{7} }{\sqrt{5} }[/tex]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 [tex]\sqrt{5}[/tex] and we would get:[tex]\frac{4\sqrt{35} }{5}[/tex]we cannot simplify this any further, so this would be our answer7. Β [tex]\frac{5}{9 + \sqrt{7} }[/tex] like the last question, we need to get rid of the square root in the denominator by multiplying the entire expression by [tex]9 - \sqrt{7}[/tex]. we get:[tex]\frac{5(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) Β }[/tex]the denominator can be multiplied together to get 81 - 7 = 74, and in the numerator we get 5(9-β7) which can be distributed as 45 - 5β7. in total we get:[tex]\frac{45-5\sqrt{7} }{74}[/tex] this cannot be simplified any further, so this is the answer8. 3β50 - 3β32 to solve, we need to get the same radical. to do this, we can break each radical up into known terms. β50 can be simplified as 25 and 2. 25 is a perfect square, and is equal to 5. β50 = 5β23(5β2) = 15β2we can break up β32 as 16 and 2. 16 is a perfect square which is equal to 4. β32 = 4β2-3(4β2) = -12β2the expression looks like this: 15β2 - 12β2 < subtract normally and we get 3β2 <-- this is our final answer, and we cannot simplify further9. 2β7 - 4β13 -4β7 + 9β13 < we can combine like terms by adding/subtracting2β7 -4β7 = -2β7-4β13 + 9β13 = 5β13-2β7 + 5β13 this cannot be simplified further, so this is the answer10. β7(β14 + 2β2) < distribute β7 into the expressionβ7 Γ β14 = β98 = 7β2β7 Γ 2β2 = 2β14the answer is 7β2 + 2β1411. (β5 + β7)(β20 + β3) < to solve, we can FOIL this out(β5 + β7)(β20 + β3) = 10(β5 + β7)(β20 + β3) = β15(β5 + β7)(β20 + β3) = 2β35(β5 + β7)(β20 + β3) = β21we get the following expression: 10 + β15 + 2β35 + β21, we cannot simplify this further so this is our answer12. the perimeter of a rectangle is P = 2l + 2w. we are given the width 3β6 + 4β15 and the length 6β6 - β15. plugged into the formula we have:2(3β6 + 4β15) + 2(6β6 - β15) < distribute 2 into each expression:(6β6 + 8β15) + (12β6 - 2β15) < combine like terms, as in combine terms with like radicals6β6 + 12β6 = 18β68β15 - 2β15 = 6β15P = 18β6 + 6β15we cannot simplify this further, so this is the answerhope this helped!