Algebra 1, algebra homework help

I have listed the following questions below with the answers and explanation. I do not understand them. Please help me understand the concept and how to solve the questions correctly. Thank you.

Solve by completing the square.
-2y2 + 8y = .98
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
or y =
You answered:
y =
or y =
With quadratic equations (ax2 + bx + c = 0), you can solve by completing the square.
Step 1: Make sure that the left side of the equation looks like x2 + bx.
Step 2: Add
to both sides.
Step 3: Factor the left side as x +
Step 4: Take the square root and solve.
Step 1: Make sure that the left side of the equation looks like x2 + bx.
To make the left side of the equation look like x2 + bx, divide both sides by-2.
-2y2 + 8y = -98
y2 – 4y = 49
Step 2: Add
b 2
to both sides.
2
Since b = -4,
() = (-2)2 = 4. Add 4 to both sides.
=
2
y2 – 4y + 4 = 53
52
Step 3: Factor the left side as x +
2
In general, an expression of the form x2 + bx
b 2
can be factored as
s(x+g)?.
The expression y2 – 4y + 4 is of this form, with b = -4. So, it can be factored as (y – 2)2.
Rewrite the equation with the left side factored.
(y-2)2 = 53
Step 4: Take the square root and solve.
y-2+7.28
Take the sque
e root
Y 2 = 7.28
Add 2 to both sides
y2 + 7.28 or y a 2 – 7.28
Split into + or –
y 9.28 or ye -5.28
Simplify
Simplify. Assume j is greater than zero.
2;
9
You answered:
The multiplication property of square roots states that
ab = ab
if both a and b are greater than or equal to zero.
The division property of square roots states that
Na
b
a
=
if a is greater than or equal to zero and b is greater than zero.
To simplify this radical expression, rewrite it with a radical in the numerator and a radical in
the denominator. Then factor out any perfect squares and simplify.
8
2j
9
=
2.;
3.3
Find the prime factorizations of the numerator’s and denominator’s coefficients
.8
=
2.3
3.3
Apply the division property of square roots
8
=
jº.2
32
Group perfect square factors
=
j*.2
3
Simplify
Multiply. Assume t, u, and v are greater than or equal to zero, and write your answer in
simplest form
2t?u?v2.30u?v4
You answered:
The multiplication property of square roots states that
ab = Vab
if both a and b are greater than or equal to zero.
To simplify this radical expression, multiply the two radicals together and then factor out any
perfect squares.
12t²u²v²
30u?
2:03. 02.v2
II
Find the prime factorization of the numeric part of each
radicand
2.3.5
2
u .V
=
2.73
2
. U
2
V
2.3.5.u?
Apply the multiplication property of square roots
= 22.12.04
6
. V
3.5.0
Group perfect square factors
2tu?V3.3.5.t
=
Simplify
2tu?v3.15.t
Multiply
Multiply. Write your answer in simplest form.
-135 (2 – 135
You answered:
The multiplication property of square roots states that
ab = a.
if both a and b are greater than or equal to zero.
Multiply.
– 35 (2 – 135
= 35 2 + 35 – 35
= 5.7 -2 +-(15.7.-15.7
Apply the distributive property
Find the prime factorizations of the radicands
=
-2-/5.7 +5.7.5:7
Apply the multiplication property of square roots
= -2/5.7 +
52.72
V
Group perfect square factors
= -2/5.7 + 5.7
Simplify
= -2-/35 + 35
Multiply
It’s common practice to order the radicands from least to greatest, with rational numbers at
the front.
35 – 2-/35
Simplify. Rationalize the denominator.
9
-5 -3
You answered:
Binomials like (a + b) and (a – b) are conjugates of each other. Multiplying conjugates
results in a difference of squares, which can be useful for rationalizing some radical
expressions.
Difference of squares:
(a + b)(a – b) = a? – b2
This expression is not simplified because there is a radical in the denominator. Because the
denominator has two terms, you should use its conjugate to rationalize it.
9
-5 – 3
9
-5 + 3
-5 + 3
Multiply the numerator and denominator by the conjugate
-5 – 3
=
9-5 + 13)
(-5–3) -5+ (3)
First, simplify the numerator.
-45 + 9/3
Apply the distributive property
-5 -13)-
-5 + 13
Now, simplify the denominator.
-45 + 913
Remember that (a + b)(a – b) = a-b
(-5)2 – (13)
-45 + 9-13
Square
25 – 3
=
-45 + 9-/3
22
Subtract
Multiply. Write your answer in simplest form.
3.5
You answered:
The multiplication property of square roots states that
ab = a b
if both a and b are greater than or equal to zero.
To simplify this radical expression, multiply the two radicals together and then factor out any
perfect squares.
35
3 5
=
=
3.5
Apply the multiplication property of square roots
15
=
Multiply