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3 years ago

Complete the square to transform the quadratic equation into the form (x – p)2 = q.

Mathematics

1 answer:

ryzh [129]3 years ago

7 0

The transformed equation is:

$(x-3)^2 = 23$

Step-by-step explanation:

We have to convert the equation in the form

$(x-p)^2 = q$

Given equation is:

$x^2-6x-8 = 6$

Adding 8 on both sides

$x^2-6x-8+8 = 6+8\\x^2-6x = 14$

In the given equation

a = x

b= ?

So,

$2.x.b = 6x\\b =\frac{6x}{2x}\\b = 3\\$

So 3^2 will be added on both sides

$(x)^2-6x+ (3) = 14+ (3)^2\\(x-3)^2 = 14+9\\(x-3)^2 = 23$

Hence,

The transformed equation is:

$(x-3)^2 = 23$

Keywords: Quadratic equation, transformation

Learn more about quadratic equation at:

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Solve for a.

egoroff_w [7]

Answer: $a=\sqrt{\frac{30}{23} }$

Step-by-step explanation:

$23a^2=30$

Divide by 23

$a^2=\frac{30}{23}$

Extract the square root.

$a=\sqrt{\frac{30}{23} }$

3 0

3 years ago

What is the equation of a line that is parallel to y=47x−3 and passes through (14, 4)?

Shtirlitz [24]

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where

m = slope

c = intercept

The equation of the given line is

y = 47x - 3

Comparing with the slope intercept equation, m = 47

If two lines are parallel, it means that they have equal slope. This means that the slope of the line passing through (14, 4) is 47

We would determine the intercept, c by substituting m= 47, x = 14 and y = 4 into y = mx + c. It becomes

4 = 47× 14 + c

4 = 658 + c

c = 4 - 658 = - 654

The equation becomes

y = 47x - 654

6 0

3 years ago

Help me please? its algerbra

Nitella [24]

Answer:

Option 1

Step-by-step explanation:

option 1=243

option 2=125

6 0

3 years ago

What is the radical form of the expression (2x^4y^5)^3/8

s344n2d4d5 [400]

We are given expression: $(2x^4y^5)^{3/8}$

Let us distribute 3/8 over exponents in parenthesis, we get

$(2^{3/8}x^{4\times 3/8}y^{5\times 3/8}) = (2^{3/8}x^{12/8}y^{15/8})$

$= (2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} )$

We can get x and y out of the radical because, we get whlole number 1 for x and y exponents for the mixed fractions.

So, we could write it as.

$(2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} ) = xy(2^{\frac{3}{8} }x^{\frac{4}{8}} y^{\frac{7}{8}} )$

Now, we could write inside expression of parenthesis in radical form.

$xy\sqrt[8]{2x^{3}x^4y^7}$

8 0

3 years ago

Does 3/15 need to be simplified

Ksju [112]

Yes. 3/15 can still be simplified

Divide 3 from numerator and denomoinator.

3/3 = 1

15/3 = 5

1/5 is the simplified form.

hope this helps

8 0

2 years ago