How do you complete the square using fractions

Answers

Answer 1

alrighty
we will complete the squaer for ax²+bx+c=0 regardless of the values of a,b, or c
we will factor it into a(x-h)²=r

so
first group x terms
(ax²+bx)+c=0
factor out a
[tex]a(x^2+\frac{b}{a}x)+c=0[/tex]
take 1/2 of the linear coefinet and squaer it
[tex]\frac{1}{2} \space\ of \space\ \frac{b}{a}=\frac{b}{2a}[/tex] square it to get [tex]\frac{b^2}{4a^2}[/tex]
add positive and negative of that inside parntheasees
[tex]a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2})+c=0[/tex]
factor perfect square
[tex]a((x+\frac{b}{2a})^2-\frac{b^2}{4a^2})+c=0[/tex]
expand
[tex]a(x+\frac{b}{2a})^2-\frac{b^2}{4a}+c=0[/tex]
and that's how you complete the square, just move the constants over to the left when you're done then divide both sides by a then square root both sides, remembering to take the positive and negative roots

Answer 2

Completing the square with fractions involves transforming the quadratic equation into a perfect square trinomial by adding the square of half the coefficient of x to both sides. This enables solving the equation more easily by then taking the square root of both sides and isolating x.

Completing the square using fractions involves a few steps tailored to work with fractional coefficients. To make it understandable, let's explain the process step by step:

Start with the quadratic equation and ensure it is in the form ax2 + bx + c = 0.Divide all terms by 'a' (the coefficient of x2) if 'a' is not equal to 1, to make the coefficient of x2 equal to 1.Rearrange the equation so that the constant 'c' is on the other side of the equation.Take half of the coefficient of x, which is now 'b/a', and square it. This value is added both sides of the equation to form a perfect square on one side.Rewrite the left side of the equation as a squared binomial.Finally, solve for x by taking the square root of both sides and then add or subtract the constant term.

For example, let's complete the square for the equation x2 + (3/2)x = 4. We take half of the coefficient of x, (3/2)/2 or 3/4, and square it to get 9/16. Adding 9/16 to both sides gives us (x + 3/4)2 = 4 + 9/16. Simplify the right side to get a single fraction, and then proceed to solve for x. Additionally, in some scenarios, we might need to multiply both the numerator and denominator by a skillfully chosen factor, such as 1/2, to facilitate simplifying or cancelling out terms.

Related Questions

Three bags of of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases Of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn. Show your work

Answers

P = potato C = corn

3P + 4C = $40
5P + 2C = $34

Multiply -2 to the 2nd equation to get
-10P - 4C = -68

Add it to the 1st equation

3P + 4C = 40
-10P - 4C = -68
-----------------------
-7P = -28

Solve for P
P = $4

Substitute 4 into P(potato) to find what C(corn) is

In △ABC , m∠A=53°,m∠B=17°, and a=27. Find the perimeter of the triangle.

Answers

Using the Law of Sines (sinA/a=sinB/b=sinC/c) and the fact that all triangles have a sum of 180° for their angles.

The third angle is C is 180-53-17=110°

27/sin53=b/sin17=c/sin110

b=27sin17/sin53, c=27sin110/sin53

And the perimeter is a+b+c so

p=27+27sin17/sin53+27sin110/sin53 units

p≈68.65 units (to nearest hundredth of a unit)

Answer:

Step-by-step explanation:

I got it correct on founders edtell

Find the least common multiple of 8c4 and 6c2 .

Answers

The least common multiple is the smallest term that can be divided to both terms without any remainder. For the two terms 8c^4 and 6c^2, you can determine it into two part. First, you find the LCM for 8 and 6. You find the prime number that is common between the two. That would be 2. For the variables c^4 and c^2, the 'prime variable' is c. Therefore, the least common multiple for 8c^4 and 6c^2 is 2c.

The adams family is remodeling their family room. the room measures 14 feet by 20 feet, and the contractor wants $35 per square foot to remodel it. how much will it cost to remodel?

Answers

14 * 20 = 280 sq ft
$35 * 280 sq ft = $ 9,800

Answer:

It would cost $9800 to remodel the room.

Step-by-step explanation:

The Adams family is remodeling their family room.

Length of the room = 20 feet

Width of the room = 14 feet

To get area of the room we use the formula

Area = Length × Width

A = 20 × 14 = 280 feet²

The contractor wants $35 per square foot to remodel it.

So it would cost = 280 × 35 = $9800

It would cost $9800 to remodel the room.

What is 3y+5x=-15 written in slope-intercept form

Answers

Slope-intercept form is y=mx+b, so we simply have to solve for y...

3y+5x=-15 subtract 5x from both sides

3y=-5x-15 divide both sides by 3

y=-5x/3-5 or more neatly in my opinion...

y=(-5x-15)/3

hey broskey your answer is option B :)

There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?

Answers

There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?

The answer is 66.

The measure of angle C in triangle ABC is 66 degrees, calculated by subtracting the sum of angles A and B from 180 degrees.

The measure of angle C can be determined by using the fact that the sum of angles in any triangle is always 180 degrees. Given that the measure of angle A is 68° and the measure of angle B is 46°, we can calculate the measure of angle C as follows:

C = 180° - A - B

C = 180° - 68° - 46°

C = 180° - 114°

C = 66°

Thus, the measure of angle C in ΔABC is 66 degrees.

Find the difference.

Correct and best explained answer gets brainliest.

Answers

9-5 =4

-4 +7=3

-1-6 =-7

so 4x^3+3x^2-7

A is the correct answer

What value of x makes the denominator of the function equal zero? y= 4/3x-33

Answers

3x - 33 = 0
3x = 33
x = 11

answer is 11

Answer: 11 is your answer

Step-by-step explanation:

The following system of equations can be used to find the roots of the equation x3 + 72 = 5x2 + 18x. y = x3 + 72 y = 5x2 + 18x Graph this system of equations on the graphing calculator. How many intersection points can you see in the default viewing window?

Answers

Answer:

he following system of equations can be used to find the roots of the equation

x3 + 72 = 5x2 + 18x.

y = x3 + 72

y = 5x2 + 18x

Graph this system of equations on the graphing calculator.

How many intersection points can you see in the default viewing window?

✔ 1

Adjust the window so you can find all of the points of intersection for the system of equations.

What are the roots of the original polynomial equation? Check all that apply.

–6

✔ 6

✔ –4

✔ 3

Step-by-step explanation:

The square root of 32, expressed in terms of a simple radical is

Answers

see attached picture for answer:

Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0

Answers

The function is [tex]f(x)= x^{5} -9x ^{3} [/tex]

1. let's factorize the expression [tex]x^{5} -9x ^{3} [/tex]:

[tex]f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)[/tex]

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )

2.
The end behavior of f(x), whose term of largest degree is [tex] x^{5} [/tex], is the same as the end behavior of [tex] x^{3} [/tex], which has a well known graph. Check the picture attached.

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of [tex] x^{2} [/tex])

so, like the graph of [tex] x^{3} [/tex], the graph of [tex]f(x)= x^{5} -9x ^{3} [/tex] :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

The end behavior of f(x) has the same end behavior of [tex]x^3[/tex] and all the zeroes of f(x) wiil be: -3 with multiplicity 1, 3 with multiplicity 1, 0 with multiplicity 3.

Given :

[tex]f(x) = x^5-9x^3[/tex] --- (1)

The value of x at which f(x) becomes zero can be determine by eqaution the equation (1) to zero.

[tex]x^5-9x^3=0[/tex]

[tex]x^3(x^2-9)=0[/tex]

[tex]x^3(x-3)(x+3)=0[/tex]

Therefore, all the zeroes of f(x) will be:

-3 with multiplicity 1,

3 with multiplicity 1,

0 with multiplicity 3.

The end behavior of f(x) has the same end behavior of [tex]x^3[/tex]. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.The graph of f(x) is attached below.

For more information, refer the link given below:

https://brainly.com/question/24153248

What is the length of x-component of v?

Answers

length of x-component of v = 2

answer is B. 2

If the ratio of the sides of two similar prisms is 3:5 and the volume of the first prism is 54, what is the volume of the second prism?

Answers

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s^3}{s^3}=\cfrac{\textit{volume of smaller}}{\textit{volume of larger}}\implies \cfrac{3^3}{5^3}=\cfrac{54}{v} \\\\\\ v=\cfrac{5^3\cdot 54}{3^3}[/tex]

Is -1/2 rational or irrational

Answers

-1/2 is rational, have a good day

-1/2 is rational because it can be expressed as a ratio of 2 integers.

-1 and 2 are both integers because they are either whole numbers or of the opposite value (negative).

which of the following represents the zeros of the function f(x) = 4x3 -13x2 -37x +10

Answers

(5,0) (1/4,0) (-2,0)

(4.4*10^6)*(3.9*10^4)
Scientific notation please help and explain

Answers

(4.4*10^6) = 4400000
and
(3.9*10^4) = 39000

The exponents on top of the 10 tells you how many decimals you're supposed to move it to. If it's a negative number, you'll need to move the same amount of decimals, but to the left side instead.
for example: 4.3*10^-3 =0.0043

in this case, however, you should refer to the Laws of Exponents.
(4.4*10^6)*(3.9*10^4)
= 4.4 * 3.9 * 10^6 * 10^4
= 17.16 * 10^(6+4) <-- Law of Exponents say that when you multiply exponents with the same base, you add the exponents together.
= 17.16 * 10^10

Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.

50 in2
59 in2
85 in2
90 in2

Answers

Answer: choice B) 59 square inches

---------------------------------------------------------------------
---------------------------------------------------------------------

Work Shown:

A1 = Area of rectangle = length*width = 7*4 = 28 square inches
A2 = Area of triangle on top = 0.5*base*height = 0.5*7*6 = 21 square inches
A3 = Area of triangle on right side = 0.5*base*height = 0.5*4*5 = 10 square inches

Total Area = A1 + A2 + A3
Total Area = 28 + 21 + 10
Total Area = 59 square inches

A 12 foot rope is cut into two pieces so that one piece is 3 feet less than twice the length of the other piece. how long is each piece?

Answers

12 feet long

1st piece = x

2nd piece = 2x-3

3x-3 =12

3x=15

x = 5

1st piece = 5 feet

2nd piece = 2*5=10-3=7 feet

Find the range of the data. Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88 A) 22
B)24
C)28
D)23

Answers

Order: 96,88,88,86,81,80,79,79,73,72
96-72= 24
B.)24

Answer:

Option B - 24

Step-by-step explanation:

Given : Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88

To find : The range of the data?

Solution :

Range is defined as the difference between the smallest and the largest element of the data.

First we arrange the data into ascending order:

72,73,79,79,80,81,86,88,88,96

The smallest number is 72

The largest number is 96

The range of the data = largest number - smallest number

The range of the data = 96 - 72

The range of the data = 24

Therefore, Option B is correct.

The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)

Answers

yes, this data represents a function. A function will not have any repeating x values. It can have repeating y values, just not the x ones.
=====================
data in the table : when x = 9....this is already a point on the table (9,12)...so the value on the table, when x = 9, is 12

f(x) = 5x + 14....when x = 9
f(9) = 5(9) + 14
f(9) = 45 + 14
f(9) = 59

the relation with the greater value would be : f(x) = 5x + 14
=====================
f(x) = 5x + 14....when f(x) = 64
64 = 5x + 14
64 - 14 = 5x
50 = 5x
50/5 = x
10 = x <==

Answer:

D 17 2/9

Step-by-step explanation:

Which number produces a rational number when added to 0.42?

Answers

Any whole or rational number. For example 1 if you want to keep it simple.

What is the area of a regular pentagon with an apothem of 14 inches long and a side 20 inches long?

Answers

Answer:

[tex]\text{Area of regular pentagon is }700 inches^2[/tex]

Step-by-step explanation:

Given that a regular pentagon with an apothem of 14 inches and a side of 20 inches.

we have to find the area of pentagon.

Apothem=a=14 inches

Side of pentagon= 20 inches

[tex]Perimeter=s=20\times 5=100 inches[/tex]

[tex]\text{Area of regular pentagon=}\frac{1}[2}\times perimeter \times apothem[/tex]

[tex]=\frac{1}{2}\times 100\times 14=700inches^2[/tex]

[tex]\text{Area of regular pentagon is }700 inches^2[/tex]

Answer:700in

Step-by-step explanation:

William can run 5 laps in 9 2/3 minutes. If one lap is 2/5 of mile how fast is William running in miles per minute?

Answers

I better get some kind of special treatment for solving this one. First of all is William related to Barry Allen in any way? My mans william is running 2 miles in 9 2/3 minutes and he's running 1 mile in 4 5/6! William is running .21 miles per minute. This wasn't worth it for 5 points...

Final Answer ( 0.21 miles per minute)

how to make d the subject of V=ldh

Answers

d is being multiplied by l and h to isolate easily we can divide by lh on either side resulting in the answer equation: (V/lh)=d

V=ldh
d = V / lh

hope that helps

(20 points)In 2008, there were 6.7 × 10^9 people living on earth. What is that number in standard notation?

A. 6,700,000
B. 67,000,000
C. 6,700,000,000
D. 67,000,000,000

Answers

Answer is: 6700000000

C. 6,700,000,000

6.7*10^9;
6.7*1,000,000,000
6,700,000,000
So, the answer is
C)6,700,000,000

May I pretty please have some math help?

Answers

Answer: A.
The point on the graph of f⁻¹ (x) is (-5,4)

Explanation
Let f(x) = -(5/4)x.
This function passes through (4, -5) as specified, because
f(4) = -(4/5)*(4) = -5

Construct f⁻¹ (x) as follows:
Set y = f(x).
y = -(4/5)x
Switch x and y.
x = -(4/5)y
Solve for y
y = -(5/4)x
Set f⁻¹ (x) to y.
f⁻¹ (x) = - (4/5)x.

Test x=-5 to see if y=4.
f⁻¹ (-5) = -(4/5)*(-5) = 4 Correct!

Write a recursive formula for 16, 9, 7, 2, 5

Answers

Notice that:

7=16-9
2=9-7
5=7-2

the next term would be: 2-5=-3

so each term of the sequence is equal to its previous term, subtracted from the second previous term:

Also, in order to describe the formula, we need to express the 2 first terms, 1 is not enough.

The recursive formula is:

[tex]a_1=16[/tex]
[tex]a_2=9[/tex]
[tex]a_n_2=a_n_1-a_n[/tex]

What rank of the marine corps do you get the stripe on your pants?

Answers

A blood stripe is a scarlet stripe worn down the outside leg seams of trousers on the dress uniform of the United States Marine Corps.

This red stripe is :

2 inches (5.1 cm) for general officers,

1.5 inches (3.8 cm) for other officers, and

1.12 inches (2.8 cm) for enlisted Staff Noncommissioned Officers and Noncommissioned Officers.

Answer:

cpl and above. E-4 and above.

Step-by-step explanation:

Help plz.. Evaluate this expression: -(-(-(-1)))?
Thanks.

Answers

negative times negative=positive
every pair of negative cancel out
-(-a)=a
so we can just keep flipping the signs
go inside to out

-(-(-(-1)))=
-(-(1))=
-(-1)=
1

A cricket ball is dropped into a cylindrical tank of water.
The ball sinks to the bottom of the tank.
The diameter of the cricket ball is 7.2 cm
The diameter of the cylindrical tank is 15 cm
Calculate the increase in height of the water in the tank.

Answers

* (in this question they didn't give me the volume of the cylinder or the height of the cylinder) -- the volume and height are NOT relevant.

the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)

* (in this question they didn't give me the volume of the cylinder or the height of the cylinder) -- the volume and height is NOT relevant.

the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)

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