Solve quadratic equations using completing the square then write in vertex form

Answers

Answer 1

Assuming you are given a standard form equation, you should convert it to vertex format. If you are given root equation form, you would have to convert to standard form.

Assuming you have;

ax²+bx+c=y
a(x²+b/ax)+c=y
a(x²+b/ax+(b/2a)²-(b/2a)²)+c=y
a(x²+b/ax+(b/2a)²)+c-a(b/2a)²=y
a(x+b/2a)²+c-a(b/2a)²=y

Try to use this format to solve the problems.

Hope I helped :)

Related Questions

solving with systems of equations using elimination! please help me. thank u!

Answers

To cross out a variable (in this case, x) we can add both equations together to get -5y=10. Dividing both sides by -5, we get y=-2. Next, plugging it into -3y+5x=26, we get 6+5x=26. Subtracting 6 from both sides, we get 5x=20. Next, we can divide both sides by 5 to get x=4

What is the length of each side of a cube if its surface area is 486 in2?

Answers

The surface area of a cube = side * side *6 =
area = side^2 * 6
486 = side^2 * 6
side^2 = 486 / 6
side^2 = 81
side length = 9 inches

4x-8y=24 find the x-intercept and y- intercept on the graph

Answers

the x intercept is the value of x when y=0
the y intercept is the value of y when x=0
when y=0: 4x-0=24 => x=4
when x=0: 0-8y=24 => y=-3
so the x intercept is 4, and the y intercept is -3

4x-8y=24
move variables to the right side and change its sign
4x=24+8y
divide both sides by 4
x=6+2y

4x-8y=24
move variable to the right and change the sign
-8y=24-4x
divide both sides by -8
y=-3+1/2x

Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (h(x)) and. g (f (x))

Answers

To get f(h(x)), we simply plug h(x) into the x value(s) of f(x), resulting in
2(x²+1)-1=2x²+2-1=2x²+1

For g(f(x)), we plug f(x) into the x value(s) of g(x), resulting in
3(2x-1)=6x-3

Can someone please help?
thanks :)

Answers

This is one way to solve it.

(6-3)^2

breakdown: (6-3) (6-3)

Now using the distributive property you can further solve this problem. This means you multiply everything by each other.

6*6, 6*-3, -3*6, -3*-3

36 -18 -18 +9

Now solve what's above.
You should find 9 as your final answer.

Please vote my answer brainliest. thanks!

A certain mutual fund has net assets of $1,359,600. One share of this fund has a net asset value of $11.33. How many shares make up the fund?

Answers

You would have to divide $1,359,600 by $11.33 which comes out to 120,000
So the answer is 120,000 shares

Answer:

Step-by-step explanation:

Three consecutive integers have a sum of 114. what are the three integers

Answers

let the smallest one be x, the second one is then x+1, the third one is x+2
x+(x+1)+(x+2)=114
3x+3=114
3x=111
x=37
the three consecutive integers are: 37,38,39

Our three consecutive integers are 37, 38, and 39.

Work is provided in the image attached.

Simplify the expression, if possible. (if the expression cannot be simplified, enter the given expression.) (k − 5)13 (k − 5)

Answers

2 ( k-5) 13 you don't need two k-5 you can simplify it so you just know to do it twice

Does this figure have rotational symmetry?
A) No, pentagons cannot be rotated.
B) No, it has five lines of symmetry.
C) Yes, it has five lines of symmetry.
D) No, it only looks the same if it is rotated 360°.

Answers

D) No, it only looks the same if it is rotated 360

In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year

Answers

multiply the current price by the increase

1.39 * 2.4 = $3.34 ( price next year)

Ari writes 2 + 4 on the left-hand side of his paper. Then he writes 6 to the right of the expression. Which symbol should Ari write between the two sets of numbers?

A.
+

B.
?

C.
=
Plz help will rate 19 pts

Answers

C. 2+4=6. i believe that's what you're asking. those other answers just dont make sense for real.

The correct symbol that Ari should write between the two sets of numbers is C. =.

When Ari writes "2 + 4" on the left-hand side of his paper and then writes "6" to the right of the expression, he is indicating that the sum of 2 and 4 is 6. The symbol "=" is used to denote equality, meaning that the value on the left side of the equation is the same as the value on the right side. In this case, the sum of 2 and 4 indeed equals 6, so the complete equation should be written as:

[tex]\[ 2 + 4 = 6 \][/tex]

This shows that the operation of adding 2 and 4 results in the number 6, which is a true statement. Therefore, the correct answer to the question is option C, the equals sign "=".

a text book costs $108.00. if mathew paid a total of $113.94 for the book and sales tax, what rate of sales tax was he charged?

Answers

Okay. So to find the amount of sales tax, we have to first subtract the text book cost from the total. 113.94 - 108 = 5.94. That’s $5.94 in taxes. To find the percentage, we have to do the amount in taxes divided by the cost of the item, in this case, the textbook. 5.94 / 108 is 0.055. Multiply 0.055 by 100 in order to get the percentage. When you do that, you get 5.5%. Matthew was charged 5.5% in sales tax.

All real numbers that are less than -3 or greater than it equal to 5

Answers

is that the question?

Your answer would be
<-3 or x > 5

a family went on a vacation and used 5.4 gallons of gasoline to travel 150 miles. how many total gallons of gasoline will they need to travel 200 more miles?

Answers

Answer is 7.2 gallons for 200 miles

The expression $1.25p + $3.50 can be used to calculate the total charge for printing p pages at a business service store. How much would it cost to print 8 pages

Answers

Since one page cost $1.25 to print take the cost of per page $1.25 times the number of pages to be printed, in this case eight. $1.25 x 8 = $10.00
Remember there is still a $3.50 added to the cost of the pages printed; thus you have $10.00 + $3.50 = $13.50 which is the total charge.

Represent real-world situations a rectangular piece of sheet metal is rolled and riveted to form a circular tube that is open at both ends, as shown. the sheet metal has a perimeter of 36 inches. each of the two sides of the rectangle that form the two ends of the tube has a length of x inches, and the tube has a circumference of x - 1 inches because an overlap of 1 inch is needed for the rivets. write a volume function for the tube in terms of x. then, to the nearest tenth, find the value of x that maximizes the volume of the tube. answer

Answers

12.3 Volume function: v(x) = ((18-x)(x-1)^2)/(4pi) Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x. The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is v(x) = (18-x)pi((x-1)/(2pi))^2 v(x) = (18-x)pi((x-1)^2/(4pi^2)) v(x) = ((18-x)(x-1)^2)/(4pi) The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative: v'(x) = (x-1)(3x - 37) / (4pi) Convert to quadratic equation. (3x^2 - 40x + 37)/(4pi) = 0 3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0 Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi) The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3

What is the reciprocal of each mixed number? Drag and drop the answer into the box to match each number.
10 1/3
2 2/3
5 1/3.

Answers

Hi there!!

First, we are going to find the improper fraction of each mixed number.

10 1/3 >>>>> 10*3+1=31 31/3

2 2/3 >>>>> 2*3+2=8. 8/3

5 1/3 >>>>>> 5*3+1 = 16. 16/3

TO find the reciprocal, we switch the numerator with the denominator.

31/3 changes to 3/31, 8/3 changes to 3/8, and finally 16/3 changes to 3/16.

Your answer is:

3/31
3/8
3/16

Hope this helps! Let me know if you have any questions:)

Answer:

10 1/3 = 3 /31. 2 2/3 = 3/8. 5 1/3 = 3/16.

Step-by-step explanation:

i took the k12 test and got 100 percent hope this helps!!

ALGEBRAAA

1. What is the average rate of change? How do you find it?
2. Whats the difference between recursive and explicit formulas?

Answers

1. The average rate of change is the slope of a line to find it divide the vertical change by the horizontal change

2. recursive is a formula to calculate the next term, depending on what the previous term was

Explicit is a formula to calculate any term depending on the term number

the table shows the volume of gasoline in a gas tank at different times. Find th e rate of change for each time interval. During which time interval did the volume decrease at the greatest rate?

Answers

Final answer:

To find the rate of change for each time interval, calculate the difference in volume for each interval and divide it by the difference in time. Compare the rates of change to determine the time interval with the lowest rate of change.

Explanation:

To find the rate of change for each time interval, we need to calculate the difference in volume for each interval and divide it by the difference in time. Let's assume the time intervals are 12-18 hours, 18-24 hours, and 12-24 hours. The rate of change for each interval can be calculated as follows:

Rate of change for 12-18 hours = (Volume at 18 hours - Volume at 12 hours) / (18 hours - 12 hours)

Rate of change for 18-24 hours = (Volume at 24 hours - Volume at 18 hours) / (24 hours - 18 hours)

Rate of change for 12-24 hours = (Volume at 24 hours - Volume at 12 hours) / (24 hours - 12 hours)

The time interval during which the volume decreased at the greatest rate will be the interval with the lowest rate of change. Compare the rates of change calculated for each interval to find the time interval with the lowest rate of change.

Learn more about Rate of change here:

https://brainly.com/question/31226174

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dakota runs a half marathon every 6 weeks. madison runs a half a marathon every 15 weeks. how many weeks untill they will run together?

Answers

30 weeks they would both run30 miles

Final answer:

To determine when Dakota and Madison will run a half marathon on the same week, we calculate the least common multiple of their running intervals, which is 60 weeks.

Explanation:

The question is to find out how many weeks will pass until Dakota and Madison will run a half marathon on the same week.

We need to find the least common multiple (LCM) of their running intervals, which are 6 weeks for Dakota and 15 weeks for Madison.

To find the LCM, you can list the multiples of each number until you find the smallest number that appears in both lists.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...Multiples of 15: 15, 30, 45, 60, ...

Here, we see that the smallest common multiple is 60 weeks.

Therefore, Dakota and Madison will run a half marathon together in 60 weeks.

the angles formed by two perpendicular lines have a measure of _______.

A.45°
B.90°
C.135°
D.180°

thank in advance!! ☺

Answers

the answer is 90 degrees. SO it would be B

I think it is A because it makes the most sence

Anna is 4ft 9in tall. Express Anna's height in feet only by using a mixed number. If necessary, simplifyvthe fraction part of the mixed number

Answers

So we know that there are 12 inches in a foot. With this information we can do this:[tex]4 \frac{9}{12} [/tex] But if you look you can see that the fraction is not simplified. How can we simplify it? Well, what is the Greatest Common Factor of 9 and 12? Well, the answer is 3! So divide 9 and 12 by three! SO the answer would be: [tex]4 \frac{3}{4}[/tex] I hope this helps!

More than half of which climate type averages between 40 and 59 inches of precipitation a year?

Answers

A range between 40 and 59 inches of precipitation a year would not correspond to a dry climate or a very cold climate.
The Cfa climate is the humid subtropical climate. This climate has hot muggy summers and frequent thunderstorms. Winters are mild and precipitation during this season comes from mid-latitude cyclones. The southeastern USA good example for Cfa climate . The Cfa climate receives precipitation throughout the year.

Solve 9x-y=45, solve for y

Answers

9x - y = 45....subtract 9x from both sides
-y = -9x + 45 ...multiply both sides by -1 to make y positive
y = 9x - 45 <==

Answer: " y = 9x - 45 " .
_________________________
Explanation:
_________________________
Given: 9x - y = 45 ;

Method 1)
____________________________________________
Multiply the entire equation (both sides) by "-1" ;

-1* {9x - y = 45} ;

to get: -9x + y = -45 ;

↔ y + (-9x) = -45 ;

→ y - 9x = -45 ;

Add "9x" to each side of the equation ; to isolate "y" one side of the equation; and to solve for "y" ;

y - 9x + 9x = -45 + 9x ;

y = -45 + 9x ;

→ y = 9x + (-45) ;

→ y = 9x - 45 .
__________________________________________________
Method 2)
__________________________________________________
Given: 9x - y = 45 ; Solve for y ;

Add "y" to each side of the equation; and Subtract "45" from each side of the equation:

9x - y + y - 45 = 45 + y - 45 ;

to get: 9x - 45 = y ;

↔ y = 9x - 45 .
________________________________

Calculus: Help ASAP
Evaluate the integral of the quotient of the secant squared of x and the square root of the quantity 1 plus tangent x, dx.

Answers

[tex]\bf \displaystyle \int~\cfrac{sec^2(x)}{\sqrt{1+tan(x)}}\cdot dx\\\\ -------------------------------\\\\ u=1+tan(x)\implies \cfrac{du}{dx}=sec^2(x)\implies \cfrac{du}{sec^2(x)}=dx\\\\ -------------------------------\\\\ \displaystyle \int~\cfrac{\underline{sec^2(x)}}{\sqrt{u}}\cdot\cfrac{du}{\underline{sec^2(x)}}\implies \int~\cfrac{1}{\sqrt{u}}\cdot du\implies \int~u^{-\frac{1}{2}}\cdot du \\\\\\ 2u^{\frac{1}{2}}\implies 2\sqrt{1+tan(x)}+C[/tex]

Answer:

[tex]2\sqrt{1+tan(x)} +C[/tex]

Step-by-step explanation:

To start solving this you need to use substitution. I let u = 1+tan(x). Next you need to find du/dx, which is sec^2(x) using trigonometric properties. Solve for dx and get dx = du / sec^2(x). Next put the new dx back in. This gives you integral sec^2(x) / sqrt u * du / sec^2(x). The sec^2(x) cancels and the new expression is integral 1/sqrt u * du, which can be simplified to integral u^-1/2 * du. You then take the integral and get 2u^1/2. Lastly, substitute the original u back in and get 2 sqrt 1+tan(x) + C.

30 POINTS!!

Find the measure of angle B in isosceles triangle ABC.

Answers

C. 65 degrees.

Triangles must equal 180 degrees. The given 50 means the rest of the triangle is equal to 130. I believe because of the Side-Angle-Side theorem of triangles (if my knowledge of proofs from 3 years ago is still with me), the two remaining angles are equal to each other. Let's call them X. 2x = 130. Divide both sides by 2. 130/2 = 65. So x=65

3 angles inside a triangle = 180 degrees

since the 2 sides are equal

angle B and C are the same

180 - 50 = 130 degrees

130 / 2 =65

Angle B is 65 degrees

One 10-ounce soft drink contains about 8 teaspoons of sugar. How much sugar would be in three 10-ounce drinks ?

Answers

24 teaspoons?

since 1 10-ounce is 8 teaspoon

8 x 3 = 24

The perimeter of the isosceles ΔABC with the base
BC is equal to 40 cm. Perimeter of the equilateral ΔBCD is 45 cm. Find BC and AB.

Answers

ΔBCD is equilateral, so

|BC| = |CD| = |DA|

and

[tex]P=|BC|+|CD|+|DA|\\\\45=|BC|+|BC|+|BC|\\\\45=3\cdot|BC|\quad|:3\\\\|BC|=45:3\\\\\boxed{|BC|=15\text{ cm}}[/tex]

ΔABC is isosceles and

|AB| = |CA| (legs)

[tex]P=|AB|+|BC|+|CA|\\\\P=|AB|+|BC|+|AB|\\\\40=2\cdot|AB|+15\\\\40-15=2\cdot|AB|\\\\25=2\cdot|AB|\quad|:2\\\\\boxed{|AB|=12.5\text{ cm}}[/tex]

The length of BC is 15 cm and the length of AB is 12.5 cm.

The given parameters;

perimeter of isosceles ΔABC = 40 cmbase of the isosceles triangle = BCPerimeter of the equilateral ΔBCD = 45 cm

An equilateral triangle has three equal sides and the length of each side is calculated as;

[tex]|BC| = |BD| = |CD| = \frac{45}{3} = 15 \ cm[/tex]

Thus, the length of BC is 15 cm.

An isosceles triangle has two equal sides and a third side of different length. This third side is usually the base of the triangle.

The base of the isosceles triangle = BC = 15 cmThe two remaining sides = AB and AC

[tex]|AB| = |AC| =\frac{Perimeter \ - \ |BC|}{2} = \frac{40 - 15}{2} = 12.5 \ cm[/tex]

Thus, the length of AB is 12.5 cm.

Learn more here: https://brainly.com/question/11296804

Graph y-5 = -2/3 (x+9)

Answers

when you put the equation into y=mx+b form, it is:
y=-2/3x-1
not sure how to graph this on here, but I guess I can describe the graph to ya:
~the line intersects the y-axis at -1 and the x intersect at -1.5
~draw your line

Suppose that the time it takes to do a job is inversely proportional to the number of workers. that is, the more workers on the job the less time required to complete the job. if it takes 2 workers 8 days to finish a job, how long will it take 8 workers?

Answers

i think it would be 2 days. you would get it done 4 times faster, so 8/4 is 2

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