Answers
Answer:
For question 1 you can try dividing each of the value
For instance, you can divide 9 by 25 and see if you get a nice number
e.g. 1/8=0.125, numbers like these
For the second question, you can find the fraction by dividing 1000 starting with the decimal points
e.g 0.650, you would be plotting 650/1000 and you would simplify the fraction to the lowest value any value above the decimal point you can multiply by the denominator and add the nominator value to get your final answer.
Step-by-step explanation:
Answer:
Write the denominator in its prime factors. If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
example: 9/25
25 = 5*5, so it will be terminating
example: 7/12
12 = 3*2*2, which contains a 3, so it will be repeating.
Related Questions
1. Suzette ran and biked for a total of 80 miles in 9 hours. Her average running speed was 5 miles per hour (mph) and her average biking speed was 12 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution. (a) How many hours did Suzette run? (b) How many hours did she bike?
Answers
Answer:
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
Step-by-step explanation:
Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:
Speed = distance / time
The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.
For running:
Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:
5 = p / x
p = 5x
For biking:
Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:
12 = q / y
q = 12y
The total distance ran and biked by Suzette (d) = Distance biked + distance ran
d = p + q
80 = p + q
80 = 5x + 12y (1)
The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run
t = x + y
9 = x + y (2)
Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:
7y = 35
y = 35/7
y = 5 hours
Put y = 5 in equation 2:
9 = x + 5
x = 9 -5
x = 4 hours
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
The generic version was basedOn the brand name and was 2/3 the size of the brand name. If the generic television set is 12 inches by 24 inches what are the dimensions of the brand name television
Answers
Answer:
18 inches by 36 inches.
Step-by-step explanation:
Since we have given that
The generic version was basedOn the brand name and was 2/3
And given Dimensions of generic version is given by 12inches ×24inches
If we use the first dimensions of 12inches we have
12=2/3 × brand
12×3/2 = brand
=18inches= brand
we use the first dimensions of 24 inches we have
24=2/3 × brand
24×3/2 = brand
=36 inches= brand
brand= 36 inches
Therefore,the dimensions of brand name will be 18 inches by 36 inches.
Solve for h. 3/7=h/14-2/7
Answers
Answer:
h = 10
Step-by-step explanation:
Given
[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]
Multiply through by 14 to clear the fractions
6 = h - 4 ( add 4 to both sides )
10 = h
Answer:
10
Step-by-step explanation:
We start out with 3/7 = h/14 - 2/7
add 2/7 to both sides:
(5/7) = h/14
Multiply both sides by 14 to get rid of the fraction:
h = 10
Find the amplitude of y = -2 sin x
Answers
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x). The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.
Cheers.
Find the area of the following rectilinear figure.
Answers
Answer:
Area : 14+10+40=64 square unit
Step-by-step explanation:
the area of the top rectangle with sides 2 and 7
A=2*7=14 square unit
the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5
Area=5*2=10 square unit
the bottom rectangle : sides 10 and 4
Area=10*4=40
add the areas : 14+10+40=64 square unit
Please answer this question now
Answers
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She sold $600 in clothing on Saturday and $1200 in clothing on Sunday. How much did she earn over the two days? A. $252 B. $291 C. $392 D. $532
Answers
Answer:
I hope this helps!
Answer D
Step-by-step explanation:
Step-by-step explanation:
salary per day =$140
bonus on sales =14%
sales on Saturday =$600
bonus on Saturday sales=14/100*$600
=$84
sales on Sunday =$1200
bonus on Sunday sales=14/100*$1200
=$168
total amount she earned over the two days=$140+$84+$168
=$532
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
x=
Answers
Answer:
x = 3
Step-by-step explanation:
j(x) = 4/5(-5) + 7
= -4 + 7
= 3
Answer:
15
Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!
NEED ASAP What is the quotient and remainder of 8,595 ÷ 24?
Answers
Answer:
358.125
Step-by-step explanation:
Answer:
358 3/24
Step-by-step explanation:
PLEASE HELP
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answers
Answer:
perimeter is 4 sqrt(29) + 4pi cm
area is 40 + 8pi cm^2
Step-by-step explanation:
We have a semicircle and a triangle
First the semicircle with diameter 8
A = 1/2 pi r^2 for a semicircle
r = d/2 = 8/2 =4
A = 1/2 pi ( 4)^2
=1/2 pi *16
= 8pi
Now the triangle with base 8 and height 10
A = 1/2 bh
=1/2 8*10
= 40
Add the areas together
A = 40 + 8pi cm^2
Now the perimeter
We have 1/2 of the circumference
1/2 C =1/2 pi *d
= 1/2 pi 8
= 4pi
Now we need to find the length of the hypotenuse of the right triangles
using the pythagorean theorem
a^2+b^2 = c^2
The base is 4 ( 1/2 of the diameter) and the height is 10
4^2 + 10 ^2 = c^2
16 + 100 = c^2
116 = c^2
sqrt(116) = c
2 sqrt(29) = c
Each hypotenuse is the same so we have
hypotenuse + hypotenuse + 1/2 circumference
2 sqrt(29) + 2 sqrt(29) + 4 pi
4 sqrt(29) + 4pi cm
Step-by-step explanation:
First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.
2pi4 so the perimeter for the half circle would be 8pi/2.
The area of that half circle would be piR^2 so 16pi/2.
Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2
16+100=C^2
116=C^2
C=sqrt(116)
making the perimeter of this triangle 2×sqrt(116)
The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.
We than just need to add up the perimeters and areas for both the half circle and triangle.
The area would be equal to 8pi+40
The perimeter would be equal to 4pi+4(sqrt(29))
HELP ASAP
[tex]Given that $33^{-1} \equiv 77 \pmod{508}$, find $11^{-1} \pmod{508}$ as a residue modulo 508. (Give an answer between 0 and 507, inclusive.)[/tex]
Answers
===================================================
Work Shown:
[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]
Notice how 33*77 = 2541 and 11*231 = 2541
[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.
So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 8686 chocolate chip cookies and 42 4242 sugar cookies. Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies. What is the greatest number of identical packages that Shaquira can make?
Answers
Answer: 2
Step-by-step explanation:
Given: Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42
Prime factorization of 86 and 42:
86 = 2 ×43
42 = 2 × 3 × 7
GCD of 86 and 42 = 2 [GCD = greatest common factor]
Hence, the greatest number of identical packages that Shaquira can make =2
How many solutions does the nonlinear system of equations graphed below
have?
y
10+
-10
10
-10
A. One
B. Two
0
O
C. Four
O
D. Zero
Answers
Answer:
D. zero
Step-by-step explanation:
Since the graphs do not intersect, there are zero solutions.
The number of solutions on the graph is zero
How to determine the number of solutions?The graph shows a linear equation (the straight line) and a non linear equation (the curve)
From the graph, we can see that the straight line and the curve do not intersect
This means that the graph do not have any solution
Hence, the number of solutions on the graph is zero
Read more about non-linear graphs at:
https://brainly.com/question/16274644
#SPJ5
Solve: 5x2 + 25x = 0
Answers
Answer:
x = -0.4
x = -(2/5)
Answer:
x = ± √5
Step-by-step explanation:
Please indicate exponentiation by using the symbol " ^ ":
5x^2 + 25x = 0
Divide all three terms by 5. We get:
x^2 + 5 = 0, or x^2 = -5
Then x = ± √5
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65.
Answers
The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:
The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.
Based on the information given, the correct expression that can be used to solve the question should be:
65 - (5.50b + 7.5)
In conclusion, the correct options are B and C.
Read related link on:
https://brainly.com/question/16904821
Answer:
B and C
Step-by-step explanation:
What is the smallest positive integer $n$ such that $\frac{n}{n+101}$ is equal to a terminating decimal?
Answers
Answer:
n = 24
Step-by-step explanation:
Given the fraction:
[tex]$\frac{n}{n+101}$[/tex]
To find:
Smallest positive integer [tex]$n$[/tex] such that the fraction is equal to a terminating decimal.
Solution:
The rule that a fraction is equal to a terminating decimal states that, the denominator must contain factors of only 2 and 5.
i.e. Denominator must look like [tex]2^m\times 5^n[/tex], only then the fraction will be equal to a terminating decimal.
Now, let us have a look at the denominator, [tex]n+101[/tex]
Let us use hit and trial method to find the value of [tex]n[/tex] as positive integer.
n = 1, denominator becomes 102 = [tex]2 \times 3 \times 17[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 4, denominator becomes 105 = [tex]5 \times 3 \times 7[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 9, denominator becomes 110 = [tex]2 \times 5 \times 11[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 14, denominator becomes 115 = [tex]5 \times 23[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 19, denominator becomes 120 = [tex]5 \times 3 \times 2^3[/tex] not of the form [tex]2^m\times 5^n[/tex].
n = 24, denominator becomes 125 = [tex]2^0 \times 5 ^3[/tex] It is of the form [tex]2^m\times 5^n[/tex].
So, the answer is n = 24
Tim owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.
He sells the shorts for $12 and the T-shirts for $8 each. Tim can work 18
hours a day, at most. It takes him 30 minutes to design a T-shirt and 45
minutes to design a pair of shorts. He must design at least 12 items each
day, but he cannot design more than 30 items in one day. Which set of
inequalities below represents this scenario?
A. s 2 12 + $ ss 30 + tiss 24-0.66t, s2; 0; t2 0
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
O c. s? 12-ts? 30-tss 24 -0.66t, s 2 0;t20
D. S 2 12-tss 30-ts 24 -0.66t, s 20; t 0
Answers
Answer:
The correct option is;
B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t
Step-by-step explanation:
The given parameters are;
The number of T-shirts, t, and shorts, s, Tim must design a day = 12
The maximum number of T-shirts and shorts Tim can design a day = 30
The maximum number of hours Tim can work = 18 hours
Therefore, we have;
The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs
Which gives;
s ≥ 12 - t
Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs
Which gives;
s ≤ 30 - t
The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24
The fraction of 36 minutes in 45 minutes = 36/45 = 0.667
Therefore we have;
The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts
Which gives;
s ≤ 24 - 0.66·t
The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.
Answer:
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
Step-by-step explanation:
Hope this helps!!
Represents the solution to the inequality -9=2/3x-7<5
Answers
Answer:
-3=x <13
Step-by-step explanation:
[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]
Multiply through by 3
[tex] - 27 = 2x - 21 < 15[/tex]
Add 21 to all sides
[tex] - 6 = 2x < 36[/tex]
Divide through by 2
[tex] - 3 = x < 18[/tex]
The solutin set is
[tex]{- 3 = x < 18}[/tex]
Two stores sell the same computer for the same original price. Store A advertises that the computer is on sale for 25% off the original price. Store B advertises that it is reducing the computer’s price by $180. When Brittany compares the sale prices of the computer in both stores, she concludes that the sale prices are equal. Let p represent the computer’s original price. Which equation models this situation?
Answers
Answer:
p= 25/100 = 180/x
Step-by-step explanation:
In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.
Answer:
0.75p=p-180
Step-by-step explanation:
0.75p=p-180 is your answer
how do you solve 2m-10=44+8m
Answers
Answer:
m = -9
Step-by-step explanation:
2m-10=44+8m
Subtract 2m from each side
2m-2m-10=44+8m-2m
-10 = 44+6m
Subtract 44 from each side
-10-44 = 44-44+6m
-54 = 6m
Divide by 6
-54/6 = 6m/6
-9 = m
Answer:
solve by solving the salvation for equation don't be a slave get educated from what's gave
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answers
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Help wanted ill do brainliest!!
Answers
Answer:
x=-1
Step-by-step explanation:
0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )
- Distribute 0.5 by 5 and -7x
2.5 - 3.5x = 8 - ( 4x + 6 )
Second- Distribute the invisible one into 4x and 6
2.5 - 3.5x = 8 - 4x - 6
- Combine like terms: Subtract 6 from 8
2.5-3.5x= - 4x + 2
-Add 4x from both sides of the equation
2.5 + 0.5x = 2
-Subtract 2.5 from both sides of the equation
0.5x = 2- 2.5
0.5x = -0.5
-Then divide each side by 0.5x
0.5x = -0.5
0.5 0.5
-Cancel the common factor of 0.5
x = - 0.5
0.5
-Divide -0.5 by 0.5
X = -1
I need helps will give you a good rating.
Answers
Answer: x = 3
Step-by-step explanation:
Sqrt(x+7) - 1 = x
Sqrt(x+7) = x + 1
x+7 = x^2 + 1
x = x^2 - 6
x=3
4x + 5y = 19 , 5y - 4x = 38
Answers
Answer:
Step-by-step explanation:
Adding both equations
4x+5y+5y-4x=19+38
10y = 57
y= 5.7
Subtracting equation i from ii
5y-4x-4x-5y=38-19
-8x=9
x= -0.9
Estimate. Then determine the area. Please please please, need help!
Answers
Estimate:
2.3 rounds down to 2
So after multiplying by 2, the area is estimated to be 4 cm squared.
Actual Area:
2.3 x 2 = 4.6
The actual area of the shape is 4.6 cm squared.
Hope this helped!
Answer:
4.6
Step-by-step explanation:
Samantha’s college runs on a trimester schedule so she receives a bill 3 times a year for tuition. Each trimester costs $1,450, and Samantha must complete 2 years of college to receive her degree. The average cost for books each trimester is $350. Approximately what will be the total cost for Samantha to get her degree?
Answers
Answer:
10800
Step-by-step explanation:
1 trimesters cost = 1450 + 350 $
2 year -> 6 trimester
1800$ x 6 = 10800 $
Which statement correctly compares
1–201 and
1512
ol-201 = 151
ol-201 < 51
l-201 > 151
Answers
Answer:
Option B.
Step-by-step explanation:
Consider the correct question is "Which statement correctly compares
1. -201 and 151
-201 = 151
-201 < 51
-201 > 151"
The given numbers are -201 and 151. We need to compare these numbers.
We know that all negative numbers are less than positive numbers.
So,
-201 < 151
If both numbers are negative, then the larger negative number is the smaller number.
Therefore, the correct option is B.
I need Helpppp quick!!!!
Answers
Answer:
G
Step-by-step explanation:
let his fixed price be x and his hourly fee be y;
270 = 4y + x
420 = 7y + x
x is common in both equations
equate the two;
x = 270-4y and x = 420-7y
270-4y = 420-7y
3y = 150
y = 50
x = 270-4*50
x = 70
Complete the square to transform the expression x2 - 2x - 2 into the form a(x - h)2 + k
Answers
Answer:
A
Step-by-step explanation:
Find the vertex form of the quadratic function below.
y = x^2 - 4x + 3
This quadratic equation is in the form y = a{x^2} + bx + cy=ax
2
+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…
y = a(x - h)^2 + k
This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.
Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.
STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.
STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).
STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.
Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.
STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.
After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).
Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.
Example 2: Find the vertex form of the quadratic function below.
The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a
=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.
STEP 1: Factor out 22 only to the terms with variable xx.
STEP 2: Identify the coefficient of the xx-term or linear term.
STEP 3: Take that number, divide it by 22, and square.
STEP 4: Now, I will take the output {9 \over 4}
4
9
and add it inside the parenthesis.
By adding {9 \over 4}
4
9
inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(
4
9
)=
2
9
to the entire equation.
Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.
STEP 5: Since I added {9 \over 2}
2
9
to the equation, then I should subtract the entire equation by {9 \over 2}
2
9
also to compensate for it.
STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.
It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(
2
−3
,
2
−11
).
Example 3: Find the vertex form of the quadratic function below.
Solution:
Factor out - \,3−3 among the xx-terms.
The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}
4
1
inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(
4
1
)=
4
−3
is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}
4
3
outside the parenthesis.
Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(
2
1
,
4
11
).
Example 4: Find the vertex form of the quadratic function below.
y = 5x^2 + 15x - 5
Solution:
Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}
4
9
.
Add {9 \over 4}
4
9
inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(
4
9
)=
4
45
is the number that we need to subtract to keep the equation unchanged.
Express the trinomial as a square of binomial, and combine the constants to get the final answer.
Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}
2
−3
,
4
−65
.
Answer:
(x - 1 )^2 - 3
Step-by-step explanation:
( x - 1 )^2 + ( -3)
x^2 - 2x + 1 - 3
x^2 - 2x - 2
simplify 5 x 5^2 in index form
Answers
Answer:
5x(25)
Step-by-step explanation:
