Answer:
[tex]y-1/2=2(x+7/2)^2[/tex]
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y-k=a(x-h)^2[/tex]
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The given function is:
[tex]y=(x+3)^2+(x+4)^2[/tex]
Expanding the squares:
[tex]y=x^2+6x+9+x^2+8x+16[/tex]
Simplifying:
[tex]y=2x^2+14x+25[/tex]
Factoring 2 from the first two terms:
[tex]y=2(x^2+7x)+25[/tex]
The expression in parentheses must be completed to form the square of a binomial:
[tex]y=2(x^2+7x+49/4-49/4)+25[/tex]
Isolating the square of the binomial:
[tex]y=2(x^2+7x+49/4)-49/2+25[/tex]
Operating and Factoring:
[tex]y=2(x+7/2)^2+1/2[/tex]
Rearranging:
[tex]\boxed{y-1/2=2(x+7/2)^2}[/tex]
Comparing with the vertex form:
a=2, h=-7/2, k=1/2
What is the slope of a line perpendicular to Line AB given A (6,2) and B (-3,2)
Answer:
slope is undefined
Step-by-step explanation:
Calculate the slope m of AB using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(6, 2) and (x₂, y₂ ) = B(- 3, 2)
m = [tex]\frac{2-2}{-3-6}[/tex] = [tex]\frac{0}{-9}[/tex] = 0
A line with a slope of zero is a horizontal line, parallel to the x- axis.
Thus a line perpendicular to AB is a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
X-5=20 show work pleaseeeeeee
Answer:
x-5=20
x=20+5 (When bringing -5 to the other side of the equal, it changes to +5)
x=25
1/3 of 12 = 2/3 of ?
Answer:
I think it's 6
Dhdneoemd
Answer:
6
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] of 12 = [tex]\frac{12}{3}[/tex] = 4
let the number required be n , then
[tex]\frac{2}{3}[/tex] n = 4 ( multiply both sides by 3 to clear the fraction
2n = 12 ( divide both sides by 2 )
n = 6
Thus
[tex]\frac{1}{3}[/tex] of 12 = [tex]\frac{2}{3}[/tex] of 6
help me i'm crying
help me
Answer:
Get a tissue blow your nose and wipe your tears
Step-by-step explanation:
Tell Mommy
Answer:
See below and learn
Step-by-step explanation:
To solve the figure. You need to split the shape up with the lines shown.
Let's solve the top triangle first.
The formula to find the area of a triangle is y = 1/2(b*h)
So the base is 2+2+6 which equals 10. And the height is 4.
So y = 1/2(4*10)
PEMDAS solve parentheses first.
y = 1/2(40)
y = [tex]20cm^{2}[/tex]
Now solve the bottom left one.
y = 1/2(2*2)
y = 1/2(4)
y = [tex]2cm^{2}[/tex]
Now the bottom right triangle.
y = 1/2(6*2)
y = 1/2(12)
y = [tex]6cm^{2}[/tex]
And to solve area of a square is
y = b*h
y = 2*2
y = [tex]4cm^{2}[/tex]
And add all of it up to get
y = [tex]20cm^{2}+2cm^{2} +6cm^{2} +4cm^{2} = 32cm^{2}[/tex]
Area = [tex]32cm^{2}[/tex]
The graph of a line in the xy-plane passes through the point (1, 4) and crosses the x-axis at the point (2.0). The
line crosses the y-axis at the point (0, b). What is the value of b?
Answer with step-by-step explanation:
The graph passes through both (1,4) and (2,0)
Thus it's slope is the difference of ordinates over difference of abscissae or -4
Thus the equation becomes y = -4x + b
This b is the required b
At x=2 ; y=0
Thus 0= -8 + b
b=8
Real quick question. need help plz
identify the sequence 18,13,8,3,-2 PLZ HELPPPPP
The common difference between each term is -5. The nth term of the sequence as follows: aₙ = 18 - 5(n-1)
The given sequence is 18, 13, 8, 3, -2.
To identify the pattern in the sequence, we can observe that each term is decreasing by 5. Starting from 18, we subtract 5 to get the next term, and so on. The common difference between each term is -5.
Using this pattern, we can continue the sequence as follows:
-2 - 5 = -7
-7 - 5 = -12
-12 - 5 = -17
-17 - 5 = -22
The extended sequence would be -2, -7, -12, -17, -22.
In terms of the general formula, we can represent the nth term of the sequence as follows:
aₙ = 18 - 5(n-1)
For more such questions on sequence
https://brainly.com/question/7882626
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The temperature fell from 0 degrees farenheight to 6 3/5 in 2 1/5 hours. What was the temperature change per hour?
A. -3
B. -4 2/5
C. 3
D. 4 2/5
Answer with step-by-step explanation:
C: 3
This is because 6 3/5 is a positive number, and 6 3/5 ÷ 2 1/5 = 3
Hope this was helpful! (brainliest please)
Consider the linear function that is represented by the equation y = 2 x + 2 and the linear function that is represented by the graph below.
Which statement is correct regarding their slopes and y-intercepts?
A. The function that is represented by the equation has a steeper slope and a greater y-intercept.
B. The function that is represented by the equation has a steeper slope, and the function that is represented by the graph has a greater y-intercept.
C. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.
D. The function that is represented by the graph has a steeper slope and a greater y-intercept.
Answer:
A
Step-by-step explanation:
Answer:
C. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.Step-by-step explanation:
Given function
y = 2x + 2And a graph. We can see it is
y = 2.5x + 1A. The function that is represented by the equation has a steeper slope and a greater y-intercept.
FalseB. The function that is represented by the equation has a steeper slope, and the function that is represented by the graph has a greater y-intercept.
FalseC. The function that is represented by the graph has a steeper slope, and the function that is represented by the equation has a greater y-intercept.
TrueD. The function that is represented by the graph has a steeper slope and a greater y-intercept.
Falseequations that are equivalent to 6x-4/2
Using Oliver’s table, how can you find the unit rate?
Answer:
Is there a table I can see if I'll be able to help
Answer:
Oliver’s table indicates that for every increase of 2 strides, the distance he travels increases by 7 feet. So, the change in distance divided by the change in stride gives the unit rate.
Step-by-step explanation:
This Is The Sample AnswerMarcus is a recent college graduate. He has $18,000 in student loans. He took out a loan to buy a car and owes $16,000. The car is now worth $14,000. He got his first paycheck and has $1400 in his checking account. What is Marcus' net worth? (Enter the positive or negative dollar amount only.)
Given :
Marcus is a recent college graduate. He has $18,000 in student loans. He took out a loan to buy a car and owes $16,000. The car is now worth $14,000. He got his first paycheck and has $1400 in his checking account.
To Find :
Marcus's net worth.
Solution :
We know, net worth is given by :
Net worth = $( Total amount owns - Total loan )
Net worth = $( 16000+1400) - ( 18000+14000)
Net worth = $(17400 - 32000)
Net worth = $-14600
Therefore, Marcus' net worth is $-14600 ( He is in a loan of $14600).
Hence, this is the required solution.
what is the area of tile 10 in.6 in.and 8 in
Answer:
480
Step-by-step explanation:
u multiply 10x6x8=480
Convert 65.000.000 to scientific notation.
Answer:
6.5 x 10^4
Step-by-step explanation:
Answer:0*10^0
Step-by-step explanation:
Name a pair of numbers which would represent the slopes of perpendicular lines.
132 days to 110.4 days
382.4 days from 132 days t 110.4 days
Amanda has four boards that are each 64 inches long. She needs to cut each board into multiple pieces that are each 12 45 inches long. How many pieces will she have after she cuts all four boards?
Answer:
You need to divide 64 by 12/45. Whenever you divide fractions you keep the first number as it is, change the sign to multiplication and write the reciprocal of the second fraction which is you have to flip the fraction. It is going to be 64 times 45/12. Which is 240/1 which is 240.
Step-by-step explanation:
Using simple algebra, it is found that Amanda will be able to cut 20 pieces of [tex]12\frac{4}{5}[/tex] inches length.
What is algebra?Algebra is the branch of mathematics that deals with mathematical operations and symbols operating on numbers, variables and expressions
Let Amanda cut total x pieces
Given that length of each piece =[tex]12\frac{4}{5}[/tex] inches = 64/5 inches
Total length cut for all the pieces can be found by multiplying the number of pieces with length of each piece
∴ Total length cut for x pieces = x × 64/5 = 64/5 x
Given that Amanda has 4 boards for cutting
Length of each board = 64 inches
Total length offered by 4 fours boards for cutting is calculated by multiplying length of each board by 4 .
Total length offered for cutting by 4 boards = 4 × 64 = 256 inches
Therefore,
Total length cut for x pieces = Total length offered for cutting by 4 boards
⇒ 64/5 x = 256
⇒ x = 256/(64/5) = (256×5)/64 = 4×5 = 20
Therefore, There will be 20 pieces cut from all four boards .
Also, Learn more about algebra from the link below:
https://brainly.com/question/24875240
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Which equation is correctly setup to solve for x?
The formula for the hypotenuse of a triangle is:
[a squared] plus [b squared] = c squared
a and b represent the two sides of the triangle.
You would have to square 8 and 4, add them, then take the square root of it to find the length of the hypotenuse.
The first equation is correct.Pls easy geometry !! Help asp for Brainly, pls !!
graph the solution to the inequality on the number line 3b + 17 _< 4b +23 + 2b
Answer:
b_>-2 so the circle is going to be on top of -2 and it is going to be closed, going to the right
ANY HELP IS GREATLY APPRECIATED What is the sign of the product (−4)(6)(9)(3)?
A. Positive, because the products (−4)(6) and (9)(3) are negative and the product of two negative numbers is positive
B. Positive, because the products (−4)(6) and (9)(3) are positive and the product of two positive numbers is positive
C. Negative, because the product (−4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative
D. Negative, because the product (−4)(6) is negative and the product (9)(3) is negative, and the product of two negative numbers is a negative number
Answer:
c
Step-by-step explanation:
there's only one negative in the whole equation making it all negative. if there were two negatives it would become a positive
Casey is using a recipe that requires 23cups of flour for every 2 cups of milk. If Casey uses 5 cups of milk, how many cups of flour are needed?
Answer: 57.5
Step-by-step explanation:
To solve this problem, you need to multiply the number of cups of flour per cup of milk times 5.
Step 1: Find how many cups of flour per cup of milk.
23/2 = 11.5 cups of flour per cup of milk
Step 2: Multiply the cups of flour per cup of milk, times the 5 cups of milk.
11.5 * 5 = 57.5 total cups of flour
math - algebra (9th grade) please include work
Answer:
Step-by-step explanation:
Y) [tex]\frac{x+4}{8}[/tex] = 3
*multiply both sides by 8 - cancels out 8 in denominator*
x + 4 = 24
*subtract 4 from both sides*
x = 20
E) [tex]\frac{x-5}{2}[/tex] = 1
*multiply both sides by 2 - cancels out 2 in denominator*
x - 5 = 2
*add 5 on both sides*
x = 7
N) [tex]\frac{x+2}{4}[/tex] = 2
* multiply both sides by 4 - cancels out 4 in denominator*
x + 2 = 8
*subtract 2 from both sides*
x = 6
A father's age is three times the sum
of the ages of his two children.After 5
years his age will be two times the sum
of their ages.Find the present age of the
father
Enzo and Beatrice are playing games at their local arcade incredibly ends wins five tickets from every game in the trees wins 11 tickets from every game when they stop playing games Enzo in the trees had won the same number of total tickets what is the minimum number of games that Enzo could have played
Answer:
22 games
Step-by-step explanation:
In order to find the minimum number of games that Enzo played we need to find the least common multiple of tickets where both Enzo and Beatrice are equal. To do this we simply find all the multiples of the number of games each could have played by the number of tickets per game until we find one in common.
5*1 = 5 11*1 = 11
5*2 = 10 11*2 = 22
5*3 = 15 11*3 = 33
5*4 = 20 11*4 = 44
5*5 = 25 11*5 = 55
... ...
... ...
... ...
5*22 = 110 11*10 = 110
Finally, we can see that the minimum amount of games that Enzo needs to play in order for both Enzo and Beatrice to have the same amount of tickets is 22 games.
x + y = -7
-x+ 4y = 17
X=
y =
Answer:
x= -9, y= 2
Step-by-step explanation:
5y=10
y=2
x+2=-7
x=-9
Answer:
x=-9y=2Step-by-step explanation:
[tex]x + y = - 7[/tex]
[tex] - x + 4y = 17[/tex]
[tex]y = - 7 - x[/tex]
[tex]x = 4y - 17[/tex]
[tex]y = - 7 - 4y + 17[/tex]
[tex]5y = 10 \\ y = 2[/tex]
[tex]x = 4y - 17 = 4 \times 2 - 17 = 8 - 17 = -9 \\ x = -9[/tex]
someone please help!!
Chelsea and her friends are making small fruit baskets for their neighbors. They have 90 pears, 45 peaches, and 75 apples. What is the greatest number of baskets they can make if each basket has the same number of pears, the same number of peaches, and same number of apples, with no fruit leftover?
Answer:
15 baskets
Step-by-step explanation:
This question is a GCF question
The first step would be to find the factors of 45, 75 and 90
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 75 are: 1, 3, 5, 15, 25, 75
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The greatest common factor is 15.
Therefore, the greatest number of baskets they can make if each basket has the same number of pears, the same number of peaches, and same number of apples, with no fruit leftover is 15 baskets
HELP ME HELP ME HELP ME HELP ME
Answer:
i think it's A i hope it is
Answer:
D
Step-by-step explanation:
A music sharing service has an initial fee of $25 and a monthly fee of $6. When a person joins the service, it costs the company $70 to create the new account. Which inequality can be used to determine how many months, m, it would take for the company to stop losing money on a new customer?
Answer: [tex]25+6m > 70[/tex]
Step-by-step explanation:
Let m = Number of months
Combined charges for music sharing service = 25+6m
Cost of joining to company = $70
According to the question,
Combined charges > Cost of joining to company (To find number of months it would take for this)
[tex]25+6m > 70[/tex] (required inequality)
