The vertex of the parabola will be;
⇒ (3, - 11)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ f (x) = 2x² - 12x + 7
Now,
Since, The equation is,
⇒ f (x) = 2x² - 12x + 7
It can be written as;
⇒ f (x) = 2(x² - 6x) + 7
⇒ f (x) = 2(x² - 6x + 9 - 9) + 7
⇒ f (x) = 2(x² - 6x + 9) - 18 + 7
⇒ f (x) = 2 (x - 3)² - 11
By comparing with standard form of parabola y = a (x - h)² + k, we get;
⇒ (h, k) = (3, - 11)
Thus, The vertex of the parabola will be;
⇒ (3, - 11)
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(-4,1); perpendicular to y= -5/6x +3
Answer:
y = (6/5)x + 29/5
Step-by-step explanation:
To avoid confusion please enclose the fractional exponent inside parentheses: y= -5/6x +3 => y= (-5/6)x +3
The new line is to be perpendicular to the given line (above). The slope of this new line must be the negative reciprocal of (-5/6), which is (6/5).
Usig the slope-intercept formula, we get y = mx + b, or
1 = (6/5)(-4) + b
The LCD here is 5. Multiplying all 3 terms by 5, we get:
5 = 6(-4) + 5b, or
5 = -24 + 5b, or
5b = 29
Then b = 29/5, and the desired equation is:
y = (6/5)x + 29/5
if the breadth of rectangle is one-fourth of its length and perimeter in60 CM find the length and breadth of rectangle
Answer:
Step-by-step explanation:
Let length be x
So breadth will be 1/4x
2(x+1/4x)=60
x+1/4x=60/2=30
find lcm and the lcm would be 4 and make denominators equal and add it
4/4x+1/4x=30
5/4x=30
x=30*4/50=6*4=24
Therefore the length is 24/4=6cm and breadth is 24cm.
Cesar is excited that he only has 12 months left before he pays off his credit card completely. His current balance is $3,750 and his APR is 17. 5%. But when he is involved in a car accident, he is forced to use his credit card to pay a $1,000 deductible to get his car fixed. How much will Cesar’s minimum monthly payment increase if he still wants to pay off his credit card in 12 months? a. $83. 33 b. $91. 44 c. $342. 91 d. $434. 35.
The amount by Cesar’s minimum monthly payment increase will be $91.44.
What will be the amount?Cesar only has 12 months left before he pays off his credit card completely.
His current balance = $3,750
APR = 17.5%
Now we use the formula :
[tex]\rm Present \ value \ of \ anuity= P=( 1-\frac{1+r}{r} })^{-n}[/tex]
PV = Present Value
P = Periodic payment
r = rate per period
n = number of period
Now for the first case:
PV of annuity = $3,750
P =?
r = 17.5% annually = % monthly monthly
n = 12 months
Now we put the values in the formula
[tex]3750=P(1-\dfrac{(1+\dfrac{17.5}{1200})^{-12}}{\dfrac{17.5}{1200} } )[/tex]
[tex]P=\dfrac{3750}{\dfrac{1-0.8405}{0.01458} }[/tex]
[tex]P=342.91[/tex]
Now for the second Case :
PV of annuity = 3750 + 1000 = 4750
P =?
r = 17.5% annually = % monthly = monthly
n = 12 months
Putting the values in the formula
[tex]4750=P(1-\dfrac{(1+\dfrac{17.5}{1200})^{-12}}{\dfrac{17.5}{1200} } )[/tex]
[tex]P=\dfrac{4750}{1-\dfrac{1+\frac{17.5}{1200} }{\frac{17.5}{1200} } }[/tex]
[tex]P=\dfrac{4750}{\dfrac{0.1595}{0.01458} } =434.35[/tex]
Cesar's increased monthly payment will be
434.35 - 342.91 = 91.44
Hence, the amount by Cesar’s minimum monthly payment increase will be $91.44.
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Bella was out at a restaurant for dinner when the bill came. Her dinner came to $24. After adding in a tip, before tax, she paid $29.04. Find the percent tip.
Answer:
21%
Step-by-step explanation:
So we have to use percent change
The formula is subtracted/original multiply 100=percent change
so she added a $5.04 tip
5.04/24=0.21, then multiplied by 100=21
so she tipped 21%
Solve the equation for x 1/2(12x-10)=1/3(9+6x)
Answer:
x =
Exact form:
- (63/2)
Decimal Form:
- 31.5
Mixed Numbers Form:
- (31 1/2)
Who is this you tuber
Answer:
theodd1sout pretty cool guy
Answer:
the odd ones out
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
126 Degrees
Step-by-step explanation:
Angel Z is going to be 42 degrees so 3*42 is 126
Factors of 81q^2 –25r^2 are
Answer:
(9q + 5r)(9q - 5r)
Step-by-step explanation:
Given :-
81q² - 25r²
To Find :
Factors
Formula :-
a² - b² = (a + b)(a - b)
Solution :-
(9q + 5r)(9q - 5r)
Justin has 64 ounces of lemonade to divide among 9 people. When he types 64÷9 into his calculator, the number that appears is 7.111111111. How much lemonade should he give to each person?
The number of lemonade should Justin give to each person is 7 with one lemonade still left.
It is given that Justin has 64 ounces of lemonade to divide among 9 people.
We have to find out that how much lemonade should he give to each person.
What will be the value of each part , if 120 is divided in 6 equal parts ?
The value of each part will be 120 divided by 6 or 120 ÷ 6 or 20 i.e., 120 is divided into 6 equal parts of 20 each.
As per the question ,
No. of ounces of lemonade to divide among 9 people = 64
No. of lemonade each people will get = 64 ÷ 9
or
64 ÷ 9 = 7.1111
So , we can't equally divide it because if 7 each is divided between 9 people , one lemonade will still be left.
i.e.,
7 × 9 = 63
64 - 63 = 1
1 still left
Thus , the number of lemonade should Justin give to each person is 7 with one lemonade still left.
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Direction. Read and analyze the following word problem. Choose and write the letter of the correct answer on the blank.
Answer:
22- b
23- d
24- b
Step-by-step explanation:
22- perimeter =2(length + width)=2(40+20)=120
23- width =100m
length = 3×width =3×100=300
perimeter =2(300 +100)= 800
24= hanz perimeter = 40m
Arthur's perimeter =42m
hence Arthur needs more fence
The price of a gas increases from 2.20 per gallon on Monday to 2.31 per gallon on Tuesday. What is the percent of increase?
Answer:
4.9%
But I guess you may round to 5%, just be sure to say that you rounded from 4.9%.
which of these is a factor in this expression 5z^4-3+8(y^3+4)
A. -3+8(y^3+4)
B. 5z^4 - 3
C. (y^3+4)
D. 8(y^3+4)
Answer:
Step-by-step explanation:
(y^3+7)
The correct expression is 5[tex]z^{4}[/tex] + 29 + 8[tex]y^{3}[/tex]
What is multiplicative distribution law ?distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac.
according to the question
Apply multiplicative distribution law
5[tex]z^{4}[/tex] - 3 + 8[tex]y^{3}[/tex] + 32
Combine like terms
5[tex]z^{4}[/tex] + 29 + 8[tex]y^{3}[/tex]
Hence, the correct expression is 5[tex]z^{4}[/tex] + 29 + 8[tex]y^{3}[/tex]
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A high school track is shaped as a rectangle with a half circle on either side. A rectangle has a length of 85 yards and width of 25 yards. 2 semicircles with diameters of 25 yards are on each end of the rectangle. Jasmine plans on running three laps. How many yards will Jasmine run? Use 3. 14 for Pi. 248. 5 yd 490. 5 yd 725. 5 yd 745. 5 yd.
perimeter=2(85)+π(12.5)=220+2×12.5π
=170+25×3.14
=170+78.5
=248.5
distance ran=3×248.5=745.5 yards.
i hope this work for you
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
go 3 forward make a dot. and 8 down make a dot. then connect dots.
Answer:
all u do is get your mouse and move it and then do it TA-DA boom the answer XD
Step-by-step explanation:
comment below what u would say
Solve for X Show and explain your work Please
x=8.385
Step-by-step explanation:
Angle EBD is a right angle since it's facing the diameter ED
Hence triangle BED is a right isosceles triangle since we also know that EB=BD
so A is the midpoint of ED since it's the center of the circle and ED is a diameter
which implies ED=2×AD=2×6=12
Using the Pythagorean theorem on a right isosceles triangle which states:
a²+b²=c²
x²+x²=12²
2x²=144
x²=72
x=√72=8.485
5 units 2 units 2 units 3 units 2 units the area of the figure is blank square units
Answer:
Your answer is 8 Square Units
Step-by-step explanation:
3 x 2 = 6
2 x 2 = 4 / 2 = 2
6 + 2 = 8
Hope this Helps!
100 points and brainlyest
Part 2 - Writing Equivalent Expressions - You will now use mathematical properties to create two expressions that are equivalent to Sara’s expression.
Property Used
Original/Changed Expression
New expression with property used
Commutative Property of Addition (rearrange the added terms in the parentheses to group like terms together.)
5(2j + 3 + j)
Combine Like terms after rearranging them
(put your answer from the previous row here)
Distributive Property of multiplication over addition (multiply the number outside the parentheses)
(put your answer from the previous row here)
(Use this final expression that you write in this box on the next slide.)
Answer:
Commutative Property of Addition: to change the order of numbers in an addition or multiplication operation does not change the sum or the product.
New expression with property used: 5(2j + j + 3)
Combine like terms: when combining like terms, add their coefficients
The like terms are 2j and j. Add their coefficients: 2 + 1 = 3, which means that the combination of like terms is 3j.
New expression with property used: 5(3j + 3)
Distributive Property of multiplication over addition: multiplying a sum by a number gives the same result as multiplying each added term by the number and then adding the products together.
So 5(3j + 3) = 5 · 3j + 5 · 3 = 15j + 15
New expression with property used: 15j + 15
Annete completes a 6.8-mile bike route in 90 minutes. She rides her bike at a constant speed for the entire route. To find how fast she traveled, she solves the equation 6.8=x(90). What does x represent?
Answer:
Her speed in miles per minute
Step-by-step explanation:
Not sure if that's true but yeah
You need to earn at least $300 for a school fundraiser washing cars. You charge $12 for trucks
and SUVs and $8 for cars. Write an inequality that represents how many vehicles need to be washed
to earn your goal.
What is the constant of proportionality from the following equation: s = 0.75u
u
A
0.75
u
S
Answer:
0.75
Step-by-step explanation:
The equation representing direct proportion is
y = kx ← k is the constant of proportionality
s = 0.75u ← is in this form
with k = 0.75
6. In a set of 10 questions ,4 marks are awarded for every correct answer and -2 marks
every wrong answer. Sunil gets 6 correct answers and 4 wrong answers. What is his
score?
Answer this question right , then I will award u brainlist and points
16 points
Step-by-step explanation:Hi there !
What is his score?
6×4 - 4×2 =
= 24 - 8
= 16 points
Good luck !
Answer:
marks awarded for each correct answer = 4
marks awarded for each incorrect answer = -2
No.of Sunil's correct answer = 6
therefore, mark of Sunil's correct answer = 6 x 4 = 24
No.of Sunil's incorrect answer = 4
therefore, mark of Sunil's incorrect answer = 4 x -2 = -8 (here + and - is multiplied therefore the final answer will be -)
Sunil's total score = 24(positive marks) - 8(negative marks)
=24-8 = 16
This also is an integer question right? ^_^
Don't mind answer. Not sure if it's correct
#3`1
A castle has to be guarded 24 hours a day. 7 knights are ordered to split each day's guard duty equally. How long will each knight spend on duty? Record your answer in minutes
Answer:
≈206 Minutes
Step-by-step explanation:
We know that the castle has to be guarded for 24 hours a day. Since there are 60 minutes in an hour, that means it must be guarded for 1,440 minutes (60 * 24 = 1,440). If we split this evenly between each of the 7 knights, through division, we know that they must each be on guard for 205.714285714 minutes, or approximately 206 minutes.
The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. a) What is the amount of increase in computers needed? b)What is the new amount of computers the team must sell?
Answer: a. 14 Computers
b. 62 Computers
Step-by-step explanation:
a) What is the amount of increase in computers needed?
Number of Computers sold last month = 48
Percentage increase required = 30%
Amount of increase in computers needed= 30% × 48
= 0.3 × 48
= 14.4
= 14 approximately
b)What is the new amount of computers the team must sell?
This will be the amount of Computers sold last month plus the increase.
= 48 + 14
= 62 Computers
Trey started an assignment at 3:44 PM and finished it at 4:23 PM. How long did it take him? Give your answer in minutes.
Write the equation of a line with slope -1/3 and y-intercept -7
A. y=-7x-1/3
B. y=-1/3x+7
C. y=-1/3x-7
Solve the equation and enter the value of y below.
4y + 15 = 39
y=--
Answer:
y=6 is the answer
Step-by-step explanation:
4y=39-15
4y=24
y=6
A bag has three marbles: one red, one blue, and one yellow. The marbles are pulled from the bag one at a time without replacing them. In how many different orders could the marbles be pulled from the bag?
The number of different orders that the marbles can be pulled from the bag is 6 ways
Combination and permutation of numbersIf a bag contains one red, one blue, and one yellow, then the total number of marbles contained is 3 marbles.
If the marbles are pulled from the bag one at a time without replacing them, the number of different orders that the marbles can be pulled from the bag is expressed as:
[tex]3C_1=\frac{3!}{(3-2)!} \\3C_1=\frac{3!}{1!}\\ 3C1=3! = 6ways[/tex]
Hence the number of different orders that the marbles can be pulled from the bag is 6 ways
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Algebra 1
> U.15 Solve a system of equations using any method: word problems GDQ
Tutor
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Victor and Susan each want to run for president of their school's student body council. In
order to do so, they must collect a certain number of signatures and get a nomination. So far,
Victor has 23 signatures, and Susan has 19. Victor is collecting signatures at an average rate
of 9 per day, whereas Susan is averaging 11 signatures every day. Assuming that their rate of
collection stays the same, eventually the two will have collected the same number of
signatures. How long will that take? How many signatures will they both have?
In
days, Victor and Susan will each have collected
signatures.
Submit
O
к
Answer:
cl jsjsjsjnsmamansnsnannananann
find f(-1)+g(2)
f(x)=5x-20
g(x)=x^2+5x-11
Step-by-step explanation:
f(x) = 5x - 20
f(-1) = 5(-1) - 20 = - 5 - 20
= - 25
g(x) = x² + 5x - 11
g(2) = 2² + 5(2) - 11 = 4 + 10 - 11
= 3
Thus, f(-1) + g(2) = - 25 + 3 = - 22
Answer:
Step-by-step explanation:
Substituting x as -1 in f(x), f(-1)
F(-1)=5(-1)-20
F(-1)=-5-20
F(-1)=-25
Substituting x as2 into g(x), g(2)
G(x) =2^2+5(2)-11
G(x)=4+10-11
G(x)=3
F(-1)+g(2)=-25+3
=-22