The vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
What is the Equation of a parabola?The general equation of a parabola is given as,
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As we want to write a function g(x) = 40x + 4x² in vertex form, and we know that the vertex form of a parabola, with vertex at (h,k) is written as,
[tex]f(x) = a(x-h)^2 + k[/tex]
Also, the algebraic identity [tex](x + a)^2[/tex] is written as,
[tex](x + a)^2 = x^2 + 2ax + a^2[/tex],
Therefore, [tex]x^2 + 2ax[/tex] can be written as
[tex]x^2 + 2ax = (x + a)^2 - a^2[/tex]
Further, we try to write the g(x) in the vertex form it can be written as,
[tex]\begin{aligned}g(x) &= 4x^2 + 40x\\\\ &= 4[x^2 + 10x]\\\\ &= 4[(x + 5)^2 - 5^2]\\\\ &= 4(x + 5)^2 - 100\\\end{aligned}[/tex]
Hence, the vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).
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What value of x makes this equation true?
2x = 4x – 10
Answer:
5
Step-by-step explanation:
2x = 4x - 10
4x - 2x = 10
2x = 10
x = 10/2
X = 5
2(5) = 4(5) - 10
10 = 20-10
10=10
Answer:
x = 5
Step-by-step explanation:
put x on one side (subtract the x on the left from both sides)
-2x = -10
divide the extra number with the x from both sides
x = 5
hope this helps!
have a wonderful day :)
coach P is deciding which job he would like to take. Job A will pay him time bonus of $10,000 plus $500 per day. Job B will pay him a one time bonus of $17,000 plus $300 per day. How many days would Coach P have to work for the two job offers to pay the same?
Answer:
35 days
500x35=17500
17500+10000=27500
300x35=10500
10500+17000=27500
Suppose A,B,C and D are different points on the same line. How many segments have endpoints at these points?
The number of line segments that can be formed on the same line is A = 6
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
If A, B, C, and D are different points on the same line, then the number of line segments with endpoints at these points can be calculated by counting the number of ways to choose 2 points from the 4 points.
The number of ways to choose 2 points from 4 points is given by the binomial coefficient 4 choose 2, which is:
So , the combination is ⁴C₂
4 choose 2 = ⁴C₂ = (4!)/(2!(4-2)!) = (4 x 3)/(2 x 1) = 6
Hence , there are 6 line segments with endpoints at A, B, C, and D.
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Two groups of hikers take two different routes from Camp A to Camp B. The first group leaves Camp A at 9:00 AM and takes a route that is 30 miles longer than the second group's route.
The second group leaves Camp A at 1:00 PM. Their hiking speed is 2 mph slower than the first group's speed.
Both groups reach Camp B at 4:00 PM. How fast does each group hike?
Answer:
6 and 4 because its correct 100%
Step-by-step explanation:
Trevor has an investment worth $6,774. 50. He made his only deposit in it 22 years ago. Given that the investment yields 2. 7% simple interest annually, how big was the initial deposit? a. $2,524. 50 b. $4,024. 03 c. $4,250. 00 d. $11,404. 88 Please select the best answer from the choices provided A B C D.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6774.50\\ P=\textit{original amount deposited}\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ t=years\dotfill &22 \end{cases} \\\\\\ 6774.50=P[1+(0.027)(22)]\implies \cfrac{6774.50}{1+(0.027)(22)}=P\implies 4250=P[/tex]
Would appreciate the help :))
Answer:
blank one: -1 blank two: -15
Step-by-step explanation:
I'm not sure but I think its correct
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x). F(x)+6
Answer:
Step-by-step explanation:
the answer is in the attachment below the graph.
Which is a factor of 6x2 x − 7? x 1 2x 1 6x 7 3x 7
The factor of the polynomial 6x² + x − 7 using factorization is (x − 1) and (6x + 7). Then the correct option is C.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The polynomial is given as 6x² + x − 7
On factorization, we have
6x² + x − 7
6x² + 7x − 6x − 7
x (6x + 7) −1 (6x + 7)
(x − 1)(6x + 7)
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Ryan bought 2 pounds of almonds and 3 pounds of peanuts. He mixed them together and divided them into bags. He put 1/8 pound of mixed nuts into each bag. Write an equation to represent the number of bags, b, Ryan filled.
Answer:
8(2A+3P) 40 bags
Step-by-step explanation:
(2A+3P)/ (1/8) 8(2A+3)
2 pounds of almonds (2A) + 3 pounds of peanuts(3P) = 5pounds of the mix
5/1 divided into 1/8 , that is the same as 5/1 multiplied be 8/1
5/1 x 8/1 =40
15) through: (5, -3), parallel to y=-x-4
A) r-2y=-2 B) 2x + y= 2
C) x + y = 2 D) x+y=-2
Step-by-step explanation:
C
parallel to y=-x-4 is C or D
(5,-3)=> C
PLEASE HELPPP!!! my teacher doesn’t teach right and im extremely confused
5. ALGEBRA Sandy Schabel owns 400 shares of Exxon
Mobil (XOM) stock. After the quarterly dividends are reinvested
under a dividend reinvestment program (DRIP), she owns
401.6 shares. XOM is selling at $86.40 a share. Find the annual
dividend per share and the annual yield for XOM.
$34,698.24 is the total amount of money if you sell the stocks, im sorry I don't think this is what you are looking for I barely understood the question.
>-<
PLEASE HELP ASAPPPPP!!!!
Answer:
(3,-2)
Step-by-step explanation:
All the others are either negative, 0, or 1. The outlier is 3,-2 because no other coordinate has a positive 3 in the x position.
Hope this helps!!
Have an amazing day!!
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What is the difference between a copay and coinsurance?
Answer:
A deductible is the amount you pay for a service before the plan shares the cost of the service with you. A copay is a set amount you pay for the service. Coinsurance is when you pay a percentage of the cost for an item or service.
e total weight of two garden statues was 714 pounds. If one statue weighed 342 pounds, how heavy was the other one?
Answer:
372
Step-by-step explanation:
Since we know the total weight which is 714 and we know the weight of one garden which is 342, all we need to do now is subtract:
714 - 342 = 372
3. Atile warehouse has Inventory at hand and can put in for a
der from a supplier of bundles of tiles.
Currently they have 38 tiles of a certain kind in stock, and can
as Inventory at hand and can put in for a back order from a su
bundle. The equation that represents this order is as follows;
in kind in stock, and can only order more in groups of 12 tiles per
The number of tiles = 12b+38, where b is the number of bundles ordered
(a) If a customer needs 150 tiles, how many bundles will need to be ordered?
answer. Why do we need to round our answer up in this problem?
undles will need to be ordered? Explain how you got your
Step-by-step explanation:
Given the equation that represents this order expressed as;
The number of tiles = 12b + 38 where;
b is the the number of bundles ordered
If a customer needs 150 tiles, the total number of bundles ordered can be gotten by simply substituting The number of tiles into the modeled equation and find the value of b. This is as shown below;
On substituting;
150 = 12b + 38
12b = 150 - 38
12b = 112
b = 112/12
b = 9.33
b ≈ 9 bundles
We need to round up the problem because the number of tiles can not be in fraction but as whole numbers.
The inequality compare between two parameters with a certain extent. The number of bundles to be ordered are 10.
Given that:
Number of tiles the customer needs is 150.
Number of tiles supplier already has is 38.
Tiles per bundle is 12.
And we don't want to supply less tiles to the customer, that is why we will order equal or more tile bundles that will satisfy the customer's needs.
Let b be the number of bundles.
Or symbolically, using inequality, we can say that:
[tex]12\times b \: + 38 \geq 150\\\\b \geq \dfrac{112}{12}\\\\b \geq 9.333...\\[/tex]
Since bundles ordered will be counted in positive integers, thus we have:
b = 10
Thus, the number of bundles to be ordered are 10.
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Is the open sentence8−4x=4x true or false when x = 0?
Answer:
FLASE
Step-by-step explanation:
8 - 4(0) = 4(0)
8 - 0 = 0
8 ≠ 0
4 (-3x+ 6)=4 (-3x) + 4 (6)
Answer:
I think its 0= 0
Step-by-step explanation:
Peter has 90 mild peppers and 36 hot peppers.
If Peter wants to put the peppers into baskets so that each basket has
the same number of mild peppers and the same number of hot pep-
pers, what is the greatest number of baskets he can make with how
many of each type of pepper?
Find the greatest common factor of 90 and 36.
pls I'm begging for help T-T
Q1. I will use team A's results to claim that their shoes are larger because the mean of team A is 13.92 whereas the mean of team B is 12.83.
Q2. I will use team B's results to claim their shoes are larger because the table of team A stops at 16, however team B's top shoe size is 18, therefore team B has the largest shoe size.
Q3. Both teams have the same average shoe size because the results are only 1 size away from each other most times.
(sorry about Q3 I'm not entirely sure about that one.)
Answer:
b is 23.7
a is 17.6
d is 9m8
Step-by-step explanation:
these are based on my calculations
hope i helped :)
1 The graph below shows a relationship between x and y. }
Answer:
C. 1/2x +2
Step-by-step explanation:
We can see in the graph that the value of y for 2 its 3, so we have to test each equations to see which one is going to give us a 3 whit 2 as the x.
A. 2x2=4 (4≠3)B. 2+2=4 (4≠3)C. 1/2 x 2+2=3 D. 2x2+1/2= 4.5 (4.5≠3)its a math question!!! please help! Find the image points given the following triangle reflected across the line y = -1
D(-1,-1), E(1,3), F(3, -2)
Question options:
D'(-2,-2), E'(0,-6), F'(2,-1)
D'(2,-1), E'(21,3), F'(0,-2)
D'(1,1), E'(-1,-3), F'(-3,2)
D'(-1,-1), E'(1,-5), F'(3,0)
Answer:
Step-by-step explanation:
Point D lies on the line, so it is invariant.
Point E is a distance of 4 units away from the line y=-1, so E is now (1, -1-4)=(1, -5).
By the same logic, F' is now (3, 0).
The image points of triangle reflected across the line y = -1 is D'(-1,-1) ,E'(1,-5) , F'(3, 0) .
What is image point?The given point P is "reflected" in the mirror and appears on the other side of the line an equal distance it. Drag the point P to see this. The reflection of the point P over the line is by convention named P' (pronounced "P prime") and is called the "image" of point P.
According to the question
Triangle points given
D(-1,-1), E(1,3), F(3, -2)
and reflected across the line y = -1
As, we have to reflect from y = -1 , there will be no change in x axis in image points only y axis will be change .
D(-1,-1)
x axis = -1
y axis = -1
x' axis = -1
y' axis = distance from -1 to -1 = 0
therefore,
y' axis = -1
D'(-1,-1)
E(1,3)
x axis = 1
y axis = 3
x' axis = 1
y' axis = distance from 3 to -1 = |3 -(-1 ) |= 4 unit
therefore, 4 unit form -1 in negative
y' axis = - 5
E'(1,-5)
F(3, -2)
x axis = 3
y axis = -2
x' axis = 3
y' axis = distance from -2 to -1 = |-2 -(-1 )| = 1 unit
therefore, 1 unit form -1 in positive
y' axis = 0
F'(3, 0)
Hence, the image points of triangle reflected across the line y = -1 is D'(-1,-1) ,E'(1,-5) , F'(3, 0) .
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Can someone please help me?
Step-by-step explanation:
the upper answered person is correct
kindly give her brainlist
thw
What is that decimal value of 4/11
Answer:
0.3636
Step-by-step explanation:
Using your understanding of the cause and effect relationship between volume and temperature, explain what happens to the motion of the particles and the kinetic energy of the particles inside a basketball after it has been left out in the cold. Use a model to support your answer.
Answer:
See explanation
Step-by-step explanation:
Temperature is defined as a measure of the average kinetic energy of the molecules of a body. A very important deduction from the kinetic theory of gases is that temperature is proportional to the kinetic energy of gas molecules.
A basketball is filled with gas particles. The higher the temperature of the surrounding, the greater the kinetic energy of the gas particles inside the basketball and the faster their motion and vice versa.
Hence, if a basketball is left in the cold, the kinetic energy of the gas particles in it will decrease and the particles will move very slowly at low velocities.
Shaun's parents agreed to pay 2/5 of the cost of a
bike, if he was able to save the rest. If his parents
gave him $92, how much did the bike cost?
Answer:
The bike was $230
Step-by-step explanation:
If 2/5 is $92 you can divide 92 by two like so,
92 ÷ 2 = 46
So ONE fifth is 46 to find out the total (5/5) you multiply by 5 so it would turn up like this,
46 × 5 = 230
The bike was $230
Hope that helps and have a great day!
Lesson name: I write/solve systems of linear equations word problems
Problem: Tickets for the school play sell for $3 for a student and $5 for an adult. one night, 595 people bought tickets for a total sale of $1951. how many adults and how many student tickets were sold?
Let S=#of student tickets
Let A=#of adult tickets
Equation= 3s+5a=1951
Answer:
Long division calculator with decimals shows the work step by step. Solve long division with decimal numbers. Calculate the quotient showing long division ...
Step-by-step explanation:
Long division calculator with decimals shows the work step by step. Solve long division with decimal numbers. Calculate the quotient showing long division ...
Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. The interest rate for his 401(k) is 7. 3%. If he puts away 10% of his $32,000 salary every year, what would the total of his 401(k) be in 10 years? Round your answer to the nearest cent. A. $67,266. 16 b. $72,176. 59 c. $33,250. 60 d. $35,677. 89 Please select the best answer from the choices provided A B C D.
The best answer from the choices provided will be B. The total of his 401(k) be in 10 years will be $72,176. 59.
What is the interest rate?The interest rate is a proportion of the principal that a lender charges a borrower. The annual percentage rate (APR) is the term used to describe the interest rate on a loan (APR).
Trent calculates the future value of the contribution using the Future Value formula with an increased contribution each year.
On doing the annual Contribution calculation we get;
The formula for calculating the future value of a yearly donation is as follows:
If F is the future value, P is the present value,n is the time period and I is the interest rate then;
Future value = Present value(1+ Interest rate)ⁿ
[tex]\rm F= P(1+I)^n \\\\ \rm F= 3200(1+7.3 \%)^{10} \\\\ \rm F= \$\ 34443.6[/tex]
Similarly, the formulas may be used to obtain a total contribution value of $72176.59.
Hence the best answer from the choices provided will be B. The total of his 401(k) be in 10 years will be $72,176. 59.
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Solve for X. Show your work.
Answer:
x=9
Step-by-step explanation:
since the location of 4x+2 and 7x-25 is across from each other that means that they are equal to each other so you have to set them equal to each other by doing 4x+2=7x-25 then you add like terms you add 25 and 2 together which gives you 27 and the equation will look like 4x+27=7x and then you subtract 4x from 7x which gives you 3x and u get the equation 27=3x now you divide 27 by 3 and get 9 so the equation will be x=9
What is the value of x in the equation −x = 6 − 4x + 18? (1 point) 24 8 −8 −24
Answer: 8
Step-by-step explanation:
What is the volume of this oblique cone?
Answer:You need π (Pi = ~ 3.14) over 3, then multiply by the radius to the power of two and finally multiply by the height.
Step-by-step explanation:
YW!!! =^.^= please mark branlest!