what is this equation rewritten in the form that reveals the minimum of the function
Answers
We are given the quadratic function c(p) = p^2 - 28p + 250 and we need to rewrite this in such a way that the minimum value is easy to find.
Remember that the vertex
[tex]f(x)=a(x-h)^2+k[/tex]where (h, k) is the vertex or the minimum point.
We use completing the squares method to do this. We divide the second term, -28p, by 2p, then square it.
[tex](\frac{-28p}{2p})^2=(-14)^2=196[/tex]We add 196 to p^2 - 28p to make it equal to (p - 14)^2, but since it will change the value of the equation, we need to subtract the same value from 250 so that the net effect is zero.
[tex]\begin{gathered} c(p)=p^2-28p+250 \\ c(p)=(p^2-28p+196)+250-196 \\ c(p)=(p-14)^2+54 \end{gathered}[/tex]The equation is c(p) = (p - 14)^2 + 54.
Related Questions
Wat 8x3 to get a answer
Answers
Answer:
24
Step-by-step explanation:
What percent of 240 is 132? pls I need it now
Answers
Answer:
55%
Step-by-step explanation:
Answer:
55%
132 is 55% of 240
Step-by-step explanation:
Evaluate the expression: No 4m2 when m = 3
Answers
We solve as follows:
[tex]f(3)=4(3)^2\Rightarrow f(3)=36[/tex]The solution is 36.
Reduce 36/60 to simplest terms
Answers
Answer:
3/5
Step-by-step explanation:
You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.
Answer:
3/5
Step-by-step explanation:
You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.
Use inductive reasoning to find a pattern for the answer then use the pattern to guess the result of the final calculation and perform the operations to see if your answer is correct
Answers
Given:
1 = 1²
1 + 3 = 2²
1 + 3 + 5 = 3²
1 + 3 + 5 + 7 = 4²
1 + 3 + 5 + 7 + 9 = 5²
1 + 3 + 5 + 7 + 9 + 11 = ___
Let's find the answer and determine the pattern.
Here, we have:
1 + 3 = 4
Now, write the sum as a perfect square:
4 = 2²
For the third equation:
1 + 3 + 5 = 9
Now, write the sum as a perfect square:
9 = 3²
This means the result will be the sum written as a perfect square.
Thus, we have:
1 + 3 + 5 + 7 + 9 + 11 = 36
Now, let's write the sum (36) as a perfect square:
36 = 6²
Therefore, we have:
1 + 3 + 5 + 7 + 9 + 11 = 6²
• ANSWER:
6²
2yd - 1ft = _____yd ______ft?
Answers
Answer: 1yd 2ft
Explanation
s we have a subtraction, we have to have the same units. Thus, in order to do so we have to consider that 1 yd = 3ft:
[tex]\frac{3ft}{1yd}[/tex]Then, converting 2yf to ft:
[tex]2yd\cdot\frac{3ft}{1yd}=6ft[/tex]Now, we can make the subtraction:
[tex]6ft-1ft=5ft[/tex]Finally, we can convert 3 ft to one yd:
[tex]3ft\frac{1yd}{3ft}=1yd[/tex]and we have 2 ft left.
Which is a function?
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}
Answers
Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Step-by-step explanation:
Each value of x corresponds to only one value of y, making the relation a function.
What is the slope of a line that passes through the points: (3, 1) and (-2, 2)? Please no links, and get to the point quickly.
Answers
Answer:
-1/5 is the slope
Step-by-step explanation:
the equation
y2-y1 over x2-x1
the linear equation 3x- 4y =7 has:
a, unique solution
b, two solutions
c, infinitely many solutions
d,no solution
Answers
The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.
Given that,
The linear equation is 3x+4y=7
Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.
There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.
The x and y are positive integers so it is a unique solution.
Therefore, The solution to the equation 3x+4y=7 is unique.
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1 over 6 divided by 6 divided by 6
Answers
Answer:
1/216
Step-by-step explanation:
[tex] \frac{1}{6} \div 6 \div 6[/tex]
[tex] \frac{1}{6} \div \frac{6}{1} \div \frac{6}{1} [/tex]
[tex] \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} [/tex]
[tex] \frac{1}{216} [/tex]
check whether x=1 is a solution of 3x-8
Answers
Answer: its 3
Step-by-step explanation: i looked it up and i found a quiz with the same question it was correct
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is 70% pure fruit juice?
Answers
20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.
What is percentage ?A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.
First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).
We know that there are 30 total pints of the mixture. Thus:
x+y=30
We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.
For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:
.65x+.90y=30 ×0.7
Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:
65x+90y=2100
Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:
65x+65y=1950
Subtract the second equation from the first equation:
25y=250
y=10
Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).
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Suppose
f
(
x
)
f
(
x
)
is an nth order polynomial, with a leading coefficient of 1. Find the compact expression
f
(
n
)
(
x
)
f
(
n
)
(
x
)
. That is, what is the solution (in terms of n) if you take the derivative to respect of
x
x
some n times?
Answers
Answer:
Hi
Step-by-step explanation: how are you doing
In the diagram below ∠1≅∠2 and m∠CFB=124°. Find each of the following.m∠1=___m∠2=___ m∠3=___m∠4=___m∠CFB= 124°
Answers
Angles and lines
We are given the following information
Angle 1 is congruent with angle 2. They have equal measures
Angle CFB measures 124°
Note that angles 4 and F are linear because they are formed by the intersection of two lines.
Linear angles add up to 180°
This means that the measure of angle 4 is:
m angle 4 = 180° - m CFB
m angle 4 = 180° - 124°
m angle 4 = 56°
now note angle 4, 1, and 2 form a straight angle of 180°. This means that
m angle 4 + m angle 1 + m angle 2 = 180°
Since angles 1 and 2 are congruent:
m angle 4 + 2* m angle 1 = 180°
Knowing that m angle 4 = 56°:
56° + 2* m angle 1 = 180°
Subtracting 56°:
2* m angle 1 = 124°
Solving:
m angle 1 = 124° / 2 = 62°
Thus, both angles 1 and 2 measure 62°
Finally, being angles 3 and 4 vertical angles (opposed by a vertex), they are congruent, thus
m angle 3 = m angle 4 = 56°
The solution is given below:
Can someone help me with the answer
Answers
The area of triangle ABC is 17.5 or 35/2
To solve this, we need to know the base and height of the triangle.
In this case, the base is the side AB, and the height is the side BC
Now we can count the units to get the lenght of the sides:
AB is 7 units long
BC is 5 units long.
Now we can use the formula for the area of a triangle:
[tex]A=\frac{bh}{2}[/tex]Where A is the area, b is the base and h is the height.
Putting the values of b and h:
[tex]A=\frac{7\cdot5}{2}=\frac{35}{2}=17.5[/tex]Then the area is 35/2 or 17.5 square units
Can you explain the steps for the y intercept and slope. x-10 = 4y
I came up with (10, 0)
Answers
What is the volume??
Answers
what is volume answer the volume is your topic for to day
Find the equation of the exponential function that goes through the points (0,3) and (3,375).
Answers
The equation of the exponential function that goes through the points (0,3) and (3,375) is y = 5(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (0,3) and (3,375).
The equivalent equations are;
375 = ab^3
3 = ab^0
From equation2;
a= 3
Substitute into equation 1;
375 = 3b^3
b^3 = 375/3
b^3 = 125
b = 5
Determine the equation
y = 3ab^x
y = 3(5)^x
This gives the required exponential equation
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Write an expression for the amount of money (in nickels) in n dollars.
PLEASE HELP ITS DUE IN AN HOUR
Answers
An expression for the amount of money (in nickels) in n dollars is 20n nickels.
How many nickels are in a dollar?A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.
To write an expression for the amount of money (in nickels) in n dollars,
Convert the n dollars to nickels.
1 dollar = 20 nickels
So, n dollars = 20n nickels
The required expression for the amount of money (in nickels) in n dollars is 20n nickels.
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Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answers
Answer:
500
Step-by-step explanition
12-children
20-adults
400 sold for 6000
c-children were
500
Which of the following shows a correct way of simplifying 6+(3-5x)
Answers
Answer: 9 - 5x
Step-by-step explanation:
6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x
Please help me solve this problem 20 points
Answers
Answer:
56
Step-by-step explanation:
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
What is the ratio of blue paint to total paint in the mixture?
Answers
The ratio of blue paint to the total paint in the mixture is 5:8.
How is a ratio calculated?Ratios contrast two figures by ordinarily dividing them. The term "antecedent" refers to the dividend and "consequent" to the divisor. A ratio in mathematics demonstrates how many times one number is present in another.It is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is expressed as a/b or a: b.Given:
In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.
Total paint in the mixture = 10+6 = 16
Ratio of blue paint to total paint = 10/16 = 5/8
Therefore, the required ratio is 5:8.
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Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?
Group of answer choices
1/2 cup of broccoli per beef
1 and ½ cup of broccoli per beef
2/3 pound of broccoli per beef
5/4 cup of broccoli per beef
Answers
Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.
What is proportion?Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.
Proportions, like ratios, use fractional values because they show the quantity of one variable in another.
We state proportions in fractions, decimals, or percentages.
The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli
3/4 pound = 0.75 pound
9/8 cups = 1.125 cups
The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)
1.5 cups = 1½ cups
Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.
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Find the coefficient of the x^2 term in the expansion of (5x-2)^6 //Series and sequences precalculus
Answers
We need to expand the term:
[tex](5x-2)^6[/tex]This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'
I'll paste an image of it above
We will use it in this way:
Each one of the rows, represent the n in the term:
[tex](x+y)^n[/tex]So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.
In our case, we need the 6th row.
Now, usually a term of the form
[tex](x+y)^6=ax^6+bx^5y+cx^4y^2+dx^3y^3+ex^2y^4+fxy^5+gy^6[/tex]As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!
[tex]\begin{gathered} a=1 \\ b=5 \\ c=10 \\ d=10 \\ e=5 \\ f=1 \end{gathered}[/tex]And we need the term that corresponds to x^2, we need the number e=5!
So, after the expansion, the coefficient of the term x^2 will be equal to 5
Write a system that would produce the graph below
Answers
Answer:
2x -y ≥ -53x +y < 10x +2y > 0Step-by-step explanation:
You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.
Linear equationsAn equation through points (x1, y1) and (x2, y2) can be written as ...
(y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1
Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.
For points (-2, 1) and (1, 7), the equation of the line can be ...
(7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)
6x -3y = -15 . . . simplify
2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)
For points (1, 7) and (4, -2), the equation of the line can be ...
(-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)
-9x -3y = -30 . . . simplify
3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)
For points (4, -2) and (-2, 1), the equation of the line can be ...
(1 -(-2))x -(-2 -4)y = (4)(1) -(-2)(-2)
3x +6y = 0 . . . simplify
x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)
InequalitiesIn each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.
There will be an "or equal to" symbol when the line is solid.
This means our inequalities are ...
2x -y ≥ -53x +y < 10x +2y > 0The image shows a quadrilateral inscribed in a circle. 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 -7 -10 -11 -12 -12-11-10 9 8 7 012 3 4 5 6 7 8 9 10 11 12 hat is the value of x ? A 23.1 B 21.1 C 25.1 D 22.6 E 19.1
Answers
We have a quadrilateral inscribed in a circle.
The quadrilateral is a trapezoid.
When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle C+m\angle B=180\degree \\ 4x+(4x+11)=180 \\ 8x=180-11 \\ 8x=169 \\ x=\frac{169}{8} \\ x=21.125 \\ x\approx21.1 \end{gathered}[/tex]Answer: x = 21.1
Evaluate the following expression
28-(-2/3)x 9.6
Answers
Answer:
34.4
Step-by-step explanation:
Use numerals instead of words.
Explain how to compare the products of two expressions without multiplying the numbers.
Since 40 x (951-686) can be rewritten as * 5x (951-686), the value of 40 x (951-686) is
of 5 x (951-685).
Answers
Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).
In what ways does multiplication compare?A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.
You must be able to distinguish between the given expressions in order to do that.
So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.
Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.
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dean is going to deliver some goods. he charges £7.00 an hour and 40p per mile for delivery.
he writes down his mileage before and after he has made his journey. this journey takes 2h and 45minutes.
how much does he charge to deliver these goods?
Answers
Answer:
See below
Step-by-step explanation:
Time charge = 2.75 hr * £7.00/hr = £ 1`9.25
Mileage charge = ( 25423 - 25263) mi * 40p / mile = 6400 p
(edited: forgot to multiply by 40p)
Now add the two charges together : 19 + (.25 * 240) + 6400/240 =
£ 45.92
( I think <===if I correctly did the monetary conversion between pence and pounds! <=== I used 240 p = 1£ )
Step-by-step explanation:
what we were not told is, if he charges a full hour for a fraction of an hour, or only a corresponding fraction of his hourly rate.
I assume the first : charging a full hour for any fraction of an hour spent.
it took him 2h and 45 minutes, so that is 3 hours charged.
and he was driving
25423 - 25263 miles = 160 miles
so, he charges
3×7 + 160×0.40 = 21 + 64 = £85
if he charges also fractions of his hourly rate, then his hourly charge would be
2 3/4 × 7 = (2×4 + 3)/4 × 7 = 11×7/4 = 77/4 = £19.25
in total that would be
19.25 + 64 = £83.25