the standard form of the quadratic function is f(x) = 3x² - 4x.
What is quadratic equation ?
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one squared term, but no higher powers. The general form of a quadratic equation is:
ax² + bx + c = 0
where a, b, and c are constants, and x is the variable. The coefficient a cannot be equal to 0, or else the equation would become a linear equation.
Quadratic equations have a variety of applications in different fields, including physics, engineering, and finance. They are used to model phenomena that involve parabolic shapes or trajectories, such as the motion of projectiles or the shape of a satellite dish.
To solve a quadratic equation, we can use several methods, including factoring, completing the square, or using the quadratic formula. The solutions to a quadratic equation are called roots, or zeros, and they can be real, complex, or imaginary.
To rewrite a quadratic function in standard form, we need to express it in the form:
f(x) = ax² + bx + c
where a, b, and c are constants. To achieve this, we can follow a few steps:
Step 1: Collect like terms
f(x) = 3x² - 4x
Step 2: Rearrange the terms so that the x² term comes first, then the x term, and finally the constant term.
f(x) = 3x² - 4x + 0
Step 3: Check the coefficient of x² is positive. If it's negative, we can multiply both sides of the equation by -1 to make it positive.
In this case, the coefficient of x² is already positive, so we don't need to multiply by -1.
Thus, the function f(x) = 3x² - 4x can be rewritten in standard form as:
f(x) = 3x² - 4x + 0
or
f(x) = 3x² - 4x + 0x^0
Note that the constant term is zero, which is not necessary to write, but it is standard to include it.
So, the standard form of the quadratic function is f(x) = 3x² - 4x.
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Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.
No. of players = 29
No. of coaches = 4
Total fabric used for headbands = 773.85 inches
Total no. of people for headbands = 29 + 4
= 33
Fabric used for headband for 1 person = 773.85/33
= 23.45 inches
Total fabric used for wristbands = 279.56 inches
Total no. of people for wristbands = 29
Fabric used for headband for 1 person = 279.56/29
= 9.64 inches
Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.
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Suppose Deandre places $5000 in an account that pays 8% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
The amount in the account at the end of 1 year is $5400.
The amount in the account at the end of 2 year is $5832.
What do you mean by interest rate?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
According to data in the given question,
We have:
Deandre places $5000 in an account that pays 8% interest compounded each year.
And no withdrawals are made from the account.
Now, we need to determine the amount of 8% interest on the $5000,
\(=\frac{5000}{100}*8\\ =400\)
Then, the amount in the account at the end of 1 year =$5000+$400
=$5400.
Now, we need to determine the amount of 8% interest on the $5400,
\(=\frac{5400}{100}*8\\ =432\)
So, the amount in the account at the end of 2 year =$5400+$432
=$5832.
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chase deposits $7440.93 into a savings account that pays a simple annual interest rate of 1.23%
Answer:
To find how much money Chase will get in a certain amount of years, set up the following equation:
(7440.93*0.0123)*x = y
Plug in x. "x" stands for how many years Chase keeps the money in his account while earning interest.
Keep "y" unknown, as that stands for what you are trying to solve for, which is how much interest money Chase will make.
AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC
Answer:
60°
Step-by-step explanation:
Arc BC and Angle BWC are the same number of degrees.
When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.
Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.
180° - 120° is 60°
Angle BWC is 60° so Arc BC is 60°
Please help. What is the solution to this system of equations using the linear combination method? {5x+y=24x+y=5 (0, 2) begin ordered pair 0 comma 2 end ordered pair. (−3, 17) begin ordered pair negative 3 comma 17 end ordered pair. (1, −8) begin ordered pair 1 comma negative 8 end ordered pair. (−2, 12)
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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HELP PLEASE.. Which of the following functions is graphed below?
Write an expression using the distributed property to dind the product of 7x63
The product of the expression 7 x 63 is 441.
We have,
To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:
7 x 63 = 7 x (60 + 3)
Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:
7 x (60 + 3) = 7 x 60 + 7 x 3
Simplifying further:
7 x 60 + 7 x 3 = 420 + 21
Therefore,
The product of 7 x 63 is 441.
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Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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A Solve each problem.
1. Henry flies his plane at 240 mph for 3 hours. How far does he travel?
Distance = speed x time
Distance = 240 x 3 = 720 miles
Answer:
henry doesn't travel but plane travel
Step-by-step explanation:
240m×3hour240m×60×60sec2592000m/sHi :) I was wondering if you could help, I'm mixed up about this one.
Answer:
the image is sideways
Step-by-step explanation:
Answer:
well buddy see you thinking to hard its right there just relax and look closely
Step-by-step explanation:
6. Rewrite y = √√4x+16 +5 to make it easy to graph using a translation. Describe the graph.
Answer:
~
Step-by-step explanation:
To make it easier to graph using a translation, we can rewrite the given equation as:
y - 5 = √√4x + 16
This is obtained by subtracting 5 from both sides of the equation.
The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.
Name the property shown.
(9 + 3) + 2 = 9+ (3 + 2)
Answer:
associative property
Step-by-step explanation:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like
Write an explicit formula for An, the nth term of the sequence 3,9, 27, ...
Step-by-step explanation:
Apparently the common ratio is
3
Explanation:
The 2nd term is 3
the 3rd=9=3²
the 4th= 27=3³
To get to the n
th term we will have to multiply n−1
times by 3
Or: tn=3n−1
PLS HELP I ONLY HAVE 30 MINS
Question 5 (4 points)
(04.02)
Determine whether the graph represents a proportional relationship. (4 points)
A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 10. Four points are shown on the graph on ordered pairs 0, 0 and 1, 3 and 2, 6 and 3, 7. These points are joined by a line. The label on the x-axis is Number of pans. The title on the y-axis is Number of cakes.
a
Yes, it is a proportional relationship because the graph goes through the origin
b
Yes, it is a proportional relationship because the graph is a straight line
c
No, it is not a proportional relationship because the graph is not a straight line
d
No, it is not a proportional relationship because the graph does not go through the origin
Answer:
C. It is not proportional because it is not a straight line.
Step-by-step explanation:
You can check to see if it is a straight line by setting up a table and ensuring that the values increase by the same amount every ordered pair.
------> The Answer Is C <------
Hope this helps have a good day :D
Miss Lianto mowed 2 7 of her lawn. Her son mowed 1 3 of it. Who mowed most of the lawn? How much of the lawn still needs to be mowed?
HURRY!!!!!!!!!!!!!!!!!!!!!!!!!
8/21 of the lawn still needs to be mowed.
To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.
Miss Lianto's fraction: (2/7) x (3/3) = 6/21
Son's fraction: (1/3) x (7/7) = 7/21
To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:
Combined fractions mowed: 6/21 + 7/21 = 13/21
So, Remaining fraction: 1 - 13/21 = 8/21
Therefore, 8/21 of the lawn still needs to be mowed.
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I NEED HELP WITH THIS ASAP!!
Answer:
no you can't get help in that
30
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining
eggs were white in color. Which equation can be used to solve for w, the number
of white eggs used last week?
A 231 +46w=0
B 46+ w = 231
C w = 231 +46
D 231 = 46w
D 231 = 46w can be used to solve for w, the number of white eggs used last week.
One of the corners of a cube is sliced off. The resulting cross section will have a minimum of how manysides.
A cross section is the plane resulting from cutting a solid.
If we cut a corner of a cube the resulting cross section will be a triangle and therefore it will have 3 sides.
5/2 is what in decimal form?
kathy plans to bake 2 types of cookies to take to the party. She needs to be sure she has enough ingredients. The chocolate chip cookies use 2 1/4 cups of flour, the sugar cookies use 2 2/3 cups of flour. How much flour will she need?
Answer:
I think she will need One and 1/2 cups of flour
Step-by-step explanation:
please let me if I RIGHT
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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Lydia sold pumpkin seeds at the County Fair. She used a graph to document
her sales. On the graph, what point represents the unit price?
Answer:
dang it can someone pls do this
Step-by-step explanation:
2
5. Many people believe that criminals who plead guilty tend to get lighter sentences than those
who are convicted in trials. The accompanying table summarizes randomly selected sample
data for defendants in burglary cases in a specific city. All of the subjects had prior prison
sentences. Use a 0.05 significance level to find the critical value needed to test the claim that
the sentence (sent to prison or not sent to prison) is independent of the plea.
Sent to prison
Not sent to prison
Guilty Plea
392
564
Not-Guilty Plea
58
14
(1 point)09.488
03.841
042.557
05.991
Answer:
Is 03.841
Step-by-step explanation:
To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.
In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.
To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.
The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.
Therefore, the correct answer is 03.841.
Letttt me jnowwwwwwww aspapppp!!!
am going through this and will send me an update tomorrow when you can get back in touch if we have time I would love for a bf of you and I was wondering what I could see for my bad credit cards at least once said that they have no interest and they are not going on the right back side and it doesn't look at the world with me anymore but it will take a little more longer then it might have gone out of there so much more to do it all the
Step-by-step explanation:
Firstly thaj, that's not her. that's not a real picture
Secondly, it's C. The answer is C because all the purple is below the line, making it negative so < since it's all bottom, we use y.
all bottom = y
all top = y
all left = x
all right = x
HELP ASAP NO LINKS PLEASE HELP
When 12x +10y is subtracted from -13x + 7y, we get
Answer:
- 25x - 3yStep-by-step explanation:
-13x + 7y - (12x +10y)
= - 13x + 7y - 12x - 10y
= - 13x - 12x + 7y - 10y
= - 25x - 3y (Ans)
-2 1/3 - (-5) =
Solve please
Answer:
2 2/3
Step-by-step explanation:
What is the area of this acute isoceles trinagle? It doesnt have a height so I am stumped.
Answer:
11.8 cm²
Step-by-step explanation:
Cosine rule: a ² = b ² + c ² - 2bc COS A
COS A = (b ² + c ² - a ²) / (2bc)
Area of triangle = ½ ab sin C
name the angle that joins the '3' side to either of the '8' sides. label that angle as A.
now, Cos A = (8² + 3² - 8²) / [(2)(3)(8)]
= 3/16.
A = inverse Cos (3/16)
= 79.193°.
Area of triangle = 1/2 ab Sin C (we'll just use letter A instead of C)
= 1/2 (3)(8) sin (3/16)
= 11.8 cm².
another way you can find it is by this simpler method:
think of one side of 8, the side of 3 and the height that you do not know by using Pythagoras' Theorem for right-angled triangle. (a² + b² = c²). go halfway up the '3' side, then cut across straight to where the '8' sides meet. we now have right-angled triangle. let's call the height you don't know h.
we have 1.5² + h² = 8²
h² = 8² - 1.5²
h² = 61.75
h = √61.75
so area = 1/2 X 1.5 X √61.75
= 11.8 cm²
What is the length of EF in the right triangle below?
D
26
10
E
F
The measure of side length EF in the right triangle is 24.
What is the measure of side length EF?The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the diagram:
Hypotenuse DE = c = 26
Leg DF = a = 10
Leg EF = b = ?
Plug in the values and solve for b:
c² = a² + b²
26² = 10² + b²
676 = 100 + b²
b² = 676 - 100
b² = 576
b = +√576 ( we take the positive value since we are dealing with dimensions)
b = 24
Therefore, the length EF is 24.
Option C)24 is the correct answer.
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