The minimum value of the expression 3x² + 6x + 6 is 3.
Therefore the answer is 3.
A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.
Minimum value of a quadratic equation of form ax² + bx + c is when
x = -b/ 2a
Then minimum value is
a( -b/ 2a )² + b( -b/ 2a ) + c
= (b²a + -2ab² + 4a²c)/ 4a²
= ( - b² + 4ac)/ 4a
= c - b²/4a
In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is
= 6 - 6²/ (4×3)
= 3
--The question is incomplete, answering to the question below--
"What will be the minimum value of the expression 3x² + 6x + 6?"
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when 7/11 is written as a decimal what is the sum of the fisrt twenty digits after the decimal point
PLEASE i relaly need help I just got brainly
I give twenty points
The first twenty digits after the decimal point of 7/11 when written as a decimal are: 6363636363636. The sum of these digits is 108.
At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $\$3.15$. Mary orders a bagel and a muffin, which comes out to $\$3.30$. Mary orders a piece of toast, two bagels, and three muffins, which comes out to $\$9.15$. How many cents does one bagel cost
On solving the question, by linear equation One bagel is 100*1.55 = 155 cents in dollars.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept.
A toast costs = x dollars.
A bagel costs = y dollars.
A muffin costs = z dollars.
It costs $3.15 for two pieces of toast and a bagel.
As a result, 2x + y = 3.15. To get the price of a bagel, we express x as a function of y,
2x = 3.15 —Y
x = -o.5y+ 1.575
It costs $3.30 for a bagel and a muffin.
Since x and z are functions of y,
—0.5y + 1.575 + + 3(3.3 — y) 9.15
—0.5y + 1.575 +2y + 9.9—3y = 9.15
—1.5y + 11.475 = 9.15
1.5y = 2.325
2.325
Y = 1.55
One bagel is 100*1.55 = 155 cents in dollars.
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Consider the rotation of figure WXYZ shown. Complete the statements about the transformation shown.
Answer:
Can you please show the picture
Step-by-step explanation:
5-115. Let us consider the difference between t(n) = 2 · 3" and f(x) = 2. 3
a) Is f(x) = 2 · 3 a function? Is t(n) = 2 · 3" a function? Why or why not?
Both f(x) = 2.3 and t(n) = 2.3" is not a function as they does not has any input variable.
f(x) = 2.3 is not a function because it's a constant value, it doesn't have any input x that could be used to produce a different output. It's just a number, and it's not a mathematical function.
t(n) = 2 · 3^n also doesn't represent a function because, again, it doesn't have any input n that could be used to produce a different output. It's also just a number, and it's not a mathematical function.
A mathematical function is a set of ordered pairs (input, output) such that for each input, there is only one output. A function must have at least one variable that can take different values and the output must depend on the input value. In other words, for each value of the independent variable, there is only one value of the dependent variable.
So, in the case of f(x) = 2.3 and t(n) = 2 · 3^n, there is no input variable that can produce different output, so they're not functions.
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Help please with this maths
The radius of the sphere is 9 cm.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere is 4/3πr³.
We have,
The surface area of a sphere = 324π cm²
4πr² = 324π
r² = 324/4
r² = 81
r = √81
r = ±9
r = -9 cm (rejected)
r = 9 cm
Thus,
The radius is 9 cm.
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h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does hhh have a negative average rate of change?
The required interval is (-∞, 0) for which the given function h(x) = x² - 1, has the negative rate of change.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given expression,
h(x) = x² - 1
Since the above expression is of parabola, which has a decreasing curve from (-∞, o), simultaneously the function shows the negative rate of change until the function is decreasing, So the required interval for which the function shows the negative rate of change is (-∞, 0).
Thus, The required interval is (-∞, 0) for which the given function h(x) = x² - 1, has the negative rate of change.
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Start with a circle whose equation is (x-a)^2 + (y-b)^2=r. Dilate that circle by a scale factor of 1/r with center of dilation (a,b). What does this transformation demonstrate
The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).
A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.
To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor
k, (x,y) --> (a + k(x-a), b + k(y-b)).
Substituting in our values, we get
(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).
Setting this equal to (a,b), we get
(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).
Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).
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find the rate of change y=−√x−4 +5
The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
what is a square root ?A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.
given
Use the average rate of change formula to substitute.
(√1)−(√−4) / (1)−(−4)
Condense the phrase.
1/5−2i/5
The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.
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g(n)=-3n-4; Find g(-8)
Answer:
g(- 8) = 20
Step-by-step explanation:
substitute x = - 8 into g(x) , that is
g(- 8) = - 3(- 8) - 4 = 24 - 4 = 20
Jaimie ran 3 1/2 on Monday. She ran half
as far on Tuesday as she did on Monday. How
far did Jaimie run in all on Monday and
Tuesday?
Answer: So Jamie ran 3 1/2 miles on Monday and half that distance on Tuesday. We need to know how far she ran "in all" which are key words for "addition".
We need to add 3 1/2 + (1/2)(3 1/2)
It's probably easiest to do this by converting to an improper fraction.
So let's convert:
3 1/2 is the same as 7/2. now we can rewrite the problem:
7/2 + (1/2)(7/2)
= 7/2 + 7/4 . Now we need a common denominator:
7/2 = 14/4
Now we have 14/4 + 7/4 = 21/4. Now we should convert to a mixed number.
21/4 = 5 1/4
So Jamie ran 5 1/4 miles in all.
Step-by-step explanation:
Answer:
5.25 or 5 1/4 (Whichever you prefer)
Step-by-step explanation:
To make it simpler, we will convert 3 1/2 to decimal format.
First, take 3 and multiply it by the denominator 2 of 1/2, then add that number to the numerator of 1/2
3 x 2=6 -> 6+1=7
now add the denominator 2 under 7 and we now have 7/2, the equivalent to the mixed number 3 1/2
Afterward, to get the decimal, divide the numerator by the denominator:
7 divided by 2= 3.5
Now halve 3.5 to get the number Jaimie ran on Tuesday -> 1.75
Then add both 3.5 (3 1/2) and 1.75 (1 3/4), to get 5.25 or 5 1/4, which is your answer.
What is a zero degree polynomial?
Any polynomial whose coefficients are all equal to zero is said to be a zero polynomial. As a result, the zero polynomial's degree is either undefined or set to -1.
The largest exponential power in a polynomial equation is called the polynomial's degree. Any polynomial's degree is determined only by its variables; coefficients are should be disregarded. The degree of a polynomial is given for an nth degree polynomial function with real coefficients and x as the variable with the largest power n, where n accepts whole integer values: p (x) = [tex]$$p(x)=a_n x^n+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+\ldots+a_1 x^1+a_0$$[/tex] in standard form is given as 'n'.
The largest power of a variable in a polynomial equation is the polynomial's degree. Only terms with variables are taken into consideration when calculating the degree of a polynomial function. The degree of a polynomial is determined by the variable term's maximum exponential power.
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four-part spinner is spun once. spinner with four parts labeled Q, R, S, and T List the sample space for the experiment. S = {Q, R, R, T} S = {Q, R, S, T} S = {R, A, T} S = {S, Q, Q}
The list of the sample space is s = {Q, R, S, T}. Option B is the correct option.
What is the sample space?
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
The random experiment's sample spaces are written in curly brackets, "{ } ".
Given that a spinner wheel has four parts. It is labeled with the names Q, R, S, and T.
The elements of sample space are Q, R, S, and T.
The sample space is a set, thus write the elements in curly brackets.
The sample space is s = {Q, R, S, T}.
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Find the number of terms and the degree of this polynomial.
Answer:
Terms = 2
Degree = 10
Step-by-step explanation:
Terms are the values appearing separated by the the mathematical sign. for this question we have 2 terms only.
the degree of a polynomial is usually the largest degree of the individual terms. for our question it's degree 10 since it's the highest.
I have 460 less than dotun.altogether we have 1280.how much do we each have
The main unknown at this point is "the number of adult tickets." The "number of children's tickets" is another factor that is unknowable. In order to assign two variables, do as follows:
Let a = # of adult tickets
and c = # of children's tickets.
What is meant by variables?Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.
Setting up the equations using the unknowns that follow the word problem is the next step. Here are the details:
There are 460 tickets total because there are an adult ticket and a child ticket.
a + c = 460.
Now that we know we want to find the number of adult tickets, we can translate the basic equation a + c = 460 into terms of a:
a + c = 460
-a = -a (For example, use -a to delete a from the left side of the equation on either side.)
c = 460 - a
We can now enter the equation c into the other equation, 8.75a + 3.50c = 3143, since we have the equation c expressed in terms of a.
Now, we need to find the value of c in the first equation so that we can plug it into the second equation:
292 + c = 460
-292 = -292
c = 168
(8.75 × 292) + (3.50 × 168) = 3143
2555 + 588 = 3143
3143 = 3143
Therefore, We each have 3143
The complete question is:
For a show adult tickets are $8.75 and children's tickets are $3.50. 460 tickets were sold for a total of 3143 how many adults tickets were sold?
Adult ticket = 8.75
child ticket = 3.50
460 tickets we're sold totaling 3143
how many adults tickets were sold
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During a science experiment, a chemist boils a liquid and then sets it on the lab table and records the temperatures as it cools. The graph shows , the temperature in degrees Centigrade, and is the number of after the liquid is set on the table. Liquid Temperature Time () Which equation is the best model for this data?
The exponential function that best models this data is given as follows:
C. y = 80(0.75)^x + 20.
How to define the exponential function?An exponential function, considering it's asymptote, is defined as follows:
y = a(b)^x + c.
In which the parameters are given as follows:
a is used to define the initial value.b is the rate of change.c is the horizontal asymptote.From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:
c = 20.
When x = 0, y = 100, hence the parameter a is obtained as follows:
100 = a(b)^0 + 20
a + 20 = 100
a = 80.
When x = 5, y = 40, hence the parameter b is obtained as follows:
40 = 80b^5 + 20
80b^5 = 20
b^5 = 1/4
b = (1/4)^(1/5)
b = 0.75. (approximately).
Hence the function is defined as follows:
y = 80(0.75)^x + 20.
Meaning that the correct option is given by option C.
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What function f(x) has the property where f'(x) is equal to 2f(x)?
Answer:
u not get the answer
Step-by-step explanation:
A bag contains 10 pieces of paper, numbered 1 through 10with a different number on each piece of paper. A second bag contains 8 pieces of paper, numbered 20 through 27with different number on each piece of paper. One piece of paper is drawn random from each bag. What is the expected value of the sum of the numbers on the two selected pieces of paper
To find the expected value of the sum of the numbers on the two selected pieces of paper, we need to calculate the probability of each possible outcome and then multiply that probability by the value of the outcome. The expected value of the sum of the numbers on the two selected pieces of paper is 6.1625.
Therefore the answer is 6.1625.
The possible outcomes for the first bag are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, each with a probability of 1/10.
The possible outcomes for the second bag are 20, 21, 22, 23, 24, 25, 26, 27, each with a probability of 1/8.
The possible outcomes for the sum of the numbers on the two selected pieces of paper are:
(1,20) ,(1,21) ,(1,22) ,(1,23) ,(1,24) ,(1,25) ,(1,26) ,(1,27)
(2,20) ,(2,21) ,(2,22) ,(2,23) ,(2,24) ,(2,25) ,(2,26) ,(2,27)
(3,20) ,(3,21) ,(3,22) ,(3,23) ,(3,24) ,(3,25) ,(3,26) ,(3,27)
...
(10,20) ,(10,21) ,(10,22) ,(10,23) ,(10,24) ,(10,25) ,(10,26) ,(10,27)
The expected value of the sum of the numbers on the two selected pieces of paper is the sum of the products of each possible outcome and its corresponding probability.
The probability of each outcome is (1/10) * (1/8) = 1/80
So the expected value of the sum of the numbers on the two selected pieces of paper is
(1 + 21)×(1/80) + (1 + 22)×(1/80) + (1 + 23)×(1/80) + (1 + 24)×(1/80) + .... + (10 + 27)×(1/80) = (21 + 22 + 23 + 24 + ... + 37)/80
= (20×17 + 1 + 2 + ... + 17)/80
= (340 + 17×(17 + 1)/ 2)/ 80
= (340 + 17×9)/ 80
= 6.1625
So the expected value of the sum of the numbers on the two selected pieces of paper is 6.1625
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Helpppp pleaseeeeeeeee
Answer:
Step-by-step explanation:
What is the slope of the line passing through the points − 3 4 and 2 − 1?
Therefore, the slope of the line passing through the points (-3,4) and (2,-1) is -1
What is a Straight Line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. The term "line" may also be used to describe a line segment in daily life that contains two locations that serve as its endpoints.
Define Slope.A line's steepness may be determined by looking at its slope. The slope is computed mathematically as "rise over run" (change in y divided by change in x). Also, The slope of a line is known as "m", is the ratio of the change in the y-coordinate to the change in the x-coordinate of two points on the line.
To find the slope of a line passing through the points (-3,4) and (2,-1), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, using the given points:
m = (-1 - 4) / (2 - (-3))
m = -5 / 5
m = -1
Therefore, the slope of the line passing through the points (-3,4) and (2,-1) is -1
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if you do 44 push ups in 4 minutes how many will he do in 5 minutes
Answer:
55
Step-by-step explanation: i think
Answer:
Step-by-step explanation:
it would be 55 because he does 11 each minute.
What is the range of f?
A. -3<_f(x)<_7
B. The f(x)-values -3,3,6, and 7
C. -6<_f(x)<_6
D. The f(x)-values -6,-4,-3, and 6
The range of f is C.
What is range?
Range is the difference between the highest and lowest values in a set of data. It is a measure of variability, providing an indication of how widely values in the data set are dispersed from one another. In statistics, range is an important tool that helps to describe and summarize data. Range is also used to measure the dispersion of data within a data set, including the degree of spread or variability in the data.
-6<_f(x)<_6. This means that the f(x)-values range from -6 to 6, including -4 and -3. The range of f does not include -3, 3, 6, and 7, which are not within the range of -6 to 6.
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Given f(x) = -x² - 2x + 12, find f(8)
Answer:
f(8) = -68
Step-by-step explanation:
f(x) = -x² - 2x + 12
f(8) = ?
We just need to put 8 in for the x and solve it
f(8) = -(8)^2 -2(8) + 12
f(8) = -64 -16 +12
f(8) = -80 + 12
f(8) = -68
Can someone please help me? :(
Step-by-step explanation:
send the pic clearly i will help surely im sorry
The local sports team donated 200 meal vouchers and 24 jerseys for a fundraising event. 125 vouchers and 20 jerseys were part of a raffle . The ratio of tickets sold to raffled items was 8:1; each ticket was sold for $3.50. How much money was raised from the raffle
On solving the provided question, we can say that by linear equation $249.67 money was raised from the raffle
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
the linear equation that can be formed is
200x + 24 y = 3.50
125 x + 20y = 5
ratio = 8:1
so, $249.67 money was raised from the raffle
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What is the range of the data set please help out!
4 is the range of the data set in the given set.
What is range data set?The space between the highest and lowest values in a data collection is known as the range. Similar units to the data are used to quantify variability. Variability is increased with larger values. The range has several limitations but is the most straightforward statistical measure of dispersion to compute and comprehend.
This means that the range might alternatively be described as the distance between the highest and lowest observation.
In the given data set,
range = maximum frequency - minimum frequency
range = 5 - 1
range = 4
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What is the domain of the function y=^3 sqrt X
The circumference of a circle B is 80% of the circumference of circle A.
a) Find the ratio of the area of circle A to the area of circle B, giving your
answer in the form 100:n
100 :
(2)
Square E has sides of length e cm.
Square F has sides of length fcm.
The area of square E is 69% greater than the area of square F.
b) Work out the ratio of e:f
Your final line should say, Ratio of e:f is
(2)
The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.
The area of the circle is equal to the multiplication of the square of the circle's radius and π.
A = πr²
where 'r' is the radius
Circumference of circle A × 0.8 = circumference of circle B
So, taking r as the radius of A,
2πr = circumference of circle A
2πr × 0.8 = circumference of circle B
So the radius of B is r × 0.8.
Now we can substitute that in the area equations :
Area of A = π×r²
Area of B = π × (r × 0.8)² = π × r² × 0.64
The circumferences of the A to B ratio is
Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)
= 1: 0.8 = 100: 80,
The areas of circle A to circle B ratio is
Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64
e² = f² × 1.69
69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.
We have this equation:
e² = f² × 1.69
Apply the square root on both sides.
e = f × √(1.69) = f × 1.3
e/f = 1.3 = 1.3/1 = 13/10
the ratio e:f = 13: 10
Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.
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what is m for y = 7x - 17
On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y = 7x - 17
at x= 0
y = -17
and m = -17
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could one side length of a function ever produce two different perimeters?
Answer: A perimeter is the total length of all the sides of a polygon. It is calculated by adding up the lengths of all the sides of the polygon. For a polygon with distinct and non-overlapping sides, each side length contributes exactly once to the perimeter. So in such case, a side length of a polygon can never produce two different perimeters.
However, it's worth mentioning that, one side length of a function could be a side of a polygon and the other could be a side of another shape. Also, it's possible that a single side length of an object is connected to a different set of side length, generating different perimeters.
For example, the length of an arc of a circle can be considered as a "side length" of the circle and it can be used to calculate both the perimeter of the arc and the circumference of the full circle, which are different measurements.
Also, a circular pool has a radius, but it's perimeter is the circumference, and this length is produced by the same radius but it's a different perimeter from the length of the radius.
In summary, a side length can produce different perimeter if we are talking about different shapes and measurements.
Step-by-step explanation:
Which of the following is a perfect square trinomial?
(A) 5x2 - 5x + 1
(B) 5x2 - 10x + 5
(C) 10x2 - 20x + 5
(D) 25x2 - 20x + 3
(E) 25x2 + 20x + 4
Answer:
B is the perfect square
Step-by-step explanation: