Answers
Answer:
3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21
4. The solutions are, x = -2 + √10 and x = -2 - √10
5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;
f(x) = x² - 6·x + 10
Step-by-step explanation:
3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c
The vertex form of the of a quadratic function can be presented based on the above standard form as follows;
f(x) = a(x - h)² + k
Where;
(h, k) = The coordinate of the vertex
h = -b/2a
k = f(h)
Comparing with the given equation, we have;
f(x) = a·x² + b·x + c = x² - 4·x - 17
a = 1
b = -4
c = -17
∴ h = -(-4)/(2 × 1) = 2
h = 2
k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21
k = -21
The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;
f(x) = (x - 2)² - 21
4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12
Dividing the given equation by 2 gives;
x² + 4·x = 6
Which is of the form, x² + b·x = c
Where;
a = 1
b = 4
c = 6
From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²
Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;
x² + 4·x + 4 = 6 + 4
(x + 2)² = 10
x + 2 = ±√10
x = -2 ± √10
The solution are, x = -2 + √10 and x = -2 - √10
5. Given that the value of the vertex = (3, 1), and a = 1, we have;
The vertex, (h, k) = (3, 1)
h = 3, k = 1
Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)
∴ -b = 2 × 3 = 6
b = -6
k = f(h) = a·h² + b·h + c, by substitution, we have;
k = f(3) = 1 × 3² + (-6) × 3 + c = 1
∴ c = 1 - (1 × 3² + (-6) × 3) = 10
c = 10
The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;
f(x) = x² - 6·x + 10
Related Questions
A school had 300 students in 2013 and 450 students in 2015. What was the average rate of growth in student per year?
Answers
[tex]450 - 300 = 150 \\ 150 \div 2 = 75t \\ the \: average \: rate \: of \: growth \: per \: year \: is \: 75 \: student \: per \: year[/tex]
carol decides to send out a survey to see what her coworkers think of the new dress code policy. if she chooses a sample of the population that gives each person an equal chance of participating, this would be a(n) sample.
Answers
This is the random sampling is used in the statement.
According to the statement
We have to find that the about the sampling.
So, For this purpose, we know that the
A sample is an outcome of a random experiment. once we sample a chance variable, we obtain one specific value out of the set of its possible values. that exact value is termed a sample.
From the given information:
if she chooses a sample of the population that offers everyone an equal chance of participating, this might be a(n) sample.
Then
According to this, there is random sampling is used.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
So, This is the random sampling is used in the statement.
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This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other.
A
M
B
b. Name a pair of line segments with the same length.
Answers
Here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. Since both segments begin at point B, their lengths are equal.
Both segments begin at point B, their lengths are equal.
Since the radius of the smaller circle is the distance from its center (B) to its edge, length BD equals length AB.
Using the attached diagram
The larger circle's center is at C, while
Point B is the location of the smaller circle's center.
The smaller circle passes through the larger circle, dividing it into two segments, BD and AB, which extend from the smaller circle's center to their intersecting edges.
As a result, since both segments begin at point B, their lengths are equal.
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F (n) = 3n-1
(n) = n² - 2n-3.
д.с
Find F(g(9))
Answers
The function F(g(9))= 179
Given ,Function F (n) = 3n-1
g(n) = n² - 2n-3
g(9)= 9²-2(9)-3
= 81-18-3
g(9) = 60
F(g(9))=F(60)
= 3(60)-1
= 179
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.
The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.
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enter the expression −2c⃗ 6d⃗ in the answer box using the notation just described. express your answer in terms of c⃗ and d⃗ . use the vector button under the templates menu in the answer box to create vectors.
Answers
The expression [tex]-2\vec C+6\vec D[/tex] in the ordered pair notation is (16,-16).
The vector components of a vector are represented as the ordered pair of its x and y components.
For example, if a vector has x - component 'a' and y- component 'b' , then the ordered pair notation for the vector is (a, b), where the vector is [tex]a \vec i+b \vec j[/tex].
Now the vector C has its x- component = -2
y- component of C = -1
Therefore, ordered pair notation of C = (-2, -1)
x- component of D = 2
y-component of D = -3
Therefore, ordered pair notation of D = (2,-3)
So the expression [tex]-2\vec C+6\vec D[/tex] = -2 (-2,-1) +6 (2,-3) = (4,2) + (12, -18)
= (16, -16) in the ordered pair notation.
That is, the vector [tex]\bold {-2\vec C+6\vec D}[/tex] is a vector with x-component 16 and y-component -16.
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is a proper subset different from a regular subset? is an empty set a proper subset? provide an example of a set for your classmates to solve for both a proper subset and an empty set. check and respond to the replies to your examples.
Answers
yes proper subset is different from a regular subset. The empty set is a proper subset of every set except for the empty set
A proper subset of a set A is a subset of A that cannot be equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.
Subset: If A and B are sets and every element of A is also an element of B, then:
A is a subset of B, denoted by A ⊆ B.
or equivalently, B is a superset of A, denoted by B ⊇ A.
Any set is considered to be a subset of itself. No set is a proper subset of itself. The empty set is a subset of every set. The empty set is a proper subset of every set except for the empty set.
For example, A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A = {1, 2, 3} and B = {1, 2, 3}
Here, A is a subset of B, or we can say that B is the superset of A.
Proper Subset: If A is a subset of B, but A is not equal to B (that is, there exists at least one element of B which is not an element of A), then
A is also a proper (or strict) subset of B; this is written as A ⊊ B.
For example A = {1, 2, 3} and B = {1, 2, 3, 4}.
Clearly, A is not equal to B and element {4} belongs to set B but is absent in set A, so we have one element in set B which is not an element of set A. Thus, A can be called a proper subset of B.
Hence, a proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B, thus the proper subset may or may not be the same.
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2(3x-2)-4x+1= 9 solve for x
Answers
Answer:x=6
Step-by-step explanation:
6x-4-4x+1=9
subtract 1 from both sides
6x-4-4x=8
add 4 to both sides
6x-4x=12
subtract 6x by 4x
2x=12
divide by 2 on both sides
x=6
Graph the image of the
quadrilateral below using a scale
factor of & = 3/2.
Answers
The coordinates of the vertices of the image are Q'(x, y) = (- 1.5, 6), T'(x, y) = (0, - 3), R'(x, y) = (1.5, 3) and S'(x, y) = (3, - 3), respectively.
What is the image of a quadrilateral after applying a dilation factor?
A dilation is a kind of rigid transformation, that is, a transformation applied on geometric loci such that its Euclidean distance is conserved. According to the statement, we must the following dilation to generate the image:
P'(x, y) = (3 / 2) · P(x, y)
If we know that Q(x, y) = (- 1, 4), T(x, y) = (0, - 2), S(x, y) = (2, - 2) and R(x, y) = (1, 2), then the vertices of the images are:
Q'(x, y) = (3 / 2) · (- 1, 4)
Q'(x, y) = (- 1.5, 6)
T'(x, y) = (3 / 2) · (0, - 2)
T'(x, y) = (0, - 3)
R'(x, y) = (3 / 2) · (1, 2)
R'(x, y) = (1.5, 3)
S'(x, y) = (3 / 2) · (2, - 2)
S'(x, y) = (3, - 3)
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2. Does being able to use a sequence of rigid transformations to specify how one shape
got to another shape prove that two shapes are congruent? Why or why not?
Answers
If two shapes can be mapped onto one another using rigid transformations, then yes, they can be said to be congruent.The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.
Two shapes are considered to be congruent if they can be mapped onto one another using rigid transformations (a sequence of one or more rotations, translations, and reflections). A congruent triangle is produced by any series of rigid transformations applied to a triangle.
Now, let's learn about Rigid transformation
A rigid transformation of the plane, also known as an isometry, keeps length intact. "Rigid transformations" include reflections, translations, rotations, and combinations of these three transformations.
Example: The preimage of right angle triangle and a right angle triangle are the example of congruent shapes.
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Graph y = -1/-3 x + 4
Answers
can someone help me please
Answers
Answer:
-175
Step-by-step explanation:
thats the answer to the question
Find value of x.
3x + 6 - 6 = 248
Answers
Answer:
x=82.7
Step-by-step explanation:
3x+6-6=248
3x=248
x=82.7
Answer:
[tex]82.6[/tex]Step-by-step explanation:
Simplify both sides of the equation:3x + 6 − 6 = 248
3x + 6 + − 6 = 248
( 3x ) + ( 6 + − 6 ) = 248 (ℂ )
3x = 248
Divide both sides by 3:3x / 3 = 248 / 3
x = 248 / 3
x = 82.6
if the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. find the third integer.
Answers
The value of third consecutive odd is 23
• In Mathematics, algebra is a branch which only deals with symbols and the rule for the manipulation of these symbols. Algebra is divided into different sub branches such as advanced algebra, linear algebra, elementary algebra, abstract algebra etc.
• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic four operations of algebra are addition, subtraction, multiplication, division.
Let the first consecutive odd integer be x
Second consecutive integer = x+2
Third consecutive integer = x+4
We are given that
First + third = 5(Second) – 63
x + x + 4 = 5 (x+2) -63
2x + 4 = 5x +10 -63
-3x = -57
3x = 57
x = 19
First Consecutive odd = 19
Second Consecutive odd = 21
Third Consecutive odd = 23
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convert 15 feet per second into yards per hour using unit cancellation
Answers
Answer:
626 times 6261 plus 276262
Step-by-step explanation:
i buy 626 cookies and 1000 million water how much did i eat and drink?
5. What is the missing side length, x, in this
right triangle?
16 yd
20 yd
A.
4 yards
B.
8 yards
C. 12 yards
D. 16 yards
X
5
Answers
Answer: 12
Step-by-step explanation: we know that a^2 + b^2 = c^2, pythagorean theorem. We're given a and c in this case, which are 16 and 20 respectively. so that means 16^2 + x^2 = 20^2. After evaluating the equation, we get 256+ x^2 =400. now subtract 256 from both sides and then we get x^2 = 144. take the square root of both sides and we end up with x = 12.
If 1 is added to a number and the sum is tripled, the result is 11 more than the number. Find the number
Answers
[tex] \large{ \star \boxed{ \tt \: Answer : \boxed{ \tt{4}}}}[/tex]
Please see the attached picture for full solution !
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what the product of 6 and x
Answers
Answer:
6x
Step-by-step explanation:
Because, 6 multiplied by x, we know that if there is just an x, we add a 1, so it would be 1x. 1x multiplied by 6 is 6x.
Hope this helps you!
Answer:
6x
Step-by-step explanation:
The product means multiply
6*x
6x
Suppose a function has a local max of (-1, 3) what can you conclude if the function is even? what can you conclude if the function is odd?
Suppose your function is increasing from the interval [2,5] what can you conclude if the function is even? what can you conclude if it is odd?
Answers
Using the concept of even and odd functions, it is found that, considering the function has a local max at (-1,3):
If the function is even, it will have another local max at (1,3).If the function is odd, it will have a local min at (1,-3).For a function increasing on [2,5], we have that:
If the function is even, it will be decreasing on [-5,-2].If the function is odd, it will be increasing on [-5,-2].What are even and odd functions?In even functions, we have that f(x) = f(-x) for all values of x.In odd functions, we have that f(-x) = -f(x) for all values of x.If none of the above statements are true, the function is neither.Hence, considering the function has a local max at (-1,3):
If the function is even, it will have another local max at (1,3).If the function is odd, it will have a local min at (1,-3).For a function increasing on [2,5], we have that:
If the function is even, it will be decreasing on [-5,-2].If the function is odd, it will be increasing on [-5,-2].For even functions it will decrease because we have that f(4) > f(3), for example, hence f(-4) > f(-3).
For the odd function it will increase because if f(4) > f(3), then f(-3) > f(-4) due to the negative signal.
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Part B
A new machine with better technology produces 210 gel pens every fifteen minutes. What is the constant of proportionality in the relationship between the number of gel pens and the number of minutes
The constant of proportionality i
Answers
Proportionality constant of p is = 14 t
WHAT IS PROPORTIONALITY CONSTANT ?The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.
CALCULATIONy = kx
The rate k = 210 ÷ 15 = 14 gel pens per minute
"p" is number of pens, "t" is number of minutes
p = 14t
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Which has the greater area, the space between the circle and the inside square or the space between the circle and the outside square. The length between one corner to the opposite corner of the inside square is equal to 10
Answers
Answer:The space between the circle and the outside circle
Step-by-step explanation:
The space between the circle and the outside circle
What is the image point of (9, -2) after a translation right 1 unit and down 1 unit
Answers
Answer:
( 10 , -3 )
Step-by-step explanation:
→ See which coordinate is affected by a translation right
x
→ Apply
( 10 , y )
→ See which coordinate is affected by a translation down
y
→ Apply
( 10 , -3 )
Nesecito ayuda es con procedimiento
Answers
Evaluando la expresión:
b^2*(c + d) - a^2*(m + n) + 2x
En los corresopondientes valores obtendremos:
b^2*(c + d) - a^2*(m + n) + 2x = 161/6
¿Como evaluar expresiones matematicas?
Veamos la segunda expresión en la imagen, está es:
b^2*(c + d) - a^2*(m + n) + 2x
Uso está por que es la unica que puedo leer bien en la imagen.
Queremos evaluar está expresion, se nos dan los valores:
a = 1 d = 4
b = 2 m = 1/2
c = 3 n = 2/3
p = 1/4 x = 0
Solo hay que reemplazar las variables por los números correspondientes. Si reemplazamos x por 0 obtendremos:
b^2*(c + d) - a^2*(m + n) + 2*0 = b^2*(c + d) - a^2*(m + n)
Ahora reemplacemos c = 3 y d = 4:
b^2*(3+ 4) - a^2*(m + n) = b^2*7 - a^2*(m + n)
Ahora remplazamos m y n, asi obtendremos:
b^2*7 - a^2*(1/2 + 2/3) = 7*b^2 - (3/6 + 4/6)*a^2 = 7b^2 - (7/6)*a^2
Finalmente reemplazamos b y a, asi obtendremos:
7*(2)^2 - (7/6)*1^2 = 7*4 - 7/6 = 28 - 7/6 = 161/6
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What is the measure of angle ABE?
Please help!
Answers
Answer:
50 degrees
Step-by-step explanation:
The angle of ABE is opposite to angle CBD, which means that ABE = CBD
It is a math rule, all opposite angles are equal.
The festival that the total attendance for 2014 will be twice the attendance in 2012. What is the projected attendance for 2014?
Answers
The projected attendance for 2014 in the form of linear equation is written as y = 2x.
What is linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero.
For instance, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.The solution to such an equation is just a pair of values, one is for x and one for y, which also equalizes the 2 sides of an equation.Now, for the given question;
Let us consider that the total attendance in 2012 be 'x'.
And the total attendance in 2014 be 'y'.
Then, the total attendance for 2014 will be twice the attendance in 2012.
Thus,
y = 2x.
Therefore, the linear equation which shows the condition that the total attendance for 2014 will be twice the attendance in 2012 is y = 2x.
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can you simply sq 3 + 5? yes or no and why?
Answers
Without decimals no
solve for x
3/9 = x/12
Simplify your answer as much as possible.
Answers
Answer:
Step-by-step explanation: We can begin by rewriting the equation. That would look like so:
3/9 = x/12
We need to solve for x. Our first step is to identify a common denominator. Let's list the multiples of each denominator.
9: 9, 18, 27, 36
12: 12, 24, 36
Our common denominator is 36.
Now, let's cross multiply:
3 x 12 = 36
9 x ? = 36
36 ÷ 9 = 4
x = 4
Final answer: 3/9 = 4/12, where x = 4.
What expressions are equivalent to the given expression
Answers
The value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex], that is, option 5.
An exponent is a number or variable that is placed above and to the right of the expression to which it applies. It tells us the number of times the expression is used as a factor.
Here, we are given an expression as follows-
To simplify this expression we can use the following property of exponentials-
[tex]a^{l} a^{k} = a^{k+l}[/tex]
This holds true for all real values of a, k and l.
Thus, we can write the given expression as-
[tex]y^{-8} y^{3} x^{0} x^{-2} = y^{-8+3} x^{0-2}[/tex]
= [tex]y^{-5} x^{-2}[/tex]
Thus, the value of the given expression is equivalent to [tex]y^{-5} x^{-2}[/tex].
From the given options, thus, option number 5, is the correct answer.
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A rectangular carpet measures 10 m by 6m
Part of the carpet is covered by a square rug of length 2 m
2m
10m
Diagram not drawn accurately
6m
What fraction of the carpet is
covered by the rug?
Give your answer in its simplest form.
Optional working
Answer:
Answers
Hope it helps …
The fraction of the carpet covered by the rug will be 1/15.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L×W square units
A rectangular carpet estimates 10 m by 6m. Some portion of the rug is covered by a square rug of length 2 m.
The area of the carpet is given as,
A = 10 x 6
A = 60 square meters
The area of the rug is given as,
a = 2 x 2
a = 4 square meters
A fraction of the carpet is covered by the rug is given as,
⇒ 4 / 60
⇒ 1 / 15
A fraction of the carpet covered by the rug will be 1/15.
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The missing diagram is attached below.
7. One hundred three and one half gallons drained in the last 9 minutes from a pool. The water drains at a constant rate. How many gallons drain per minute from the pool?
Answers
The Number of Gallons drained per minute from the pool is; 931.5 gallons drained per minute
What is the constant rate?Constant rate is simply a rate that remains unchanged regardless of change in parameters.
Now, we are told that One hundred three and one half gallons drained in the last 9 minutes from a pool. Thus;
Amount of gallons that drained from pool = 103¹/₂ gallons = 207/2 gallons
Time it took to drain = 9 minutes
Thus;
Number of Gallons drained per minute from the pool = (207/2)/9
Number of Gallons drained per minute from the pool = (207 * 9)/2
Number of Gallons drained per minute from the pool = 931.5 gallons drained per minute
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Consider the data set
5 2 2 4 9 2 3 1
Find the average (mean):
Find the median:
Answers
Answer:
Step-by-step explanation:
4+2=6
6/2=3