Answer:
[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]
Step-by-step explanation:
Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)
So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]
we can change the function by changing the value of the constant "a".
we can use two arbitrary values, but in this example I'll use -1 and 1.
this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]
these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.
In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form
[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]
We can also expand the other function similarly.
[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]
In ΔEFG, is it possible for segment GE to measure 6 units?
According to the triangle inequality theorem, the measure for the third side can be GE = 6 units, because: A. 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that the set of side measurements that will form a triangle will be the set of side lengths whereby the sum of any two sides will be greater than the third side of the triangle.
For example, if a, b, and c are the side lengths of a triangle, then:
a + b > ca + c > bb + c > aThus, we have the given lengths:
FE = 3 units
FG = 5 units
Therefore, the third side length would be GE = 6 units based on the triangle inequality theorem because:
3 + 5 > 6
5 + 6 > 3
6 + 3 > 5
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write an equation in form of y=mx+b for a line with slope =7 and y-intercept =4
$m\angle U=2x\degree$ , and $m\angle V=2\left(m\angle U\right)$ . Find the value of $x$ that makes $\angle U$ and $\angle V$ complementary angles
The value of x that makes ∠U and ∠V a complement of each other is; x = 9
How to find Complementary Angles?
There are different equal angle theorems in math's such as complementary angles, supplementary angles, linear pairs e.t.c
Now, complementary angles are defined as angles that sum up to 90 degrees.
We are given that;
m∠U = 2x°
m∠V = 4m∠U = 4(2x)°
We want to find the value of x that makes ∠U and ∠V a complement of each other.
This means that by the definition of complementary angles, they will sum up to 90 degrees. Thus;
2x + 4(2x) = 90
2x + 8x = 90
10x = 90
x = 90/10
x = 9
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Complete question is;
m∠U = 2x°, and m∠V = 4m∠U. Which value of x makes ∠U and ∠V complement of each other? A. 25 B. 9 C. 36 D. 18
What is the remainder of 5x3 - 7x² + 2x + 1 divided by (x - 3)?
A.) 126
B.) 79
C.) 203
D.) 205
Answer: A
Step-by-step explanation:
To describe a specific geometric sequence, Jamie wrote the recursive formula: (Formula in picture)
Write the first five terms of this sequence.
If Jamie wrote the recursive formula [aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence, then the first five terms of this sequence are [2, 8, 32, 125 and 512]
As per the question statement, Jamie wrote the recursive formula
[aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence.
We are required to determine the first five terms of this sequence.
To solve this question, first we have to determine the values of "n" which goes as (n = 1, 2, 3, 4, 5, 6...)
Now, for (n = 1), (an = a₁ = 2), given in the question statement itself,
And using the question mentioned formula, for (n = 2),
[a₂ = {(a₍₂₋₁₎ * 4}]
Or, [a₂ = (a₁ * 4)]
Or, [a₂ = (2 * 4)]
Or, (a₂ = 8).
Similarly, for (n = 3), [a₃ = {(a₍₃₋₁₎ * 4}]
Or, [a₃ = (a₂ * 4)]
Or, [a₃ = (8 * 4)]
Or, (a₃ = 32).
For (n = 4), [a₄ = {(a₍₄₋₁₎ * 4}]
Or, [a₄ = (a₃ * 4)]
Or, [a₄ = (32 * 4)]
Or, (a₄ = 128).
For (n = 5), [a₅ = {(a₍₅₋₁₎ * 4}]
Or, [a₅ = (a₄ * 4)]
Or, [a₅ = (128 * 4)]
Or, (a₅ = 512)
Hence, the first five terms of this sequence are [2, 8, 32, 125 and 512].
Sequence: In mathematics, a sequence is an enumerated collection of objects in a particular order, and repetitions being allowed.To learn more about Sequences, click on the link below.
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(8r
2
−7r−9)+(−r
2
+r)
Answer:
12r -9
Step-by-step explanation:
(8r2−7r−9)+(−r2+r)
= 16r -7r -9 +2r +r
= 12r -9
is the number 19 a prime or composite number
Answer:
prime
Step-by-step explanation:
because 19 can only divide 1 and itself
Compute the probability of randomly drawing 10 cards from a deck and getting exactly 5 spades.
Enter the exact answer.
The probability of randomly drawing 10 cards from a deck and getting exactly 5 spades is 0.0468
Formula Required:
Given a set of n items, a group of k items can be chosen in any of the 'n' ways, where 'k' is the number of possibilities. The order in which the choices are made is not significant.
A typical deck of cards contains 52 cards in total. Therefore, there exist (52, 10) scenarios in which 10 cards could be chosen (without replacement) that are exhaustive, mutually exclusive, and equally likely.
Again, there are 13 spades in the entire deck of 52 cards. The remaining (10 - 5) = 5 cards can be drawn from the remaining (52 - 13) = 39 cards in the deck in (39, 5) ways, and 5 spades can be drawn from the 13 spades in (13, 5) ways.
As a result, there are (13, 5) * advantageous scenarios for choosing exactly 5 spades (39, 5)
Consequently, the necessary probability:
= Favorable number of cases for the event / Total number of all possible cases.
= (13 , 5) * (39 , 5) / (52 , 10)
(n, k) = n! / k! (n-k)!
= 0.0468
Therefore, the probability of 5 spades will be 0.0468
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2.if the m∠5 is 63° , find the measure of ∠3.
Show your work
Answer:
117°
Step-by-step explanation:
180-63=117°
so hope it help
Draw the graph of your= 2x +1
The graph of the equation y = 2x+1 has been plotted
The equation of the line is
y = 2x+1
The domain is defined as the set of all possible inputs of the function.
The range is defined as the set of all possible outputs of the function
Here the equation is y =2x+1, we have to substitute the different values for the x and find the values of y.
The values of the x will be the domain and the values of the y will be the range
At x= -2
y = 2(-2)+1
= -3
At x= -1
y = 2(-1)+1
= -1
At x= 0
y = 2(0)+1
= 1
At x=1
y = 2(1)+1
= 3
At x=2
y = 2(2)+1
= 5
Plot the graph using the values
Hence, the graph of the equation y = 2x+1 has been plotted
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Which 2 of the following are correct equations of the line passing through (2, -3) with a slope of five?
y+3 = 5 (x-2)
y= 5x -3
y= 5x + 13
y-3= 5 (x+2)
y= 5x -13
Answer:
The two equations that passes through (2, -3) and has a slope of five are:
y + 3 = 5(x - 2) and y = 5x - 13
Step-by-step explanation:
For the first equation, you get y equal to itself. To do that, you need to simplify the right side of the equation. For 5(x - 2), you will distribute the 5 to the x and -2, equalling to 5x - 10. Next, we subtract 3 from both sides to cancel out the 3 on the left side. The equation is now y = 5x - 13. The -13 is the y intercept so we start at the point (0, -13). Since the slope goes up by 5 for every one point it moves to the right, it will eventually reach the point (2, -3). In other words, you add 1 to the x value and 5 to the y value. The points will look like this: it starts at (0, -13) and goes to (1, -8) and goes to (2, -3). The second equation is equivalent to the first equation. Hopefully this helps you out!
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3≤x≤7 goes from least to greates
Given
Function f(x) , g(x) and h(x)
Find
Order of the function according to average rate of change
Explanation
Average rate of change can be given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex][tex]3\leq x\leq7[/tex]for f(x)
[tex]\begin{gathered} \frac{f(7)-f(3)}{7-3} \\ \\ \frac{-10-(-8)}{4} \\ \\ -\frac{2}{4} \\ \\ -\frac{1}{2} \end{gathered}[/tex]for g(x)
[tex]\begin{gathered} \frac{g(7)-g(3)}{7-3} \\ \\ \frac{7-(27)}{4} \\ \\ -\frac{20}{4} \\ \\ -5 \end{gathered}[/tex]for h(x)
[tex]\begin{gathered} \frac{h(7)-h(3)}{7-3} \\ \\ \frac{60-24}{4} \\ \\ \frac{36}{4} \\ 9 \end{gathered}[/tex]Final Answer
least to greatest = g(x) , f(x) . h(x)
correct option is 2.
f(x)=72/x - 11
f(72)=
How do I solve with fractions? (with answers)
Answer:
The answer is r = 3
Step-by-step explanation:
Hope this helps! :))
Please let me know if its incorrect
Trixie exclaimed , “hey! Arithmetic sequences are just name for linear functions.” What do you think ? justify your idea based on multiple representations
An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
"Arithmetic sequences are just name for linear functions", what you think?An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
By picking two consecutive words in the sequence and deducting the first from the second, we may get the common difference for a particular sequence.
The graph of linear function is a straight line. A function with the formula y=f(x)=ax+by=f(x)=ax+b is said to be linear.
Although not quite the same, arithmetic progressions resemble linear functions.
If the value nn is a full number, then the expression t(n)=2n-4t(n)=2n4 denotes a series, and the graph of this sequence will have distinct points (as shown below).
The expression f(x)=2x-4f(x)=2x4, where xx is any real number, on the other hand, denotes a function, and this function's line graph will be continuous (as shown below).
Although not quite the same, arithmetic progressions resemble linear functions.
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2x - 3y = -6please solve and graph
2x - 3y = -6
Solve for y:
-3y= -6-2x
y= (-2x-6) /-3
y= 2/3x+2
Slope intercept form:
y= mx+b
Where:
m= slope (2/3)
b= y-intercept (2)
So, to graph the function, we have to draw a line that crosses the y axis at 2, and for every 3 units moved to the right along the x-axis it goes up 2 units along the y-axis.
S. SURVEY In a survey of their favorite
subjects, 390 students said math was
their favorite. One tenth as many...
students said that history was their
favorite subject. How many students
said history was their favorite?
The total number of students who participated in the survey are 100.Given to us The number of students who choose other as their favorite subject = 20 studentsMath = 30%English = 45%Let the total number of students in the survey be x.What is the percentage of students who choose other as their favorite subject?We know that percentage is always 100%, therefore,Total number of students in the survey = other + Math +English100% = other + 30% + 45%100% - 30% - 45% = otherother = 25%Thus, the percentage of students who choose another as their favorite subject is 25%.What is the total number of students who participated in the survey?We know that the number of students who choose English as their favorite subject in the surveys is 20, therefore,25% of the total number of students = 20Hence, the total number of students who participated in the survey is 100.
Expand the brackets and simplify the
expression below.
8(3y + 2) + 4y
Answer:
28y+16
Step-by-step explanation:
8(3y+2)+4y
24y+16+4y
28y+16
The simplification of the given expression is 28y+16.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
We are given an expression as;
8(3y+2)+4y
we need to solve the expression
First open the bracket;
24y+16+4y
Solve the like terms;
28y+16
Therefore, the simplification of the given expression is 28y+16.
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Write your answer as a fraction in simplest form. 4/25x10
What type of reasoning is used to find the next amount of train cars? Explain your answer.
Answer: It's using the table of 2 to continue the pattern of trains.
in the first fig the no. of carton is 0.
for the next one it is 2 and the next 4.
the pattern will thus continue with the multiplication table of 2.
X =
y =
(3y + 2)
4x°
52°
TO GET Y I WILL USE THE REASON SUM OF ANGLES IN A TRIANGLE:
[tex]52 + 90 +( 3y + 2) = 180 \\ 52 + 90 + 2 +3 y = 180 \\ 3y = 180 - 90 - 52 - 2 \\ 3y = 36 \\ \frac{3y}{3} = \frac{36}{3} \\ y = 12[/tex]
y=12°
TO FIND X I WILL USE THE REQSON ALTERNATE ANGLES
[tex]4x = 52 \\ \frac{4x}{4} = \frac{52}{4} \\ x = 13[/tex]
x=13°
THEE ANGLES ARE INSIDE THE PARALLEL LINES :NOTE.
Evaluate XYZ squared if x = -2, y = 7, and z= -4.
The required value of XYZ squared would be 3136 which is determined by substituting x = -2, y = 7, and z = -4.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have to evaluate xyz squared if x = -2, y = 7, and z = -4.
⇒ (xyz)²
Substitute the values of x = -2, y = 7, and z = -4 in the above expression
⇒ [(-2) × (7) × (-4)]²
Apply the multiplication operation and we get
⇒ (56)²
⇒ 3136
Therefore, the obtained value of XYZ squared would be 3136 if x = -2, y = 7, and z = -4.
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Find the value of x *
55°
X
Step-by-step explanation:
Since right angle is equal to 90°,
90°-55°=35°
Solve for the value of w. * (8w+8)(9w-5)°
The solution for the value w is 13 in the equation 8w+8 = 9w-5.
What is an angle?Two rays, referred to as the angle's sides and vertex, come together to form an angle. Angles created by two rays are located in the plane where the rays are located.
Dihedral angles are formed when two planes intersect. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can also be used to define an angle between two intersecting curves.
Angle is a term used to describe the size of an angle or of a rotation. This metric represents the proportion of a circular arc's length to radius. In the case of a geometric angle, the arc is centred at the vertex and is bound by the sides.
We know that vertical angles of intersection are equal, so here
⇒ (8w+8) = (9w-5)
⇒ 8w+8 = 9w-5
⇒ 9w - 8w = 8 + 5
⇒ w = 13
Angle measure = 8(13)+8
= 112°
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Write a condition Pls
A ball is thrown upward from the top of a building that is 160 feet tall. The height, H, of the ball T seconds after being thrown is given by the equation H = -16t^2 + 48t + 160.
After how many seconds will the ball hit the ground?
a. 2
b. 3
c. 5
d. 10
Answer:
10
Step-by-step explanation:
because 10 is 10 gsjivfhnvv thkgfhlmbbbctb. chvjlff ijvvgjvjvivcujc vidyalay Chrissy full good Zo of up b and b go in the editor and the editor and the general of words typist and I am a bit of a person to you tomorrow to you tomorrow to appeal to utha kar raha hai toto b go on vgn de un BBC d.
There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of fruit in the bowl are apples?
40%
0.06%
6%
0.4%
Answer: 40% of the fruit pieces are apples
Step-by-step explanation:
[tex]\frac{6}{15}[/tex] = .4
.4 x 100% = 40%
Describe the transformations to the basic function. Then, write the equation of the function.
The given function is a graph transformation of the absolute value function.
What are Function Transformations?A function transformation "moves," "resizes," or "reflects" the parent function's graph. Function transformations are classified into three types: Translation, Dilation, and Reflection. Only dilation alters the size of the original shape; the other two transformations change the shape's position but not its size.
Step 1: Parent function y = f₁(x) = |x|
Step 2: f₁(x) is reflected (Reflection) about x-axis to form f₂(x) = -f₁(x) = -|x|
Step 3: f₂(x) is moved to left by 5 units(Horizontal translation) to form f₃(x) = f₂(x + 5) = -|x + 5|
Step 4: f₃(x) is moved up 1 unit (Vertical translation) to form f₄(x) = f₃(x) + 1 = -|x + 5| + 1
The equation of the given graph is:
y = |x + 5| +1
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If f (x) = x/2 - 3 and g(x) = 4 x^2 + x-4, find (f+g)(x).
The sum of the two functions can also be expressed as follows;
[tex](f+g)(x)=f(x)+g(x)[/tex]This is not a difficult process. We just put the terms of the two functions together.
We have to be careful to add or subtract the coefficients of similar terms, taking into account their signs.
[tex]f(x)=\frac{x}{2}-3[/tex][tex]g(x)=4x^2+x-4[/tex][tex](f+g)(x)=f(x)+g(x)[/tex][tex](f+g)(x)=4x^2+x+\frac{x}{2}-7[/tex]Answer:
Step-by-step explanation:
x2 – 2x – 8
Find an expression which represents the difference when (9x-4)is subtracted from (7x-2) in simplest terms.
The expression when (9x-4) is subtracted from (7x-2) in simplest terms is 2(1-x).
According to the question,
We have the following information:
(9x-4) is subtracted from (7x-2).
(We know that an expression written after the word from should be written first and the expression before it should be written after the sign of subtraction.)
So, we have the following expression:
(7x-2)-(9x-4)
7x-2-9x+4
(We know that the number with the same variables are added or subtracted. For example, 7x is added to -9x.)
-2x+2
Taking 2 as a common factor from these two terms:
2(-x+1)
2(1-x)
Hence, the difference of the two expressions is 2(1-x).
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