Part b how do these functions differ from functions you have used in algebra in the past?
Answers
The functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
What is a function?It should be noted that a function simply means an equation where the x that is plugged into the equation will yield exactly on e y from the equation.
In this case, the functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
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Related Questions
Given the function f(x) = x² + 8x + 12, determine the average rate of change of
the function over the interval -10 < x < -2.
Answers
The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is
[tex]\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}[/tex]
Simplify this radical.
[tex]\sqrt{84} \\\\1; 2\sqrt{21} \\2; 2\sqrt{42} \\3; 4\sqrt{21} \\or 4; 4\sqrt{42} \\[/tex]
Answers
The radical is 2√21.
What is radical?The √ symbol that is used to denote square root or nth roots.
Given :
√84
= √2*2*21
=2√21
Hence, the radical is 2√21.
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please help fr , like i acc need help
Answers
Step-by-step explanation:
first a little help, how they got the equations :
in total they need 15 liters.
so, whatever x and y are, but together they must be 15 L.
x + y = 15
then, we are mixing x liters of 20% alcohol with y liters of 100% alcohol, that have to result in a 40% solution of (x+y) liters :
0.2x + y = 0.4(x+y)
we know from the first equation that x+y = 15, so the second equation is actually
0.2x + y = 0.4 × 15 = 6
so, we have
x + y = 15
0.2x + y = 6
do you notice something ? there is a "+ y" in both equations.
so we can actually subtract the second equation from the first, eliminate y and solve for the remaining x. and then use one of the original equating to get also y :
x + y = 15
- 0.2x + y = 6
---------------------
0.8x 0 = 9
0.8x = 9
x = 9/0.8 = 11.25 liters
x + y = 15
11.25 + y = 15
y = 15 - 11.25 = 3.75 liters
Hey guys, need help here
Answers
Assuming [tex]a[/tex] is a non-negative real number...
Raise both sides to the power 2 :
[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^2 = 8^2 \implies a^{3/2} = 64[/tex]
which follows from the exponent product property, [tex](x^y)^z=x^{yz}[/tex]. In particular, 3/4 × 2 = 6/4 = 3/2.
Raise both sides to the power 1/3 :
[tex]\left(a^{3/2}\right)^{1/3} = 64^{1/3} \implies a^{1/2} = 4[/tex]
where we use the same property as before, and 4³ = 64. This time, 3/2 × 1/3 = 3/6 = 1/2.
Take the reciprocal of both sides. This negates the exponent, so we end up with
[tex]\dfrac1{a^{1/2}} = \dfrac14 \implies \boxed{a^{-1/2} = \dfrac14}[/tex]
Of course, you could also solve for [tex]a[/tex] immediately by raising both sides of the original equation to the power 4/3. We have 4/3 × 3/4 = 12/12 = 1, so
[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^{4/3} = 8^{4/3} \implies a = 8^{4/3}[/tex]
Now 2³ = 8, so [tex]8^{4/3} = \left(8^{1/3}\right)^4 = 2^4 = 16[/tex], and since 4² = 16, it follows that
[tex]a = 16 \implies a^{1/2} = \sqrt{16} = 4 \implies a^{-1/2} = \dfrac14[/tex]
775 tickets were sold for a game for a total of $1,587.50. If adult tickets sold for $2.50 and childrens tickets sold for $1.50,how many of each kind of tickets were sold?
Answers
350 tickets sold of children and 425 tickets sold for adult.
What is algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Let x be the number of adult tickets that were sold and y be the number of children's tickets that were sold.
Total 775 tickets were sold for the game.
So,
x + y = 775
If adults tickets sold for 2.50 and children's tickets sold for 1.50 and all the tickets were sold for a total of 1587.5, it means that
2.5x + 1.5y = 1587.5
put x = 775 - y
2.5(775 - y) + 1.5y = 1587.5
1937.5 - 2.5y + 1.5y = 1587.5
-y = 1587.5- 1937.5
y = 350
and, x = 775 - y = 775 - 350
x = 425
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please help .. . . .
Answers
Answer:
Step-by-step explanation:
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is (
,
).
Answers
Answer:
(-4,-18) and (5,90)
Step-by-step explanation:
I'll assume the first equation is supposed to be y – 10 = 11x + x^2
This is a parabola. The second equation is a straight line:
y – 12x = 30
We want to find the points at which these lines intersect. They will intersect for any (x,y) that
Let's rearrange the second equation to isolate y:
y – 12x = 30
y = 30 + 12x
Now we can take the this value of y and substitute it into the first equation:
y – 10 = 11x + x^2
(30 + 12x) – 10 = 11x + x^2
20 + 12x = 11x + x^2
0 = x^2 -x -20
We can factor this into (x+4)(x-5)
That means x can be either -4 or 5.
Find the value of y using these values of x in both original equations:
For x = -4
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(-4)+(-4)^2 +10
y = -44 + 16 + 10
y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.
For x = 5
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(5) + (5)^2 + 10
y = 55 + 25 + 10
y = 90
The second point both lines meet is (5,90).
We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.
Find the area of the rectangle
Answers
Answer:
Option A = 1*3 = 3 unit²[tex]area \: of \: rectangle \: = length \: \times breath[/tex]
[tex]length \: = distance \: between \: f \: and \: g \: or \: between \: e \: and \: h \: [/tex]
Distance between f and G = distance between E and HF = (3,7)
G = (6,4)
H = (5,3)
E= (2,6)
= (3 units)
Distance between FE = GH= 1 units
Area = 3* 1
= 3 units²
HELP ME PLS 40 POINTS HELP ME
Answers
Answer:
y=4/5x-3.5
Step-by-step explanation:
You should keep the Y and X as variables in your slope-intercept equation. The slope-intercept formula is y=mx+b. Your M would be your slope which is rise over run. Based on the points, you go up four and right five. Your b is where the line intersects the Y-axis. You're welcome.
50 people were asked if they speak French or German or Spanish. Of these people, 31 speak French 2 speak French, German and Spanish 4 speak French and Spanish but not German 7 speak German and Spanish 8 do not speak any of the languages all 10 people who speak German speak at least one other language How many people only speak Spanish?
Answers
The number of people that speak only spanish = 6
How to Interpret Venn Diagrams?We are given;
Total number of people surveyed = 50
31 speak French 2 speak French, German and Spanish.
4 speak French and Spanish but not German.
7 speak German and Spanish.
8 do not speak any of the languages.
All 10 people who speak German speak at least one other language.
Thus;
From the Venn diagram;
Number of people that speak only French and German = 10 - 5 - 2 - 0 = 3
Number that speak only spanish = 50 - 22 - 3 - 2 - 4 - 5 = 6
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Which graph represents the function of f(x) = 4x^2-16/2x-4 ?
Answers
See the graph in the image.
y = (4x² - 16)/(2x - 4)y = [4(x-2)(x+2)]/[2(x-2)]y = 2(x+2), with a domain of all real numbers other than 2A function is a relationship between inputs where each input is related to exactly one output.
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Function:
f(x) = (4x² - 16) / (2x - 4)
This can be written as,
f(x) = (2x)² - 4² / (2x - 4) [ a² - b² = (a + b)(a - b) ]
f(x) = (2x - 4)(2x + 4) / (2x - 4)
f(x) = 2x + 4
Now,
We will find the coordinates from the function f(x) = 2x + 4
x = 0, f(x) = 4
(0, 4)
x = 1, f(x) = 6
(1, 6)
x = 3, f(x) = 10
(3, 10)
And so on.....
The graph is given below,
Thus,
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
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Which of the expressions are equivalent to the one below? Check all that
apply.
(14+4) 6
A. 14 (4+ 6)
B. (14+6) + 4
C. (4+6) (14+6)
D. (4+14) ÷ 6
Answers
Answer:
none of them match
Step-by-step explanation:
maybe something is typed wrong. the answer I got for the equation was 108 and none of them match
Write functions for each of the following transformations using function notation. Choose a different letter to
represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in
the counterclockwise direction.
• translation of a units to the right and b units up
reflection across the y-axis
• reflection across the x-axis
• rotation of 90 degrees counterclockwise about the origin, point O
• rotation of 180 degrees counterclockwise about the origin, point O
• rotation of 270 degrees counterclockwise about the origin, point O
Answers
Answer:
Step-by-step explanation:
1) = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
Five siblings decide to buy their father a birthday present that costs b dollars, splitting the cost evenly amongst themselves. In terms of B, how much money does each sibling save by buying the gift as a group rather than alone?
A = b/25
B = b/5
C = 4b/5
D = 4b
Answers
Answer: b/5
Step-by-step explanation:
They divide the total by 5 to get the cost each person has to pay
Please Help
What does the missing angle in the triangle measure?
Answers
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle is 180
95+25 +x = 180
120 +x = 180
Subtract 120 from each side
120+x-120 = 180-120
x = 60
Which equation can be used to solve for x in the triangle below?
Answers
Using the cosine rule, the equation to use to solve for x is: x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41)) ≈ 3.1 cm.
How to Use the Cosines Rule to Solve a Triangle?The cosine rule is given as, c = √(a² + b² − 2ab × cos(C))
Given the following:
c = x = ?a = 4.0 cmb = 4.7 cmC = 41°Plug in the values:
x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41))
x ≈ 3.1 cm
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Are the equations 9x=5x+4 and 14x=4 equivilant?
Answers
Answer:
No
Step-by-step explanation:
First solve both equations:
1) 9x = 5x + 4
Simplifying
9x = 5x + 4
Reorder the terms:
9x = 4 + 5x
Solving
9x = 4 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
9x + -5x = 4 + 5x + -5x
Combine like terms: 9x + -5x = 4x
4x = 4 + 5x + -5x
Combine like terms: 5x + -5x = 0
4x = 4 + 0
4x = 4
Divide each side by '4'.
x = 1
Simplifying
x = 1
2) 14x = 4
14x = 4 (divide both sides by 14 to get x)
14x/14 = 4/14
x = 0.285714285714
As you can see, the value of x in the second equations is less than one, therefore making these algebraic equations not equivalent.
Answer:
No
Step-by-step explanation:
9x=5x+4 and 14x=4
9x= 5x+4
Subtract 5x from each side
9x-5x = 5x+4-5x
4x= 4
The equations are not the same
A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same time and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point (the right angle) is changing at 2 sq. meter per seconds, then how fast are the people moving when they are 5 meters from the right angle? (Round your answer to two decimal places.)
Answers
definetly not a
Step-by-step explanation:
because it is an incompetent answer
Select the correct answer from each drop-down menu.
Consider this equation.
- 1-5 = x - 8
The equation has
and
.A valid solution for x is
Answers
Answer:
-1-5=x-8
or, -1-5+8=x
or, x= -1-5+8
or, x= -6+8
or, x=2
therefore, x=2
Which equation describes the same line as y- 5 = -2(x+4)?
OA. y=-2x-8
B. y=-2x - 2
OC. y=-2x - 3
OD. y=-2x+9
SUBI
Answers
Answer:
C
Step-by-step explanation:
We have
y - 5 = -2(x + 4)
Expanding the RHS by multiplying by 2 gives us
y - 5 = -2x -8
Moving -5 from LHS to RHS (reverses sign)
y = -2x -8 + 5 or
y = -2x -3
C. y=-2x - 3 , equation describes the same line as y- 5 = -2(x+4).
Here, we have,
We have been given an equation in point-slope form and we are asked to find the equation of same line.
y- 5 = -2(x+4)
Upon using distributive property , we will get,
=> y- 5 = -2x - 8
We have
y - 5 = -2(x + 4)
Expanding the RHS by multiplying by 2 gives us
y - 5 = -2x -8
Moving -5 from LHS to RHS (reverses sign)
y = -2x -8 + 5 or
y = -2x -3
Therefore, the equation y = -2x -3 represents the same line as our given equation.
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what is the value of k such that 5x-2y=9 and 6x+ky=4 are perpendicular?
Answers
15
5x-2y=9......(1)
6x+ky=4......(2)
slope of eqn i= -5/-2
=5/2
slope of eqn ii = -6/k
since the line are perpendicular
5/2 * -6/k = -1
-30= -2k
k=15
its math help me out?
Answers
Answer:
D IS THE BEST IS WHAT MY TEACHER TOLD ME
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
To determine the correct table of input/outputs, take each input, substitute it into the function for "x", evaluate, and see if it equals the output. If it works for ALL of the pairs, then it is the correct table. Since functions only have one output for any input, there can't be two correct answers.
[tex]f(x)=\frac{3}{x}+4[/tex]
Check x = -3
[tex]f(-3)=\frac{3}{(-3)}+4\\=-1+4\\=3\\f(-3)\overset{\checkmark}{=}3[/tex]
Check x = -2
[tex]f(-2)=\frac{3}{(-2)}+4\\=-1.5+4\\=2.5\\f(-2)\overset{\checkmark}{=}2.5[/tex]
Check x = 1
[tex]f(1)=\frac{3}{(1)}+4\\=3+4\\=7\\f(1)\overset{\checkmark}{=}7[/tex]
Check x = 2
[tex]f(2)=\frac{3}{(2)}+4\\=1.5+4\\=5.5\\f(2)\overset{\checkmark}{=}5.5[/tex]
Check x = 3
[tex]f(3)=\frac{3}{(3)}+4\\=1+4\\=5\\f(3)\overset{\checkmark}{=}5[/tex]
a bag contains 4 white marbles , 7 red marbles , and 5 black marbles. you randomly select 3 marbles from the bag. without replacement.the random variable represents the number of black marbles
Answers
5/4+7+5 = 0.3125
type an equation for the line shown on the graph
(0,2)
Answers
Answer: Hope this helps you.
Y = MX + 2
Step-by-step explanation:
Since you don't have a picture of the line I cant find the slope but with the info I know the equation is.
Y = MX + 2
(Replace M with the slope or post the graph so I can identify the slope)
The product of 2 more than 3 times a number and 6 less than 4 times the number (z)
Answers
Answer:
[tex]12z^{2} -10z -12[/tex]
Step-by-step explanation:
Let the number be z
2 more than 3 times z ==> 3z + 2
6 less than 4 times z ==> 4z - 6
Product of the above two is
[tex](3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12[/tex]
point-slope equation for perpendicular lines y=-2x-7 that passes through (-2,-3)
Answers
Answer: below! ^^
Step-by-step explanation:
Hii, do you need an answer to your question? Let me help you out! (;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part 1 ⚜Perpendicular lines have slopes that are opposite inverses of each other.
The slope (m) of the line that is perpendicular to y=-2x-7 is [tex]\sf -\cfrac{1}{2}[/tex].
Part 2 ⚜⚜ Point slope formula[tex]\boldsymbol{y-y1=m(x-x1)}[/tex]
⚜Stick in the known values[tex]\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}[/tex]
⚜ Simplify[tex]\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}[/tex]
Voila! There's our answer, cheers! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hope I helped! Best wishes!
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
A boat is heading towards a lighthouse, where Mason is watching from a vertical
distance of 122 feet above the water. Mason measures an angle of depression to the
boat at point A to be 16°. At some later time, Mason takes another measurement and
finds the angle of depression to the boat (now at point B) to be 66°. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
Answers
The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.
We can draw the above situation as a form of a right-angle triangle.
From the figure, the distance between AB is x ft
From the right angle triangle DBC:
tan66 = 122/CB
CB = 54.31 ft
From the right angle triangle DAC
tan16 = 122/AC
AC = 425.46 ft
x = AC - CB
x = 425.46 - 54.31
x = 371.15 ft ≈ 371 ft
Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
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which greek mathematician wrote the most definitive text on geometry, one that is still referred torday.
Answers
Answer:
Pythagoras
Step-by-step explanation:
please mark me as brainlest
A main area of mathematics is called Euclidean Geometry.
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. find the missing term. the roots of x2 − ( ) 34 are 5 ± 3i.
Answers
The missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have the roots of a quadratic equation:
5 ± 3i
To find the quadratic equation:
(x - (5+3i))(x - (5-3i))
[tex]\rm =x^2+x\left(-\left(5-3i\right)\right)-\left(5+3i\right)x-\left(5+3i\right)\left(-\left(5-3i\right)\right)[/tex]
= x² -10x + 34
The missing value is 10x
The quadratic equation is:
= x² -10x + 34
Thus, the missing term in the provided quadratic equation is 10x if the roots of a quadratic equation are 5 ± 3i.
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A ball is thrown from the top of the school. The height of the ball (in feet) written in
terms of the time (in seconds) is modeled by f (t) = -16t² + 32t + 48. At what time
will the ball hit the ground?
Answers
Answer:
3 seconds
Step-by-step explanation:
When the ball hits the ground, the height will be 0. Therefore, you can substitute 0 in for the value of f(t), hence the equation will be:
0 = -16t^2 + 32t + 48
You can then factor out -16:
0 = t^2 - 2t - 3
Factor:
0 = (t-3)(t+1)
t = 3, -1
However -1 is an extraneous solution because time cannot be negative. Therefore, the answer is 3 seconds.
