The conclusions that can be drawn about f–1(x) are:
[tex]f^-^1(x)[/tex] has an x-intercept of (-36, 0)[tex]f^-^1(x)[/tex] has a range of all real numbers.Calculations and Parameters:Given:
[tex]f(x) = \frac{-2}{3}x - 24[/tex]
[tex]f(x) + 24 = \frac{-2}{3}x[/tex]
To find x, we would multiply both sides by -2/3
= [tex]x= \frac{-3}{2} (f(x) + 24)[/tex]
[tex]f^-^1(x) = -\frac{3}{2} (0) - 36[/tex]
[tex]f^-^1(x) = -36[/tex]
Therefore, [tex]f^-^1(x)[/tex] has an x-intercept of (-36, 0)
Furthermore, [tex]f^-^1(x)[/tex] has a range of all real numbers.
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What causes the economy to move from its short-run equilibrium to its long-run equilibrium?
Answer:
Nominal wages, prices, and perceptions adjust upward to this new price level
Step-by-step explanation:
why do some numerical expressions contain parentheses
The most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.
What are parentheses?In mathematics, parenthesis is used to arrange numbers in the sequence of operations, clarify numbers, and denote multiplication.
Suppose you have an expression as:-
E = { ( 5-2 )8} 6
In this case, you would calculate 5 minus 2 first (parentheses), then multiply by 8 (brackets), then complete the part inside the curly braces, and finally multiply by 6.
Therefore the most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.
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Lines RS, TV, and SW are shown.
10-
8-
R
S
6
4-
2-
-10-8-6-4-22-
2 4 6 8 10 x
T
-6
8
W
-10-
☎ do
N
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answer:
b
Step-by-step explanation:
The statements true about the slopes and lines are
a) Line TV has a slope of 0.
b) Lines RS and TV are parallel.
c) Line SW has an undefined slope.
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be S ( 2 , 6 )
Let the second point be R ( -8 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 6 ) / ( -8 - 2 ) = 0
So , the slope of line RS = 0
Let the point T = T ( -6 , -4 )
Let the point V = V ( 8 , -4 )
Slope m = ( -4 - (-4) ) / ( 8 - (-6) ) = 0
So , the slope of line TV = 0
And , the lines RS and TV are parallel as they have the same slope
Now , the x coordinate of the point S and W does not change
So , it has an undefined slope
Hence , the equation of line is solved
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The complete question is attached below :
Lines RS, TV, and SW are shown.
Which statements are true about these lines? Select
three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Rebecca rolls a 6-sided number cube 1290 times. How many of the rolls are expected to show a factor of 6?
Answer:
215
Step-by-step explanation:
1/6 chance to roll a 6
1/6 * 1290
Two exponential functions are shown in the table.
X
f(x)=2*
g(x) =
2
2
4
1
2
0
-1
-2
2
71111
4
141212
4
Which conclusion about f(x) and g(x) can be drawn
from the table?
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
O The function f(x) has a greater initial value than g(x).
Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.
How to compare the functions f(x) and g(x)?In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:
If, f(-x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
f(-x) = 2⁻ˣ = ½ˣ = g(x).
Similarly, two functions are considered to be reflections over the x-axis under the following condition:
If, -f(x) = g(x).
Evaluating the given functions, we have:
f(x) = 2ˣ
-f(x) = -2ˣ ≠ g(x).
Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.
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which expression is equivalent to 15n – 20
2(8n – 6)
6(2n – 9)
5(3n – 4)
5(4n – 3)
A. 36
B. 52
C. 148
D. 168
Answer:
B) 52
Bodmas rule:
BracketsOrderDivisionMultiplicationAdditionSubtractionSolving Steps:
⇒ 2 × (3 - 1)⁴ + 5 × 4
⇒ 2 × (2)⁴ + 5 × 4
⇒ 2 × 16 + 5 × 4
⇒ 32 + 20
⇒ 52
Option B
A rifle is aimed horizontally at a target on a screen some distance away. The bullet hits the target 2.8 cm below the aim point. The initial velocity of the bullet is 750.0 m/s.
Find the flight time?
Answer:
0.03 second time the flight
2/3(cx+1/2)-1/4=5/2 solve
Answer:
2/3(cx+1/2)-1/4=5/2. CX=29/8
Write each expression in radical form
[tex]\sqrt[4]{6^5}[/tex]
Step-by-step explanation:
This expression in radical form :4√65 =2.838412
If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0.
Answer:
a=2
Step-by-step explanation:
[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]
[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]
the curve is a right parabola.
here b=0,and a=4a for x
we are finding the area between x-axis and x from 0 t0 4a.
curve is symmetrical about x-axis so we multiply by 2.
If the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
What is area of the region bounded by the curve ?An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.
Area bounded by the curve [tex]=\int\limits^a_b {x} \, dx[/tex]
We have,
[tex]y^2 =4ax[/tex]
⇒ [tex]y=\sqrt{4ax}[/tex]
[tex]x= 4a[/tex],
Area of the region [tex]=\frac{256}{3}[/tex] Sq units
Now comparing both given equation to get the intersection between points;
[tex]y^2=16a^2[/tex]
[tex]y=4a[/tex]
So,
Area bounded by the curve [tex]= \[ \int_{0}^{4a} y \,dx \][/tex]
[tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]
[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]
[tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]
[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]
On applying the limits we get;
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]
[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]
[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]
⇒ [tex]a^{3} =8[/tex]
[tex]a=2[/tex]
Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex] and the line [tex]x= 4a[/tex] is [tex]\frac{256}{3}[/tex] Sq units, then the value of [tex]a[/tex] will be [tex]2[/tex] .
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Select whether the pair of lines is parallel, perpendicular, or neither. x=−2, y=10
Answer:
perpendicular
Step-by-step explanation:
x = -2 is a vertical line at x = -2
y is a horizontal line the two lines are perpindicular
the lines x=−2, y=10 are perpendicular to each other.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, The given equations are :
x=−2 and y=10
First, consider x = -2 equation :
equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.
Consider second line y = 10 :
line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.
Therefore, the lines x=−2, y=10 are perpendicular to each other.
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Multiply
k+3/4K - 2 (12k2 +2k -4)
Answer:
-204kk+3+32k/4k
Hope this helps!!
PLEASE HELP THIS IS DUE AND I NEED IT DONE
Answer:
The answers are in the picture. Remember that first is x and then y when you see those coordinated again. (10,11) X=10 and Y=11.
Step-by-step explanation:
An ordinary die is a cube with numbers 1 through 6 on the sides. Imagine that the die is rolled twice in sucession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
What is the probability that the sum is not divisible by 2 and not divisible by 4?
Answer:
1/2Step-by-step explanation:
NOTE : we have 6×6=36 possible outcome.
we can resume the set of outcomes in the table below :
Then
the probability that the sum is not divisible
by 2 and not divisible by 4 :
= 18/36
= 1/2
Savannah is 1.75 meters tall. At 11 a.m., she measures the length of a tree's shadow to
be 43.75 meters. She stands 39.2 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
The height of the tree is 1.95 meters.
At 11 AM, we have
Savannah = 1.75 m
Tree Shadow = 43.75 m
Savannah Shadow = 39.2 m
So, we make use of the equivalent ratio
Savannah :Tree::Savannah Shadow:Tree Shadow
Now, 1.75:Tree::39.2:43.75
In fraction Tree/1.75 = 43.75/39.2
Multiply both sides by 1.75
Tree =43.75/39.2 ×1.75
Tree=1.95
Therefore, the height of the tree is 1.95 meters.
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a wall contains a rectangular window. the area (in square feet) of the window is represented by x^2-4x+3. write a bionominal that represents the height of the window. find the permiteter when the wall is 10 feet. the square on the inside is (x-3) ft
The height of the wall would be x - 1 and the perimeter of the wall is 32 feet
How to determine the height?The area of the window is given as:
A = x^2 - 4x + 3
Expand
A = x^2 - 3x - x + 3
Factorize
A = x(x - 3) - 1(x - 3)
Factor out x - 3
A = (x - 1)(x - 3)
The width of the wall is given as: x - 3
So, the height of the wall would be x - 1
How to determine the perimeter?
The perimeter is calculated using:
P = 2 *(Width + Height)
This gives
P = 2 * (x - 1 + x - 3)
When x = 10, we have:
P = 2 * (10 - 1 + 10 - 3)
Evaluate
P = 32
Hence, the perimeter of the wall is 32 feet
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100 points! halp...
Which point could be removed in order to make the relation a function? ((-4.3). (-5. 6), (1, 0). (-4. 5). (9, 5), (0.-7))
(-5.6)
(1.0)
(-4, 5)
(9.51
Answer:
it is 3rd option C. -4, 5
Step-by-step explanation:
all the elements are associated with only one second element except -4
for -4 there are two second elements 3 and 5 from the ordered pairs (-4, 3) and (-4, 5)
so we can remove one of them to make R a function
since (-4, 3) is not in the options so the correct option is (-4, 5)
so c is the right one
Hope This Helped
As per defination of function
Every domain has an unique range
or
f(x)=yHere
f(-4)=3f(-4)=5One point need to be removed to get it function
Hence the point is (-4,5)
need help with this asap pls really need the answer
In the diagram, the area of the given shape is 102 cm²
Area of a KiteFrom the question question, we are to determine the area of the given shape
The given shape is a kite
The area of a kite is given by the formula,
[tex]A =\frac{pq}{2}[/tex]
Where A is the area
p and q are the diagonals
In the given diagram,
p = 6cm + 6 cm = 12 cm
q = 3 cm + 14 cm = 17 cm
Thus,
Area of the kite = [tex]\frac{12 \times 17}{2}[/tex]
Area of the kite = 6 × 17
Area of the kite = 102 cm²
Hence, the area of the given shape is 102 cm²
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Which function has the same domain as y= 2√x?
Oy= √2x
O y=2³√x
0₁y = √x-2
O y=³√x-2
The option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
y= 2√x
From the above function the domain should be:
x ≥ 0 (because square root of negative values does not exist)
The function:
y = √(2x)
2x ≥ 0
x ≥ 0
Thus, the option first is correct because y= 2√x and y= √2x have same domain which is x ≥ 0.
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Write the equation of the line that passes through (1, 5) and (−2, 14) in slope-intercept form.
The equation of line is y = -3x + 8
What is slope?Slope is the ratio of the change in the y coordinates to the change in the x coordinates.
Analysis:
slope (m) = y2 - y1 / x2 - x1
m = 14 -5 / -2-1 = 9/-3 = -3
when y = 5, x = 1
y = mx + c
5 = -3(1) + c
5 = -3 + c
c = 5+3 = 8
Y = -3x + 8
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9. Find the area:
25
19
13
Answer:
162.5
Step-by-step explanation:
25=height
13=base
to find the area of a triangle you do (h(b)b)/2
The Other Number Your first number was 8. Is the other one 0? How did we know that? Can we read your mind?
Answer:
???
Step-by-step explanation:
Graph the set {x|x≤-5} on the number line.
Then, write the set using interval notation.
The interval notation that defines this set is: (-∞, -5]
And the graph can be seen below.
How to graph the inequality?Here we want to graph the inequality:
x ≤ -5
This refers to all the values of x equal or smaller than -5.
To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.
The interval notation that defines this set is: (-∞, -5]
The first end is open, and the second is closed (because of the symbol ≤).
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Drag the expressions into the boxes to correctly complete the table. Polynomial Not a polynomial
The answer to the given question is as below:-
Polynomials:-
x³-7x²+9x-5x⁴-20
x⁵-5x⁴+4x³+2x-1
3x²-5x⁴+2x-12
Non-polynomial:-
x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
[tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]
[tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]
What are polynomials?A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.
So the table will be formed as:-
Polynomials:- Non-polynomial:-
x³-7x²+9x-5x⁴-20 x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
x⁵-5x⁴+4x³+2x-1 [tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]
3x²-5x⁴+2x-12 [tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]
Therefore the polynomials and non-polynomials are shown in the table above.
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T=mv^2/L
Write an equation that shows the given formula solved for V
Answer:
v = √(LT/m)
Step-by-step explanation:
Given :
T = mv²/LMultiply both sides with L :
T × L = mv²/L x LLT = mv²Divide both sides by m :
LT × 1/m = mv² × 1/mLT/m = v²Take the square root on each side :
√v² = √(LT/m)v = √(LT/m)Answer:
[tex]v = \sqrt{ \frac{tl}{m} } [/tex]
Step-by-step explanation:
[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]
Help help help help help help help help
A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has a y intercept of 6. What is the equation of the function described?
Equation of the function: f(x) = 4 sin (x/2) + 6.
What is sinusoidal function ?The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).
Given: max value= 6, min value= -2, y-intercept= 6.
As, standard form f(x) = A sin (ωx +φ) + k,
where A is the amplitude, ω is the angular velocity with ω=2πf.
Now,
A = |6- (-2)/2|
A = |6 +2/2| = 8/2
A = 4
Also, ω:
The period of a sinusoidal is T = 1/f
so, f = 1 / T
ω = 2πf
ω = 2π ( 1/T) with T = 4π
ω = 2π (1/(4π) = 2π (2)
ω = 1/2
The y-intercept k = 6
So, equation with values A =4, ω = 1/2, k = 6, φ = 0.
f(x) = A f(x)
f(x) = A sin (ωx +φ) + k
f(x) = 4 sin (x/2) + 6.
Hence, equation of the function f(x) = 4 sin (x/2) + 6.
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6. Janet spent $25, $30, $10, and $8 for
recreation in the last four weeks. What
was her average weekly expense for
recreation?
A. $12.50
B. $18.25
C. $25.25
D. $36.50
Answer:
B
Step-by-step explanation:
Total money spent = 25 + 30 + 10 + 8 = 73
Per week = 73 / 4 = 18.25
I need a thorough explanation for question 4 please. It’s about Operations of Powers/Exponents.
Simplify
I need help for finals
Answer:
goto gauth maths and ask again