Answer: Option B
Step-by-step explanation:
By definition, only those functions that are one to one have an inverse function.
A function is one by one if there are not two different input values, [tex]x_1[/tex] and [tex]x_2[/tex], that have the same output value y
Note that the function [tex]f(x)= \frac{|x+3|}{5}[/tex] is not a one-to-one function
When x=2 [tex]f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1[/tex]
When x=8 [tex]f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1[/tex]
Note that the function [tex]f(x)= \frac{x^4}{7}+ 27[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
When x=-1 [tex]f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
Note that the function [tex]f(x)= \frac{1}{x^2}[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{1}{(1)^2}\ ,\ \ y=1[/tex]
When x=-1 [tex]f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1[/tex]
Then the answer is the option B.
You can verify that The function [tex]f (x) = x ^ 5-3[/tex] is a one-to-one function and therefore its inverse is a function
How can i find the value for R
Answer:
R = 134
Step-by-step explanation:
This is a 5 sided figure. The interior angles add to (n – 2)180 where n is the number of sides
(5-2) * 180 = 540
Add up all the angles and set it equal to 540
R+ 78+109+113+106 = 540
Combine like terms
R + 406 = 540
Subtract 406 from each side
R +406-406 = 540-406
R = 134
Solve for x. (x - 8)(x - 8) = 0
Answer: x=8
Step-by-step explanation:
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
Set the first factor equal to 0 and solve.
x−8=0
x−8=0
Help me please! BRAINLIEST
Answer:
1. 53 by 58 , 222 ft
2. 321000
3.1080
4. 3.5
Step-by-step explanation:
1. 23+15+15 = 53
28+15+15= 58
53+53+58+58= 222
Can someone please help??
Answer:
24 + 32p = 8(3 + 4p)Step-by-step explanation:
24 = 8 · 3
32p = 8 · 4p
24 + 32p = 8 · 3 + 8 · 4p = 8 · (3 + 4p)
f(x) = x2 + 5x - 1 is shifted 3 units left. The result is g(x). What is g(x)?
Answer:
g(x) = (x + 3)^2 + 5(x + 3) - 1
Step-by-step explanation:
Please use " ^ " to denote exponentiation: f(x) = x^2 + 5x - 1.
Shifting the graph of this function 3 units left results in
g(x) = (x + 3)^2 + 5(x + 3) - 1
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answer:
1st option
Step-by-step explanation:
By observation, we can see that the graph crosses the y-axis at y = -2. Therefore the y-intercept is -2.
we can also see that the graph intersects the axes at (0,-2) and (3,0)
the formula for a linear slope when given two points (x1, y1) and (x2,y2) is given by :
m = (y2 - y1) / (x2 - x1)
In our case, x1 = 0, y1 = -2, x2= 3 and y2 = 0
hence m = (0 - (-2)) / (3-0) = 2/3
Hence the slope is 2/3
Only option 1 satisfies the values for both y-intercept and slope that we calculated.
Answer:
A) The slope is 2/3 and the y intercept is -2
Step-by-step explanation:
This is the correct answer for edge
one fifth of a number plus five times that number is equal to seven times the number less 18
To solve the equation, we can use algebraic techniques to find the value of 'x'.
Explanation:To solve the equation, we can let the number be represented by 'x'. The equation can then be written as: (1/5)x + 5x = 7x - 18. Simplifying this equation gives us: (1/5)x + 5x - 7x = -18. Combining like terms, we get: (6/5)x = -18. Dividing both sides by 6/5 gives us the value of 'x'.
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Follow below steps:
The question involves solving a linear equation to find an unknown number. To solve "one fifth of a number plus five times that number is equal to seven times the number less 18", the first step is to let "x" represent the unknown number and then create an equation based on the given information.
We start by translating the words into an equation:
One fifth of a number can be written as "(1/5)x".
Five times that number is written as "5x".
Seven times the number less 18 is written as "7x - 18".
So our equation becomes "(1/5)x + 5x = 7x - 18". Simplifying, we get "(6/5)x = 7x - 18".
Combining like terms yields "(1/5)x = -18", and we solve for x to find the value of the unknown number: "x = -90".
Through this process, the student can identify the value of the number in question.
The library is located 1.8 miles west of Callie’s house. The grocery store is located 2.4 miles south of the library. What is the length of a straight line between Callie’s house and the grocery store? Enter your answer in the box.
Check the picture below.
By using a right triangle rectangle, we will see that the distance is equal to 3 miles.
How to find the distance?You can think of the distance as the hypotenuse of a right triangle with legs that measure 1.8 miles and 2.4 miles.
Then, using the Pythagorean theorem we can write:
H^2 = (1.8 mi)^2 + (2.4 mi)^2
H = √((1.8 mi)^2 + (2.4 mi)^2) = 3mi
So the distance between Callie's house and the grocery store is 3 miles.
If you want to learn more about right triangles, you can read:
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Monique has $20 available to buy some sweet corn and lima beans to make succotash. If she buys 8 lb of corn, how many pounds of lima beans can she buy
Answer:
It’s a
Step-by-step explanation:
Answer:
It's A: 4.8 lb
Step-by-step explanation:
The following two-way table shows the data for the students of two different grades in a school:
Member of Science Club Not Member of Science Club Total
Grade 7 20 2 22
Grade 8 20 8 28
Total 40 10 50
Based on the relative row frequency, the students of which grade are more likely to be members of the science club?
Grade 7
Grade 8
The students of both grades are equally likely to be members of the science club
No conclusion can be drawn about the chances of a student being a member of the science club
Answer: grade 7
Step-by-step explanation:
Grade 7: 20/22 students in club
Grade 8: 20/28 students in club
Grade 7 has higher % of students in science club
Answer:
Grade 7
Step-by-step explanation:
The relative row frequency of members of the Science Club is: Member of Science Club / Total
in Grade 7: 20/22 = 0.91.
And in Grade 8 is: 20/28 = 0.71.
Then, students of Grade 7 are more likely to be members of the science club.
Help with inscribed polygons. Me and my daughter do not understand this.
Answer:
Part 1)
a.1) The central angle of pentagon is 72°
a.2) The central angle of hexagon is 60°
a.3) The central angle of decagon is 36°
a.4) The central angle of dodecagon is 30°
b.1) The measure of each interior angle of pentagon is 108°
b.2) The measure of each interior angle of hexagon is 120°
b.3) The measure of each interior angle of decagon is 144°
b.4) The measure of each interior angle of dodecagon is 150°
Part 2) The central angle and the interior angle are supplementary angles
Part 3) As the number of sides increases, the central angle decreases and the interior angle increases.
Step-by-step explanation:
Part 1. For each polygon, include the following information in the paragraph box below:
a) What was the central angle you used to locate the vertices? Show your calculation.
we know that
To find the central angle divide 360 degrees by the number of sides of the polygon
case a.1) Pentagon
The pentagon has 5 sides
so
The central angle is equal to
360°/5=72°
case a.2) Hexagon
The pentagon has 6 sides
so
The central angle is equal to
360°/6=60°
case a.3) Decagon
The pentagon has 10 sides
so
The central angle is equal to
360°/10=36°
case a.4) Dodecagon
The pentagon has 12 sides
so
The central angle is equal to
360°/12=30°
b) What is the measure of each interior angle of the polygon? Show your calculation
we know that
The sum of the interior angle of the polygon is equal to
S=(n-2)*180°
where
n is the number of sides
To find each the measure of each interior angle, divide the sum of the interior angles by the number of sides
case b.1) Pentagon
The pentagon has 5 sides
so
S=(n-2)*180°
S=(5-2)*180°=540°
Divide by the number of sides
The measure of each interior angle is equal to
540°/5=108°
case b.2) Hexagon
The hexagon has 6 sides
so
S=(n-2)*180°
S=(6-2)*180°=720°
Divide by the number of sides
The measure of each interior angle is equal to
720°/6=120°
case b.3) Decagon
The hexagon has 10 sides
so
S=(n-2)*180°
S=(10-2)*180°=1,440°
Divide by the number of sides
The measure of each interior angle is equal to
1,440°/10=144°
case b.4) Dodecagon
The hexagon has 12 sides
so
S=(n-2)*180°
S=(12-2)*180°=1,800°
Divide by the number of sides
The measure of each interior angle is equal to
1,800°/12=150°
Part 2. What is the relationship between the central angle and the interior angle?
we know that
The sum of the central angle plus the interior angle is equal to 180 degrees
therefore
The central angle and the interior angle are supplementary angles
Verify
Pentagon
72°+108°=180°
Hexagon
60°+120°=180°
Decagon
36°+144°=180°
Dodecagon
30°+150°=180°
Part 3. As the number of sides increases, how do the angles change?
we know that
As the number of sides increases, the central angle decreases and the interior angle increases.
Which of the following terms best describes the three side lengths of the
triangle below?
Answer:
B. Pythagorean triple
Step-by-step explanation:
To prove Pythagorean triple, we must prove that
ML² + LN² = MN²
or MN = √( ML² + LN²)
= √( 9² + 12²)
= √( 81 + 144)
= √( 225)
= 15 = value of MN given in diagram (proven)
in order to graph a linear equation in slope-interceot form, what do you need to know? what does the equation look like when the y-intercept of the line is equal to 0? what does the equation look like when it also has a slope equal to 1?
Answer:
(a) Slope and y-intercept; (b) y = mx; (c) y = x + b
Step-by-step explanation:
1. Need to know
Slope and y-intercept.
You use these numbers to calculate one other point. Then you draw a straight line between the y-intercept and the other point to get the graph.
2. y-Intercept = 0
The form of the equation is y = mx + b, where b is the y-intercept.
If the intercept is zero, b = 0, and the equation has the form
y = mx
The graph is a straight line passing through the origin.
3. Slope = 1
m represents the slope. If m = 1, the equation has the form
y = x + b
If the axes are scaled equally, the graph is a straight line that crosses the y-intercept at an angle of 45°.
Which of the following shows the true solution to the logarithmic equation below?
log(x)+ log(x+5) = log(6x +12)
©
X=-3
x=4
X=-3 and x = 4
X=-3 and x=-4
Answer:
x = 4.
Step-by-step explanation:
log(x) + log(x+5) = log(6x +12)
log x(x +5) = log(6x + 12)
Therefore x(x + 5)= 6x +12
x^2 + 5x - 6x - 12 = 0
x^2 - x - 12 = 0
(x - 4)(x + 3) = 0
x = -3, 4.
logs of negative values do not exists so the anser is x = 4.
©
The value of x is -3 , 4 ; option C is the solution to the equation
What is an Equation ?
An equation is a mathematical statement between two algebraic expressions equated by an equal sign.
A logarithm equation is given in the question.
log(x)+ log(x+5) = log(6x +12)
The equation of Logarithm says
log (x .y) = log x + log y
From the equation
log(x)+ log(x+5) can be written as log (x(x+5))
log (x(x+5)) = log(6x +12)
We can relate this as
(x(x+5)) = 6x +12
x² + 5x = 6x +12
x² -x -12= 0
x² -4x +3x -12 = 0
x (x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x = -3 , x=4
Therefore the option C is the solution to the equation
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If h(x) is the inverse of f(x), what is the value of h(f(x))?
OO
0 1
f(x)
Answer:
x.
Step-by-step explanation:
h(f(x) = x.
For example the inverse of f(x) = 2x is g(x) = x/2
f((gx)) 2 (x/2)
= 2x / 2
= x.
If h(x) is the inverse of f(x), then the value of h(f(x)) is:
x
Step-by-step explanation:Inverse of a function-
The inverse of a given function is a function which reverses the action of the other function.
Also, the composition of a function and it's inverse no matter in which order they are applied always gives us the identity function.
( Identity function-- Identity function is a function which when applied to some other function always retains that function )
i.e. If h(x) is the inverse of f(x) ; then we have:
[tex]h(f(x))=f(h(x))=x[/tex]
Should teens be allowed to play dangerous sports? Why or why not?
Answer:
I mean if it's there dream then why stop it? Its there life and we can't really stop that cause regardless what you say or do they're gonna find a way to do it. So I would say yes.
I am going to assume this is a poll? For our opinions?
If so then yes, I think that kids should be allowed to play dangerous sports..Football fatalities remain rare, but the game can be dangerous. That doesn't mean kids shouldn't play, same with hockey and any other
The diagonal of a square is x units. What is the area of the square in terms of x? square units square units 2x square units square units
For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:
[tex]l ^ 2 + l ^ 2 = x ^ 2[/tex]
Where:
l: It's the side of the square.
[tex]2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}[/tex]
We know that the area of a square is given by:
[tex]A = l ^ 2[/tex]
So, the area is:
[tex]A = \frac {x ^ 2} {2}[/tex]
Answer:
[tex]A = \frac {x ^ 2} {2}[/tex]
Answer:
Option A: 1/2 x^2
Step-by-step explanation:
what is the difference between the mean of each set?
a) 4
b) 5
c) 7
d) 9
please divide 4⁄6 ÷ 2⁄6
4/6 divided by 2/6 is 2.
you multiply the 4/6 by 6/2 to get 24/12. You then simplify it and get 2 as your answer.
What is the volume of a cardboard box that measures 1 inch by 5 inches by 7 inches?
The volume of the cardboard is __________ cubic inches.
Enter your answer as the number that correctly fills in the blank in the previous sentence. If necessary, round your answer to the nearest tenth, like this: 42.5
Answer:
35 cubic inches
Step-by-step explanation:
V= lwh
1*5*7= 35
Answer:
The answer is 35 cubic inches.
Step-by-step explanation:
For volume problems (with prisms, such as cardboard boxes) all you have to do is multiply all the dimensions, height, width, and length.
Wyatt claims that _ is equivalent to _ Which statement about his claim is true in every aspect?
The statement that is true in every aspect regarding his claim is:
False, because when combined in this manner, the alternating signs of the series are lost ( Wyatt ignored the negative in the first factor)Step-by-step explanation:The series is given as:
[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9[/tex]
which could also be written by:
[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n(\dfrac{1}{3})^n\cdot 3^2[/tex]
i.e.
[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{-n}\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{2-n}[/tex]
which is not equivalent to: [tex]\sum_{n=0}^{3} 3^{2-n}[/tex]
Since, on expanding the actual series we get the sum as:
[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=(-\dfrac{1}{3})^0\cdot 9+(-\dfrac{1}{3})^1\cdot 9+(-\dfrac{1}{3})^2\cdot 9+(-\dfrac{1}{3})^3\cdot 9\\\\\\=9-\dfrac{1}{3}\times 9+\dfrac{1}{3^2}\times 9-\dfrac{1}{3^3}\times 9\\\\\\=9-3+1-\dfrac{1}{3}\\\\\\=\dfrac{22}{3}[/tex]
Now, the expansion of:
[tex]\sum_{n=0}^{3} 3^{2-n}[/tex] is:
[tex]\sum_{n=0}^{3} 3^{2-n}=3^2+3^1+3^0+3^{-1}\\\\\\=9+3+1+\dfrac{1}{3}=\dfrac{40}{3}[/tex]
Answer:
D in short
Step-by-step explanation:
Ed2021
What value is bigger. .65 or 3/5
Answer:
0.65 > 3/5
Step-by-step explanation:
3/5 is 0.6 in fraction form
0.65 is greater than 0.6.
Therefore, 0.65 is greater than 3/5.
hope this helps!
The graph of y= - 3x^2– 4x + 2 opens downward true or false
Answer:
True
Step-by-step explanation:
This is a parabola. The coefficient of the x^2 term is -3
Since it is negative, the parabola opens downward
Answer: False
Step-by-step explanation: A-Pexw
Which inequality is shown below ?
Answer:
b.
Step-by-step explanation:
Which describes the correlation shown in the scatterplot?
Answer:
None
Step-by-step explanation:
For there to be a correlation it needs to either be in a line or have equal stuff on both sides
Answer:
Option c is right
Step-by-step explanation:
Given is a scatter plot with points scattered.
We have to find from the shape the correlation coefficient
The points on the scatter plot do not support a linear correlation between the two variables.
There does not seem to be a line of fit which has minimum deviations from the line.
Hence there is no correlation is the correct answer.
From the given graph, we can say that option c is right.
which expression is equivalent to (5x2 + 2x + 1) + (6x2 − 3x + 9) -A. -3x2 + 11x − 3 B. 11x2 − x + 10 C. 4x2 + 27x − 28 D. -3x2 + 11x + 31
Answer:
B. 11x^2 − x + 10
Step-by-step explanation:
(5x^2 + 2x + 1) + (6x^2 − 3x + 9)
I like to line them up vertically
(5x^2 + 2x + 1)
+ (6x^2 − 3x + 9)
---------------------------
11 x^2 - x + 10
Solve for x in the equation 2x2 -5x+ 1 = 3.
Answer:
[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]
Step-by-step explanation:
[tex]2x^2-5x+1=3[/tex]
To solve for x, we make right hand side 0
Subtract 3 from both sides
Given equation becomes
[tex]2x^2-5x-2=0[/tex]
We apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=2, b=-5, c=-2
[tex]x=\frac{5+-\sqrt{5^2-4(2)(-2)}}{2(2)}[/tex]
[tex]x=\frac{5+-\sqrt{41}}{4}[/tex]
[tex]x=\frac{5+\sqrt{41}}{4}[/tex] and [tex]x=\frac{5-\sqrt{41}}{4}[/tex]
Find the surface area of this cube. Be sure to include the correct unit in your answer.
8 yd
8 yd
8 yd
The circle given by x^2+y^2-6y-12=0 can be written in standard form like this: x^2+(y-k)^2=21 What is the value of k in this equation?
Answer:
The value of k =3
Step-by-step explanation:
[tex]x^2+y^2-6y-12=0[/tex] We need to solve this equation to become in standard form to find the value of k.
[tex]x^2+y^2-6y-12=0\\x^2+y^2-6y = 12\\(x)^2 +(y^2-2(y)(3)+(3)^2) = 12 +(3)^2\\(x)^2+(y-3)^2 = 12+9\\(x)^2 +(y-3)^2 = 21[/tex]
The given standard form is:
[tex]x^2+(y-k)^2=21[/tex]
Comparing it with [tex](x)^2 +(y-3)^2 = 21[/tex]
The value of k =3
Answer:
k = 3
Step-by-step explanation:
Equation of the given function has been given as x² + y² - 6y - 12 = 0.
We have to convert this equation in the standard form of x² + (y - k)² = 21 to get the value of k.
x² + y² - 6y - 12 = 0
x² + y² - 6y + 9 - 9 - 12 = 0
x² + [y²- 2(3y) + 3²] - 21 = 0
x² + (y - 3)²- 21 = 0
x² + (y - 3)² = 21
Now by comparing this equation with the standard form of the equation we get the value of k = 3
If f(x) = 5x + 40, what is f(x) when x = –5?
First note that f(x) means the same thing as y. To solve for f(x) or y you need to plug in -5 for x and solve using the rules of PEMDAS
5(-5) + 40
-25 + 40
15
When x is -5 then y is 15
Hope this helped!
~Just a girl in love with Shawn Mendes