Answer:
The inverse of the function is
-2x-3
Step-by-step explanation:
The inverse of the function f(x) = -\dfrac{1}{2}(x+3) is f(x)⁻¹ = -2x - 3
What is the inverse of a function?The inverse of a function is a function that gives us the actual value for which the desired function has a given result.
The given function is:
[tex]\mathbf{ f(x)=-\dfrac{1}{2}(x+3)}[/tex]
To find the inverse, we need to follow the following steps
replace the role of f(x) by y;[tex]\mathbf{ y=-\dfrac{(x+3)}{2}}[/tex]
Swap x and y variables[tex]\mathbf{ x=-\dfrac{(y+3)}{2}}[/tex]
Solve for y;2x = - (y + 3)
2x = -y - 3
y = -2x - 3
Writing back in inverse notation, we have:
f(x)⁻¹ = -2x - 3
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Anton bought a picnic cooler. His total bill, with tax, was $7.95.
He paid 6 percent sales tax. How much did he pay for the cooler
alone without the tax?
Answer:
$ 7.50
Step-by-step explanation:
The cost of the picnic cooler would be 100%.
With the 6% sales tax, Anton would pay 106% of the cost if the picnic cooler.
(since 100% +6%= 106%)
106%(picnic cooler)= $7.95
Cost of picnic cooler= 100%(picnic cooler).
Cost of picnic cooler
[tex] = \frac{7.95}{106} \times 100 \\ = 7.50[/tex]
Thus, he paid $7.50 for the cooler alone.
Calvin took his friends to a movie for his birthday. The movie tickets cost $12 per person. He spent less than $180. If x is the number of friends he took along, then the inequality that represents the situation is 12x≤180 180x ≥12 x+12≤180 12+x≥180 . Calvin took at most friends to the movie. 13 14 15 16
Answer:
12x<180
14
Step-by-step explanation:
12x<180
x<180/12
x<15
Since x has to be less than 15, he took at most 14 people.
HELP! pleaseeee!!!!!!
Answer:
1,2, and 4.
Step-by-step explanation:
Hi there! I know that i am kind of late, but the answer on Edge 2020 are options 1,2, and 4. I hope this helps, have a great rest of your day :D
From the figure the correct options are ΔABC ~ ΔDEC, ∠B ≅ ∠E, 3DE = 2AB.
Given that a right triangle ΔABC is being dilated by a scale factor of 2/3 and reflected over the side AC to form the ΔDEF.
Since we know that in reflection transformations the object are similar so we can conclude that ΔABC ~ ΔDEC.
Also, by the definition of similar triangles,
∠B ≅ ∠E, ∠A ≅ ∠D and ∠ACB ≅ ∠DCE.
Now since the scale factor is 2/3,
so,
2AB = 3DE
2BC = 3CE
2AC = 3DC
Hence the correct options are ΔABC ~ ΔDEC, ∠B ≅ ∠E, 3DE = 2AB.
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A box that has a width of 5 inches and a length of 12 inches is used to ship a part. The part lies along the diagonal of the bottom of the box. What is the longest possible length of the part?
Answer:
13 inches
Step-by-step explanation:
Draw a square and draw a diagonal line through it. It creates a right triangle. So we can then use the Pythagoras theorem to find the length of the object at it's max. so we do a^2+b^2=c^2. So we do (12*12) + (5*5) = 169 and the square root of 169 is 13.
Identify the sequence as arithmetic or geometric. f(n+1)=17 f(n), for n≥1 and f(1)=49
Answer:
.
/
/
.
.
Step-by-step explanation:
Answer:
Step-by-step explanation:
f(1) = 49
f(n+1) = 17f(n)
n = 1 ; f(1+1) = 17* f(1)
f(2) = 17 * 49 = 833
This is a geometric sequence. Each term is got by multiplying 17 with the previous term, Which means 17 is the common ratio
Calculate the volume and surface areas of the following
Answer:
(VOLUME) A=24 cubic units B=98 cubic units C=36 cubic units D=64 cubic units
Step-by-step explanation:
To find Volume you multiply length, height and width.
Plot the points A(-3, 2), B(-5, -4), C(-2, -4) and D(0, 2). What figure do you
get on joining the points in order (plz answer properly plz I beg you guys )
Answer:
It is a trapezium, I guess
Step-by-step explanation:
To know more see the picture attached
Walter lost his favorite book. He used the map below to discover that he is currently at point (1, 6). He determined that his book is 5 units either to the west or south of his current location. Which of these could be the location of the book? (-4, 6) (1, -1) (-4, 1) (6, 6) (6, -4) (1, 1)
Answer:
(-4, 6)
Step-by-step explanation:
If his book was 5 units to the west, it would be at (1 - 5, 6) = (-4, 6) and if it was 5 units to the south it would be at (1, 6 - 5) = (1, 1). Therefore, (-4, 6) is the answer because (1, 1) isn't an answer choice.
PLEASE HELP!!
Match the expression to its simplified form.
5*-2
1/25
2*5
1/16
2*-4
32
5*3
125
Step-by-step explanation:
5^-2= 1/25 (as when taken up 25 it becomes 5^-2).2^5= 32 (when we multiply 2 for 5 times, we get 32).(2×2×2×2×2)2^-4=1/16 (as when we take up 16 we get 2^-4)5^3=125 (when we multiply 5 for 3 times we get 125)(5×5×5)Hope it helps...
Answer:
The picture should be easier to look at :)
Step-by-step explanation:
Just got it right on edge 2020
please hurry!
The pie chart shows the number of students signing up for various athletic classes. Which bar diagram shows the percent of students signing up for Track and Field class?
Athletic Class Sign Up
1.) A bar diagram with 2 shaded squares and 8 unshaded squares.
2.) A bar diagram with 3 shaded squares and 7 unshaded squares.
3.) A bar diagram with 4 shaded squares and 6 unshaded squares.
4.) A bar diagram with 8 shaded squares and 10 unshaded squares.
Answer:
1) A bar diagram with 2 shaded squares and 8 unshaded squares.
Step-by-step explanation:
There are 100 students (40+15+20+25).
20 signed up for Track and Field.
20 out of 100 would equate to 20/100, or 2/10, or:
1) A bar diagram with 2 shaded squares and 8 unshaded squares.
Answer:
a
Step-by-step explanation:
the two squares are shaded and eight are not
A sample of 353 people is surveyed. The people are classified according to political affiliation ("Democrat", "Republican", or "Independent"). They are also
classified according to opinion on a bill ("in favor of", "opposed to", or "indifferent to"). The results are given in the contingency table below.
In favor of
Opposed to
Indifferent to
Democrat
37
33
47
Republican
29
49
35
Independent
41
41
41
What is the relative frequency of respondents who are Republican?
Round your answer to two decimal places.
Х
?
Answer:
[tex]Relative\ Frequency = 0.32[/tex]
Step-by-step explanation:
Given
The table in the attached diagram
Total population of the survey = 353
Required
Relative frequency of respondents who are Republican
First we consider the data in the republican row; this is presented as follows;
Republican: 29 ------ 49 ----- 35
Next, we add up this data to give the total number of respondents who are republicans
Republicans = 29 + 49 + 35
Republican = 113
Recall that
Total population of the survey = 353
The relative frequency is calculated as follow;
[tex]Relative\ Frequency = \frac{Republican}{Total\ Population\ of\ the\ survey}[/tex]
[tex]Relative\ Frequency = \frac{113}{353}[/tex]
[tex]Relative\ Frequency = 0.3201133145[/tex]
[tex]Relative\ Frequency = 0.32[/tex] (Approximated)
if the standard deviation of a variable is 8, what is the variance?
Answer:
r]
Step-by-step explanation:
Please help !!!The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is
yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use
for
.
Answer:
1,788
Step-by-step explanation:
You calculate the volume of the cylinder minus the volume of the cube
[tex]volume = (\pi*r^2*height) - (width*lenght*height)\\ volume = (\pi*10^2*6) - (4*4*6) [yards]\\volume = 1,788[/tex]
The volume of solid in cubic yards is 1,788 cubic yards
What is the Volume of a Rectangle?
The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
The radius of the solid = 10 yards
The height of the solid = 6 yards
The length of the box = 4 yards
The width of the box = 4 yards
Now ,
The volume of the solid = Volume of the cylinder - Volume of box
And ,
The Volume of cylinder = π x r² x h
The Volume of box = length x width x height
So , substituting the values in the equation , we get
Volume of Cylinder = π x r² x h
= ( 22/7 ) x 10 x 10 x 6
= ( 22/7 ) x 600
= 1884.95 yards³
Volume of the box = length x width x height
= 4 x 4 x 6
= 96 yards³
Therefore ,
The volume of the solid = Volume of Cylinder - Volume of the box
The volume of the solid = 1884 yards³ - 96 yards³
= 1788 yards³
Hence , the volume of the solid is 1788 cubic yards
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which dimensions cannot create a triangle? Three angles measuring 10, 25, and 145, three sides measuring 9m,15m, and 9m, three sides angles measuring 40,70, and 65, three sides measuring 6cm,8cm, and 10cm
Answer:
Three angles measuring 40, 70, and 65
Step-by-step explanation:
The angles of a triangle must total 180.
40+70+65=175, so it cannot be a triangle.
What number should replace the ?
Answer:
94
Step-by-step explanation:
There is a common pattern.
4² = 16
Switch digits 16 ⇒ 61
5² = 25
Switch digits 25 ⇒ 52
6² = 36
Switch digits 36 ⇒ 63
7² = 49
Switch digits 49 ⇒ 94
Plz help me 3(x + 1) = 5 + x
Answer:1
Step-by-step explanation:distribute 3 through the parentheses, move variable to the left hand side and change it’s sign, move constant to the right hand side and change its sign , collect like terms , subtract the numbers and then divide .
The graph shows a journey in a car. Which of the statements most likely describes the journey back to the starting point at the the portion of the graph labeled O?
Answer:
The car travels different distance per unit of time.
Step-by-step explanation:
Distance per unit time on graph will be = Distance for a given point time/ Time
if we see this in terms of x and y , it will be the slope of the curve on given graph.
y/x = slope of graph
Now solving it becomes easier.
We know that
slope = [tex]tan\alpha[/tex] where [tex]\alpha[/tex] is the positive angle with x axis
For part I
The slope will be tan of some acute angle and we know that
tan of acute angle varies between 0 to 1.
Distance per unit time on graph will be between 0 to 1
for part J
Line is parallel to x axis and hence angle with x axis will be 0
thus,
tan 0 = 0
slope of part j is 0
Distance per unit time on graph will be = 0
For part k the distance is changing at each point hence we have to find
distance for each point and time for each point on coordinate and hence
Distance per unit time on graph for part k will be different at each point.
part L and N can be explained on similar grounds as J
O can be explained by explanation for part K.
Part M can be explained by explanation of part I
here difference will be that slope is obtuse and hence
slope or distance per unit time will be negative
as tan for obtuse angle is between -1 to 0.
Thus, correct option will be
The car travels different distance per unit of time.
Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (8, 10), parallel to the graph of y = x +7.
Select one:
Answer:
y=8/3x-34/3
Step-by-step explanation: If the line is parallel to y=8/3x+7, then the slope must be 8/3. So, we can eliminate A and B. Now, let's take C, and plug in (8, 10) into the equation. We end up with 10=64/3-34/3. 64-34=30. 30/3=10. 10 = 10. So, C is the correct answer. No need to check for D.
Giving Brainly Please Help I Am In A Rush: A 2-column table with 5 rows titled Games Played. Column 1 has entries a percent, a percent, a percent, a percent, b percent. Column 2 has entries c, c, c, c, d. So far this season, a team has won 51 out of 68 games. Identify the values of a, b, c, and d that complete the bar diagram for this situation. a = 10, 25,51,100 b = 25,51,68,100 c = 12.75,14,17,51 d = 30,51,68,100
Answer:
the answer is below
Step-by-step explanation:
a = 25
b = 100
c = 17
d = 68
Answer:
The correct answer is
a= 25
b = 100
c = 17
d = 68
Step-by-step explanation:
At the beginning of the year, Adrian's savings account balance was $28. Each week, he deposits another $15 into that account, and he doesn't spend any of his savings.
Answer:
808$
Step-by-step explanation:
This isn't very clear, when does he stop saving?
I'm going to assume that he stops at the end of the year at which case that would just be 15 multiplied by 52 plus 28
A pharmacist is filling small empty bottles with cough syrup from a larger bottle. He can solve the inequality to find the number of small bottles, x, that can be filled from the larger bottle and still have 250 milliliters left in the larger bottle. Which statement describes the number of small bottles the pharmacist can fill?×
Answer:
1000 -25x >250.
Step-by-step explanation:
Let us assume the capacity of a large bottle = 1000 ml.
And the capacity of each small bottle = 25 ml.
Reaming milliliters in large bottles = 250 milliliters.
Number of bottles = x bottles.
The total capacity of the large bottle - capacity of a small bottle × number of bottles > Remaining milliliters in a large bottle.
Therefore, we can set up an inequality.
1000 - 25 × x > 250.
1000 -25x >250.
Brad wants to open a new savings account. He finds one that returns 3% on his investment each year.
Question 1
Assign a variable to each of the following płeces of information:
• final balance
• initial investment
• return rate
use the variable to write a formula for the final balance after 2 years
Answer:
1.03x
Step-by-step explanation:
1 year b would be the inital investment added with interest
i believe this is the equation
b = x + r(x)= (1 + r)x
and since it says 3% each year we know its 0.03 (r)
and when you solve it out you get that answer
Drag the tiles to the correct box?
Answer:
1. (3,-1) and (5,4)
[tex]Distance\ = 5.39[/tex]
2. (2,3) and (4,5)
[tex]Distance\ = 2.83[/tex]
3. (-5,7) and (8,5)
[tex]Distance = 13.15[/tex]
4. (-2,4) and (3,-1)
[tex]Distance = 7.07[/tex]
Step-by-step explanation:
Given
The attached
Required
Calculate the distance between each points;
Distance between points is calculated using;
[tex]d =\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
1. (3,-1) and (5,4)
Here; [tex]x_1 = 3; x_2 = 5; y_1 = -1; y_2 = 4[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(3 - 5)^2 + (-1 - 4)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-5^2)}[/tex]
[tex]d =\sqrt{4 + 25}[/tex]
[tex]d =\sqrt{29}[/tex]
[tex]d = 5.39[/tex] (Approximated)
2. (2,3) and (4,5)
Here; [tex]x_1 = 2; x_2 = 4; y_1 = 3; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(2 - 4)^2 + (3 - 5)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-2^2)}[/tex]
[tex]d =\sqrt{4 + 4}[/tex]
[tex]d =\sqrt{8}[/tex]
[tex]d = 2.83[/tex] (Approximated)
3. (-5,7) and (8,5)
Here; [tex]x_1 = -5; x_2 = 8; y_1 = 7; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-5 - 8)^2 + (7 - 5)^2}[/tex]
[tex]d =\sqrt{- 13^2 + 2^2}[/tex]
[tex]d =\sqrt{169 + 4}[/tex]
[tex]d =\sqrt{173}[/tex]
[tex]d = 13.15[/tex] (Approximated)
4. (-2,4) and (3,-1)
Here; [tex]x_1 = -2; x_2 = 3; y_1 = 4; y_2 = -1[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-2 - 3)^2 + (4 - (-1))^2}[/tex]
[tex]d =\sqrt{- 5^2 + (4+1)^2}[/tex]
[tex]d =\sqrt{- 5^2 + 5^2}[/tex]
[tex]d =\sqrt{25 + 25}[/tex]
[tex]d =\sqrt{50}[/tex]
[tex]d = 7.07[/tex] (Approximated)
Find the value of x. please help will give brainliest
Answer:
24°
Step-by-step explanation:
Bigger Triangle
180°-94°-41°= 45° ( Angles sum in a triangle)
Smaller Triangle
180° - 45°- 111° = 24° (Angles sum in a triangle)
Therefore X = 24°
Hope this helps.
Answer:
24
Step-by-step explanation:
First we will find the last angle of the big triangle.
1). 94 + 41 + y = 180
y = 45
Now we know the value of 2 angles in the smaller triangle, so we can find x.
1). 111 + 45 + x = 180
x = 24
Hope this helps))
17 points geometry question i need help asap.
Question 1: Classify the system of equations and identify the number of solutions. 3 = 4x + y 2y = 6 − 8x Answers: inconsistent; none consistent, independent; one consistent, dependent; one consistent, dependent; infinite Question 2: Using substitution, identify the ordered pair that is not an element of the solution set of the system of equations. 6x + 3y = 6 2x + y = 2 Answers: (0, 2) (1, 0) (2, −2) (−2, 0)
Answer:
1st: consistent and dependent
2nd: (-2,0). Simply put the called and check.
Answer:
Question 1 Answer: consistent, dependent; infinite
Question 2 Answer: (2, -2) y= 2 - 2x
Step-by-step explanation:
Question 1 explanation: Solve the first equation for y.
3 = 4x + y
3 − 4x = y Subtract 4x from both sides.
y = 3 − 4x Rewrite the equation.
Simplify the second equation by dividing.
2y = 6 − 8x
y = 3 − 4x Divide both sides of the second equation by 2.
Rewrite the system.
y = 3 − 4x
y = 3 − 4x
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 22 and 15
Answer:
7 < (third side length) < 37
Step-by-step explanation:
Add these two side lengths together. We get 37. Unless the 3rd side is LESS than 37, we cannot form a triangle.
Next, subtract 15 from 22, obtaining 7. The 3rd side has to be GREATER than 7 in order for the sides 7+, 15 and 22 to form a triangle.
7 < (third side length) < 37
Answer:
26.63 ??
Step-by-step explanation:
I think you use pythagorean theorum to solve.
do 22^2 and 15^2 and get 709.1569
sqrt of that is 26.63
ΔPQR is located at P (−3, −3), Q (0, 0), and R (3, −3). Which statement correctly classifies ΔPQR?
Answer:
Isosceles Triangle
Step-by-step explanation:
An equilateral triangle is a triangle that has all of its 3 sides at an equal length. After drawing out the given points on a graph, you can clearly see that the foundation is longer than the other 2 sides. Because the 2 sides that I just mentioned happen to be of equal length, however, means that this triangle can be none other than an Isosceles triangle. If I did anything wrong here, let me know. Have a good rest of your day. :D
Answer:
ΔPQR is an isosceles triangle.
Step-by-step explanation:
A rectangle is graphed on the coordinate grid.
Which represents the equation of the side that is parallel to sider?
y=-X+9
y=-x+ 5
y=x-3
y= X+3
Let’s see if I can help you :)!
With two points you can define a line.
So, the line parallel to s is q, which has these two pointS: (3,6) and (6,3)
There are different ways to get the line. For instance, this one:
Y = a*x+b
a = slope = difference_y/difference_x = (3-6)/(6-3) = -1,
y = -x + b,
Now use any point, say (3,6) to get b:
6 = -3+b-> b - 9.
Line is y = -x + 9,
It checks out in the other point: (6,3) —> 3 = -6+9 = 3. Good.
Other method:
y-y2 = a*(x-x2), where (x2,y2) is one of the two points and a is the slope as defined before.
Really hope this helped you!
Answer:
The answer is B
Step-by-step explanation:
need help refer to picture
Answer:
-6x + 54y + 4.83 xy + 9.32
Step-by-step explanation:
line up like terms next to each other:
7x - 13 x + 18y + 36y + 4.83xy + 9.32
solve:
-6x + 54y + 4.83xy + 9.32