Answer:
( x - 3 ) 3 .
Step-by-step explanation:
Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=3√x+3 f - 1 ( x ) = x 3 + 3 is the inverse of f(x)=(x−3)3 f ( x ) = ( x - 3 ) 3 .
Find the area of the shaded region.
80°
5 cm
A≈ [?] cm²
Enter a decimal rounded to the nearest tenth.
[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]
Hawa models a can of ground coffee as a right cylinder. She measures its radius as
3/4 in and its volume as 8 cubic inches. Find the height of the can in inches. Round your answer to the nearest tenth if necessary
Answer: The height is 4.5 in
Step-by-step explanation:
We can use the given formula for volume, transform it to solve for height (h), and then substitute our given values to solve.
Given formula:
[tex]\displaystyle V=\pi r^2h[/tex]
Transformed to solve for height:
[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]
Substitute given points:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.75\; \text{inches})^2}[/tex]
Square:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.5625)}[/tex]
Multiply:
[tex]\displaystyle h=\frac{8}{1.767146}[/tex]
Divide:
[tex]\displaystyle h=4.527[/tex]
Round to the nearest tenth:
[tex]\displaystyle h=4.5[/tex]
In Martha's food storage, she has 13 cans of chicken noodle soup, 15 cans of tomato soup, and 17 cans of mushroom soup. If she randomly chooses a can of soup from her food storage, what is the probability it is a can of tomato soup?
Answer:
1/3
Step-by-step explanation:
p(event) = (number of desired outcomes)/(total number of outcomes)
total number of outcomes = 13 + 15 + 17 = 45
number of desired outcomes = 15
p(can of tomato soup) = 15/45 = 1/3
In the following diagram, triangle EFG is similar to triangle MNP and cos E=4/7. If MP=20 then find the length of MN to the nearest tenth. Show the work that leads to your answer.
The length of MN to the nearest tenth is 11.4 units
Finding the length of MN to the nearest tenthFrom the question, we have the following parameters that can be used in our computation:
cos E = 4/7
MP = 20
Because the triangles are similar triangles, we have
cos M = cos E = 4/7
So, we have
cos M = MN/MP
This gives
MN/MP = 4/7
So, we have
MN/20 = 4/7
Evaluate
MN = 20 * 4/7
So, we have
MN = 11.4
Hence, the length is 11.4
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Find all intersection points of the parabola y = x^2 and the circle with a radius √6 and center at (0,4).
The requried, intersection points are (√5, 5), (-√5, 5), (√2, 2), and (-√2, 2).
To find the intersection points of the parabola y = x² and the circle with radius √6 and center at (0,4), we need to solve the system of equations:
x² + (y - 4)² = 6 (equation of circle)
y = x² (equation of parabola)
We can substitute y = x² into the equation of the circle and obtain a quadratic equation in x:
x² + (x² - 4)² = 6
x⁴ - 7x² + 10 = 0
This equation can be factored as:
(x² - 5)(x² - 2) = 0
Therefore, the solutions for x are x = ±√5 and x = ±√2. To find the corresponding values of y, we can substitute these values of x into the equation of the parabola:
y = x²
For x = √5, we have y = (√5)² = 5, and for x = -√5, we have y = (-√5)² = 5.
For x = √2, we have y = (√2)² = 2, and for x = -√2, we have y = (-√2)² = 2.
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The Cruiser Bicycle Company makes two styles of bicycles: the Traveler (x), which sells for $300, and the Tourister (y), which sells $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production.
Write an inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products).
An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:
x + y ≤ 300
x1 + y3 ≤ 360
What is an inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
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I don’t understand this problem
The area of the composite figure is equal to 521.080 square milimeters.
How to determine the area of a composite figure
In this problem we have the representation of a composite figure, whose area should be found. This figure is the consequence of the combination of three figures: a semicircle, a rectangle and a triangle. The area formulas for each case are introduced below:
Semicircle
A = 0.5π · r²
Where r is the radius, in milimeters.
Rectangle
A = b · h
Triangles
A = 0.5 · b · h
Where:
b - Base, in milimeters.h - Height, in milimeters.A - Area, in square milimeters.Now we proceed to compute the area of the composite figure:
A = 0.5π · (10 mm)² + (20 mm) · (14 mm) + 0.5 · (12 mm) · (14 mm)
A = 50π mm² + 280 mm² + 84 mm²
A = 521.080 mm²
RemarkThe statement is absent. Complete statement is introduced below:
Find the area of the figure.
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In a standard deck of cards (NOT including jokers), there are:
4 suits (diamonds, hearts, clubs, spades)
13 number and face cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King)
2 colors (red, black)
Face cards are Jack, Queen, King
a) What is the probability of drawing a red or black card?
b) What is the probability of drawing a 7 of spades?
c) What is the probability of NOT drawing a Diamond?
d) What is the probability of drawing a black 2?
hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((
Need help with this please
The area of the original figure is 1/9 times the area of the new figure
The perimeter of the original figure is 1/2 times the perimeter of the new figure
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The figures
The areas of the new figures is calculated as
Area = Old area * scale factor
So, we have
Area Figure 1 = (1 * 3) * 3
Area Figure 1 = 9
The perimeter of the new figures is calculated as
Perimeter = Old Perimeter * scale factor
So, we have
Perimeter Figure 2 = (4 * 4 + 4 * (2 + 3)) * 1/2
Perimeter Figure 2 = 18
See attachment for the dilates figures
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Applying the Right Triangle Altitude Theorem. Which similarity statement is true?
The true similarity statement are using Right Triangle Altitude Theorem :
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.
By the Right Triangle Altitude Theorem,
If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.
Using this,
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.
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The complete question is given below.
Find each angle and arc measure.
⌢
mDGF= degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
Answer: 226
Step-by-step explanation:
The angle is half of the arc angle
so mDGF is 2 times as big as the angle
mDGF=113*2
mDGF=226
Yoshi is driving across the United States. If Yoshi's map is 20 inches across, and the United States is 3,000 miles across, what is the scale of the map?
how many paperclips that weigh 2 grams would balance a scale of 1 pound?
Answer: 226.795 paperclips
Step-by-step explanation:
First, we need to know how many grams are in a pound.
[tex]\boxed{\text{1 pound = 453.59 grams}}[/tex]
Next, we will divide 453.59 grams by the 2 grams per paper clip to see how many paper clips would balance the scale with one pound.
453.59 / 2 = 226.795 paperclips
Which of the following represents the symmetric property of equality?
A) If a = b and b = c, then a = c
B) If a = b, then ac = bc
C) If a = b, then b = a
D) a(b + c) = ab + ac
Answer:
C) a = b ⇒ b = a
Step-by-step explanation:
You want to identify the statement that represents the symmetric property of equality.
A.If a = b and b = c, then a = c. This is the transitive property of equality.
B.If a = b, then ac = bc. This is the multiplication property of equality.
C.If a = b, then b = a. This is the symmetric property of equality.
D.a(b +c) = ab +ac. This is the distributive property of multiplication over addition.
Help me solve and show my work please
The simplified form of trigonometric functions by trigonometric formulas are listed below:
Case 1: 0.5√(2 - √3)
Case 2: (0.5√2) / (1 + 0.5√2)
Case 3: sin 6x
Case 4: sin θ
How to simplify and evaluate trigonometric functions
In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:
Case 1
sin 15° = √[(1 - cos 30°) / 2]
sin 15° = √[(1 - √3 / 2) / 2]
sin 15° = √[(2 - √3) / 4]
sin 15° = 0.5√(2 - √3)
Case 2
tan 22.5° = sin 45° / (1 + cos 45°)
tan 22.5° = (0.5√2) / (1 + 0.5√2)
The last two expressions are simplified and evaluated by double angle formulas:
Case 3
2 · sin 3x · cos 3x
sin 6x
Case 4
2 · sin 0.5θ · cos 0.5θ
sin θ
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An ordinary fair dice is a cube with the numbers 1 through 6 on the sides
The probability values are P(A) = 0.722 and P(B) = 0.50
Calculating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
A fair die
The sample space of the events are
A = Sum is greater than 5
B = Sum is an even number
From the sample space of the sum of outcomes, we have
n(A) = 26
n(B) = 18
So, we have
P(A) = 26/36 = 0.722
n(B) = 18/36 = 0.50
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maria and joan went shopping. maria bought 3 pair of jeans that each cost the same amount and 4 t-shirts that each cost the same amount. joan bought 2 pair of jeans that each cost the same amount, and 1 t-shirts that each cost the same amount. what is the cost of the jeans and shirts
Result:
The total cost of the jeans and shirts = 5(x + y)
How do we determine the cost?Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.
Let x = the cost of one pair of jeans.
Let y = e the cost of one T-shirt.
Given:
Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:
3x = cost of Maria's jeans
4y = cost of Maria's T-shirts
Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:
2x = cost of Joan's jeans
y = cost of Joan's T-shirt
To find the total cost of all they bought, add up the costs:
Total cost = Maria's cost + Joan's cost
Total cost = 3x + 4y + 2x + y
Total cost = 5x + 5y
So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.
Simplify the expression by factoring out a common factor of 5, and we get:
Therefore, total cost = 5(x + y)
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can someone help me with number 2 and 3
The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;
PerpendicularParallelNeitherPerpendicularParallelNeitherWhat are parallel lines?Parallel lines or line segments are line segments that have the same slope.
1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5
The slope of the segment [tex]\overline{CD}[/tex] is; (3 - 0)/(10 - (-5)) = 3/15 = 1/5
The slope of [tex]\overline{AB}[/tex] is the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex], [tex]\overline{AB}[/tex] is perpendicular to [tex]\overline{CD}[/tex]
2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3
The slope of the segment [tex]\overline{CD}[/tex] is; (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3
The slope of [tex]\overline{AB}[/tex] is the same as the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex], [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]
3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2
The slope of the segment [tex]\overline{CD}[/tex] is; (-7 - 11))/(5 - (-1)) = -18/6 = -3
The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1
The slope of the segment [tex]\overline{CD}[/tex] is; (2 - 6)/(-8 - (-4)) = -4/(-4) = 1
The slope of [tex]\overline{AB}[/tex] is the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]
5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4
The slope of the segment [tex]\overline{CD}[/tex] is; (6 - (-3))/(12 - 0) = 9/12 = 3/4
The slope of [tex]\overline{AB}[/tex] is the same as the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex]
6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2
The slope of the segment [tex]\overline{CD}[/tex] is; (7 - (-5))/(-4 - 2)) = 12/(-6) = -2
The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.
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How many rectangles can you make that will fit on a 4 ✕ 4 geoboard such that none of them are congruent?
The answer is NOT: 100, 20, 36, 4, 354, 273, or 73
Answer:
9
Step-by-step explanation:
You want the number of non-congruent rectangles that can be drawn on a 4 × 4 geoboard.
RectangleA rectangle will have right-angle corners and opposite sides the same length. The attachment shows the 9 rectangles we believe exhaust the possibilities for a grid of 4 dots by 4 dots.
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What is the range of |x|-7?
Answer:
3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!
If you know what question this is please answer I couldn’t fit everything in the picture :(
Restaurant
No commute 3
0-1 Hr Commute 10
> 1 Hr Commute 28
Sum 41
The correct groupings for each probability are given below as follows:
The probability that you have more than a 1 hour commute: Marginal-57/134 = 42.5% chanceThe probability that you make a home-cooked meal and you have more than a 1-hour commute: Joint-7/134 = 5% chanceThe probability that you eat at a restaurant given that you have no commute: Conditional-3/37 = 8% chanceThe probability that you get takeout food: Marginal-50/134 = 37% chanceThe probability that you eat at the restaurant and have no commute: Joint probability 3/134 = 2% chanceThe probability that you commute 0-1 hour given that you get take-out food: Conditional-18/50 = 36% chanceWhat is joint probability?The possibility of two events occurring simultaneously and at the same time is known as joint probability.
Joint probability is the likelihood that event Y will take place at the same time as event X.
An example of a joint probability is the probability that you eat at the restaurant and have no commute
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Garnier's Opera House is a revival of the________style.
Romantic
Gothic
Renaissance
Baroque
Answer: Garnier's Opera House is a revival of the Baroque style.
I need help with this question. please help!!
The value of x in the heptagon is 38.6 degrees.
How to find the angle of an heptagon?An heptagon is a polygon with 7 sides. A regular heptagon is an heptagon with all sides equal to each other.
Therefore, sum of angles in an heptagon is equal to 900 degrees.
Let's find each angle of the heptagon.
each angle in the regular heptagon = 900 / 7
each angle in the regular heptagon = 128.57 degrees
Therefore, each angle of a square is 90 degrees.
Hence,
x = 128.57 - 90
x = 38.5714285714
Finally,
x = 38.6 degrees
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find the measure of TDC
The measure of angle TDC in the triangle is 32 degrees.
How to find the angle of a triangle?The tangent CD forms a right angle with the radius CT of the circle. This forms a right angle triangle.
Therefore, the sum of angles in the triangle is 180 degrees.
Hence,
∠C = 90 degrees
Therefore,
3x + 14 + 8x + 10 + 90 = 180
11x + 114 = 180
11x = 180 - 114
11x = 66
divide both sides by 11
x = 66 / 11
x = 6
Therefore,
∠TDC = 3x + 14 = 3(6) + 14 = 18 + 14 = 32 degrees.
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one less than two times a number is equal to 11 more than four times the number
Answer:
n = -6
Step-by-step explanation:
We can allow n to represent the unknown number.
Two times the number is 2n and 1 less than gives us 2n - 1Four times the number is 4n and 11 more than gives us 4n + 11Now, we can set the two expressions equal to each other to find the number, n:
[tex]2n-1=4n+11\\2n=4n+12\\-2n=12\\n=-6[/tex]
Finally, we can check if the number fits the equation and the verbal expression by plugging in -6 for n:
Algebraically:
2(-6) - 1 = 4(-6) + 11
-12 - 1 = -24 + 11
-13 = -13
Verbally:
Two times the number -6 is -12 and 1 less than - 12 is -13
Four times the number -6 is -24 and 11 more than this is -13
Answer: x= -6
Step-by-step explanation:
Each word in a word problem translates to a mathematical symbol
> 1 less than => - 1
> two times a number => 2x
put that together 1 less than two times a number means:
2x-1
> is => =
> 11 more => 11+
> four times the number => 4x
put it all together
2x-1=11+4x bring all like terms to each side
-2x = 12 solve for x
x= -6
what is the area of triangle ADC, if A is (-1, 3), D is (-1, 7), and C is (0, 4)?
Answer:
e
Step-by-step explanation:
g
1-The tangent line to the curve y = x³ at point A(a, a³) intersects the curve at point B. Let
R be the area of the region bounded by the curve and the tangent line. The tangent line at B
intersects the curve at another point C. Let S be the area of the region bounded by curve and
the second tangent line. How are the areas R and S related?
Answer:
The areas R and S are equal.
Step-by-step explanation:
Since, the tangent line to the curve y = x³ at point A(a, a³) is given by y = 3a²(x - a) + a³. This line intersects the curve at point B(a, a³), and we can find the x-coordinate of point B by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point B.
The slope of the tangent line at point B is 3a², so the equation of the tangent line at point B is y = 3a²(x - a) + a³. This line intersects the curve at another point C, and we can find the x-coordinate of point C by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point C.
The region bounded by the curve and the tangent line at point A is a triangle with base a - (a - a) = 0 and height a³ - a³ = 0, so its area is 0. The region bounded by the curve and the tangent line at point B is a triangle with base a - a = 0 and height a³ - a³ = 0, so its area is also 0. Therefore, the areas R and S are both equal to 0, which means they are equal to each other.
not sure why I cant get the right answer
The composite figure has an area of 142 square yards
The composite figure has one square, right triangle, two rectangles
Area of square = side × side
=8×8
=64 yards
Area of triangle =1/2×8×6
=24 square yards
Area of 1st rectangle = 3×6
=18 square yards
Area of 2 nd rectangle = 9×4
=36 square yards
Total area is sum of square, rectangles and triangle
total area = 64+24+18+36
=142 square yards
Hence, the composite figure has an area of 142 square yards
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10011 base 2 +P + 11100 base 2+ 101 base 2=1001111 base 2
The value of P in the equation (10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2) is 11011 base 2.
What is the value of P in the base 2 addition?The value of P in the equation is found as follows from the given equation:
10011 base 2 + P + 11100 base 2 + 101 base 2 = 1001111 base 2
Hence;
P = 1001111 base 2 - (10011 base 2 + 11100 base 2 + 101 base 2)
Summing the values in the bracket: 10011 + 11100 + 101 = 110100
Then the value of P will be:
P = 1001111 base 2 - 110100 base 2
P = 11011 base 2
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HELP ME ALSO WITH THIS!!!!!