since 87 calories = ³/₄ cup
let x calories = 1 cup
⇒ 87 = ³/₄ x
x = (87)(⁴/₃)
x = 116 calories
∴ if 87 calories is in 3/4 cup, then 1 cup contains 116 calories.Match each function with its inverse function. Use function composition to determine your answers.
Please help
Answer:
For f(x) = x^2 - 2x + 1, the inverse is g(x) = √x + 1
For f(x) = 2 - 5*x the inverse is g(x) = (2 - x)/5
For f(x) = 5*(x - 2) the inverse is g(x) = x*(1/5) + 2
for f(x) = (x - 2)^2 - 1 the inverse is g(x) = √(x + 1) + 2
Step-by-step explanation:
If we have two functions f(x) and g(x) such that these functions are inverse, then we have:
f( g(x)) = x
and
g( f(x)) = x
Let's start with the function:
f(x) = x^2 - 2x + 1
Notice that we can rewrite this as:
f(x) = x^2 - 2*x + 1 = (x - 1)^2
Because this is a quadratic function, the inverse function needs to have a square root, then the inverse function can be the third or fourth one.
Let's try with the last one:
g(x) = √x + 1
Then:
f( g(x)) = ( √x + 1 - 1)^2 = (√x )^2 = x
g( f(x)) = √(x - 1)^2 + 1 = (x - 1) + 1 = x
Then for the function:
f(x) = x^2 - 2x + 1, the inverse is: g(x) = √x + 1
Now let's find the inverse for the second function:
f(x) = 2 - 5*x
The inverse of this function will be also a linear function, and the slope of the inverse will be the inverse of this slope, then the inverse may be the first or second options.
Let's try with:
g(x) = (1/5)*x - 2
Then:
f( g(x) ) = 2 - 5*((1/5)*x - 2) = 2 - x + 10
Then this g(x) is not the inverse of the function.
Let's try with g(x) = (2 - x)/5
Then:
f( g(x)) = 2 - 5*(2 - x)/5 = 2 - 2 + x = x
g( f(x)) = (2 - 2 - 5*x)/5 = 5*x/5 = x
For the function f(x) = 5*(x - 2)
The inverse should be the remaining linear function:
g(x) = x*(1/5) + 2
Then:
f( g(x)) = 5*(x*(1/5) + 2 - 2) = 5*x*(1/5) = x
g( f(x)) = (5*(x - 2) )*(1/5) + 2 = (x - 2) +2 = x
For the last function, f(x) = (x - 2)^2 - 1
The inverse function will be:
g(x) = √(x + 1) + 2
The compositions are:
f( g(x)) = (√(x + 1) + 2 - 2)^2 - 1 = (√(x + 1))^2 - 1 = (x + 1) - 1 = x
g(f(x)) = √((x - 2)^2 - 1 + 1) + 2 = √((x - 2)^2 + 2 = x
Answer:
PLATO ANSWER
Step-by-step explanation:
if a water jug has a volume of 5000cm3 and a height of 45cm, what is the diameter of the jug?
a) 22cm
b) 9.5cm
c) 12cm
d) 15.6cm
If anyone can help :)
Answer:
irrational
Step-by-step explanation:
reason
[tex] - \frac{5}{52} [/tex]
In a sale, the price of a sofa is reduced by 70%. The sale price is £255 What is the price before the sale?
Answer:
850
Step-by-step explanation:
Price x .30 (100%-70%)=sales price
price x .30 = 255
price = 255/.30
price = 850
What is the mean for the data set below
Answer:
B) 8.5
Step-by-step explanation:
[tex]8+10+6+4+12+6+8+14=68\\\\\frac{68}{8} =\boxed{8.5}[/tex]
Option B should be the correct answer.
Hope this helps.
Convert 60% into a decimal and a Fraction(Simplify)
Decimal
Fraction
Answer:
decimal: .6
fraction: 3/5
This year, The Springfield Times had 11,322 subscribers. That is 85% more than they had last year, before the paper was bought out. How many subscribers did the paper have last year?
Answer:
The paper had 1698.3 subscribers last year.
Step-by-step explanation:
11,322 * 85% = 9623.7
11,322 - 9,623.7 = 1698.3
So, the answer is 1698.3
Hope this helps! :)
Write the values in the boxes that make the statement true
Answer:
[tex]\frac{5}{3}xz^8*9x^6y^0z^2 = 15x^7z^{10}[/tex]Step-by-step explanation:
Given
[tex]\frac{5}{3}xz^a*bx^cy^dz^2 = 15x^7z^{10}[/tex]Simplify
[tex]\frac{5}{3}b*x^{1+c}z^{a+2}y^d = 15x^7z^{10}y^0[/tex]Compare left and right sides and
Find b:
[tex]\frac{5}{3}[/tex] b = 15 ⇒ b = 15*3/5 = 9Find c:
1 + c = 7 ⇒ c = 7 - 1 = 6Find a:
a + 2 = 10 ⇒ a = 10 - 2 = 8Find d:
d = 0Solution is:
[tex]\frac{5}{3}xz^8*9x^6y^0z^2 = 15x^7z^{10}[/tex]The area of a trapezoid is 216 in2 and it two bases are 14 and 22 inches long. Find the height of the trapezoid.
Answer:
12 inches
Step-by-step explanation:
The formula for a trapezoid is
A = 1/2(a +b)h
The formula to find the height =
h = 2A/a + b
A= 216 in²
a =14 in
b = 22 in
Hence,
h = 2 × 216/14 + 22
h = 12 inches
The height of the trapezoid = 12 inches
Amy would like to spend at most $100 on lunches for the month. After the first day, Amy had spent $25. At most, how much money can Amy still spend?
Answer:
for the whole month $75.00 for each day around $2.60
Step-by-step explanation:
$100-$25=$75
$75÷29=$2.60 (rounded)
full number is $2.586206896551724
Can I please have Brainliest?
Find the volume of a right circular cone that has a height of 16 m and a base with a
circumference of 14.7 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
Step-by-step explanation:
Start earning $78/hourly for working online from your home for few hours each day... Get regular payment on a weekly basis... All you need is a computer, internet connection and a little free time..... Read more here... www.Nifty2.com
B3BB
Which graph represents the solution set of the inequality x+226?
986
08
4
9 S
7
8
6
+
0 1 -
SS 986
1
2
3
S
6
7
6 8
1 S 986
0
1
2 3
4.
5
9
7 8 9
0
1
2
S
4
5
9
B 2
6
Answer:
C is correct
Step-by-step explanation:
Firstly, we have to solve for x in the solution set of the inequality
We have this as follows;
x + 2 ≥ 6
x ≥ 6-2
x ≥ 4
To graph this, we consider the middle sign which is greater than or equal to
So, the inequality sign has to face the right side
secondly, it has to be shaded on the point 4 due to the fact that it has the ‘equal to’ beneath the single inequality symbol
so, the correct answer here is option C
Choose the <,>,= symbols to answer the question
Answer:
1. >
2,<
3.<
4.>
5,>
6.<
7.>
8.>
Step-by-step explanation:
Please answer fast, it’s due in a hour.
Answer:
100.48 units³
Step-by-step explanation:
Volume of Cylinder: V = πr²h
volume = pi × radius² × heightV = 3.14 × 2² × 8
V = 100.48 units³
Answer:
100.84^units
Step-by-step explanation:
A number, x, rounded to 1 decimal place is 3.7
Write down the error interval for x.
Answer:
The error in rounding a number is half of the unit of measure. The number was rounded to the nearest 0.1 unit so the error is half of 0.1 which is 12⋅0.1=0.05
2
1
⋅0.1=0.05. Since 3.7+0.05=3.753.7+0.05=3.75 and 3.7−0.05=3.653.7−0.05=3.65, then the error interval is \boxed{3.65\le x<3.75}.
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs.
Match the numbers in scientific notation with the corresponding numbers in standard notation.
2.32E9
2.32E8
4.31E-13
4.31E-6
232,000,000
0.00000431
2,320,000,000
0.000000000000431
Answer:
the photo below
Answer:
2.32 · 10^9 = 2,320,000,000.
2.32 · 10^8 = 232,000,000.
4.31 · 10^-13 = 0.000000000000431
4.31 · 10^-6 = 0.00000431
AHahahaahhahhah please please help no links please
Answer:
45
The scale factor is 9
So, 5 x 9 = 45
Find the value of x.
Can someone help please?
In UVW, u=51 inches,v= 61 inches and w= 62 inches.find the measure of angle V to the nearest degree
Answer:
49degrees
Step-by-step explanation:
Using the cosine rule
u² = v²+w²-2vwcosU
Substitute the given values
51² = 61²+62²-2(61)(62)cosU
2601 = 3721+3844-7564 cosU
2601 = 7565-7564cosU
-7564cosU = 2601-7565
-7564cosU = -4964
CosU =-4964/-7564
CosU = 0.6563
U = arccos(0.6563)
U = 49degrees(to nearest degree)
I need help ASAP will give brainliest
Divide 1000 into two parts such that one part is a multiple of 47 and the other is a multiple of 19 ( Show me your working)
= 1000
I know
I think hope this helps
f(x) = -2x + 9 What is f(2h) ?
Answer:
f(2h) = -4h + 9
Step-by-step explanation:
Jacob: Start with the given function f(x) = -2x + 9 and replace 'x' with 2h:
f(x) = -2x + 9 becomes:
f(2h) = -2(2h) + 9, or
f(2h) = -4h + 9
Answer:
-4h + 9
Step-by-step explanation:
f(x) = -2x + 9
f(2h) = -2(2h) + 9
f(2h) = -4h + 9
15 m
4 m
4 m
160°
5 m
Find the area of the figure. Round your answer to the nearest tenth.
Answer:
17.3
Step-by-step explanation:
[tex](2 \sqrt{3}) \times 5 = 17.3[/tex]
6x-4(3x-5)=2 solve for x.
Answer:
x = 3
Step-by-step explanation:
6x -4(3x-5) = 2
6x - 12x + 20 = 2
-6x = 2 - 20
-6x = -18
x = 3
Nolan reports the weather for TV 12's popular afternoon news show. Last month, he tracked
the noon temperature each day in the two largest cities in the area, Hooverville and Deeson
City.
Which city had a lower median temperature?
Hooverville
Deeson City
Answer:
Hooverville
Step-by-step explanation:
The Hooverville has lower median temperature.
What is Box and Whisker Plot?A box and whisker plot is a method for abstracting a set of estimated data using an interval scale. Another name for it is simply a box plot. Most of the time, these are used to interpret data. It is one kind of graphical method that shows how the data in the dataset changes. The histogram can also be used to show the data. However, the histogram provides an adequate display. Since multiple sets of data can be displayed in the same graph, a box and whisker diagram will provide additional information, making it superior to a histogram.
Given Box and Whisker Plot of two cities which show's the noon temperature each day,
From the graph Median of Hooverville is 36 and
median of Deeson City is 38
we can say that Hooverville has lower median temperature.
Hence the lower median temperature is of Hooverville.
Learn more about Box and Whisker Plot;
https://brainly.com/question/2742784
#SPJ2
sunglasses cost 70 euros. the exchange rate is 1 euro = 0.859
Answer: 60.13 USD
Step-by-step explanation: 0.859 x 70 = 60.13
Which of the following situations are equal to 20%? Select all that apply.
A) 5 out of 25
B) 8 out of 40
C) 2 out of 8
D) 16 out of 80
E) 12 out of 24
Answer:
all except C.
Step-by-step explanation:
Answer: A AND C IT SHOULD BE A BECAUSE IF YOU LOOK AT THE %
Which of the following represents a solution to the equation d3 - 343?
WILL MARK AS BRAINLIST
The number 5.2 is which type of number?
Answer:
It is not an "integer" because it is a "decimal value".
It is not "irrational" because the decimal value terminates and does not repeat.
Expressions equivalent to 3^10
Answer:
59049+0
59048.1+0.9
59048.01+0.99
...
Step-by-step explanation:
There's infinite.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3^{10}}[/tex]
[tex]\mathsf{= 3\times 3\times3\times 3 \times 3\times 3\times3\times3\times3\times3 }[/tex]
[tex]\mathsf{3\times3 = \bf 9}[/tex]
[tex]= 9\times9\times 9\times 9\times9[/tex]
[tex]\mathsf{9\times9 = \bf 81}[/tex]
[tex]\mathsf{= 81\times81\times 9}[/tex]
[tex]\mathsf{81 \times 81 = \bf 6,561}[/tex]
[tex]\mathsf{= 6,561\times9}[/tex]
[tex]\mathsf{\bf = 59, 049}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge \bf 59,049}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The area of a triangle is 36 cm square. Give three possible sets of dimensions for the triangle and explain whether or not you can also give the triangles' side length.
Answer:
[tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
[tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
[tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
Step-by-step explanation:
Given
Shape: Triangle
[tex]Area = 36cm^2[/tex]
Solving (a): Three possible dimensions
The area of a triangle is:
[tex]Area = 0.5 * Base * Height[/tex]
Let: [tex]Base = 6cm[/tex]
So, we have:
[tex]36= 0.5 * 6* Height[/tex]
[tex]36= 3* Height[/tex]
Solve for Height
[tex]12 = Height[/tex]
[tex]Height = 12[/tex]
So, a possible dimension is: [tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
Let: [tex]Base = 4cm[/tex]
So, we have:
[tex]36= 0.5 * 4* Height[/tex]
[tex]36= 2* Height[/tex]
Solve for Height
[tex]18 = Height[/tex]
[tex]Height = 18[/tex]
So, a possible dimension is: [tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
Let: [tex]Base = 9cm[/tex]
So, we have:
[tex]36= 0.5 * 9* Height[/tex]
[tex]36= 4.5* Height[/tex]
Solve for Height
[tex]8 = Height[/tex]
[tex]Height = 8[/tex]
So, a possible dimension is: [tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
So, the three possible dimensions are:
[tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
[tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
[tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
Solving (b): Can the side lengths be given
We can only determine the base and the height of the triangle, the third side length can not be determined using the available information