Answer:
(fog)(x) = x
Step-by-step explanation:
Composite function:
[tex](f \circ g)(x) = f(g(x))[/tex]
Composite of a function and its inverse.
The composition of a function and it's inverse is the straight line x. So
[tex](f \circ f^{-1})(x) = x[/tex]
f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}
We can see that the x-values in f are the y-values for g, and the y-values for f are the x-values for g, that is, f and g are inverse functions. Thus:
(fog)(x) = x
Each question is worti 2 punts
5. The Eiffel Tower, shown to the right, has a width of 328 feet and a height of 984 feet. Maria
is designing a T-shirt for her trip to France and she wants to put a picture of the Eiffel tower on
the front of the shirt. The maximum space she can use on the shirt is a rectangle with a width of
.75 feet and a height of 1.5 feet. Maria uses a scale factor of where k is an integer, to shrink
the Eiffel Tower and fit it on the t-shirt. What is smallest possible value for k?
Answer:
The smallest possible value of k is 656
Step-by-step explanation:
The given width of the Eiffel Tower, w₁ = 328 feet
The given height of the Eiffel Tower, h₁ = 984 feet
The width of the space Maria can use on the shirt, w₂ = 0.75 feet
The height of the space she can use on the shirt, h₂ = 1.5 feet
We get;
The ratio of height to width of the Eiffel Tower = h₁/w₁ = 984/328 = 3
The height to width ratio of the space on the shirt = h₂/w₂ = 1.5/0.75 = 2
Therefore, that the aspect ratio of the space on the T-shirt is wider than the Eiffel Tower, the height of the space on the T-shirt is the limiting dimension of the scaled picture of the Eiffel Tower
Therefore, the scale factor, k = The ratio of the actual height of the Eiffel Tower, to the height of the space on the T-shirt
Where 'k' represent the integer value to shrink the Eiffel Tower and fit it on the T-shirt, and 'k' is the smallest ratios of the dimensions of width or height of the tower to the dimensions of the width or height of the space available on the shirt, given that the height to width ratio of the area on the shirt is smaller than that of the Eiffel Tower
Mathematically
k = h₁/h₂
∴ k = 984/1.5 = 656
The scale factor of the height of the Eiffel Tower to the height of the space available on the T-shirt, k = The smallest possible value of k = 656.
Help plssss I’m trying to finish this diagnostics test
Answer: 5 Seconds
Step-by-step explanation: Given the equation of the height expressed ad;
h(t) = - 16t^2 + initial height
Given that initial height = 400feet
h(t) = - 16t^2 + 400
The waste will hit the ground at when h(t) = 0
substitute
0 = - 16t^2 + 400
16t^2 = 400
t² = 400/16
t² = 25
t = √25
t = 5secs
Cual es el cociente y el resto de la siguiente división? 64:5= *
a) El cociente es 4 y el resto 5
b) El cociente es 12 y el resto 0
c) El cociente es 4 y el resto 12
d) El cociente es 12 y el resto
Answer:
D
Step-by-step explanation:
el cociente es 12 y el resto es 4, porque 12 por 5 es 60. 60 es el cociente. y 64-60 = 4 por lo tanto 4 es el resto
Brainliest + 20 points goes to whoever answers correctly also if you want more points then answer my others
hey shawty baes i’m so srry 4 asking sm but i have no clue what i’m doing
Answer:
D. x = -5y^2
Step-by-step explanation:
I used a graphing calculator.
Figure ABCD is a parallelogram
What is the value of x?
6
7
8
9
Step-by-step explanation:
Can u upload image so that i can help u
where is the sand dollar
Answer:
maybe the palm tree is at 5 the rock at -2 and the sand dollar at 0?
or, somthing like that
Step-by-step explanation:
The sand dollar is at zero which is 2 units away from rock and five units away from palm tree
What is Number system?A number system is defined as a system of writing to express numbers.
A sand dollar is 2 units away from rock and five units away from palm tree, We have to find the location of the sand dollar
Let the rock is at -2 on number line
The palm tree is at 5 on number line
So the sand dollar is at 0, as zero is two units away from rock and tree is five units away
Hence, the sand dollar is at zero which is 2 units away from rock and five units away from palm tree
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Tres amigos obtienen un premio de $1000.00 en la lotería, ¿cómo deben repartirlo si uno de ellos aportó $12.00, el otro $8.00 y el tercero $15.00?
Ayudeeen es para hoyyyy
Answer:
hii
Step-by-step explanation:
follow me please gugs
GIVE BRAINLOEST!!! see picture
Answer:
c. 60
Step-by-step explanation:
If we know that d is 90 degrees. We can make a conclusion that we have a 30, 60, 90 triangle. D is 90 and a triangle is 180 degrees. So we can automatically knock off 90 from the 180 giving us another 90. Now we know that we have a 30 and 60 to work with. F is an angle that is larger than E. So E is 30 and F is 60.
Find the exact value of cos2theta if sin2theta=3/4 and theta is between 0 and 90 degree
[tex] \boxed{ \boxed{ \cos {}^{2} ( \theta) = \dfrac{1}{4} }}[/tex]
Solution :According to a Trigonometric Identity :
[tex] \hookrightarrow \mathrm{\sin {}^{2} ( \theta) + \cos {}^{2} ( \theta) = 1}[/tex]
Now, let's solve for [tex] \cos²(\theta)[/tex]
[tex] \longrightarrow \dfrac{3}{4} + \cos {}^{2} ( \theta) = 1[/tex]
[tex] \longrightarrow \cos{}^{2}( \theta) = 1 - \dfrac{3}{4} [/tex]
[tex]\longrightarrow \cos {}^{2} ( \theta) = \dfrac{4 - 3}{4} [/tex]
[tex]\longrightarrow \cos {}^{2} ( \theta) = \dfrac{1}{4} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: \: it \: \: helps \: \: you.....}}{\orange{}}}}}[/tex]
Ivanna has bought 30 pounds of dog food. She feeds her dog 3/5 pounds for each meal. For how many meals will the food last?
Answer:50
Step-by-step explanation:
3/5 = 3 ÷ 5 = 0.6
30 ÷ 0.6 = 50
otra explicacion:
30/1 ÷ 3/5= 30/1 x 5/3 = 150/3 = 50
Which one of the following compound inequalities has no solution?
From the following compound inequalities, all the compound inequalities have a solution.
What is compound inequality?A compound inequality is a type of inequality that comprises two basic inequalities.
From the given information, we have:
2x + 3 < 3x - 4 and 3x + 7 > 5x - 92(x -6) < 3(x+6) and 6(x+3) > 9(x-1)8x + 15 ≤ 4x - 5 and -7x + 2 < -6x + 3-5x - 1 ≥ -7x + 9 and -4x - 7 < 5x + 11To determine the compound inequality with no solution, we need to solve each of the inequalities.
1.
2x + 3 < 3x - 4 and 3x + 7 > 5x - 9
Collect like terms
= 2x - 3x < - 4 - 3 and 3x - 5x > - 9 - 7
= -x < -7 and -2x > -16
= x < 7 and x > 8 (has a solution)
2.
2(x -6) < 3(x+6) and 6(x+3) > 9(x-1)
Open brackets
= 2x - 12 < 3x + 18 and 6x + 18 > 9x - 9
Collect like terms
= 2x - 3x < 18 + 12 and 6x - 9x > - 9 - 18
= - x < 30 and - 3x > - 27
= x > -30 and x > 9 (has a solution)
3.
8x + 15 ≤ 4x - 5 and -7x + 2 < -6x + 3
Collect like terms
= 8x - 4x ≤ - 5 - 15 and -7x - 6x < 3 - 2
= 4x ≤ - 20 and -13x < 1
= x ≤ -5 and x < - 1/13 ( has a solution)
4.
-5x - 1 ≥ -7x + 9 and -4x - 7 < 5x + 11
= -5x + 7x ≥ 9 + 1 and -4x -5x < 11 + 7
= 2x ≥ 10 and -9x < 18
= x ≥ 5 and x < -2 ( has a solution)
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The sixth graders at Kingston Middle School voted for their favorite sport. The results are in the circle graph below. Favorite sports 3/20 Football 1/2 Basketball 1/2 Golf Baseball 1/10 If the 180 students in sixth grade get to choose a sport to play for a special reward, how many of these students will choose basketball?
Answer:
90 Students.
Step-by-step explanation:
1/2 (Half) of 180 is 90.
Answer:
90 students will choose basketball
Step-by-step explanation:
half (1/2) choose basketball and half of 180 is 90
In the past 4 months, Alex has lost 8 pounds, gained 9 pounds, lost 2 pounds, and lost another 6 pounds. Find his total change in weight.
please provide with strategies!! ❤️
=============================================================
Explanation:
Draw a vertical number line. Let's say we start at 0 on the number line. Zero means no net change (he doesn't gain weight, nor does he lose weight either).
Losing 8 pounds means we go down 8 units. Think of it like being at the ground level and then going down 8 floors to the basement level of a large building (eg: parking garage maybe).
After this movement, we're at -8 on the number line. Then move up 9 units to arrive at +1 or just 1 on the number line. So Alex has gained those 8 pounds back to his original weight, plus an extra pound. So that's why -8+9 = 1.
Then move down 2 units to get to -1. Lastly, from -1 move 6 units down to get to -7.
So overall, Alex has lost 7 pounds when everything is said and done.
Refer to the diagram below. We start at point A, move to point B after losing 8 pounds, then to C when gaining 9 pounds, and so on until we get to point E. Point E is at -7 on the vertical number line to represent that he lost 7 pounds.
----------------
We can think of it in another way:
add up all the losses to get
loss of 8 + loss of 2 + loss of 6 = loss of 16
So he lost 16 pounds if we ignore the "gained 9 pounds", but we have to account for that. So we'll take 9 away from 16 to get 16-9 = 7.
Overall, Alex lost 7 pounds.
Given that (in picture)...
Find the values of a and b
Please help- confused on rationalising denominator but not sure
=================================================
Work Shown:
Multiply top and bottom by [tex]\sqrt{2}[/tex] to rationalize the denominator
[tex]\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\[/tex]
We end up with something in the form [tex]a+b\sqrt{2}[/tex] where a = -3 and b = 5
Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
5x3 - x2 + 2
The polynomial, [tex]5x^3 - x^2 + 2[/tex], is a trinomial and the degree of the polynomial is 3.
A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.
The given polynomial, [tex]5x^3 - x^2 + 2[/tex], has three terms separated by addition and subtraction symbols, making it a trinomial.
The highest exponent in the polynomial is 3, which determines its degree.
So, the degree of the polynomial is 3.
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A car starts from rest and acquires a velocity of 72 km/h in 5s. Find the distance travelled by car assume motion of car is uniform.
Answer:
Converting velocity into m/s
72x5/18=20 m/s²
Distance = Velocity *Time
20*5=100m
Step-by-step explanation:
hope it's helpful
Each week, Morgan walks a total of 5 miles to and from school, and Whitney walks a total of 6 miles to and from school. Part A Enter a number in each box to complete the ordered pairs showing the total number of miles that Morgan and Whitney will have walked after each week. The first term of each ordered pair is the number of miles Morgan will have walked. The second term is the number of miles Whitney will have walked.
Answer: (5,10) (6,12) (15,18) (20,24) (25,30)
Step-by-step explanation:
All you have to do is read the question carefully, and if you don’t understand than, keep doubling each number. Example: 5, 10 then you do whitneys part, which is 6,12 than you keep adding 5 and 6
Which function is graphed below?
On a coordinate plane, an exponential decay function is shown. The curve starts in quadrant 2 and decreases into quadrant 1. It crosses the y-axis at (0, 3) and approaches y = 0 in quadrant 1.
1)y = one-third (3) Superscript x
2)y = 3 (one-third) Superscript x
3)y = (one-half) Superscript x Baseline + 2
4)y = (2) Superscript x Baseline minus 1
By solving a system of equations, we will see that the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} -3[/tex]
Which rational function is graphed below?
First, we need to see the x-value of the vertical asymptote, here we can see that the vertical asymptote happens at x = -2, then the denominator will be something like:
d = (x - (-2)) = (x + 2).
Then our rational function will be something like:
[tex]f(x) = \frac{a}{(x + 2)} + c[/tex]
In the graph we can see two things, first:
f(0) = 3
f(1) = 1
Replacing that in our function, we get:
[tex]\frac{a}{(0 + 2)} + c = 3\\\\ \frac{a}{(1 + 2)} + c = 1[/tex]
This is a system of equations, that can be rewritten as:
a/2 + c = 3
a/3 + c = 1
Isolathing c in both equations, we get:
a/2 - 3 = -c = a/3 - 1
Then we have:
a/2 - 3 = a/3 - 1
Now we can solve this for a:
a/2 - a/3 = 3 - 1
a/6 = 2
a = 2*6 = 12
And the value of c is given by:
-c = a/3 - 1 = 12/3 - 1 = 4 - 1 = 3
c = -3
Then the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} - 3[/tex]
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Answer:
B. 3(1/3)^x
Step-by-step explanation:
Edg 2022
A school painted 1/2 of a wall with 3 colors.Each color takes up the same amunt of space on the wall.What fraction of the wall does each color occupy?
Answer:
1/6
Explanation:
This is because if you were to take up the entire wall with these same proportions, you would need six colors.
100 points and brianllest for whoever answer first
Answer:
5/12 hour or 25 minutes
Step-by-step explanation:
The formula is
distance = rate * time
changing minutes to hours (50 * 1 /60 ) = 5/6 hours
distance = 20 mph * 5/6 hours
distance = 50/3 miles
We need to go the same distance at 40 mph
50/3 = 40 mph * time
Multiply each side by 1/40
50 /3 * 1/40 = 40 * 1/40 *t
50/3 *1/40 =t
5/12 of an hour
Changing back to minutes
5/12 * 60 =25
How do I find the area of a triangle
Answer:
you find the area of triangle by the formula
1/2×base×height
Answer:
Area of triangle = ½ × base × height
Step-by-step explanation:
(A = ½ × b × h)
This formula is mainly used to find the area of the triangle.
Q7) A rectangular piece of land measures 8 m by 5m. It is to be fenced with four lines of wire. What length of wire is needed for fencing?
Answer:
26 m
Step-by-step explanation:
Find what length is needed for fencing by finding the perimeter of the land.
Use the perimeter formula, P = 2l + 2w
Plug in the length and width:
P = 2l + 2w
P = 2(8) + 2(5)
P = 16 + 10
= 26
So, the length of wire needed is 26 m
Which function is shown in the graph below?
1-0
319
4
$
2
-10=8 -5 22
2
2
4
B 8 10 x
6
-10
Oy=2x-2+3
y= 2X+2+3
y = 2*-+2
Oy= 2x+3 +2
answer:B
got it right on edg
The function that represents the exponential graph is, [tex]y = 2^{x+2} + 3[/tex].
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
We know a function is called an exponential function when the exponent is the independent variable, For example, aˣ.
From the graph of the function, When x = 0, y = 7.
Observing the options we have,
[tex]y = 2^{x+2} + 3[/tex].
When x = 0.
[tex]y = 2^{0+2} + 3.[/tex]
[tex]y = 2^{2} + 3.[/tex]
y = 7.
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The loudness L of sound in decibels is given by L=10log(I/I0) where I is the intensity of the sound, and I0 is the intensity of the least audible sound. If I0=10^-12 W/m^2 about how many times more intense is a 97 decibel sound than a 93 decibel sound?
A. 4.5
B. 1.5
C. 2.5
D. 3.5
97 decibel sound is 2.5 times more intense than a 93 decibel sound
Correct option is C.
What is intensity of sound?Sound intensity also known as acoustic intensity, is defined as the power transmitted by a sound wave per unit area in a direction perpendicular to that area. Sound intensity is the sound power in watts divided by the area (in square meters) covered by the sound. Sound loudness relates the intensity of a particular sound to its strength at the threshold of hearing, measured in decibels (dB).
Given expression for loudness
L = 10 log(I/I₀)
Loudness of two different sounds are
L₁ = 97 decibel and L₂ = 93 decibel.
Let the intensity for the loudness L₁ and L₂ are I₁ and I₂
Then,
L₁ = 10log(I₁/I₀) = 97
⇒ log(I₁/I₀) = 9.7
taking antilog
I₁/I₀ = antilog (9.7)
I₁/I₀ = 5011872336.27271
L₂ = 10log(I₂/I₀) = 93
⇒ log(I₂/I₀) = 9.3
taking antilog
I₂/I₀ = antilog (9.3)
I₂/I₀ = 1995262314.96888
Then,
(I₁/I₀)/(I₂/I₀) = 5011872336.27271/1995262314.96888
I₁/I₂ = 2.51188643 ≈ 2.5
Hence, 2.5 times more intense is 97 decibel sound than 93 decibel sound.
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What’s the Missing Side?
PLEASEEE HELPP
Answer:
11 km
Step-by-step explanation:
34.1 = 3.1x
solve for x
x=11 km
Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. At how many months will the cost be the same for both companies?
Answer:
5 months
Step-by-step explanation:
150 + 45x = 195 240 285 330 375 420
125 + 50x = 175 225 275 325 375 425
help pleaseeeeeeeeeee!
Answer:
See explanation below
Step-by-step explanation:
1. 10 students didn't talk on the phone because they've spent zero hours on the phone.
2. 3 hours is the largest number of hours
Line segment AB has a length of 5 units. It is translated 3 units to the right on a coordinate
plane to obtain line segment A'B'. What is the length of A'B'?
Answer:
bete a la her ha pir que yo no me use la reasouesta
please help me (: ALgebra 2!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{3x+1}{x}, x\neq -1[/tex]
Step-by-step explanation:
We can start by combining the fractions in the numerator. We can multiply them by x/x and x + 1/x + 1 respectively to get a common denominator of x(x + 1).
[tex]\frac{4}{x+1}*\frac{x}{x} +\frac{2}{x} *\frac{x+1}{x+1}\\\\\frac{4x}{x(x+1)}+\frac{2x+2}{x(x+1)}\\\\\frac{6x+2}{x(x+1)}[/tex]
Now we can rewrite an simplify:
[tex]\frac{\frac{6x+2}{x(x+1)} }{\frac{2}{x+1} }\\\\\\\frac{6x+2}{x(x+1)}*\frac{x+1}{2} \\\\\frac{3x+1}{x}[/tex]
The domain would be x ≠ -1 because the starting domain is [tex]x\neq -1; x\neq 0[/tex] and it changed to [tex]x\neq 0[/tex], so for the two fractions to be equal, the domain would be [tex]x\neq -1[/tex].