Answer:
f(x) and g(x) are inverses of each other
Step-by-step explanation:
To find the inverse of a function, swap the x's and y's and then solve for "y"
f(x) = 5x + 2
y = 5x + 2
Swap:
x = 5y + 2
-2 - 2
x - 2 = 5y
÷5 ÷5
45 POINTS!!!! HELP
A Ferris wheel at an amusement park is modeled by (x – 80)^2 + (y – 80)^2 = 5,625, where the measurements are in feet. A slingshot attraction is modeled by y = –3x^2 + 72x – 280. Which attraction reaches a greater height, and what does it represent in terms of the context?
A.The slingshot reaches a greater height at 280 feet, which is the vertex of the parabola.
B. The Ferris wheel reaches a greater height at 155 feet, which is the highest point on the circle.
C. The slingshot reaches a greater height at 152 feet, which is the vertex of the parabola.
D. The Ferris wheel reaches a greater height at 150 feet, which is the highest point on the circle.
Find a polynomial of least possible degree having the graph shown
f(x)=0
The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.
Polynomial of least possible degreeIt follows from the graph that the roots of the polynomial are; -2, 3 and 7.
On this note, the factors of such polynomial are;
Hence; (x+2)(x-3)(x-7) = f(x)
f(x) = x³-8x²+x +42Read more on polynomials;
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1 . 12+2x=16 2.12+x=26 3 . 4x-2=10
Answer:
1. x=4
2. x=14
3. x=3
Step-by-step explanation:
x is just a symbol they use as a temporary symbol to tell the person reading the problem that there is number that you do not know yet. if the x in the problem is next to a number then it needs to be multiplied with the number it's next to. in this case we know that 4 times 3=12 and if you take two away from 12 you get 10 so because 3 works in the equation it's the answer for 4x-2=10. this applies to every problem like this another way to solve it is if you add 2 to the left side it cancels out but you need to add 2 to the other side which would look like 4x=10+2 which equals 4x=12 and 4 times three equals 12. it doesn't matter how the equation changes as long as you find out whatx equals then that is the answer.
Answer:
1. x = 2
2. x = 14
3. x = 3
Step-by-step explanation:
1. 12 + 2x = 16
First, I did 16 - 12 which is 4. I did this because you want to know how much 2x is supposed to be fully, and you always want to do the opposite. like in this case it was addition so the opposite is subtracting. Next, the 2x is supposed to equal 4, and when you see 2x that means you have to multiply. So, 2 x 2 = 4. You can also do 4 divided by 2 equal 4. Finally, the answer for x is 2.
________________________________________________________
2. 12 + x = 26
So, you have to do 26 - 12 which is 14. I turned the addition problem to a subtraction problem because you always want to do the opposite. and you should already know that x will equal 14. you can double check if you want and change it back to addition which will be 12 + 14 = what ? 26 . so 14 is the answer for x !
________________________________________________________
3. 4x - 2 = 10
First, you want to do 10 + 2 which is 12. You should know by now if you read above for the other equations that you have to do the opposite. Next, 4x is going to have to be equal to 12. So, 4 x 3 = 12 or you can do 12 divided by 4 which will still equal 3. Finally the answer for x is 3.
________________________________________________________
Hope this helps !
here a fun quote
"Happiness is the secret to all beauty. There is no beauty without happiness." - Chirstian Dior
The ratio of girls to boys in the sixth grade class is seven to six. If there are 84 girls, how many boys are in the sixth grade?
Answer:
72
Step-by-step explanation:
84/7 = 12
12 × 6 = 72
84 to 72
Answer:
72
Step-by-step explanation:
divide 84 by 7, and then multiply 12(what you got from the division) by 6 and you get 72
30 POINTS! Combine the like terms of the 2 questions below:
1. y + 4 + 3(y + 2)
2. 0.5(x⁴ - 3) + 12
Answer:
[tex]\tt 1)\: \boxed{\tt 4y+10}[/tex]
[tex]\tt 2)\:\boxed{\tt 0.5x^4+10.5}[/tex]
Step-by-step explanation:
1) y + 4 + 3(y + 2)
Expand:-
[tex]\tt y+4+3y+6[/tex]
Combine like terms:-
[tex]\tt y+3y+4+6[/tex]
[tex]\boxed{\tt 4y+10}[/tex]
__
2) 0.5(x⁴ - 3) + 12
Expand:-
[tex]\tt 0.5x^4-1.5+12[/tex]
Add/Subtract Numbers:-
[tex]\boxed{\tt 0.5x^4+10.5}[/tex]
___________________
Which inequality describes the graph?
y ≥ 1/2x – 2
y < 1/2x – 2
y ≤1/2 x – 2
y >1/2 x – 2
[tex]y < \frac{1}{2} x - 2 \\ [/tex]
Have a great day ♡♡♡♡♡In the ordered pair (2, 7), the number 2 is the y-coordinate.
In the ordered pair ( 2, 7 ) , the number 2 is the y-coordinate.
In the ordered pair ( 2, 7 ) , the number 2 is the y-coordinate.
The horizontal axis in a coordinate plane is the x-axis.
The horizontal axis in a coordinate plane is the x-axis. – The horizontal axis in a coordinate plane is the x-axis.
The y-axis is also called the origin.
Answer:
The origin is at (0,0) its where the x and y coordinate intersect.
Step-by-step explanation:
what was the question here?
Dwayne bought 12 yards of wrapping paper.
How many inches of wrapping paper did he buy?
since there are 36 inches in 1 yard, 12 yards will have 12(36) = 432 inches.
Watch your cholesterol: The mean serum cholesterol level for U.S. adults was 198, with a standard deviation of 39 (the units
are milligrams per deciliter). A simple random sample of 106 adults is chosen. Use Cumulative Normal Distribution Table if
needed. Round the answers to at least four decimal places.
Part: 0/3
Part 1 of 3
(a) What is the probability that the sample mean cholesterol level is greater than 204?
The probability that the sample mean cholesterol level is greater than 204 is
Next Part
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For the mean serum cholesterol level for U.S. adults was 198, with a standard deviation of 39, the probability is mathematically given as
x=0.1379
What is the probability that the sample mean cholesterol level is greater than 204?Generally, the equation for the probability is mathematically given as
P(\=x>210)
Therefore
P=(z>\frac{204-198}{39/\sqrt{106}})
P=(z>1.583)
In conclusion, from cumulative table
x=1-p(z>1.583)
x=1-0.8621
x=0.1379
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Determine each feature of the graph of the given function.
2x + 8
f(x) =
x² + x
x - 12
[tex]x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}[/tex]
Determine whether 2x+2y= -6 is a function?
Answer:
It's a function because when you simplify it becomes y=-x-3. the only reason it wouldn't be a function would be if the equation were to be x = a random number that is not a variable. The equation would not pass the vertical line test which is the requirement to see if an equation is a function.
Simply put, it's a function.
Determine whether [3x + 12 + x] is equivalent to [4(3 + x)]. Use properties of operations to justify your answer.
Step-by-step explanation:
Using BODMAS rule
[3x+12+x] = [4(3+x)]
[4x+12] = [12+4x]
Parentheses 1 = Parentheses 2
LHS = RHS
HENCE PROVED
MARK ME AS BRAINLISTHexagon BCDEFG is shown below. Each square on the grid is a unit square. What is the area of the
hexagon in square units?
Answer:
B. 100 units
Step-by-step explanation:
What I did was I couunted the lines at the bottum and since it was 10 then I counted up and that was 10 so you would do 10x10 get 100 units.
16. Given that k is a real constant such that 0 < k < 1. Show that the roots of the equation kx2 + 2x + (1 – k) = 0, are С (i) Always real (ii) Always negative
Answer:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
Given equation: [tex]kx^2+2x+(1-k)=0[/tex]
[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]
[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]
Complete the square:
[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]
[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]
Therefore, the roots are always real.
Please help on math.
Answer:
832.5²
Step-by-step explanation:
Base x height ÷ 2 is the formula to find a triangles area.
45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²
Answer:
832.5²
Step-by-step explanation:
find the product using suitable rearrangement (-18) multiply (-10) multiply 9
Answer:
1620
Step-by-step explanation:
(-18)×(-10)×9= 1620
Solve 3 log 2x = 4. Round to the nearest thousandth if necessary.
5
2.783
10.772
best answer of this equation is 10.772
Answer: 10.772
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
exact form:
x= 10 4/3
--------- (its a fraction)
2
decimal form: 10.77217345....
after that round to the nearest thousandth.
find the amount of hydrogen in a liter of acid rain that has a pH of 5.5 math
To calculate hydronium concentration from pH, type on you calculator
10 to the power of negative pH value
10^-5.5 = 3•10^6 mol/L
Since there are 3 hydrogens in every hydronium molecule,
There are 9 • 10^6 hydrogens in that liter of acid.
Lana is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet.
How much glass is needed?
A.
680 sq ft
B.
340 sq ft
C.
2,040 sq ft
D.
1,360 sq ft
Answer:
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Hope this helps you!!
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Gretchen made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 2 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
Answer
91.67inch^3
Step-by-step explanation:
The volume of a cone can be calculated using below formula
V= 1/3 π.r^2h
Where h= height of the cone
r= radius of the cone
V= volume of the cone
Given :
height= 11 inches
radius= 5 inches
π= 3.14
Then substitute into the formula we have
V= 1/3 × 3.14× 5^2 ×11
V= 91.67inch^3
Therefore volume of the cone is 91.67inch^3
Between what two whole numbers does your answer lie in 30/8?
Answer:
3 and 4
Step-by-step explanation:
30/8=3.75
3.75 lies between 3 and 4
Hey there!
30/8
= 30 ÷ 2 / 8 ÷ 2
= 15 / 4
≈ 3 3/4
≈ 3.75
It falls in between three (3) and four (4). But, fun fact it rounds to up to four (4)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
given a force of 88N and acceleration of 4m/s what is the mass
Answer:
F = ma
m = F/a
m = 88/4
m = 22 kg
Step-by-step explanation:
Identify the trinomial that is a perfect square.
A. 9x2 + 30x + 16
B. 16x2 + 20x + 9
C. 36x2 + 60x + 25
D. 4x2 + 30x + 25
Answer:
Option C, [tex]36x^2 + 60x + 25[/tex]
Step-by-step explanation:
Step 1: Determine the perfect square
According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"
The only one that seems to work is Option C so lets factor it.
[tex]36x^2 + 60x + 25[/tex]
[tex](6x + 5)(6x + 5)[/tex]
[tex](6x + 5)^2[/tex]
Yup! We can see that Option C would give us a perfect square
Answer: Option C, [tex]36x^2 + 60x + 25[/tex]
Work out the angle below
Answer:
56
Step-by-step explanation:
two of the angles are the same meaning the bottom two are 62. angles in a triangle add up to 180° so you just do 62 + 62 and then take the answer away from 180
62+62=124
180-124=56
which of the following value, when multiplied by 2/3, results in a product that is greater than 2/3
a. 2/3
b 3/2
c 3/4
d 4/4
Answer:
b
Step-by-step explanation:
2/3 * 2/3 = 4/9
2/3 * 3/2 = 1
2/3 * 3/4 = 1/2
2/3 * 4/4 = 2/3
The variables x and y vary directly. Given the equation y = 2x , find the value of x when
y = 10.
a. 10
c. 20
b. 5
d. 8
If the probability of a family owning a cat is 0.10, the probability of owning a dog is 0.20, and the probability of owning a cat and a dog is 0.08, what is the probability of a family owning a cat or a dog?
Probability helps us to know the chances of an event occurring. The probability of a family owning a cat or a dog is 0.22.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the probability of a family owning a cat is 0.10, the probability of owning a dog is 0.20, and the probability of owning a cat and a dog is 0.08. Therefore, the probability of a family owning a cat or a dog can be written as,
Probability (family owning a cat or a dog)
= Probability (Cat) + Probability (Dog) - Probability (Cat And Dog)
[tex]\text{Probability (family owning a cat or a dog)} = 0.10+0.20-0.08 = 0.22[/tex]
Hence, the probability of a family owning a cat or a dog is 0.22.
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I can only manage to get 3/4 and i know i got the answer right so can someone please help me?
Answer:
See below.
Step-by-step explanation:
A(1, 4)
B(3, 0)
C(-3, -2)
We find the coordinates of he midpoints using the midpioint formula.
D([1 + 3]/2, [4 + 0]/2) = D(2, 2)
E([1 + (-3)]/2, [4 + (-2)]/2) = E(-1, 1)
We find the slopes using the slope formula.
slope of BC:
m_BC = (-2 - 0)/(-3 - 3) = -2/(-6) = 1/3
slope of DE:
m_DE = (1 - 2)/(-1 - 2) = -1/(-3) = 1/3
Since the slopes of BC and DE are equal, the lines are parallel.
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The Odd Man Out!
PART 2:
For each set of figures below, three are similar (meaning that they are related through a sequence of transformations including dilation), and one is an exception. Find the exception in each set of figures and answer the questions for each set.
Answer:
a. exception: C; obtuse angle with a different measure
b. corresponding angles are congruent; corresponding sides are proportional
c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar
d. corresponding sides are porportional; they are not proportional when the triangles are not similar
Step-by-step explanation:
As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.
__
a.Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.
__
b.The similar triangles have congruent corresponding angles and proportional corresponding sides.
__
c.See (b) regarding similar triangles. Non-similar triangles have different angles.
__
d.See (b) regarding similar triangles. Non-similar triangles have different side proportions.
PLEASE HELP ASAP
Describe the rate of change modeled by this graph.
A) positive
B) negative
C) no change
D) a change that is undefined