Answer:
f(f(x)) = x⁴ + 2x² + 2
Step-by-step explanation:
if f(x) = x² + 1, then f(f(x)) is equal to:
f(x)² + 1
= (x² + 1)² + 1
= x⁴ + 2x² + 1 + 1
= x⁴ + 2x² + 2
0. Folded boxes a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 5 ft by 8 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. b. Squares with sides of length x are cut out of each corner of a square piece of cardboard with sides of length /. Find the volume of the largest open box that can be formed in this way.
Answer:
Box dimensions:
L = 3 ft
D = 6 ft
H = 1 ft
Volume V = 18 ft³
Step-by-step explanation:
a) Each side of the future box is
L = 5 - 2*x D = 8 - 2*x
height of the box is x
Then the volume of the box as function of x is:
V(x) = ( 5 - 2*x ) * ( 8 - 2*x ) * x
V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x
V(x) = 40*x - 26*x² + 4*x³
Tacking derivatives on both sides of the equation:
V´(x) = 40 - 52*x + 12x² or V´(x) = 20 - 26*x + 6*x²
If V´(x) = 0
6*x² - 26*x + 20 = 0
Solving for x
x₁,₂ = (-b ± √ b² - 4*a*c ] /2*a
x₁,₂ = ( 26 ± √ 676 - 480 ) / 12
x₁,₂ = (26 ± 14 )/ 12
x₁ = 1
x₂ = 3,33 ( we dismiss this solution since is not feasible according to cardboard dimensions )
Then the sides of the box are:
L = 5 -2*x L = 5 - 2*1 L = 3 ft
D = 8 - 2*x D = 8 - 2*1 D = 6 ft
H = x = 1 ft
And the volume is V = 6*3*1 = 18 ft³
Please help meeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
h = 4.2 in
Volume = 3.6 cubic inches
[tex]\frac{1}{3}\pi r^{2}h = 3.6\\\\\frac{1}{3}*3.14*r^{2}*4.2 = 3.6\\\\r^{2}= \frac{3.6*3}{3.14*4.2}\\\\ = 0.81\\r=\sqrt{0.81}\\\\[/tex]
r = 0.9 in
Answer:
.... ..................
I'm unsure how to solve for w, can someone please help?
Answer:
w = 1/2
Step-by-step explanation:
One of the ways to solve problems using log is to use these two equations that use the same variables and plug in numbers.
log b (a) = c
b^c = a
By plugging in the numbers we get this:
log 16 (4) = w
16^w = 4
w = 1/2
In the diagram below, AB is parallel to CD. What is the value of y?
A. 45
B. 55
C. 135
D. 65
Answer:
A. 45
- as AB and CD are parallel to each other, the value of y will be equal to 45° in CD
The value of y in the given diagram is 45.
Option A is the correct answer.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
Let the corresponding angle with y is m.
Now,
y = m
Now,
45 and m are opposite angles.
So,
m = 45
Now,
The corresponding angle with y is m.
This means,
y = m
y = 45
Thus,
The value of y is 45.
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Please help me I need this due
if an angle measures 18° what is the measure of its complement
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.....
Complement Angle = 90°= 90 - 18
= 72
--> 72° is the complement angle of 18°
Hope it helps!
mark me brainliest pls.....
Follow me!
Pls answer just the answer
Answer:
588000
Step-by-step explanation:
if i am wrong pls tell me cause i think there's a different answer gl g
Answer:
$103,421.88
Step-by-step explanation:
Given:
P = 70000
r = 0.05
n = 1
t = 8
Work:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=70000(1+\frac{0.05}{1} )^{1*8}\\\\A=70000(1.05)^8\\\\A=103421.88[/tex]
how can I subtract 4/3 - 1/3
Answer:
1
Step-by-step explanation:
Since they have the same denominator, it would be:
[tex]\frac{4}{3}-\frac{1}{3}=\frac{4-1}{3} =\frac{3}{3}=1[/tex]
Can someone please help me with this!
Answer:
It's Positive
Step-by-step explanation:
Im normally good at alg ish but im confused
Answer:
The problem is telling you to find g ( f ( x ) )
Since we know that f(x) is square root of x, we can put the function this way.
g(√x)
Then, we use √x as our x in our g(x) function.
You plug in √x for x and you solve.
(√x ) ^2 is just x.
Finally the answer is
x-3
hope this helps :)
Step-by-step explanation:
Neal's room has sides 10 1/4 ft and 12 5/6 ft. What is the perimeter?
Answer:
66 1/6ft
Step-by-step explanation:
I have calculated by saying perimeter =2(length+width). I think that's the answer hope it helps.
Answer: 46 1/4
Step-by-step explanation:
Perimeter = (L+W) x 2
So basically ... (10 1/4 + 12 5/6) x 2
Which would be ... 23 1/12 x 2
Which gives you the answer of 46 and 1/4
5. If the tree's circumference is 141.3ft, what is its diameter?
Answer:
d ≈ 45 ft
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Circumference of a Circle Formula: C = πdStep-by-step explanation:
Step 1: Define
Circumference C = 141.3 ft
Step 2: Solve for d
Substitute in C [Circumference Formula]: 141.3 ft = πdSubstitute in π (approximation): 141.3 ft ≈ 3.14d[Division Property of Equality] Divide both sides by 3.14: 45 ft ≈ dRewrite: d ≈ 45 ftIdentify the terminal point for a 45° angle in a unit circle.
9514 1404 393
Answer:
(x, y) = ((√2)/2, (√2)/2))
Step-by-step explanation:
See the attached chart. The 45° angle can be found in the upper-right portion of the chart (1st quadrant).
Can someone solve for x? And maybe explain it in a simple way?
Answer:
x=10
Step-by-step explanation:
Because of the two parallel lines, the ratio between the sides must be the same. Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio. Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too. If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.
12/18=x/(x+5)
then cross multiply and solve
12(x+5)=18x
12x+60=18x
60=18x-12x
60=6x
10=x
Answer:
x=10
Step-by-step explanation:
You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.
[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]
For what values of x is the perimeter of the figure greater than 112 meters?
Select the correct choice below and fill in the answer box to complete your choice.
Answer:
John is buying shirts for his softball team. He will pay a one-time processing fee of $27.50 and $12.75 per each shirt ordered. Which equation can be used to find y, the total cost to buy xshirts? John is buying shirts for his softball team. He will pay a one-time processing fee of $27.50 and $12.75 per each shirt ordered. Which equation can be used to find y, the total cost to buy xshirts? John is buying shirts for his softball team. He will pay a one-time processing fee of $27.50 and $12.75 per each shirt ordered. Which equation can be used to find y, the total cost to buy xshirts? vv
Step-by-step explanation:
No scams. Show your work. write answer as a percent and round the nearest whole number if needed.
Answer:
Step-by-step explanation:
we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2
area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex] (where r is the radius, NOT the diameter, easy to confuse)
the radius of the inner circle is 2.5. which is half of the diameter of 5
inner circle = [tex]\pi[/tex]*(2.5)^2
inner circle = 19.6349...
outer circle = [tex]\pi[/tex]*(10^2)
outer circle = 314.1592...
the ratio is 19.6349... / 314.1592... = 0.0625
0.0625 = 6.25%
= 6% ( rounded to nearest whole number )
In order to make an A on her project, Sarah needs at least 160 points. She has already turned in part of her work and has been given 125 points so far. write and solve the inequality that models this situation and found out how many points Sarah needs for the last part of her project to get an A
I’ll give points + brainslist, if you don’t know don’t bother answering (:
Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box.
If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
A. y = 84(x - 6) + 12
B. y = 12x + 84
C. y = 84x + 12
D. y = 12(x - 6) + 84
Answer:
Step-by-step explanation:
A can of juice has a radius of 4 inches and a height of 7 inches. What is the volume of the can?
Round your answer to the nearest tenths place.
Answer:
351.7
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
V = 3.14(4²)(7)
V = 3.14(16)(7)
V = 50.24(7)
V = 351.68
Rounded to the nearest tenth:
351.7
Complete the expressions that would make them a perfect square trinomial.
a.
x² – 8x+
b. x2 + 20x +
C.
x² – 16x +
d. x2 + 9x +
Answer:
a) 16
b) 100
c) 64
d) [tex]\frac{81}{4}[/tex][/tex]
Step-by-step explanation:
Perfect square trinomial:
A perfect square trinomial has the following format:
[tex](x \pm a)^2 = x^2 \pm 2ax + a^2[/tex]
a.
x² – 8x
[tex]x^2 - 8x = x^2 - 2ax[/tex]
So 2a = 8, a = 4. Then
[tex]a^2 = 4^2 = 16[/tex]
The perfect square trinomial is [tex]x^2 - 8x + 16[/tex]
b. x2 + 20x +
2a = 20, so a = 10
[tex]a^2 = 10^2 = 100[/tex]
The perfect square trinomial is [tex]x^2 + 20x + 100[/tex]
C.
x² – 16x +
2a = -16, so a = -8.
[tex]a^2 = (-8)^2 = 64[/tex]
The perfect square trinomial is [tex]x^2 - 16x + 64[/tex]
d. x2 + 9x +
[tex]2a = 9[/tex], so [tex]a = \frac{9}{2}[/tex]
[tex]a^2 = (\frac{9}{2})^2 = \frac{81}{4}[/tex]
The perfect square trinomial is [tex]x^2 + 9x + \frac{81}{4}[/tex][/tex]
Find the following ratios. Write each answer as a fraction and as a decimal rounded to four decimal places.
Answer:
[tex]y = 56.6208[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find y
To find y, we make use of the relationship between sides lengths 44 & y and angle 39
The relationship is:
[tex]cos(39) = \frac{44}{y}[/tex]
i.e.
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
Make y the subject
[tex]y = \frac{44}{cos(39)}[/tex]
[tex]y = \frac{44}{0.7771}[/tex]
[tex]y = 56.6208[/tex] -- approximated
X 6.4.7-T
Question Help
Assume that females have pulse rates that are normally distributed with a mean of j = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 70 beats per minute and 78 beats per minute.
The probability is
(Round to four decimal places as needed.)
Enter your answer in the answer box and then click Check Answer
2 parts
remaining
Let X be a random variable denoting pulse rates of females as described, with mean µ = 74.0 bpm and standard deviation σ = 12.5 bpm. Then
P(70 < X < 78) = P((70 - µ)/σ < (X - µ)/σ < (78 - µ)/σ)
… = P(-0.32 < Z < 0.32)
… = P(Z < 0.32) - P(Z < -0.32)
… ≈ 0.6255 - 0.3745
… ≈ 0.2510
where Z is normally distributed with mean 0 and s.d. 1.
• • •
Next, you sample 25 females from the population and want to find the probability that their average falls between 70 and 78 bpm. Let [tex]X_i[/tex] denote the pulse rate of the i-th woman from the sample, and let Y be the random variable for the sample mean; that is,
[tex]Y=\displaystyle\sum_{i=1}^{25}\frac{X_i}{25}[/tex]
Recall that a sample of size n taken from a normal distribution with mean µ and s.d. σ has a mean that is also normally distributed with mean µ and s.d. σ/√n.
The mean stays the same, µ = 74.0, but now the s.d. is σ/√n = σ/5 = 2.5. So we have
P(70 < Y < 78) = P((70 - µ)/(σ/5) < (Y - µ)/(σ/5) < (78 - µ)/(σ/5))
… = P(-1.6 < Z < 1.6)
… = P(Z < 1.6) - P(Z < -1.6)
… ≈ 0.9452 - 0.0548
… ≈ 0.8904
A class consists of 1/2 freshmen, 1/8 sophomores, and 1/8 juniors; the rest are seniors. What fraction of the class is seniors?
Answer:
2/8
Step-by-step explanation:
freshman=4/8
1/8 soph 1/8 jr
add all together u get 6/8
the rest is seniors so its 2/8
1. What number will make this expression a perfect square trinomial? Show your work. x2 - 6x +
Answer:
.......
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Take half of b (6/2=3)
Square it (3^2=9)
What percent of the model is shaded green?
Answer:
1/5%
Step-by-step explanation:
The percentage of the model shaded green will be 20.
How to find how much percent 'a' is of 'b'?Suppose a number is 'a'
Suppose another number is 'b'
We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
[tex]\dfrac{a}{b} \times 100[/tex]
(in percentage)
The total number of the box in the figure is 100.
The total number of shaded green = 20
So,
[tex]\dfrac{20}{100} \times 100[/tex]
20%
Therefore, The percentage of the model shaded green will be 20.
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8a+11-2b for
a =4.b=2
Answer:
39
Step-by-step explanation:
8(4) + 11 -2(2)
32 + 11 - 4
43 - 4
39
help please i need it asap
Which category do both of these shapes belong to
Answer:
D. Parallelogram
Step-by-step explanation:
Answer:
The answer is Parallelgram(D)
two pairs of parallel sides in a quadrilateral
hope it helps...
1/3 of 36 solve using a tape diagram
