Answer:
B. 8
Function's:
Given following:
f(x) = 2x - 2 g(x) = x² + 1To solve for f(g(-2)), substitute x = -2 in function g(x)
⇒ f(g(-2))
⇒ f((-2)² + 1)
⇒ f(5)
Now, substitute x = 5 in function f(x)
⇒ 2(5) - 2
⇒ 8
Evaluate the expression [tex]\sqrt[5]{3125{e}^{\frac{11 \pi }{2} i}}[/tex], leaving your answer in polar form.
[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]
The graph shows the translation, g(x), of the function f(x). What integer represents the horizontal translation of f(x) to g(x)?
The integer that represents the horizontal translation of f(x) to g(x) is 4
How to determine the integer?The attached graph represents the missing piece in the question
From the graph, we can see that:
The function g(x) is 4 units to the left of the function f(x)
This means that:
g(x) = f(x + 4)
Hence, the integer that represents the horizontal translation of f(x) to g(x) is 4
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Use the trigonometric ratios sine, cosine, and tangent to answer the following questions
Answer:
Step-by-step explanation:
Can someone help me
The value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
What is a Function?A function is a law that relates a dependent and an independent variable.
The value of the two functions is given
The value of (g . f) (0)
= g(f(0))
From the table of f(x) at x = 0
= g(1)
From the table of g(x) at x =1
=-2
The value of (g . f) (1)
= g(f(1))
From the table of f(x) at x = 1
= g(0)
From the table of g(x) at x =0
=1
Therefore, the value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
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Which best describes the relationship between the lines?
2x – y = −1
4x – 2y = 6
same line
perpendicular
neither
parallel
same line preparations
Answer:
Parallel
Step-by-step explanation:
So the best way to compare two lines is to convert it into slope-intercept form which is given in the form of: y=mx+b where m is the slope, and b is the y-intercept, in this form it's really easy to see if they're the same line, parallel, or perpendicular.
Original Equation:
2x - y = -1
Subtract 2x from both sides
-y = -2x - 1
Divide both sides by -1
y = 2x + 1
Original Equation:
4x - 2y = 6
Subtract 4x from both sides
-2y = -4x + 6
Divide both sides by -2
y = 2x - 3
As you can see both equations have a slope of 2, but different y-intercepts, so they're not the same line, but they'll also never intersect, because they increase by the same amount, thus they are parallel
Identify the algebraic expression for the following: the quotient of 12 and a number y increased by 7
The algebraic expression for the given word problem is 12/y + 7
Writing an expressionFrom the question, we are to write the algebraic expression for the given word problem
The given word problem is
"the quotient of 12 and a number y increased by 7"
First,
"the quotient of 12 and a number y" can be expressed as
12/y
Then,
"the quotient of 12 and a number y increased by 7" becomes
12/y + 7
Hence, the algebraic expression for the given word problem is 12/y + 7
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If an object moves along the y-axis (marked in feet) so that it’s position at time X (in seconds) is given by f(x) = 108x -12x^2 , find the following:
The velocity equation is:
[tex]v(x) = 108 - 24x[/tex]
Such that:
[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]
And the velocity is zero for x = 4.5
How to find the velocity equation?
We know that the position equation is:
[tex]f(x) = 108*x - 12*x^2[/tex]
To get the velocity, we need to differentiate with respect to x, so we get:
[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]
Now we want to get the velocity for x = 0 and x = 2, we will get:
[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]
Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.
Finally, we need to solve:
[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]
The velocity is zero when x = 4.5
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enter your answer in scientific notation
Answer:
[tex]1.7x10^{4}[/tex]
Step-by-step explanation:
To divide the scientific notation, divide 5.1 to 3 then subtract the exponents of your ten - following the quotient rule.
5.1/3 = 1.7, then 9-5 = 4
final answer is [tex]1.7x10^{4}[/tex]
An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of
350 centimeters.
a. Ice has a density of 0.93 grams per cubic centimeter. Find the mass of the icicle to the nearest gram.
b. On a warm day, the icicle begins to melt. In the first hour, its diameter decreases about 0.7 centimeter in the first hour
and its length decreases by 15 centimeters. How many cubic centimeters of ice melt in the first hour?
c. The icicle's dimensions continue to decrease at a constant rate. A bucket with a diameter of 25 centimeters and a
height of 30 centimeters is placed to catch the water as it drips from the melting icicle. Will the bucket overflow after
the icicle has been melting for 5 hours? Explain. HELP PLEASE
Answer:
Step-by-step explanation:
Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.
From the question, we can tell it is a inversed-cone (upside down)
Volume of Cone = [tex]\pi r^{2} \frac{h}{3}[/tex]
a) Given Diameter , d = 15.5cm and Length , h = 350cm,
we first find the radius.
[tex]r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm[/tex]
We will now find the volume of the cone.
Volume of cone [tex]\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}[/tex]
We know the density of ice is 0.93 grams per [tex]1cm^{3}[/tex]
[tex]1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g[/tex](Nearest Gram)
b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm
and the new length, h = 350cm - 15cm = 335cm
Now we will find the volume of this newly-shaped cone.
Volume of cone = [tex]\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}[/tex]
Volume of cone being melted = New Volume - Original volume
= [tex]\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}[/tex]
c) Lets take the bucket as a round cylinder.
Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.
Volume of cylinder = [tex]\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}[/tex]
To overflow the bucket, the volume of ice melted must be more than the bucket volume.
Volume of ice melted after 5 hours = [tex]5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}[/tex]
See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.
Volume of bucket - Volume of ice melted after 5 hours
= [tex]\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}[/tex]
from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.
if anyone knows how to answer this do so please
Answer:
b = 5.3
A = 48.6
B = 41.4
Step-by-step explanation:
Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.
So for our Right-Angled Triangle we have from Pythagoras Identity that
[tex]a^{2} +b^{2} =c^{2}[/tex] ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex] where a=6 , c=8
by substituting,
[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]
Now to find A , we will use the Trigonometric Identities
Since [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]
[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]
Since in any Triangle A+B+C=180
Then B=180-A-C=180-48.6-90=41.4
Huilans age is three times Thomas age The sum of their ages is 76 what is Thomas age
Answer:
let x be thomas age
3x for huilans age since huilans age is 3 time thomas age
both of their ages add to 76
ie. x + 3x =76
solve for x
4x = 76
x = 76 ÷ 4
x = 19. thomas age
to get huilans age : take 19 × 3 = 57
find the size of the angles marked with letters in each diagram
Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x).
n=15, x=2, p=5
P(x)=
Using the binomial distribution, it is found that P(X = 2) = 0.0032.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 15, x = 2, p = 0.5.
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{15,2}.(0.5)^{2}.(0.5)^{13} = 0.0032[/tex]
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Check all of the functions that are odd. f(x)=x3-x2 f(x)=x5-3x3 2x f(x) = 4x 9 f (x) = startfraction 1 over x endfraction
The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
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Answer:
B.) f(x)=x5-3x3+2x is odd
D.) f (x) = 1/ x is odd
Step-by-step explanation:
just did it on edg
Perform the indicated operation and write the answer in the form a + bi.
(3 +81) (4-3i)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23 i[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (3 + 8i)(4 - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: (3 \sdot 4)+ (3 \sdot - 3i) + (8i \sdot4) + (8i \sdot - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: 12 - 9i + 32i - (24 {i}^{2} )[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i -( 24 \sdot - 1)[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i + 24[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23i[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex]\Large\maltese\underline{\textsf{A. What is Asked \space}}[/tex]
Perform the indicated operation and write the answer with the form a+bi.
2 numbers given, one of which is complex
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!\space\space}}[/tex]
Multiply these two numbers, just like you always multiply binomials.
[tex]\bf{(3+8i)(4-3i)}[/tex] | multiply
[tex]\bf{3\times4+3\times(-3i)+8i\times4+8i\times(-3i)}[/tex] | simplify
[tex]\bf{12-9i+32i-24i^2}[/tex] | this can be simplified A LOT
[tex]\bf{12+23i-24i^2}[/tex] | as strange as it may seem, this can be simplified even more, because isn't i^2 the same as -1?
[tex]\bf{12+23i-24\times(-1)}=12+23i+24}[/tex] | add 12 and 24
[tex]\bf{36+23i}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=36+23i}[/tex]. The answer is written in the form a+bi, as requested.
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
The original price of a mountain bike was reduced by $125 . if p= the mountain bike's original price in dollars, which algebraic expression represents the reduced price?
The algebraic expression that represents the reduced price is p - 125
How to determine the reduced price?The reduction is given as:
Reduction = $125
The original price is given as:
Original = P
The reduced price is calculated as:
Reduced price = original - reduction
This gives
Reduced price = p - 125
Hence, the algebraic expression that represents the reduced price is p - 125
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A bag contains four batteries
Answer:
If this is the question about sample space, a possible answer is 24 and 64 ways in sample space.
Step-by-step explanation:
Hopefully, this is helpful :)
Which proportion is not true?
A. 2/3 = 4/6
B. 5/8 = 25/40
C. 9/10 = 81/90
D. 4/7 = 24/28
Answer:
D. 4/7 = 24/28
Step-by-step explanation:
In any proportion, the value of the numerator and denominator does not change if is multiplied by the same value.
We know that 4*6 = 24, so the numerator holds true. However, 7*6 is 42. In the same vein, 7*4 is 28, so the denominator would hold true. However, 4*4 is 16. Thus, the proportion has not been multiplied by the same value.
In order to get 24/28 from 4/7, you would have to multiply by 6/4, which is not the same value.
A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.
Using linear function concepts, we have that from the information given:
The relationship is linear.The independent variable is the number of months.The dependent variable is the value of the card.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.x is the independent variable.y is the dependent variable.From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:
V(t) = 25 - 2.5t.
Thus:
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Adele is 5 years older than Timothy. In 3 years, Timothy will be 2/3 of Adele’s age. What is Adele’s age.
Answer:
12
Step-by-step explanation:
Let a = Adele's current age
Let t = Timothy's current age
Adele is 5 years older than Timothy:
a = t + 5 {equation 1}
In 3 years Timothy will be 2/3 of Adele's age:
(2/3)(a + 3) = t + 3 {equation 2}
Since we are looking for Adele's age, let's rearrange equation 1 to:
t = a - 5
Substitute that into equation 2 and solve for a.
(2/3)(a+3) = a - 5 + 3
(2/3)(a + 3) = a - 2
Multiply through by 3 to clear the fraction
2(a+3) = 3a - 6
2a + 6 = 3a - 6
Add 6 to both sides, subtract 2a from both sides
12 = a
Adele is 12 years old
This means Timothy is 7 years old.
Check equation 2 to verify:
(2/3)(a + 3) = t + 3
(2/3)(12+3) = 7 + 3
(2/3)(15) = 10
10 = 10
Answer is correct
I need help on these 2 questions please ASAP
Step-by-step explanation:
Q9
a) :
First, find the common difference for the sequence. add the first term to the second term
3+3= 6
add second term to the third term
3+6=9
add third term to the fourth term
6+9=15
b) 15 +24= 39
24+39=63
39+63= 102
Q10
a) 2 , 10 , 8
b) find the common difference for the sequence. Subtract the first term from the second term.
10-2= 8
Subtract the second term from the third term
8-10= -2
c) 10
A class was given 9(whole number) 1/2 litres of juice to share equally. If there are 36 pupils in the class, how many millilitres of juice will each student get?
Answer:
263 8/9 millilitres
Step-by-step explanation:
9.5 litres = 9500 millilitres
9500/36 = 263 8/9
Four dragons (red, yellow, green, and blue) are getting ready to perform. The red dragon and the yellow dragon do not want to go on stage first. In how many different ways can the dragons go on stage?
Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.For the remaining dragons, there are 3! possible ways.Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
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Answer:
Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
A_n = n!A
n
=n!
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.
For the remaining dragons, there are 3! possible ways.
Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
Which of the following is the most profitable investment for a candy shop that earns $1 revenue per pound of candy? (5 points) Group of answer choices Worker at $10 per hour, producing eight pounds of candy per hour Worker at $12 per hour, producing 16 pounds of candy per hour Machine with $5 per hour operating cost, producing 10 pounds of candy per hour Machine with $8 per hour operating cost, producing 14 pounds of candy per hour
Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.
Which of the following is the most profitable investment?The first option is a worker that costs $10 per hour and produces 8lb, then this worker gives:
8lb/$10= 0.8 pounds per dollar.
The second worker costs $12 per hour, and produces 16lb per hour, so this worker gives:
16lb/$12 = 1.33 pounds per dollar.
The third option is a machine that cost $5 per hour and produces 10lb per hour, then:
10lb/$5 = 2 pound per dollar.
The last option costs $8 per hour, and produces 14 pounds per hour, then:
14lb/$8 = 1.75 pounds per dollar.
Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.
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A construction company is building a drainage ditch that is shaped like a "V". The ditch will be 10 feet wide at ground level and 5 feet deep at its lowest point. The depth of the ditch increases at a rate of 1 vertical foot for every 1 horizontal foot out from the lowest point at the center of the ditch .If x is the horizontal distance from the left edge of the ditch, in feet, determine which absolve value function models the ditch's vertical depth below ground level, in feet.
A. f(x) = |x + 5| − 5
B. f(x) = -|x − 5| − 5
C. f(x) = -|x − 5| + 5
D. f(x) = |x − 5| − 5
The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5
How to illustrate the function?From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.
Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5
In conclusion, the correct option is B.
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Rodrick is visiting the local museum exhibit and has a maximum of $30 dollars to spend. The entry ticket cost $7. He can spend g dollars. Write an inequality that can find g and the amount of money Rodrick can spend at the gift shop.
Entry ticket = $7
Gift shop money = $g
Maximum to spend = $30
Inequality => 7+g ≤ 30
Hope it helps!
A gas can hold 10 litters of gas.
How many could we fill 7 litters of gas?
Answer:
a gas can hold 7×10=70 litters of gas
Draw the solution set for each of the following inequalities
Answer:
Step-by-step explanation:
→
Here is a list of numbers:
8.1, 1, 4.4, 0.4, 9, 5.5,
5.1, 5.7, 1.2
State the median.
Give your answer as a decimal.
A discount store had monthly sales of $86,600 and spent 14% of it on promotions. how much was spent on promotion?
The amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
The percent signifies the hundredth part of the whole.
When informed that the promotion is 14 percent of the monthly sales of $86,600.
Therefore, to calculate the total amount spent on promotion, we calculate 14 percent of 86600.
Therefore, the total amount on promotion = 14% of $86,600 = $ (14/100 * 86,000) = $ (14*866) = $12,124.
Therefore, the amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
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