Answer:
[tex]4032x^4[/tex]
Step-by-step explanation:
Use the 10th row of Pascal's Triangle to get you where you need to be. You need 10 rows because any polynomial raised to the 9th power has 10 terms. Those 10 terms are, in order:
1, 9, 36, 84, 126, 126, 84, 36, 9, 1
Setting up for the first 6 terms:
[tex]1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...[/tex]
The 6th term is the last one. It goes on from there, but I stopped at the 6th term, since that is what you need.
Simplifying gives us:
[tex]126(x^4)(32)[/tex]
and multiplying gives us:
[tex]4032x^4[/tex]
The 6th term in the expansion of (x + 2)^9 is calculated using the binomial theorem, with the result being 4032x^4.
Explanation:The 6th term in the expansion of the binomial expression (x + 2)9 is found using Binomial Theorem. The general formula for any term in the expansion of (a + b)^n, where n is a positive integer, is C(n, k) * (a^(n-k)) * (b^k), where C(n, k) is the combination of n items taken k at a time, and k is the term number minus 1.
For the 6th term, k equals 5 (since k = term number -1). By substituting these values into formula, you get: C(9, 5) * (x^(9-5)) * (2^5), which equals 126 * x^4 * 32, or 4032x^4.
So, the 6th term in the expansion of (x + 2)9 is 4032x^4.
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Which of these is the quadratic parent function?
A. f(x) = |x|
B. f(x) = x2
C. f(x) = x
D. f(x) = 2x
Answer:
B. f(x) = x^2
Step-by-step explanation:
The only quadratic equation in the choices is the answer.
B. f(x) = x^2
5 friends are going on a 3 kilometer hike. Each person is going to lead the group for an equal distance of their hike. How many kilometers should each person lead?
Answer:
0.6 km
Step-by-step explanation:
(3 km)/(5 friends) = 0.6 km/friend
Each person should lead for 0.6 km.
Answer:
3/5
Step-by-step explanation:
3 divided by 5 equals to 3/5 or 0.6
50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with windows have hardwood floors?A. 10 B. 16 2/3 C. 40 D. 50 E. 83 1/3
Answer:E 83[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
50% of the apartment in a certain building have windows and hardwood floors.
25% of the remaining 50% apartment without window have hardwood floors.
40% of the apartment do not have hardwood floors i.e. 60 % have hardwood floor
Therefore percent of the apartments with windows have hardwood floors is
[tex]=\frac{50 percent of total\ apartment }{60\ percent\ of\ apartment}[/tex]
=83[tex]\frac{1}{3}[/tex]%
Factor completely.
81x4-1
A. (3x + 1)(3x - 1)(3x + 1)(3x - 1)
B. 9x?(9x2 - 1)
C. (9x2 + 1)(9x2 - 1)
D. (9x2 + 1)(3x + 1)(3x - 1)
Reset
Next
Answer: Option D
[tex](9x^2+1)(3x+1)(3x-1)[/tex]
Step-by-step explanation:
We have the following expression
[tex]81x^4-1[/tex]
We can rewrite the expression in the following way:
[tex](9x^2)^2-1^2[/tex]
Remember the following property
[tex](a+b)(a-b) = a^2 -b^2[/tex]
Then in this case [tex]a=(9x^2)[/tex] and [tex]b=1[/tex]
So we have that
[tex](9x^2)^2-1^2[/tex]
[tex](9x^2+1)(9x^2-1)[/tex]
Now we can rewrite the expression [tex]9x^2[/tex] as follows
[tex](3x)^2[/tex]
So
[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]
Then in this case [tex]a=(3x)[/tex] and [tex]b=1[/tex]
So we have that
[tex](9x^2+1)(9x^2-1) =(9x^2+1)((3x)^2-1^2)[/tex]
[tex](9x^2+1)(9x^2-1) =(9x^2+1)(3x+1)(3x-1)[/tex]
finally the factored expression is:
[tex](9x^2+1)(3x+1)(3x-1)[/tex]
Richard ordered a coffee table that was a regular pentagon. Find the measure of an exterior angle of the table.
(JUSTIFY)
Answer:
72
Step-by-step explanation:
If you find an interior angle, its supplement will be the exterior angle. That's one way to do the problem.
Another is to take 360 and divide it by the number of sides. That is the easier way to do it.
Exterior angle = 360 / divided by the number of sides
Exterior angle = 360 /5
Exterior angle = 72
---------------
The other way is done by
(n - 2) * 180 = 540
That's the total number of degrees in the interior of the pentagon.
1 interior angle = 540 / 5 = 108
The supplement of this angle is 180 - 108 = 72
Same answer 2 different ways.
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.9% of their carbon-14. How old were the bones at the time they were discovered?
The mastodon bones are approximately 6764 years old, determined by calculating carbon-14 decay, with 42.1% of the original carbon-14 remaining after losing 57.9%, and using the known half-life of 5750 years.
Explanation:The procedure to determine the age of the mastodon bones involves the principle of radioactive decay, specifically using carbon dating. Carbon-14, a radioactive isotope of carbon with a half-life of 5750 years, is used to date materials that were once part of a living organism.
Since the mastodon bones have lost 57.9% of their original Carbon-14, less than one half-life has passed. By using the exponential decay formula, we find that the remaining amount of Carbon-14 is 100% - 57.9% = 42.1%. One half-life (5750 years) would result in 50% remaining, and since 42.1% is a bit less than 50%, we need to determine how much less in terms of time. The calculation requires solving the following equation: N/N_0 = (1/2)^(t/T), where N is the remaining amount of Carbon-14, N_0 is the original amount, t is the time passed, and T is the half-life of Carbon-14.
To solve for t, we rearrange the equation to t = T * (log(N/N_0) / log(1/2)). Substituting the known values (T = 5750, N/N_0 = 0.421), we can calculate the time t that has passed since the death of the mastodon. When we perform this calculation, we find the bones to be slightly older than one half-life, equating to approximately 6764 years old.
Suppose a rock is thrown off of a bridge into the river 120 feet below. The height, h, in feet of the rock above the river is given by h = ?16t2 + 84t + 120, where t is the time in seconds. How long does it take the rock to splash into the river below?
Answer:
about 6.418 seconds
Step-by-step explanation:
You apparently want to find t when h=0:
0 = -16t^2 +84t +120
0 = 4t^2 -21t -30 . . . . . . divide by -4
t = (-(-21 ±√((-21)² -4(4)(-30)))/(2(4)) = (21±√921)/8 . . . . only the positive time is of interest
t = 2.625+√14.390625 ≈ 6.419 . . . . seconds
It takes about 6.42 seconds for the rock to hit the water.
Answer:
6.4
Step-by-step explanation:
Consider the equation below. f(x) = 2x3 + 3x2 − 12x (a) find the interval on which f is increasing. (enter your answer in interval notation.) incorrect: your answer is incorrect. find the interval on which f is decreasing. (enter your answer in interval notation.) incorrect: your answer is incorrect. (b) find the local minimum and maximum values of f. local minimum local maximum (c) find the inflection point. (x, y) = find the interval on which f is concave up. (enter your answer in interval notation.) find the interval on which f is concave down. (enter your answer in interval notation.)
To find the intervals on which a function is increasing or decreasing, analyze the sign of the derivative. The function is increasing on (-infinity, -1) and (2, infinity), and decreasing on (-1, 2).
Explanation:To find the intervals on which a function is increasing or decreasing, we need to analyze the sign of the derivative of the function. In this case, the derivative of f(x) is f'(x) = 6x^2 + 6x - 12. We can find the critical points by setting the derivative equal to zero: 6x^2 + 6x - 12 = 0. Solving this equation gives us x = -1 and x = 2.
To determine the intervals of the function, we can create a sign chart:
x-2-1023f'(x)+0-0+
From the sign chart, we can see that the function is increasing on the intervals (-infinity, -1) and (2, infinity), and decreasing on the interval (-1, 2).
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(a) Intervals of Increase:
[tex]\[ (-\infty, -3) \cup (2, \infty) \][/tex]
Interval of Decrease:
[tex]\[ (-3, 2) \][/tex]
(b) Local Minimum and Maximum:
Local Maximum: [tex]\( x = -3 \)[/tex]
Local Minimum: [tex]\( x = 2 \)[/tex]
(c) Inflection Point:
[tex]\[ \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \][/tex]
(d) Concavity:
Concave Up: [tex]\( (-\infty, -\frac{1}{2}) \)[/tex]
Concave Down: [tex]\( (-\frac{1}{2}, \infty) \)[/tex]
(a) To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to examine the sign of its derivative, [tex]\( f'(x) \)[/tex].
[tex]\[ f(x) = 2x^3 + 3x^2 - 12x \][/tex]
First, let's find[tex]\( f'(x) \)[/tex]:
[tex]\[ f'(x) = 6x^2 + 6x - 12 \][/tex]
To find where [tex]\( f(x) \)[/tex] is increasing or decreasing, we need to find the critical points where [tex]\( f'(x) = 0 \)[/tex] or is undefined.
Setting [tex]\( f'(x) = 0 \)[/tex]:
[tex]\[ 6x^2 + 6x - 12 = 0 \][/tex]
[tex]\[ x^2 + x - 2 = 0 \][/tex]
This quadratic equation can be factored as:
[tex]\[ (x + 2)(x - 1) = 0 \][/tex]
So, the critical points are [tex]\( x = -3 \)[/tex] and [tex]\( x = 2 \)[/tex].
Now, let's test the intervals between and beyond these critical points:
For [tex]\( x < -3 \)[/tex]:
[tex]\[ f'(-4) = 6(-4)^2 + 6(-4) - 12 = 6(16) - 24 - 12 > 0 \][/tex]
Since [tex]\( f'(-4) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on[tex]\( (-\infty, -3) \)[/tex].
Between [tex]\( -3 \)[/tex] and [tex]\( 2 \)[/tex] :
[tex]\[ f'(0) = 6(0)^2 + 6(0) - 12 = -12 < 0 \][/tex]
Since [tex]\( f'(0) < 0 \)[/tex], [tex]\( f(x) \)[/tex] is decreasing on [tex]\( (-3, 2) \)[/tex].
For [tex]\( x > 2 \)[/tex]:
[tex]\[ f'(3) = 6(3)^2 + 6(3) - 12 = 6(9) + 18 - 12 > 0 \][/tex]
Since [tex]\( f'(3) > 0 \)[/tex], [tex]\( f(x) \)[/tex] is increasing on [tex]\( (2, \infty) \)[/tex].
So, the interval on which [tex]\( f(x) \)[/tex] is increasing is [tex]\( (-\infty, -3) \cup (2, \infty) \)[/tex] , and the interval on which [tex]\( f(x) \)[/tex] is decreasing is [tex]\( (-3, 2) \)[/tex].
(b) To find the local minimum and maximum values of [tex]\( f(x) \)[/tex] :
we need to examine the critical points and the endpoints of the intervals we found.
Since [tex]\( f(x) \)[/tex] changes from increasing to decreasing at [tex]\( x = -3 \)[/tex], [tex]\( f(x) \)[/tex] has a local maximum at [tex]\( x = -3 \)[/tex] .
And since [tex]\( f(x) \)[/tex] changes from decreasing to increasing at [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] has a local minimum at [tex]\( x = 2 \)[/tex] .
(c) To find the inflection point:
we need to examine the concavity of [tex]\( f(x) \)[/tex], which is determined by the sign of the second derivative, [tex]\( f''(x) \)[/tex].
First, let's find [tex]\( f''(x) \)[/tex]:
[tex]\[ f''(x) = 12x + 6 \][/tex]
Setting [tex]\( f''(x) = 0 \)[/tex]:
[tex]\[ 12x + 6 = 0 \][/tex]
[tex]\[ x = -\frac{1}{2} \][/tex]
Since [tex]\( f''(x) \)[/tex] is positive for [tex]\( x < -\frac{1}{2} \)[/tex] and negative for [tex]\( x > -\frac{1}{2} \), \( f(x) \)[/tex] is concave up on [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and concave down on [tex]\( (-\frac{1}{2}, \infty) \)[/tex].
So, the inflection point is [tex]\( \left(-\frac{1}{2}, f\left(-\frac{1}{2}\right)\right) \)[/tex], and the intervals on which [tex]\( f(x) \)[/tex] is concave up and concave down are [tex]\( (-\infty, -\frac{1}{2}) \)[/tex] and [tex]\( (-\frac{1}{2}, \infty) \)[/tex] respectively.
Suppose we want a 90% confidence interval for the average amount spent on entertainment (movies, concerts, dates, etc.) by freshman in their first semester at a large university. The interval is to have a maximum bound on the error (or simply margin of error) of $2, and the amount spent has a normal distribution with a known standard deviation $30. The number of observations required is at least
Answer:
609
Step-by-step explanation:
Standard deviation = [tex]\sigma[/tex] = $30
Margin of error = E = $2
Confidence level = 90%
Since the distribution is said to be normal, we will use z scores to solve this problem.
The z score for 90% confidence level = z = 1.645
Sample size= n = ?
The formula to calculate the margin of error is:
[tex]E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=z\frac{\sigma}{E}\\\\n=(\frac{z\sigma}{E} )^{2}[/tex]
Using the values in above equation, we get:
[tex]n=(\frac{1.645 \times 30}{2} )^{2}\\\\ n = 608.9[/tex]
This means, the minimum number of observations required is 609
HELP!!
Use the drawing tool to sketch the graph and label its parts.
Part B
Answer:
see attached graph on the graph tool
Step-by-step explanation:
The equation of the parabola is
x²-6x-16y+25=0
vertex at (3,1) and focus at (3,5)
Fluorescent light bulbs have lifetimes that follow a normal distribution, with an average life of 1,685 days and a standard deviation of 1,356 hours. In the production process the manufacturer draws random samples of 197 light bulbs and determines the mean lifetime of the sample. What is the standard deviation of the sampling distribution of this sample mean?
Answer:
3,238
Step-by-step explanation:
1,685+1,356+197=3,238
Using the Central Limit Theorem, it is found that the standard deviation of the sampling distribution of this sample mean is of 96.6 hours.
The Central Limit Theorem states that for a sample of size n, from a population of standard deviation [tex]\sigma[/tex], the standard deviation of the sampling distribution is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that: [tex]\sigma = 1356, n = 197[/tex]
Then
[tex]s = \frac{1356}{\sqrt{197}} = 96.6[/tex]
The standard deviation of the sampling distribution of this sample mean is of 96.6 hours.
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Two rectangular prisms have the same volume. The area of the base of the blue prism is 4 1/8 square units. The area of the base of the red prism is one-half that of the blue prism. Which statement is true?
Answer:
The height of the red prism must be twice the height of the blue prism
Step-by-step explanation:
The height of the red prism must be twice the height of the blue prism.
Since the height of the blue prism is twice that of the red prism, the height of the red prism must be twice as much as that of the blue prism to make the volumes equal.Volume of a prism can be calculated as the area of the base multiplied by the height.
V= b*h....
Liliana is using dark power crystals to raise an army of zombies. She has 5 55 dark power crystals, and each crystal can raise 1 0 1010 zombies. How Many Zombies Can Lilliana Raise
Answer:
56060550
Step-by-step explanation:
555x101010=56060550
That’s a lot of zombies and I’m scared now.
Answer:
56,060,550
Step-by-step explanation:
A:4
B:1
C:-1
D:-4
please help
Answer: the answer would be -4
Step-by-step explanation: it is going down 4 units
PLZ HELP ASAP 30 POINTS!!!
A farmer in China discovers a mammal hide that contains 70% of its original amount of c-14.
N=n0e^kt
No=amount of c-14 at time t
K=0.0001
T=time in years
Find the age of the mammal hide to the nearest year.
Substitute the given numbers for their letters in the equation:
N = NOe^kt
N - amount after t years
No = Original amount
K = 0.0001
t = number of years
Substitute the given numbers for their letters in the equation:
0.70 = 1 * e^-0.0001t
Take the logarithm of both sides:
log0.70 = loge^-0.0001t
-0.1549 = -0.0001t * 0.43429
t = -0.1549 / (-0.0001 * 0.43429)
t = 3566.74
Rounded to the nearest year = 3,567 years old.
The age of the mammal hide is 3,567 years old.
Calculation of the age of the mammal:Given,
N = NOe^kt
Here
N - amount after t years
No = Original amount
K = 0.0001
t = number of years
Now
[tex]0.70 = 1 \times e^{-0.0001}t[/tex]
Now Take the logarithm of both sides:
[tex]log0.70 = loge^{-0.0001}t\\\\-0.1549 = -0.0001t \times 0.43429\\\\t = -0.1549 \div (-0.0001 \times 0.43429)[/tex]
t = 3566.74
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Line r cuts a pair of parallel lines. One of the eight angles created measures 90°. Which statements about the angles are true? A. All the angles are congruent. B. Only four of the angles measure 90°. C. All the angles are right angles.D. Only the vertical angles are congruent. E. All the interior angles are congruent.
Answer:
A. All the angles are congruent. C. All the angles are right angles.E. All the interior angles are congruent.Step-by-step explanation:
Adjacent angles are supplementary. If one of them is 90°, then they both are. Another name for a 90° angle is "right angle." In this geometry, all 8 of the angles are right angles, including interior, exterior, vertical, linear, adjacent, and any other pairing you might name.
Any statement restricting the congruent angles to "only" some subset will be incorrect. Any and every subset of the angles contains congruent angles.
Answer:
A. All the angles are congruent.
C. All the angles are right angles.
E. All the interior angles are congruent.
This should be right.
Step-by-step explanation:
Yuto left his house at 10 a.m. to go for a bike ride. By the time Yuto’s sister Riko left their house, Yuto was already 5.25 miles along the path they both took. If Yuto’s average speed was 0.25 miles per minute and Riko’s average speed was 0.35 miles per minute, over what time period in minutes, t, starting from when Riko left the house, will Riko be behind her brother?
Answer:
52 minutes and 30 seconds
Step-by-step explanation:
You know that Yuto has ridden for 5.25 miles when Riko left their house and you need to know and what time they will be together:
Then you can say that:
5.25 miles+(yutos speed)*t= (Rikos speed)*t
when t=Time in minutes when they will be together
5.25 miles+(0.25miles/min)*t= (0,35miles/min)*t
5.25miles=(0.35miles/min-0.25miles/min)*t
5.25miles/(0.35miles/min-0.25miles/min)=t
t=52.5 min =52 minutes and 30 seconds
Answer:
The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.
Hope this helps!!! :) Have a great day/night.
Solve. What is 99×89-34÷2-1?
Answer:
8793
Step-by-step explanation:
Multiply and divide first, making the equation 8811-17-1. Now subtract. This leaves 8793
Answer:
8793
Step-by-step explanation:
99×89-34÷2-1 = 8793
Multiply: 99 x 89 = 8811
Divide: 32 ÷ 2 = 17
Add: 17 + 1 = 18
Subtract: 8811 - 18 = 8793
A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?
Answer:
Probability of missing two passes in a row is 0.08.
Step-by-step explanation:
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
Answer:
Probability of missing two passes in a row is 0.08.
Step-by-step explanation:
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
What is the value of e in 7x
Answer:
7x
Step-by-step explanation:
This illustrates the meaning of a logarithm.
The natural log of 7x is the power to which e must be raised to give 7x. When you raise e to that power, you get 7x.
Im stuck on this problem, can someone please help
Answer:
-8
Step-by-step explanation:
x = -2 is in the range -3 ≤ x ≤ -1, so the definition f(x) = 4x applies.
f(-2) = 4(-2) = -8
Answer:
-8
Step-by-step explanation:
The value of f(-2) is -8.
-2 if x < -3
f(x) - 4x if -3 < x < -1
x^2 if x> -1
In a group of 60 students 14 students take Algebra 1 20 students take Algebra 2 and 7 students take both subjects how many students don't take either of these subjects
Please help me I just want to finish this so I can go to sleep.
Which functions could be represented by the graph? Check all that apply.
f(x) = | x + 0.14|
f(x) = |x| + 1.3
f(x) = |x – 7|
f(x) = |x + 12|
f(x) = |x| – 17
f(x) = |x – 23|
Answer:
f(x) = |x -7|f(x) = |x -23|Step-by-step explanation:
The absolute value function graph is shifted to the right by some unknown amount. That is, the parent function p(x) = |x| has become f(x) = p(x-a) = |x-a|, a right-shift of "a" units.
The grid squares are not marked, so we cannot say exactly what the right-shift is. The only two answer choices having the correct form are ...
f(x) = |x-7|
f(x) = |x -23|
_____
Anything that looks like |x+a| will be left-shifted by "a" units.
Anything that looks like |x| +a will be shifted up by "a" units. If "a" is negative, the actual shift is downward.
Answer:
f(x) = |x – 23|
f(x) = |x – 7|
Step-by-step explanation:
Right on edge
The gas mileage for a certain vehicle can be approximated by m= -0.03x^2 +3.7x-43, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 25 mpg.
Round to the nearest mph.
The vehicle will get 25 mpg at speeds of approximately
mph ____and ____ mph
Answer:
The vehicle will get 25 mpg at speeds of approximately 22 mph and 101 mph.
Step-by-step explanation:
Given, the equation that is used to determine the gas mileage for a certain vehicle is,
[tex]m=-0.03x^2+3.7x-43----(1)[/tex]
If the mileage is 25 mpg.
That is, m = 25 mpg,
From equation (1),
[tex]-0.03x^2+3.7x-43=25[/tex]
By the quadratic formula,
[tex]x=\frac{-3.7\pm \sqrt{3.7^2-4\times -0.03\times -43}}{2\times -0.03}[/tex]
[tex]x=\frac{-3.7\pm \sqrt{8.53}}{-0.06}[/tex]
[tex]\implies x=\frac{-3.7+ \sqrt{8.53}}{-0.06}\text{ or }x=\frac{-3.7- \sqrt{8.53}}{-0.06}[/tex]
[tex]\implies x\approx 22\text{ or }x\approx 101[/tex]
Hence, the speed of the vehicle of the vehicle are approximately 22 mph and 101 mph.
To find the speed at which the car gets 25 mpg, the equation -0.03x^2 +3.7x-43 is set equal to 25 and then solved. Using the quadratic formula, the speeds are approximately 30 mph and 76 mph when rounded to the nearest whole number.
Explanation:The question requires you to find the speed(s) at which the vehicle gets 25 miles per gallon (mpg). To do this, you'll need to equate the given quadratic equation (-0.03x^2 +3.7x-43) to 25 and then solve for x (representing speed in mph). So, the equation becomes:
-0.03x^2 +3.7x-43 = 25
This simplifies to:
-0.03x^2 +3.7x - 68 = 0
This quadratic equation can be solved by factoring, completing the square or using the quadratic formula. In this case, the quadratic formula is the best solution:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
By substituting a = -0.03, b = 3.7, and c = -68 into the formula, the calculated speeds are approximately 30 mph and 76 mph.
Please keep in mind that the answers were rounded to the nearest whole number (mph). Hence, the vehicle will get 25 mpg at speeds of approximately 30 mph and 76 mph.
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Find the sum:
1/6 + squareroot of 6
Answer:
see below
Step-by-step explanation:
The sum is irrational, so can only be indicated or approximated.
[tex]\dfrac{1}{6}+\sqrt{6}=\dfrac{1+6\sqrt{6}}{6}\approx 2.61615\,64094\,49844\,76486\,39507\,4137\dots[/tex]
For this case we must find the sum of the following expression:
[tex]\frac {1} {6} + \sqrt {6}[/tex]
We have that when entering [tex]\sqrt {6}[/tex] in a calculator we obtain:
[tex]\sqrt {6} = 2.45[/tex]
On the other hand:
[tex]\frac {1} {6} = 0.16[/tex]periodic number
So, the expression is:
[tex]\frac {1} {6} + \sqrt {6} = 2.62[/tex]
Answer:
2.62
What is the equation of the line of symmetry for the parabola represented by the equation y=−2(x−3)^2+4 ? Enter your answer as the correct equation, like this: x = 42
[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=-2(x-\stackrel{h}{3})^2+\stackrel{k}{4}\qquad\qquad \stackrel{vertex}{(\underline{3},4)}\qquad \qquad \stackrel{\textit{axis of symmetry}}{x=\underline{3}}[/tex]
From the equation of the parabola in vertex-form, it's line of symmetry is given by:
[tex]l: x = 3[/tex]
The equation of a parabola of vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k[/tex]
The line of symmetry is given by:
[tex]l: x = h[/tex]
In this problem, the parabola is modeled by the following equation:
[tex]y = -2(x - 3)^2 + 4[/tex]
Hence, the coefficients of the vertex are [tex]h = 3, k = 4[/tex], and the line of symmetry is:
[tex]l: x = 3[/tex]
A similar problem is given at https://brainly.com/question/24737967
Approximately 30 million mobile devices were sold in 1998 in the United States. The number sold increased to 180 million devices in 2007. Calculate the percent increase of mobile device sales from 1998 to 2007.
Answer:
500%
Step-by-step explanation:
The percentage change is given by ...
percent change = ((new value)/(old value) -1) × 100% = (180/30 -1)×100%
= (6 -1)×100% = 500%
Mobile device sales increased 500% from 1998 to 2007.
Answer:
Number of mobiles sold in the year 1998=30 million
Number of mobiles sold in the year 2007=180 million
Percentage increase in mobile sale from year 1998 to 2007 will be
[tex]=\frac{\text{final}-\text{Initial}}{\text{Initial}}\\\\=\frac{180-30}{30}\times100\\\\=\frac{150}{30} \times 100\\\\=\frac{15000}{30}\\\\=500\text{Percent}[/tex]
=500%
Use the TVM Solver to calculate the amount you should make in monthly payments into an investment account if you want to have $1,000,000 in 60 years. The account pays 3.9% interest compunded monthly and you will make an intial investment of $25,000
Answer:
$257.95
Step-by-step explanation:
We have assumed the payment is made at the end of each month, and the last payment will bring the balance to $1 million.
1) Suppose a rhombus has 12 cm sides and a 30° angle. Find the distance between the pair of opposite sides.
2) In rectangle KLMN, the angle bisector of ∠NKM intersects the longer side at point P. The measure of ∠KML is equal to 54°. Find the measure of ∠KPM.
Answer:
1) 6 cm
2) 117°
Step-by-step explanation:
1) Draw a picture of the rhombus. The distance between opposite sides is the height of the rhombus. If we draw the height at the vertex, we get a right triangle. Using trigonometry:
sin 30° = h / 12
h = 12 sin 30°
h = 6 cm
2) Draw a picture of the rectangle.
∠KML is the angle the diagonal makes with the shorter side ML. This angle is 54°. ∠NKM is the angle the diagonal makes with the shorter side NK. ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.
The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P. So m∠PKM = 27°.
KLMN is a rectangle, so it has right angles. That means ∠KML and ∠KMN are complementary. So m∠KMN = 36°.
We now know the measures of two angles of triangle KPM. Since angles of a triangle add up to 180°, we can find the measure of the third angle:
m∠KPM + 36° + 27° = 180°
m∠KPM = 117°
Please assist with this problem. It is really difficult.
[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{\stackrel{\textit{difference of squares}}{(x^3-y^2)(x^3+y^2)}+2y^4}\implies [(x^3)^2-(y^2)^2]+2y^4 \\\\\\ x^6-y^4+2y^4\implies \boxed{x^6+y^4}[/tex]
Answer:
a) [tex](x^3-y^2)(x^3+y^2)+2y^4=x^6+y^4[/tex] is an identity.
Step-by-step explanation:
Most of the left hand sides are in this form:
[tex](a-b)(a+b)[/tex].
When you multiply conjugates you do not have to use full foil. You can just multiply the first and multiply the last or just use this as a formula:
[tex](a-b)(a+b)=a^2-b^2[/tex].
Choice a), b), and d). all have the form I mentioned.
So let's look at those choices for now.
a) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]
[tex](x^6-y^4)+2y^4[/tex] (I used my formula I mentioned above.)
[tex]x^6+y^4[/tex]
So this is an identity.
b) [tex](x^3-y^2)(x^3+y^2)[/tex]
[tex]x^6-y^4[/tex] (by use of my formula above)
This is not the right hand side so this equation in b is not an identity.
d) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]
[tex](x^6-y^4)+2y^4[/tex]
[tex]x^6+y^4[/tex]
This is not the same thing as the right hand side so this equation in d is not an identity.
Let's look at c now.
c) [tex](x^3+y^2)(x^3+y^2)[/tex]
There is a formula for expanding this so that you could avoid foil. It is
[tex](a+b)(a+b) \text{ or } (a+b)^2=a^2+2ab+b^2[/tex].
Just for fun I'm going to use foil though:
First: x^3(x^3)=x^6
Outer: x^3(y^2)=x^3y^2
Inner: y^2(x^3)=x^3y^2
Last: y^2(y^2)=y^4
---------------------------Add.
[tex]x^6+2x^3y^2+y^4[/tex]
This is not the same thing as the right hand side.