The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
For given question,
We have been given a function f(x) = 6 + 9x² - 6x³
We need to find the local maximum and local minimum of the function f(x)
First we find the first derivative of the function.
⇒ f'(x) = 0 + 18x - 18x²
⇒ f'(x) = - 18x² + 18x
Putting the first derivative of the function equal to zero, we get
⇒ f'(x) = 0
⇒ - 18x² + 18x = 0
⇒ 18(-x² + x) = 0
⇒ x (-x + 1) = 0
⇒ x = 0 or -x + 1 = 0
⇒ x = 0 or x = 1
Now we find the second derivative of the function.
⇒ f"(x) = - 36x + 18
At x = 0 the value of second derivative of function f(x),
⇒ f"(0) = - 36(0) + 18
⇒ f"(0) = 0 + 18
⇒ f"(0) = 18
Here, at x=0, f"(x) > 0
This means, the function f(x) has the local minimum value at x = 0, which is given by
⇒ f(0) = 6 + 9(0)² - 6(0)³
⇒ f(0) = 6 + 0 - 0
⇒ f(0) = 6
At x = 1 the value of second derivative of function f(x),
⇒ f"(1) = - 36(1) + 18
⇒ f"(1) = - 18
Here, at x = 1, f"(x) < 0
This means, the function f(x) has the local maximum value at x = 1, which is given by
⇒ f(1) = 6 + 9(1)² - 6(1)³
⇒ f(1) = 6 + 9 - 6
⇒ f(1) = 9
So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.
Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
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In step 2, the
property of equality was applied.
In step 4, the
property of equality was applied.
In step 2, the property of equality applied was addition property of equality.
In step 4, the property of equality applied was multiplication property of equality.
What is the Addition Property of Equality?The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:
a - c + c = b + c
a = b + c.
What is the Multiplication Property of Equality?According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:
a/c × c = b × c
a = bc
In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.
In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.
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Answer: step 2 - addition property
step 4 - multiplication property
Step-by-step explanation:
9. Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____
Answer:
x = 3√3
y = 6
Step-by-step explanation:
The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.
Altitudex = √(9·3) = 3√3
Short sidey = √((9+3)·3) = 6
__
Additional comment
These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)
Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)
The ratio of short side to long side is ...
x/9 = 3/x ⇒ x² = 9·3 ⇒ x = √(9·3)
The ratio of short side to hypotenuse is ...
y/(9+3) = 3/y ⇒ y² = (9+3)·3 ⇒ y = √((9+3)·3)
Likewise, the ratio of long side to hypotenuse is ...
w/(9+3) = 9/w ⇒ w² = (9+3)·9 w = √((9+3)·9) = 6√3
Which is a discrete random variable?
The order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is
The order of magnitude for total attended for a high school football team is 3
How to determine the order of magnitude?The given parameters are:
Average number of fan = 1000
Number of home games = 5
The total number of fans in the 5 games is:
Total number of fans = Average number of fan * Number of home games
Substitute known values in the above equation
Total number of fans = 1000 * 5
Express 1000 as 10^3
Total number of fans = 10^3 * 5
Rewrite the equation as:
Total number of fans = 5 * 10^3
The power of 10 represents the order of magnitude
Since the power of 10 is 3, the order of magnitude is 3
Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3
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A clock has a diameter of 16 inches. How far does the hour hand travel during 5 hours? Use 3.14 for pi.
Therefore the hour hand travels 40.192in in 5 hours
A sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;
β = 360/5
β = 72 degrees
Given the following parameters
r = 16/2
r = 8in
Substitute into the formula
A = 8²(72π)/360
A = 40.192in
Therefore the hour hand travels 40.192in in 5 hours
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Which number has a repeating decimal form?
A. sqrt{15
B. 11/25
C. 3/20
D. 2/6
Answer:
D It repeats
Step-by-step explanation:
square root of 15 is 3.87298334621
11/25= 0.44
3/20=.6
D = 0.33333333333
Does anyone know this? Evalute the power type your answer in the open box. Look at picture.
Help me asap! I will give you marks
Recall the binomial theorem.
[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]
1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is
[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]
Observe that
[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]
[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]
When we multiply these by [tex]8-9x[/tex],
• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]
• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]
and the sum of these terms is
[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]
2. The binomial expansion is
[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]
We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :
[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]
Last week the value of an investment changed at a rate of -$3.15 each day. After How many days was the total change in value -$12.60?
In four days,the total change in value -$12.60.
According to the statement
we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.
So, here we use division rule to find the solution.
The given change value is :
-$3.15 each day.
The desired change value is :
-$12.60.
Number of days required = -12.60 / -3.15
Number of days required = 12.60 / 3.15
Number of days required = 4 days.
So, in four days the change in value reaches at the desired value of change.
So, In four days,the total change in value -$12.60.
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Evacuate the following using suitable identities (102)^3
The value of [tex](102)^3[/tex] exists 1061208.
How to estimate the value of [tex](102)^3[/tex]?Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]
Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get
a = 100 and b = 2 then substitute the values of a and b then
[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]
= 1000000 + 8 + (600 × 102)
= 1000000 + 8 + 61200
= 1061208
Hence, [tex](102)^3=1061208[/tex]
Therefore, the value of [tex](102)^3[/tex] exists 1061208.
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If no denominator equals zero , which expression is equivalent to
Answer: Choice D
[tex]\frac{-19}{\text{x}-5}[/tex]
=================================================
Work Shown:
[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]
[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]
This matches with choice D as the final answer.
Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]
Last week a painter painted 6 houses in 2 days. this week she painted 5 houses in 4 days. in which week was the painter more productive?
Answer:
The painter was more productive in week a.
Step-by-step explanation:
Find the unit rate. How many houses could be painted in 1 day?
6/2 means that she could paint 3 houses per day
5/4 means that she could paint 1.25 houses per day.
The painter was more productive in the last week.
Explanation:In this problem, we need to find in which week did the painter paint the most.
To find the solution to this problem, first, we need to divide 6 by 2 (last week)
which equals 3.
Next, divide 5 by 4 (this week)
which equals 1.25
Now, compare the two quotients and identify the larger number (3 and 1.25).
Basically, we can see that the number 3 is larger.
This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.
Therefore, we can say that the painter was more productive in the last week.
I hope this helps :)
A sports teacher divided a class into two groups. Three-fifth of the first group and 80% of the second group play soccer.
What fraction of the class plays soccer?
Answer:
7/5
Step-by-step explanation:
80/100 = 0.8 = 8/10 = 4/5 (to the simplest fraction).(three-fifth) 3/5 + 4/5 = 7/57/5 of the class plays soccer ✅Hope this helpsGood luck ✅Do the data in the table represent a direct variation or inverse variation? Write an equation to model the data in the table?
x 2 4 8 12
y 4 2 1 2/3
Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x
VariationDirect variationy = k × x
4 = k × 2
4 = 2k
k = 4/2
k = 2
when y = 2 and x = 4
y = k × x
= 2 × 4
y = 8
Indirect variationy = k/x
4 = k / 2
8 = k
when y = 2 and x = 4
y = k/x
2 = k/4
2 × 4 = k
k = 8
So,
y = k/x
y = 8/x
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A boat traveled 27 miles in 2 hours. at this rate how many miles will the boat travel in 1/2 hour
Answer:
6.75
Step-by-step explanation:
Distance in Miles
MPH -------------------------
Time in Hours
27/2 = 13.5. That is 1 hour. Half that and you get 6.75 MP1/2H
A population of n = 10 scores has = 50 and = 5. what is the population variance? 5
The value of the Population Variance is 100.
According to the statement
we have given that the A population of N = 10 scores has μ = 50 and σ = 5. And we have to find the population variance.
So, For this purpose,
we know that the population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population.
Population variance = mean /(standard deviation/number of samples)
Population variance = μ / (σ /N )
Substitute the values in it and then
Population variance = 50 / (5 /10 )
Population variance = 50 / (0.5 )
Population variance = 100.
So, The value of the Population Variance is 100.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
A population of N = 10 scores has μ = 50 and σ = 5. What is the population variance?
a. 10
b. the square root of 5
c. the square root of 50
d. 25
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please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p\\}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Natasha got the power right. The power is 295 hp.
How to calculate power?t = 5.825∛w / p
where,
w = weight of the carp = power delivered by the engine in horsepowerquarter mile time = tTherefore,
t = 13.4 s
p = 3590
13.4 = 5.825∛ 3590 / p
cube both sides
13.4³ = 5.825³ × 3590 / p
2406.104 = 197.645890625 × 3590 / p
cross multiply
2406.104 p = 709548.747344
p = 709548.747344 / 2406.104
p = 294.895294361
p = 295 hp
Therefore, Natasha got the power right
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Two parallel lines are cut by a transversal. Complete the following statements.
The consecutive interior angles is...
supplementary, complementary, congruent
The alternate interior angles is...
supplementary, complementary,congruent
To complete the statements;
The consecutive interior angles is supplementary
The alternate interior angles is congruent
Properties of parallel lines cut by a transversal
The properties are;
Corresponding Angles are congruentAlternate Exterior Angles are congruentAlternate Interior Angles are congruentConsecutive Interior Angles sum to 180 degrees, that is, they are supplementaryConsecutive interior angles are supplementary
Alternate interior angles are congruent
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Please Help me its a math question i will give brainlist please !!! the image is attached
Answer:
D
Step-by-step explanation:
When you reflect the point it goes to point (-2,5). From that point, go 4 left and 8 down. That gets you to (-2,-3)
what is 4.22 x 10^17 seconds
We can rewrite the given time as:
7.03x10^15 mins 1.17x10^14 hours.4.88x10^12 days.What is 4.22x10^17 seconds in minutes and hours?First, remember that:
60s = 1 min
Then to write that amount in minutes, we just need to divide by 60, so we get:
(4.22x10^17)/60 mins= 7.03x10^15 mins
Now, remember that:
1 hour = 3600s
Then to get the time in hours, we need to divide by 3600:
(4.22x10^17)/3600 h = 1.17x10^14 hours.
Similarly, you can change to any time unit that you want, for example:
1 day = 24*3600 s
Then the time in days is:
(4.22x10^17)/(24*3600) days = 4.88x10^12 days.
And so on.
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A bin in the school gymnasium holds different colored balls. a ball is picked at random and then replaced. the probability of picking a green ball is 0.5, the probability of picking a blue ball is 0.4, and the probability of picking a red ball is 0.1. if a ball is picked and replaced 140 times, how many times should you expect a blue ball to be picked? a. 14 b. 48 c. 56 d. 70
Correct answer is C. the number of times blue ball appears is 56
Given,
probability of picking a green ball is 0.5,
the probability of picking a blue ball is 0.4,
the probability of picking a red ball is 0.1.
a ball is picked and replaced = 140
Probability = (the number of ways of achieving success) / (the total number of possible outcomes)
Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.
For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times and the probability of picking a blue ball (which is equal to 0.4)
= (140)(0.4) = 56
Therefore, we should expect that the blue ball will be picked 56 times.
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A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. event a is defined as drawing a black tile from the bag on the first draw, and event b is defined as drawing a white tile on the second draw. if two tiles are drawn from the bag, one after the other without replacement, what is p(a and b) expressed in simplest form?
P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To express P(A and B) in the simplest form:
P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
In the year 2000, there were 200,000 cell phone subscribers in a city in new york. the number of subscribers increased by 60 percent per year after 2000. which equation can be used to model the number of subscribers, y, in the city t years after 2000?
The equation can be used to model the number of subscribers, y, in the city t years after 2000 is y = 200,000(1+60)t.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The first step is to calculate the percentage increase for each year.
If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.
(100+60)% = (100/100 + 60/100)
= (1 + 0.6)
After 2,000, the subscribers will be 200,000×(1+0.6).
For the following years the 200,000×(1+0.6)t
So, the value of y will be given by,
Y=200,000(1+0.6)t
Hence,The equation Y=200,000(1+0.6)t .
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The equations of two lines are given below.
3 x minus y equals 5
3 y equals x minus 15
Are these lines parallel, perpendicular, or neither?
The lines are neither parallel nor perpendicular
How to determine the relationship between the lines?The equations of the lines are given as
3 x minus y equals 5
3 y equals x minus 15
Rewrite the equations properly
3x - y = 5
3y = x - 15
Make y the subject in both equations
In 3x - y = 5, we have
y = 3x + 5
In 3y = x - 15, we have
y = 1/3x - 5
The slopes of the two lines are
m1 = 3
m2 = 1/3
The above values are not equal, and they are not opposite reciprocal
This means that the lines are neither parallel nor perpendicular
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What is the focus point of a parabola with this equation? y = 1 8 (x2 − 4x − 12)
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).
How to estimate the focus point of a parabola?Given: [tex]$y=\frac{1}{8} (x^{2} -4x-12)[/tex]
[tex]$y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$[/tex]
Use the form [tex]$a x^{2}+b x+c$[/tex] to find the values of a, b, and c.
[tex]$a=\frac{1}{8}$[/tex], [tex]$b=-\frac{1}{2}$[/tex] and [tex]$c=-\frac{3}{2}$[/tex]
Consider the vertex form of a parabola [tex]$a(x+d)^{2}+e$[/tex]
To estimate the value of d using the formula [tex]$d=\frac{b}{2 a}$[/tex].
Substitute the values of a and b into the formula
[tex]$d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$[/tex]
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]
Cancel the common factor 2 and 8.
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$[/tex]
[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]$d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$[/tex]
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]
equating, we get
[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]
[tex]$d=-\frac{1}{2} \cdot 4$$[/tex]
The value of [tex]$d=-2$[/tex]
Find the value of e using the formula [tex]$e=c-\frac{b^{2}}{4 a}$[/tex].
Substitute the values of c, b and a into the above formula, and we get
[tex]$e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$[/tex]
simplifying the equation, we get
[tex]$e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$[/tex]
Apply the product rule to [tex]$\frac{1}{2}$[/tex].
[tex]$e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$[/tex]
simplifying the above equation, we get
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]$e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$[/tex]
[tex]$e=\frac{-3-1}{2}$$[/tex]
[tex]$e=\frac{-4}{2}=2$[/tex]
Substitute the values of [tex]$a, d_{t}$[/tex] and e into the vertex form [tex]$\frac{1}{8}(x-2)^{2}-2$[/tex].
Set y equal to the new right side.
[tex]$y=\frac{1}{8} \cdot(x-2)^{2}-2$[/tex]
Use the vertex form, [tex]$y=a(x-h)^{2}+k$[/tex], to determine the values of a, h, and k.
[tex]$a=\frac{1}{8}$[/tex]
[tex]$h=2$[/tex]
[tex]$k=-2$[/tex]
Find the vertex [tex]$(h, k)$[/tex]
[tex]$(2,-2)$[/tex]
Find [tex]$\boldsymbol{p}$[/tex], the distance from the vertex to the focus.
To estimate the distance from the vertex to a focus of the parabola [tex]$\frac{1}{4 a}$[/tex]
Substitute the value of a into the formula
[tex]$\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$[/tex]
[tex]$\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$[/tex]
[tex]$\frac{1}{\frac{1}{2}}=2$[/tex]
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)
Substitute the known values of h, p, and k into the formula, we get
(2,0).
Therefore, the correct answer is (2,0).
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Find lim f(x) if f(x)
x->5
=
{
-x² -1, x #5
-3, x=5
Given
[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]
we have
[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]
since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.
Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . use 3.14 for π as necessary.
The area of the shaded region = 810.66 ft²
What is rectangle?
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since, the opposite sides are equal and parallel, in rectangle, therefore, it can also be termed as a parallelogram.Area of Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =
14*20 + 530.66 =
810.66 ft²
Therefore, the area of the shaded region = 810.66 ft²
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An78swer:
Step-by-step explanation:
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
2, x - 2, x + 4
Step-by-step explanation:
The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)
Factoring a Quadratic expressionFrom the question, we are to determine the each of the factors of the given quadratic expression
The given quadratic expression is
2x² - 4x - 16
Factoring
2x² - 4x - 16
First, factor out 2
That is,
2(x² - 2x - 8)
Now, we will factor x² - 2x - 8
x² - 2x - 8
x² - 4x + 2x - 8
x(x - 4) +2(x -4)
(x +2)(x -4)
Thus,
2x² - 4x - 16 = 2(x +2)(x -4)
Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)
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Find the volume of the triangular prism below if B = 12 cm, h = 8 cm, and L = 27 cm.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{Formula \rightarrow \dfrac{1}{2} \times \bold{b}ase\times\bold{h}eight\times \bold{l}ength}[/tex]
[tex]\mathsf{Your\ equation\ should\ look\ like\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{Solving\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{ \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{= \dfrac{1}{2}\times\dfrac{12}{1}\times\dfrac{8}{1}\times\dfrac{27}{1}}[/tex]
[tex]\mathsf{= \dfrac{1\times12\times8\times27}{2\times1\times1\times1}}[/tex]
[tex]\mathsf{= \dfrac{12\times8\times27}{2\times1\times1}}[/tex]
[tex]\mathsf{= \dfrac{96\times27}{2\times1}}[/tex]
[tex]\mathsf{= \dfrac{2,592}{2}}[/tex]
[tex]\mathsf{= 2.592\div2}[/tex]
[tex]\mathsf{= 1,296}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ C.\ }\frak{1,296\ cm^3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]i don't know how to solve this. help please?
Answer:
51 74
Step-by-step explanation:
x = smaller
x +23 = larger
added together (x + x+23) equal to 28 less than 3x = 3x-28
x + x+23 = 3x-28 subtract 2x from both sides of the equation
23 = x -28 add 28 to both sides
51 = x then the larger = 51 + 23 = 74
Answer:
51 and 74
Step-by-step explanation:
Let the smaller of the two numbers be represented by x. The larger of the two numbers is 23 greater than the smaller, and therefore can be written as x + 23.
Set up an EquationFirst, we can write the sum of the two numbers in terms of the smaller number. "three times the smaller" is 3x, and "28 less" is 3x-28.
Therefore our equation is:
[tex]x+x+23=3x-28[/tex]
Solve the EquationStart by adding like terms
[tex]2x+23=3x-28[/tex]
Subtract 23 from both sides
[tex]2x=3x-51[/tex]
Subtract 3x from both sides
[tex]-x=-51[/tex]
Divide both sides by -1
[tex]x=51[/tex]
The larger term is: [tex]x+23\Rightarrow51+23\Rightarrow74[/tex]
Check[tex]51+74=125[/tex]
[tex]3(51)-28=153-28=125[/tex]
[tex]125=125[/tex]
The smaller number is 51 and the larger number is 74