Answer:
x = -6 and x = 4
Step-by-step explanation:
In math, the critical points of a function are the points where the derivative equals zero.
So, first we will find the derivative of the function. The derivative is:
[tex]f'(x)=3x^2 +6x-72[/tex]
Now, we are going to make the derivative equal zero and find the answers of the equation.
[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]
So we have that the critical points are the answers to this equation:
[tex]x+6= 0 \\x= - 6[/tex]
and
[tex]x-4=0\\x=4[/tex]
Thus, the critical points are x=-6 and x=4
Using it's concept, it is found that the critical numbers of the function are:
x = -6 and x = 4.
The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:
[tex]f^{\prime}(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = x^3 + 3x^2 - 72x[/tex]
The derivative is:
[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]
[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]
Then:
[tex]f^{\prime}(x) = 0[/tex]
[tex]3(x^2 + 2x - 24) = 0[/tex]
[tex]x^2 + 2x - 24 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.
[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]
[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]
[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]
The critical numbers of the function are x = 4 and x = -6.
A similar problem is given at https://brainly.com/question/16944025
easy khan academy math. please answer asap
Answer:
[tex]\boxed{\sf B \ and \ C}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(60)=\frac{5.2}{KL}[/tex]
[tex]\sf KL=\frac{5.2}{sin(60)}[/tex]
[tex]\sf sin(90-60)=\frac{3}{KL}[/tex]
[tex]\sf KL=\frac{3}{sin(90-60)}[/tex]
[tex]20+3x-15+x=27[/tex]
Answer:
x=11/2
Step-by-step explanation:
First we can combine similar terms on the left side. 3x + x is 4x and 20-15 is 5
Now that we have combined them, we are left with 4x+5=27
Subtract 5 on both sides to cancel out the 5.
4x=22
Divide both sides by 4
x=22/4
Simplify
x=11/2
Answer:
[tex] \boxed{\sf x = \frac{11}{2}} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x: \\ \sf \implies 20 + 3x - 15 + x = 27 \\ \\ \sf Grouping \: like \: terms, \: 20 + 3x - 15 + x = \\ \sf (3x + x) + (20 - 15) : \\ \sf \implies \boxed{ \sf (3x + x) + (20 - 15)} = 27 \\ \\ \sf 3x + x = 4x : \\ \sf \implies \boxed{ \sf 4x} + (20 - 15) = 27 \\ \\ \sf 20 - 15 = 5 : \\ \sf \implies 4x + \boxed{ \sf 5} = 27 \\ \\ \sf Subtract \: 5 \: from \: both \: sides: \\ \sf \implies 4x + (5 - \boxed{ \sf 5}) = 27 - \boxed{ \sf 5} \\ \\ \sf 5 - 5 = 0 : \\ \sf \implies 4x = 27 - 5 \\ \\ \sf 27 - 5 = 22 : \\ \sf \implies 4x = \boxed{ \sf 22} \\ \\ \sf Divide \: both \: sides \: of \: 4x = 22 \: by \: 4 : \\ \sf \implies \frac{4x}{4} = \frac{22}{4} \\ \\ \sf \frac{ \cancel{4}}{ \cancel{4}} = 1 : \\ \sf \implies x = \frac{22}{4} \\ \\ \sf \implies x = \frac{11 \times \cancel{2}}{2 \times \cancel{2}} \sf \implies x = \frac{11}{2} [/tex]
In a multiple regression, the following sample regression equation is obtained:yˆ = 152 + 12.9x1 + 2.7x2.a. Predict y if x1 equals 20 and x2 equals 35. (Round your answer to 1 decimal place.)
Answer:
The predicted value of y is 504.5.
Step-by-step explanation:
Let be [tex]y = 152 + 12.9\cdot x_{1} + 2.7\cdot x_{2}[/tex], for all [tex]x_{1}, x_{2} \in \mathbb{R}[/tex]. If [tex]x_{1} = 20[/tex] and [tex]x_{2} = 35[/tex], the predicted value of y is:
[tex]y = 152 + 12.9\cdot (20) + 2.7\cdot (35)[/tex]
[tex]y = 504.5[/tex]
The predicted value of y is 504.5.
It is urgent plz answer
Answer:
my class is 8 th is I don't now this answer
Which expression is equivalent to (x^1/2 y ^-1/4 z)^-2
Answer:
x^-1 y^½ z^-2
What is the value of $\sqrt{36 \times \sqrt{16}}$?
Answer:
24
Step-by-step explanation:
If we have two square roots like [tex]\sqrt{36}\cdot\sqrt{16}[/tex], we could do this either of two ways.
1. Multiply 36 by 16 and find the square root of that
[tex]\sqrt{36\cdot16} = \sqrt{576} = 24[/tex]
2. Find the square root of both of them then multiply.
[tex]\sqrt{36} = 6, \sqrt{16} = 4, 6\cdot4 = 24[/tex]
Hope this helped!
The average child will wear down 727 crayons by his or her tenth birthday find the number of boxes of 64 crayons this is equivalent to.round to the nearest tenth
Answer:
11.4
Step-by-step explanation:
You just need to divide this one.
727/64=11.3593
Answer:
11.4
Step-by-step explanation:
727/64=11.359375
We have to round to the nearest tenth so, it would be 11.4.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
In graphing a trigonometric function, how does one establish which are the EXTREMUM coordinates and which are the MIDLINE INTERCEPTION coordinates. I can find the x values and the y values but do not know which X goes with which Y and the graphs end up incorrect! It is EXTREMELY frustrating. How do I discern which is which!!!!! Thank You.
Answer:
If I getting the question correctly, your doubt is the order of the values you get after doing the math. I mean, you can do the calculations, but in the end, you don't form the coordinate pairs correctly, that's why I understand from your question. So, here is what you need to do.
One way to graph is by using the definitions of those kinds of functions. For example, let's say we want to find the points to draw the function: [tex]y=sin(x)[/tex]
Remember that trigonometric functions have a specific period, that means, their drawing repeats over and over again after a certain number. That period is [tex]2 \pi[/tex], that means this number represents a cycle.
So, the main thing you need to do is to pick a starting point to then, draw the curve according to the [tex]2 \pi[/tex] period.
Now, we know that sine functions intercept the origin of the coordinate system, as you can observe in the image attached, there you can see that from the origin you draw those waves making sure you intercept the x-axis at every [tex]\pi[/tex] number. In the end, you will have a sine function.
On the other hand, if you want to have a chart with all x-values and y-values. First, you need to set x-values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Then, you need to find each y-values for each of them.
Now, you have to draw a chart value, to keep in other the coordinate pairs, that way, you'll have the correct pairs at the end.
For example, for [tex]x=-5[/tex], we get [tex]y=-0.09[/tex], that means in the chart value, you are gonna form the pair [tex](-5, -0.09)[/tex], and now you have your first point of the drawing. Then, you keep repeating the process until you complete all the chart values.
As you can imagine, you're going to get really small decimal numbers, that's why I explained to you the first method, it's faster and easier.
If mBC in circle Ais 60°, what is mZ BDC?
a. 60 degrees
b. 45 degrees
c. 30 degrees
d. 25 degrees
Answer:
Option (C)
Step-by-step explanation:
Measure of the arc BC of a circle A = 60°
Since, measure of an arc is equal to the measure of the central angle that intercepts the arc.
Therefore, m∠A = 60°
Since, measure of the inscribed angle is half of the central angle subtended by the same arc.
Therefore, m∠A = [tex]2\times m(\angle {BDC})[/tex]
60° = 2 × m(∠BDC)
m∠BDC = 30°
Therefore, Option (C) will be the answer.
Answer:
It’s C
Step-by-step explanation:
helppppppppppppppppsdss
Answer:
t = p * n
Step-by-step explanation:
* - multiplication
t is the total cost
in order to find total cost we need to multiple cost per mile on the number of miles so we will receive cost of all miles that we went
Answer:
[tex]\boxed{t=pn }[/tex]
Step-by-step explanation:
t is total cost
The formula is in terms of t (total cost).
p is price per mile
Suppose the price per mile is £60. For every mile he travelled, he has to pay £60.
n is the number of miles travelled.
For example, Carlos travelled 4 miles and the price per mile is £30.
[tex]t=30 \times 4\\t=120[/tex]
His total cost will be £120.
butter and flour are mixed in the ratio 2:3. paul has 640 grams of butter and 880 grams of flour. how much more flour does he need? Can you explain again in a simpler format.
Answer:
80 grams of butter
Step-by-step explanation:
640/2=329
3x320=960
960-880=80
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
Which transformation is needed to be used on x^2, to get the graph of f(x) = 2x2 - 12x + 22?
Select one:
O a. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 13 units
O b. Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O c. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O d. Shift right by 3 units and shift upwards by 4 units
Please I need help
Answer: A
Step-by-step explanation:
The required transformation is Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units. Hence option B is correct.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Since, both curve of x² and 2x² - 12x + 22 is in the graph.
Now, the steps of transformation of x² into 2x² - 12x + 22 is as follows.
1) Shift left by 3 units.
2) Stretch vertically by a factor 2.
3) Shift upward by 4 units
Thus, the required result will be seen graph.
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Suppose Grant is going to build a playlist that contains 6 songs. In how many ways can Grant arrange the 6 songs on the playlist?
Grant can arrange the 6 songs on the playlist in
different ways.
Grant can arrange the songs 720 different ways
The different ways Grant can arrange the 6 songs on the playlist is 720.
What is the different ways to arrange a certain number of objects?The different ways to arrange 'n' number of objects are n!.
The number of songs in the playlist are 6.
Therefore, the number of ways Grant can build the playlist is
[tex]= 6!\\= (6)(5)(4)(3)(2)(1)\\= 720[/tex]
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Show all work! I don't understand this! Brainleist!
I attached a picture this time!
Answer:
2.94 seconds.
Step-by-step explanation:
The ball will hit the ground when the height of the ball is 0 meters.
The equation is...
h = 61 - 6t - 5t^2.
-5t^2 - 6t + 61 = 0
5t^2 + 6t - 61 = 0
We can use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex], where a = 5, b = 6, and c = -61.
= [tex]\frac{-6 ± \sqrt{6^2 - 4 * 5 * (-61)} }{2 * 5}[/tex]
= [tex]\frac{-6 ± \sqrt{36 - 20 * (-61)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{36 + 1,220)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{1,256} }{10}[/tex]
= [tex]\frac{-6 ± 35.44009029}{10}[/tex]
Since time cannot be negative, we will not minus the 35.44009029.
(-6 + 35.44009029) / 10 = 29.44009029 / 10 = 2.944009029
That is approximately 2.94 seconds.
Hope this helps!
Answer:
[tex]\boxed{t = 2.94 \ seconds}[/tex]
Step-by-step explanation:
When the ball hits the ground, h = 0
Putting this in the equation:
=> [tex]0 = 61-6t-5t^2[/tex]
=> [tex]61-6t-5t^2 = 0[/tex]
Taking -1 as common
=> [tex]-1(5t^2+6t-61) = 0[/tex]
Dividing both sides by -1
=> [tex]5t^2+6t-61 = 0[/tex]
Using Quadratic Equation:
=>t = [tex]\frac{-b+ / - \sqrt{b^2-4ac} }{2a}[/tex]
=> [tex]\frac{-6 +/- \sqrt{6^2-4(5)(-61)} }{2(5)}\\\frac{-6 +/- \sqrt{36+1220} }{10}[/tex]
=> t = [tex]\frac{-6 +/- 35.44}{10}[/tex]
Either:
t = [tex]\frac{-6+35.44}{10}[/tex] OR t = [tex]\frac{-6-35.44}{10}[/tex]
t = 29.44/10 OR t = -41.44/10
t = 2.94 OR t = -4.14
Time can never be negative so t = 2.94 secs
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?
[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]
Answer:
1/13
Step-by-step explanation:
MATH HELP ASAP :( Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest possible leading positive integer coefficient. Polynomial of lowest degree with lowest possible integer coefficients, and with zeros 9-41 and 0 (multiplicity 2).
Answer:
[tex]f(x)=((x-9)^2+16)x^2[/tex]
[tex]f(x)=x^4-18x^3+97x^2[/tex]
Step-by-step explanation:
If you want to, I could add the explanation as well. Just notify me.
Something really important I want to note is that since 9-4i is a zero, then 9+4i must must also be a zero.
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
15 pt
Step-by-step explanation:
Answer:
15 pintsStep-by-step explanation:
1 quarts = 2 pints
From the question we were given 7.5 quarts to to get the desired result multiply 7.5 by 2
Which is 7.5 × 2 = 15 pints
Hope this helps you
PLEASE ANSWERRR The ordered pair for the standard equation 3y – 2x = 12 is: (0, 4). (0, -4). (6, 2). None of these choices are correct.
Answer:
(0, 4)
Step-by-step explanation:
3y - 2x = 12.
Check each one by substituting:
(0,4):
3(4) - 2(0) = 12
12 = 12. - so its this one.
The ordered pair (0, 4) is for the equation 3y - 2x = 12 and the ordered pairs (0, -4). (6, 2) does not satisfy the equation.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The equation:
3y - 2x = 12
Plug x = 0 and y = 4
3(4) - 2(0) = 12
12 = 12 (true)
SImilarly for checking the other ordered pairs.
Thus, the ordered pair (0, 4) is for the equation 3y - 2x = 12 and the ordered pairs (0, -4). (6, 2) does not satisfy the equation.
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a hat contains 2 red apples and 3 green apples. a bucket contains 7 red apples and 3 green apples. a container is selected at random and an apple is drawn out. what is the probability that it will be a red apple
Answer:
15
Step-by-step explanation:
URGENT It is given that a regular n-sided polygon has 5 sides more than a
regular m-sided polygon. If the sum of interior angles of the regular
n-sided polygon is twice that of the latter, find the values of m and n.
Answer:
m = 7; n = 12
Step-by-step explanation:
"a regular n-sided polygon has 5 sides more than a
regular m-sided polygon"
n = m + 5
The sum of the measures of the interior angles is
180(n - 2) for the n-sided polygon and
180(m 2) for the m-sided polygon.
"If the sum of interior angles of the regular
n-sided polygon is twice that of the latter"
180(n - 2) = 2(180)(m - 2)
We have a system of equations with 2 equations.
n = m + 5
180(n - 2) = 2(180)(m - 2)
Simplify the second equation:
n - 2 = 2m - 4
n + 2 = 2m
Substitute m + 5 for n.
m + 5 + 2 = 2m
7 = m
m = 7
n = m + 5 = 7 + 5 = 12
Answer: m = 7; n = 12
Rewrite the equation by completing the squares x^2-x-20
Answer: x = ¹/₂ ± √⁸¹
------------
2
Step-by-step explanation:
First write out the equation
x² - x - 20
Now we now write the equation by equating to 0
x² - x - 20 = 0
We now move 20 to the other side of the equation. So
x² - x = 20,
We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes
x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²
x² - ( ¹/₂ )² = 20 + ¹/₄
( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction
( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4
Taking the square root of both side to remove the square,we now have
x - ¹/₂ = √⁸¹/₄
x - ¹/₂ = √⁸¹/₂
Therefore,
x = ¹/₂ ± √⁸¹
-----------
2
A mechanic earns $5 more per hour than his helper. On a six-hour job the two men earn a total of $114. How much does each earn per hour?
Answer:
Step-by-step explanation:
m= the amount of money the mechanic makes.
h= the amount of money the helper makes.
m=h+5
m+h=114
h+5+h=114
2h+5=114
h=54.50
m=59.5
Helper makes $9 an hour.
Mechanic makes $9.92 an hour.
The earning of helper each earn per hour is 7$ /hr.
To find earning of helper per hour.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and also the properties and manipulation of numbers.
Given that:
let the cost /per hour of helper be x
and that of the mechanic is x+5
now for 6 hour job total earning is
6(x+x+5) = 114
=> 2x+5 = 19
so, 2x = 14 or x = 7
the earning of helper is = 7$ /hr
and earning of mechanic is = 12$/hr
So, the earning of helper each earn per hour is 7$ /hr.
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Which system type is a linear system with infinitely many solutions?
Answer:
down b3low
Step-by-step explanation:
The point where the two lines intersect is the only solution. An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions.
A rectangle has a width of 3/4 inches and a length of 9/10 inches. Another rectangle
is larger but still proportional to the first rectangle. It has a width of 30 inches and a length of 36 what proportion could model this situation
Answer:
Bigger size / smaller size = 40
Step-by-step explanation:
Notice that we
36 / (9/10) = 30 / (3/4) = 40
Therefore the proportion model would be
Bigger size / smaller size = 40
A new city Mayor would like to determine the proportion of community voters who are ages 18 to 20 years. He has heard it is 10%. To test this prediction, he surveys 1000 random community voters and found that 111 of them are aged 18 to 20. The following is the setup for this hypothesis test: H0:p=0.10 H0:p≠0.10 The p-value for this hypothesis test is 0.04. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer: He should reject the null hypothesis.
Step-by-step explanation: When using P-Values to decide if you accept or not the alternative hypothesis, compare the p-value with the chosen significance level (α).
In the Mayor's survey:
p-value = 0.04
α = 5% or 0.05
If the p-value is less than α, reject the null hypothesis and accept the alternative. If p-value is greater than or equals α, fail to reject the null hypothesis and don't accept the alternative.
Analysing the Mayor's survey:
p-value = 0.04 < α = 0.05
In conclusion, the Mayor should reject the null hypothesis and accept that the proportion of voters who are aged 18 to 20 is not equal to 10%, i.e., accept the alternative hypothesis: [tex]H_{a}[/tex]: p≠0.10
Help ASAP!!!
Find sin(c). Round to the nearest hundredth if necessary.
A: 0.38
B: 0.92
C:0.42
D:1.08
Answer:
The answer is option A
0.38Step-by-step explanation:
sin ∅ = opposite / hypotenuse
Since we are finding sin (c)
From the question
The opposite is BA
The hypotenuse is AC
So we have
sin c = BA/ AC
BA = 5
AC = 13
sin c = 5/13
sin c = 0.384615
sin (c) = 0.38 to the nearest hundredth
Hope this helps you
Answer:
[tex]\boxed{Sin C = 0.38}[/tex]
Step-by-step explanation:
Sin C = opposite/hypotenuse
Where opposite = 5, hypotenuse = 13
Sin C = 5/13
Sin C = 0.38
6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
No solutionStep-by-step explanation:
6x – 3y = 3
–2x + 6y = 14
lets solve by substitution:
1) lets isolate y:
6x–3y=3
-3y=-6x+3
y=(-6x+3)/-3
y=2x-1
2) plug in 2x-1 for y in order to find x:
6x-3(2x-1)=3
6x-6x+3=3
3=3
since x cancels out, it means that there is no solution to this linear system of equations
Answer:
No Solution :)
Step-by-step explanation:
What are the zeros of the quadratic function f (x) = 2x^2 -10x-3?
Answer:
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
Step-by-step explanation:
1. Need to factor or can use the quadratic formula
2x^2-10x-3=0
a=2, b=-10, c=-3
[-b+-sqrt(b^2-4*a*c)]/(2*a)
[10+-sqrt(100-4*(-200)]/4
[10+- sqrt(300)]/4
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
The item below is based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:
Excerpt:
"Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ2 (4, N = 100) = 11.73, p < .05."
The phi coefficient for this study is:________.
Answer:
φ = 0.34
Step-by-step explanation:
Given:
total number of observations = N = 100
chi-square test for independence χ2 = (4, N = 100) = 11.73
To find:
phi coefficient φ
Solution:
phi coefficient φ is computed as:
φ = √( χ2 / n )
= √ (11.73 / 100 )
= √0.1173
φ = 0.3425