p(1) = 1
Let p(x) = x2 + bx = c
then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c
Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)
= -2b/c2+bc+c = f(a,b) (say)
For critical points,
∂f/∂c = 0 and ∂f/∂b = 0
= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0
= b(2c+b+1) =0
= b= 0 or b= - (1+2c) = -(2c(c+1))/c2+bc+c = 0
If c=0 , b= -1 => c= 0 or c=-1
If c = -1 ,b = 1
thus we have the following possibility for (b,c)
(0,0) , (0,-1) , (-1,0) ,(1,-1).
At (0,0) f(0,0) = not defined
(0,-1) f(0,-1) = 0
(1,-1) f(1,-1) = 2
(-1,0) is not possible.
p(x) = (x2 +x-1)² + (x2 +x-1) -1
= p(1) = (1+1-1)² + (1+1-1) -1
= 1
Hence, p(1) = 1
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A pyramid has 24 edges and 13 faces, find the number of vertices in the figure -geometry
Answer: 13 vertices
Step-by-step explanation:
We can use the following formula to find the number of vertices in the figure. V is the number of vertices, F is the number of faces, and E is the number of edges.
V = 2 - F + E
V = 2 - (13) + (24)
V = 13
the second statement is the blank of the first x ⇒ y ¬x = ¬y
The second statement is the inverse statement of the first conditional statement.
What is the second statement?If x and y are two propositions, then:
x ⇒ y
Is a conditional statement:
"If x, then y".
The other statement is:
¬x ⇒ ¬y
Where:
¬x means "not x"
So the statement is:
"If not x, then not y".
That would be the inverse statement of the given conditional statement.
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Madeline uses a mirror on the ground to measure the height of her school building. She walks a distance of 9.5 m from the building, then place is a mirror flat on the ground. she then walks 2.75 more meters
The height of the building is 5.33m.
How to calculate the height?The question is to calculate the height of the building.
Based on the information given, the height will be:
Madeline eye height/Distance from X = Height of building/Building distance from X
1.55/2.75 = x/9.45
x = (1.55 × 9.45)/2.75
x = 5.33 m
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By what factor should -1 - 4i/ 2 + 9i be multiplied to find the quotient? Enter any complex numbers in the form a + bi
The factor by which the complex rational number be multiplied is; 2 -9i.
What value should be used to multiply to find the quotient?The expression given in the task is a fraction made up of complex numbers.
Hence in a bid to evaluate the quotient of the expression; -1 - 4i/ 2 + 9i.
The numerator and denominator must be multiplied by the conjugate of the denominator which in this case is; 2 -9i.
This is to help reduce the denominator to a real number.
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A company has 12 000 employees. During the financial crisis in 2008, 2.5 % of them were retrenched
50.75 % of them had a pay cut and the rest were unaffected. Find the number of employees who
were unaffected by the financial crisis.
Answer:
5610
Step-by-step explanation:
unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:
[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]
pls help asap.........
11. The value of x is [tex]13\frac{3}{4}[/tex]
12. From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x
Linear equationsFrom the question, we are to solve the given equation
The given equation is
[tex]5 + \frac{1}{2}(4x +5) = 35[/tex]
This becomes
[tex]\frac{1}{2}(4x +5) = 35-5[/tex]
[tex]\frac{1}{2}(4x +5) = 30[/tex]
[tex]4x +5 = 2 \times 30[/tex]
[tex]4x +5 = 60\\[/tex]
[tex]4x= 60-5[/tex]
[tex]4x= 55[/tex]
[tex]x = \frac{55}{4}[/tex]
[tex]x = 13\frac{3}{4}[/tex]
Hence, the value of x is [tex]13\frac{3}{4}[/tex]
12.
From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x
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Will give brainliest and about 45 points
Answer:
[tex]\sf C. - \dfrac{3}{4}[/tex]
Explanation:
[tex]\sf Given \ equation : 4x - 3y = 12[/tex]
Rewrite in slope intercept form "y = mx + b"
[tex]\rightarrow \sf 4x - 3y = 12[/tex]
[tex]\rightarrow \sf - 3y = 12 - 4x[/tex]
[tex]\rightarrow \sf y =\dfrac{ 12 - 4x}{-3}[/tex]
[tex]\rightarrow \sf y =\dfrac{ 4}{3}x - 4[/tex]
Here the slope is 4/3 and y-intercept is -4
Perpendicular lines has negatively inverse slope.
→ per. slope = -(slope)⁻¹ = -(4/3)⁻¹ = -3/4
Answer:
[tex]-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slopeb is the y-interceptGiven linear equation:
[tex]4x-3y=12[/tex]
Find the slope of the given linear equation by rewriting the equation so that it is in slope-intercept form (i.e. make y the subject):
[tex]\implies 4x-3y=12[/tex]
[tex]\implies 4x-3y+3y=12+3y[/tex]
[tex]\implies 4x=12+3y[/tex]
[tex]\implies 4x-12=12+3y-12[/tex]
[tex]\implies 4x-12=3y[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{4}{3}x-\dfrac{12}{3}[/tex]
[tex]\implies y=\dfrac{4}{3}x-4[/tex]
Therefore, the slope of the given line is 4/3.
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to the given line is:
[tex]\implies m \times \dfrac{4}{3}=-1[/tex]
[tex]\implies m=-\dfrac{3}{4}[/tex]
If -8. min 19 are in an AP, find the values of m and n
Answer:
m = 1 and n = 10.
Step-by-step explanation:
I am assuming you mean -8, m , n, 19.
If they are in AP the 4 terms will have a common difference.
19 - (-8) = 19 + 8 = 27.
So the increase over 3 terms (from -8 to 19) is 27 so we have:
27 / 3 = 9
Therefore the common difference is 9 and the A P is
-8, 1, 10, 19.
HELP HELP HELP
Quick algebra 1 question for 50 points!
1. Provide a brief overview of graphing a linear equation using slope.
2. Create 2 original problems and solve it using the graphing a linear equation using slope method, show your work as you solve the problem and explain each step.
The standard equation of a straight line is given by y = mx + b, where m is the slope (rate of change) and b is the y intercept of the line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a straight line is given as:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept of the line.
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soybeans have a conversion factor of 36.744 (bu/t). how much do 45 bushels weight. Show your work pls
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
How many tonnes are a given quantity of bushels?
In this question we have an application of direct proportionality model, whose form is shown below:
y = k · x (1)
Where:
x - Quantity of bushelsk - Conversion rate, in tonnes per bushel.y - Quantity of tonnesIf we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:
y = (1/36.744 t/bu) · (45 bu)
y = 1.225 t
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
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Differentiation question, please explain :)
The Logistic Law of Population Growth, first proposed by Belgian mathematician
Pierre Verhulst in 1837, is given by [tex]\frac{dN}{dt}= kN-bN^2[/tex], where k and b are constants.
Show that the equation [tex]N= \frac{KN0}{nMN0+(k-bN0)e^{-kt} }[/tex] is a solution of this differential equation (N0 is a constant).
Answer:
dN)/(dt)=(rN(K-N))/K is the answer.
Step-by-step explanation:
The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst.
The continuous version of the logistic model is described by the differential equation is:
(dN)/(dt)=(rN(K-N))/K. (where r is the Malthusian parameter (rate of maximum population growth) and K is the so-called carrying capacity (i.e., the maximum sustainable population).
So, the correct option is ' (dN)/(dt)=(rN(K-N))/K'.
Mark as brainlist pls!
5. Given (x + 1) and (x-3) are factors of P(x) = x4-5x³-7x² + cx + d. Determine the values
of the constants c and d.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
How to determine the missing coefficients of a quartic equation
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of linear equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
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HELP ME ASAP PLEASE
A statistics student is taking a poll of his high school classmates and their senior prom
preferences. He asks those polled, "Last year tickets for the senior prom were $60 each.
This year tickets will need to be $70 if we have a live band perform. Would you like to see
a live band perform at this year's senior prom?" Is this a valid question?
According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).
Why is this question invalid?This question is not valid because it specifies information that would surely change the answer of the respondent.
The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.
According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.
Note: This question is incomplete because the options are missing. Here are the options:
A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.
B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.
C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.
D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.
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You are looking at a map of the united states, and it is assumed that you already know which direction is north
When one is looking at a map of the united states, and it is assumed that you already know which direction is north, this illustrates a theorem.
What is a theorem?It should be noted that a theorem simply means a statement that has been proved.
In this case, when one is looking at a map of the United States, and it is assumed that you already know which direction is north, this illustrates a theorem. This is because it's proven.
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Angela is starting a new business, selling shirts and dresses that she sews herself, The materials for the skirts cost 13.56 and the materials for the dresses cost 18.79. She only has $80 to spend. She still has a regular job, so she is limited on the time she has to sew her products. She only wants to spend 15 hours sewing; it takes 2 hours to sew a skirt, and 4 hours to sew a dress
How does this graph change between point D and point G?
A graph increases from point D to point G, and then decreases.
The graph increases.
The graph decreases.
The graph increases, then decreases.
The graph remains constant.
Answer:
The graph increases.
Step-by-step explanation:
hope this helps!!
Answer: the graph increases
Step-by-step explanation: did test
The question is on the picture
Answer: 68
Step-by-step explanation:
By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.
Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2?
Truth Value for p^ q when x is replaced by 2 is also true. ( p^q is True)
What is a prime number?The prime numbers are those numbers that have only one factor namely 1 and the number itself.
Given that p = x is prime and q = x is even. If we replace x by 2 then we would get
p = 2 is prime
q = 2 is even
p^q will be held true only if p and q both are true.
The statement for p and q both are true because 2 only has two factors only 1 and 2 themselves.
2 is also considered an even number (2,4,6,8,...)
Since p = true and q = true then
p and q = p^q = true
Thus, p^q is True.
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Answer:
p^q is true
Step-by-step explanation:
If both p and q are true, the statement p^q is true. If both p and q are false, the statement p^q is still true. All other options yield a false result.
someone solve this plsss
Lacey has $36 to spend. She buys a pair of sunglasses for $14.89 and a hat for $9.33. Lacey buys a scarf with the remaining money. How much does Lacey spend buying a scarf?
Answer:
$11.78
Step-by-step explanation:
14.89+9.33=24.22
36-24.22=11.78
a car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector
The magnitude of the resultant vector is 27 miles
How to determine the vector magnitudeResultant vector = Distance of A - Distance of B
This is so because of the opposite direction of the car's movement
A = 87 miles
B = 114 miles
Resultant vector = 114 - 87
Resultant vector = 27 miles
Thus, the magnitude of the resultant vector is 27 miles
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Please help! Billy just received $10 for his birthday and immediately spent $2.50 on a pack of baseball cards. He then wants to buy some boxes of candy that cost $1.50 each.
If Billy has $7.50 remaining, which of the following equations will give you the number of boxes, x, that Billy could buy?
Answer:
1.5x = 7.5 (a)
Step-by-step explanation:
If Billy has $7.50 remaining, then he can buy x no. of boxes.
Each box costs $1.50
So, 1.5x = 7.5
Baby rabbits were sorted into three groups, based upon which food they preferred when given a choice: Brand A rabbit food, Brand B rabbit food, or a diet of raw vegetables. For two months each group was restricted to their preferred diet (they were no longer given a choice in diet). Measurements for the height, weight, and length of the rabbits was taken each week for two months. The rabbits in the group with the diet of raw vegetables had significantly more growth that the other two groups. What conclusion can be drawn from this study?
Answer: That raw vegetables are better for the rabbit's growth than rabbit food.
Answer:
The rabbit food that was strictly a diet of raw vegetables is healthier for the rabbits.
Step-by-step explanation:
Solve the following....
4(5-2x)+3=7
Answer:
x = 2
Step-by-step explanation:
1) If there is a number right next to a bracket, then it means that it should be multiplied. --> 4(5 -2x) = 25 - 10x
2) (20 - 8x) + 3 = 23 - 8x
3) 23 - 8x = 7
4) 16 = 8x
5) We divide both sides with 8 to leave x. --> 2 = x
6) x = 2
A cylinder has a cross-sectional area of 17m² and a length of 14 m what is the volume of the cylinder
Answer:
your answer please mark me as brainlist
Step-by-step explanation:
V
=
238
m³
You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s residence. Explain how you can use the diagram to locate the meeting place.
6x+7=-5 i got it wrong
Answer:
x = -2
Step-by-step explanation:
Subtract 7 from both sides :
6x = -12
Divide both sides by 6 :
x = -2
Hope this helped and have a good day
. Expand: 31og2 (9n)
By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists
[tex]$ 6(log _2(3) +3 log _2(n))[/tex].
What is a logarithm?A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.
From the definition of a logarithm, we get
aˣ = b exists the same as x = logₐb
Given: [tex]$3log _2(9n)[/tex]
Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]
[tex]$= 3(2log _2(3) + log _2(n))[/tex]
Expanding the equation, we get
[tex]$3(2log _2(3) + log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].
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Oak street and elm street run parallel to each other when Main Street intersects them it forms interior <6 measuring70 what is the measure of <4
IfIf it forms interior <6 measuring70. The measure of <4 is: B. 110°.
Measure of <4Using this interior angle theorem
Measure of <4=180° - <6
Where:
<6 measure 70
Hence:
Measure of <4=180°-70°
Measure of <4=110°
Therefore the measure of <4 is: B. 110°.
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Y=
Help me please thank you
Answer:
-135689;456+((888888888