The absolute maximum of the function is 184 and the minimum value of the function is -72.
What is the absolute maximum value?If the graph of an absolute value function opens downward, the y-value of the vertex is the maximum value of the function.
Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the absolute maximum and minimum values at this endpoints are as calculated;
At end point x = -5
f(-5) = (-5)⁴-18(-5)²+9
f(-5) = 625-450+9
f(-5) = 184
At end point x = 5
f(5) = (5)⁴-18(5)²+9
f(5) = 625-450+9
f(5) = 184
To get the critical point, this point occurs at the turning point i.e at
dy/dx = 0
if y = x⁴-18x²+9
dy/dx = 4x³-36x = 0
4x³-36x = 0
4x (x²-9) = 0
4x = 0
x = 0
x²-9 = 0
x² = 9
x = ±3
Using the critical points [0, ±3]
when x = 0, f(0) = 0⁴-18(0)+9
f(0) = 9
Similarly when x = 3, f(±3)= (±3)⁴-18(±3)²+9
f(±3) = 81-162+9
f(±3) = -72
It can be seen that the absolute minimum occurs at x= ±5 and the absolute minimum occurs at x =±3
absolute maximum = 184
absolute minimum = -72
Hence, the absolute maximum of the function is 184 and the minimum value of the function is -72.
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please help!!!!!!!!!!
Answer: which one ? ill edit this w/ the answer
Step-by-step explan
The triangles are congruent by SSS and HL
Answer:
D
Step-by-step explanation:ik
PLEASE HELP I NEED TO GET DONE IN 10 MINUTES!!
The marbles below (with colors green, orange, red, pink, and blue) are placed into a bag and mixed up. Kevin is asked to pick a marble from the bag without looking. What is the probability that he will not choose a green or a red marble?
Answer:
11 over 20
Step-by-step explanation:
There are 20 altogether and 9 are green and red 20 - 9 = 11
I WILL GIVE YOU BRANILEST!
This is a really important question that I need to know before 1! Please explain your answer! PLEASE EXPLAIN!
What is the length of the line segment?
Answer:
[tex]l(\overline {AB})\approx9.22\: units[/tex]
Step-by-step explanation:
A = (-2, -3), B = (-8, 4) (Given)[tex]\implies x_1= -2,\: y_1=-3,\: x_2=-8,\: y_2= 4[/tex]By distance formula length of segment AB can be given as:[tex]l(\overline {AB})=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex][tex]l(\overline {AB})=\sqrt{[-8-(-2)]^2 +[4-(-3)]^2}[/tex][tex]l(\overline {AB})=\sqrt{[-8+2]^2 +[4+3]^2}[/tex][tex]l(\overline {AB})=\sqrt{[-6]^2 +[7]^2}[/tex][tex]l(\overline {AB})=\sqrt{36 +49}[/tex][tex]l(\overline {AB})=\sqrt{85}[/tex][tex]l(\overline {AB})=9.21954446\: units[/tex][tex]l(\overline {AB})\approx9.22\: units[/tex]Helppppp fastttt !!! Pleaseeee and tyyyyy
Answer:
x ≤ -4
Step-by-step explanation:
-7x + 13 ≥ 41
Rearrange the terms
-7x ≥ 41 - 13
Calculate
-7x ≥ 28
Divide both sides
x ≤ -28/7
Simplify
x ≤ -4
HOPE THIS HELPS AND HAVE A NICE DAY <3
Find the value of x in the figure.
Answer:
120
Step-by-step explanation:
Because triangle is always 180.
180-30-30=120
Can somebody help me with this question?
Answer:
D. tanθ = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Trigonometric applied here :
tanθ = 1/cotθ
=============================================================
In Quadrant III, all values of tan and cot are positive.
⇒ tanθ = 1/(3/4)
⇒ tanθ = 4/3
helppppppppppppppppppppppp meeeeeeeeee
Solve the equation
x²+4x-7=0
by completing the square
give your answers to 2 decimal places.
Need steps with the answer and fast as possible. i will grant you 50 points literally Meena's mother is four times as old as meena. after 5 years,her mother will be three times as old as she will be then. whats their present ages
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Meena mother is 4 times as old as Meena After 5 years, Her mother will be 3 times as old as she will be then. To Find :-We have to find the present ages of Meena and her mother. Let's Begin :-Let the present age of Meena be ' x ' years.
Now, It is given in the question that her mother is 4 times as old as MeenaThat means,
Present age of her mother
[tex]\sf{ = 4x \: years }[/tex]
Now,
After 5 years
The age of the Meena will be
[tex]\sf{ = x + 5 \: years }[/tex]
Therefore,
According to given condition,
The age of her mother will be
= [tex]\sf{ = 4x + 5 \: years ...eq(1)}[/tex]
But, It is given that,
After 5 years, Her mother will be 3 times as old as Meena.That is,
After 5 years, Her mother age will be
[tex]\sf{ = 3(x + 5) \: years ...eq(2)}[/tex]
From eq(1) and (2) :-
[tex]\sf{ 4x + 5 = 3(x + 5) }[/tex]
[tex]\sf{ 4x + 5 = 3x + 15}[/tex]
[tex]\sf{ 4x - 3x = 15 - 5 }[/tex]
[tex]\sf{ x = 10 \: years }[/tex]
Thus, The present age of the Meena will be 10 years.
Therefore,
The present age of her mother will be
[tex]\sf{ 4x = 4 × 10 }[/tex]
[tex]\sf{ = 40 \: years }[/tex]
Hence, The present of Meena and her mother is 10 years and 40 years.
The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals
, then the quadrilateral is a parallelogram.
The midpoint of HJ is
and the midpoint of IK is (2, 2).
Therefore, HIJK is a parallelogram because the diagonals
, which means they bisect each other.
Check the picture below.
well, HIJK is a parallelogram only if its diagonals bisect each other, if that's so, the midpoint of HJ is the same as the midpoint of IK, let's check
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad J(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 + 0}{2}~~~ ,~~~ \cfrac{ -1 + 5}{2} \right)\implies \left( \cfrac{4}{2}~~,~~\cfrac{4}{2} \right)\implies \boxed{(2~~,~~2)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ I(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad K(\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \left(\cfrac{ 1 + 3}{2}~~~ ,~~~ \cfrac{ 1 + 3}{2} \right)\implies \boxed{(2~~,~~2)}[/tex]
Answer:
1. bisect each other 2. (2,2) 3. have the saem midpoint
Step-by-step explanation:
The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals
✔ bisect each other
, then the quadrilateral is a parallelogram.
The midpoint of HJ is
✔ (2, 2)
and the midpoint of IK is (2, 2).
Therefore, HIJK is a parallelogram because the diagonals
✔ have the same midpoint
, which means they bisect each other.
Question provided in image:
Answer:
the slope of parallel lines are - the same
i.e,m1=m2
the slope of perpendicular lines are- negative reciprocals
i.e,m1*m2= -1
where, m1 and m2 slopes of two lines
A. The slope of parallel lines are: the same/equal
B. The slope of perpendicular lines are negative reciprocals.
What are the Slopes of Parallel and Perpendicular Lines?If two lines are parallel to each other, they will have the same slope. If the slope of one is 4, the slope of the other line that is parallel to it would also be 4.
On the other hand, the slope of perpendicular lines are negative reciprocal of each other. That is, if the slope of one is, -1, the slope of the other line would be 1.
Therefore, parallel lines have the same slope, while perpendicular lines have slope values that are negative reciprocal to each other.
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More people leave Anytown, AL each year than move into it. The population over the past 20 years is shown in the table. Use technology to find an equation that models the exponential decline. Report the rate of decline below, rounding to the nearest hundredth.
Year Population
2000 30,000
2005 27,000
2010 25,500
2015 24,000
2020 22,400
The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
Let's suppose the equation that models the exponential decline is:
[tex]\rm y = a(b^x)[/tex]
From the data given, we can calculate the value of a and b:
a = 46348587109809610
b = 0.9861
y = 46348587109809610(0.9861)ˣ
Thus, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
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can someone help me with " |-3|-10 " please.
Answer:
-7
Step-by-step explanation:
| anything inside these vertical lines becomes positive when the lines are removed. These lines are absolute value lines |
So |-2| becomes 2 when absolute bars are removed.
Using this logic, |-3| becomes 3 when bars removed. Thus 3 - 10 = -7
the address by ronald reagan is one of his most famous speeches. Taking into consideration the principles of effective public speaking you have studied so far, list at least 4 reasons why you feel this speech is still considered great?
ASAP 100 POINTS
Answer:
nation's leader
Step-by-step explanation:
As the nation's leader, President Reagan decided to address the country about the Challenger tragedy. Putting aside his scheduled State of the Union address before Congress, the President instead delivered an Oval Office address to comfort the people as the nation mourned.
find the product and simplify your answer 5x/x^2-1 * x+1/x^2
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of the given expression can be done as,
[tex]\dfrac{5x}{x^2-1} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{x^2-1^2} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{(x+1)(x-1)} \times \dfrac{x+1}{x^2}\\\\= \dfrac{5}{(x-1)x}[/tex]
Hence, the simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).
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Convert the polar equation to rectangular coordinates. (use variables x and y as needed. )
The rectangular coordinates will be (x=7cot(θ), y=7).
What are polar coordinates?A pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.
We have the standard conversion toolbox:
[tex]x=rcos(\theta)\\\\y=rsin(\theta)[/tex]
Here it is given that
[tex]r=7cosec(\theta)[/tex]
so
[tex]x=7cosec(\theta)\times cos(\theta)=\dfrac{7cos(\theta)}{sin(\theta )}=7cot(\theta)\\\\\\y=7cosec(\theta)\times sin(\theta)=\dfrac{7sin(\theta)}{sin(\theta)} = 7[/tex]
therefore the rectangular coordinates are (7cot(θ), 7)
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In trapezoid PQRS, if segment XY is the midsegment, which could be the lengths PQ and SR? Select all that apply.
17 cm and 31 cm
18 m and 30 m
4 cm and 8 cm
9 cm and 15 cm
12 cm and 36 cm
18 cm and 30 cm
please explain how you get the answer :)
Answer:
17 cm and 31 cm
12 cm and 36 cm
18 cm and 30 cm
Step-by-step explanation:
The midsegment of a trapezoid is equal to the average of the two bases. When taking an average of two numbers, you add them and divide by 2. So the equation will be as follows:
[tex]\frac{PQ + SR}{2} = XY[/tex]
XY is given to be 24, so:
[tex]\frac{PQ + SR}{2} = 24[/tex]
Multiplying on both sides gets us:
[tex]PQ + SR = 48[/tex]
So any values of PQ and SR that add to 48 work. Therefore, we will sum the given options:
17 cm + 31 cm = 48 cm
18 m + 30 m = 48m (Did you mean meters?)
4 cm + 8 cm = 12cm
9 cm + 15 cm = 24cm
12 cm + 36 cm = 48cm
18 cm + 30 cm = 48 cm
8. A school official calculated that the school bus arrives by 8 a.m. 90% of the time. If the
bus runs 200 days, on how many days can the school official expect it to arrive after
8 a.m.?
Answer:
20 days of the 200 total days
Step-by-step explanation:
1. 200/100=2
2. 2x90=180
3. 200-180=20
Solve the system with elimination.
x - 2y = 4
3x + y = 6
? ]
help with practice problem
Answer:
y = 2x - 6
Step-by-step explanation:
For parallel lines, the mx (the slope) stays the same but the y-int changes.
Can someone help real quick? I know x=15 but I can't figure out the length.
Answer:
23
Step-by-step explanation:
AB and BC are tangent to circle P, which means that both lines are congruent. Set AB and CB equal to each other:
2x-7=5x-52
3x=45
x=15
Plug 15 into AB:
2(15)-7 = 23
Length of AB is 23.
50 cm = _____ km
1000 g = _____ cg
Answer:
0.0005 and 100000
Step-by-step explanation:
solve them in the answer.
artem is inviting 3 friends each friend wants 8 cookies and each box has 4 cookies how many boxes should artem get
Answer:
6 boxes
Step-by-step explanation:
2 boxes for each friend
:)
Answer:
So there's Artem and his 3 friends so thats 4 people and everyone wants 8 cookies each box has 4 cookies so he would buy 32 boxes.
Step-by-step explanation:
Which is the correct quotient with a letter as the remainder?
Answer:
A) 913 / 29 = 31 r 14Step-by-step explanation:
31 × 29 + 14 = 913
Then
913 / 29 = 31 r 14
One factor of this polynomial is (2x - 1). Use long division to determine which expression represents the other factor. 2x³+ 5x² - 27x + 12
-> 3rd answer is correct
Name each indicated part of the algebraic expression.
4x + y
3
- 2.2
Answer:
4 Coefficient-2.2 Constant1/3 Coefficienty/3 Termx VariableStep-by-step explanation:
Some qucik lil definitions of these words
Coefficient - A multiplicative factor in some term of a polynomial, a series, or any expression.
Constant - A value that is unchanging.
Term - A single mathematical expression.
Variable - A letter used to represent an unknown.
Michael is investing $2500 at his bank. The savings account he chooses earns interest at a rate of 6%
annually. How much is in the account after four years?
So
P=2500R=6%T=4yearsInterest
I=PRT/100I=2500(6)(4)/100I=25(24)=$600Amount
2500+600$3100find the value of x in each of the following
2x/3=8
Answer:
The value of x is 12.
Step-by-step explanation:
I took extra ciricular math classes in high school, So I am a pro at equations
Nerys checks her tax bill from last year
the tax rates were as follows:
•No tax on the first £11,000 of earnings
•Earnings in excess of £11,000 and up to £43,000 taxed at a rate of 20%
•Earnings in excess of £43,000 and up to £ 150,000 taxed at a rate of 40%
•Earnings over £150,000 taxed at a rate of 45%
Last year Nerys earned £162,700 before tax.
how much tax did she pay in total?
Answer:
£54,915
Step-by-step explanation:
The tax table is applied as follows:
first 11,000 -- no tax
11,000 to 43,000 -- tax is 0.20 × (43,000 -11,000) = 6,400
43,000 to 150,000 -- tax is 0.40 × (150,000 -43,000) = 42,800
150,000 to 162,700 -- tax is 0.45 × (162,700 -150,000) = 5,715
Then the total tax on earnings of £162,700 is ...
£6,400 +42,800 +5,715 = £54,915
Nerys paid a tax of £54,915.
_____
Additional comment
The tax computation could be simplified to ...
f(x) = max(0, 0.2x -2200, 0.4x -10800, 0.45x -18300)
In this instance, the value 0.45x -18300 is the highest, at £54,915. Not all the computations are required if you realize the lines cross at x = 11,000, 43,000, and 150,000.