The expression |ab^3| if a>0 and b>0 is even.
What is Parity Definition?
Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]
[tex]f(a): \quad|a|\left|b^3\right|[/tex]
[tex]f(-a): \quad|a|\left|b^3\right|[/tex]
[tex]-f(a):-|a|\left|b^3\right|[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
The expression |ab^3| if b>0
[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
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A square garden is surrounded by a concrete walkway of width x. The length of the walkway is 15 feet long
a) Write an expression for the area of the garden.
The formula for the area of a square is A = s^2, where s is
a side length of the square.
A(x) = (15 + 2x)
b) Consider the information given above and discuss the maximum and minimum size of the concrete walkway. Be sure to explain your estimates.
Considering the information, the minimum and maximum size of the concrete walkway is is -900 and -450 units respectively
How to determine the minimum and maximum values?Minimum and maximum values of the area of the square garden is the area the square garden can occupy.
The given parameters are
A=S²
S= a side of the square= A(x) = (15+2x)
Now, hence A=S²
This implies that
(15+2x)(15+2x)
Expand the brackets to get
225+60x+4x=0
Solving the equation using the quadratic formula
x=± (√b²-4ac)÷2a
This implies that
x= -60±(√60²-4*4*225)÷2*4
Simplifying the equation we have
(-60±0)÷8
x=-30
Now if x= -3
Therefore (15+2*-30) = -45 and (15*x)
= 15*-30=-450 units
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Mr. Ramli is a small entrepreneur, he wants to invest RM 2000 in a spice business. He
is confident that his investment, RM y will increase at a rate 2(x+121) which x is time
in year.
Find the number of years it takes for his investment money to be doubled from his
original investment.
Mr. Ramli's investment in the small entrepreneurship will be doubled in 8 year.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate which something evolves over time. Thus, it is not the amount of specific changes themselves but rather the acceleration or slowdown of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.For the stated equation-
rate of increase is given as-
dy/dx = 2(x + 121) < - rate of the change
dy = 2(x + 121)dx
Integrating;
∫dy = ∫2(x + 121)dx
y = x² + 242x + C
At x = 0, y(0) = 0 Thus,
(0)² + 242(0) + C = 2000
C = 2000
Now, y = x² + 242x + 2000
Calculate 't' to get the y(t) = 40,000 (double the amount)
4000 = x² + 242x + 2000
x² + 242x - 2000 = 0
Find the factor;
x = 8 and x = -250
As, x is time in year. So, x = 8 years.
Therefore, it takes eight years for his investment capital to double from what he initially put up.
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A knife cot 3 time the cot of a poon. 9 poon and 12knive cot 82. 80
How much doe one knife cot
One knief costs 5.52 dollars
Let the cost of knief be x dollars and the cost of spoon be y dollars.
A knife costs 3 times the cost of a spoon.
So, we get an equation,
x = 3y ..............(1)
9 spoons and 12 knives cost $82.80
So, we get an equation,
12x + 9y = 82.80 .........(2)
Substitute above value of x in equation (2),
12(3y) + 9y = 82.80
45y = 82.8
y = 1.84
Subatitute above value of y in equation (1),
x = 5.52
Therefore, the cost of knief is 5.52 dollars
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Given a triangle with a=80, b=51 and c=113, find C
Using cosine law of triangle and using the provided value for the sides, the value of angle C is [tex]118^{o}[/tex] .
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
How does cosine law work?It is especially helpful for filling in the gaps in a triangle's information. The cosine rule, for instance, enables one to determine any of the angle measurements when all three sides of a triangle are known. Similar to this, using the cosine rule, one can determine the length of the third side given two sides and the angle between them are known.
a=80
b=51
c=113
[tex]cos(C) = \frac {a^{2}+b^{2} - c^{2}}{2ab}[/tex]
cos(c)= -0.4617
C= [tex]118^{o}[/tex]
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Can anyone help solve for x
Answer:
X = 33.19
Step-by-step explanation:
You're welcome.
Choose the system with one solution. (Hint: Try graphing each one on your calculator)
A. y = 7
1
y=-2
B. y = 5x + 2 C. y = 5x + 2 D. 2x + 4y = 6
y = 5x
y = -4x + 2
x + 2y = 3
Problem 9
72 = 2³ x 3²
150 = 2 × 3 × 5²
Work out the lowest common
multiple of 72 and 150, giving
your answer in prime factor form.
Answer:
1800
Step-by-step explanation:
You want the least common multiple (LCM) of 72 and 150 given their prime factorizations:
72 = 2³ × 3²150 = 2 × 3 × 5²Least Common MultipleThe LCM is found as follows:
Identify the unique prime factors (2, 3, 5)Identify the highest power of each (3, 2, 2)Raise those factors to those power to get the LCMLCM(72, 150) = 2³ × 3² × 5² = 1800
Linear quadratic systems
The solution of the given system of equations is (-1, 2).
What is system of equations?
A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.
Consider, the given system of equations.
x^2 - x + 3y - 8 = 0 ..(1)
x - y + 3 = 0 ..(2)
From equation (2),
x = y - 3 ..(3)
Plug the value of x in equation (1).
⇒ (y - 3)^2 - (y - 3) + 3y - 8 = 0
y^2 - 6y + 9 - y + 3 +3y - 8 = 0
y^2 - 4y + 4 = 0
y^2 - 2y - 2y + 4 = 0
y(y - 2) - 2(y - 2) = 0
(y - 2)(y - 2) = 0
(y - 2)^2 = 0
y = 2
Now plug y = 2 in equation (3)
x = 2 - 3
x = -1
hence, the solution of the given system of equations is (-1, 2).
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Extended Response
1. (6) The weights of grapefruits, G, of a certain variety are approximately Normally
distributed with a mean of 1 pound and a standard deviation of 0.12 pounds.
a. Let T = 3G. Find the mean and standard deviation of T.
b. Let R = G+ G + G. Find the mean and standard deviation of R.
c. Let Q=T-R. Find the mean and standard deviation of Q.
The mean and standard deviation of T, the mean and standard deviation of R, and the mean and standard deviation of Q.
0.120.20.2236What is the mean and standard deviation of Q.?a. The mean and standard deviation of 7-G is
7-1=6 and 0.12, respectively.
b. Let X be the weight of a single grapefruit, so the mean and standard deviation of X are 1 and 0.12, respectively.
The mean and standard deviation of R=G+G+G are
3*1=3
and
√(3)*0.12=0.2, respectively.
c. The mean and standard deviation of
Q=T-R are 7-3=4
√0.2((0.12^2)+(0.2^2))=0.2236 respectively.
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A computer store buys a computer system at a cost of $436.80. The selling price was first at 728, but then the store advertised a 20% markdown on the system. Answer part b.
A= 582.40
Members of the store's loyalty club get an additional 20% off their computer purchases. How much do club members pay for the computer with their discount?
The price for club members is $______
please help
The price that that club members pay for the computer is $465.92.
How to calculate the price?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
Since the selling price was first at 728, but then the store advertised a 20% markdown on the system and members of the store's loyalty club get an additional 20% off their computer purchases.
The cost will be calculated thus:
582.40 - (20% × $582.40)
= $582.40 - $116.48
= $465.92
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This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blank question. PARKS Rachelle wants to determine the best state park for hiking and fishing. She has developed a metric based on the information she has gathered and the best catch from her previous fishing trips to the parks. Part A Use the metric to calculate a score for each park. Round to the nearest tenth. Park Score = 100[0.2(online rating5)+0.4(miles of trails25)+0.4(fish weight10)] State Park Online Star Rating Hiking Trails (mi) Best Fish (lb) Park Score Gooseberry Falls 4.8 20 9.8 Lake Maria 4.3 14 8.2 Maplewood 4.9 25 7.3 Camden 4.3 15.8 10.1 Part B Part B How might someone who enjoys hiking much more than fishing change this metric? 100 words remaining Tools are not currently accessible
Answer:
Step-by-step explanation:
What are the roots of the equation x² - 12x + 72 = 0 in simplest a + bi form?
Step-by-step explanation:
[tex] {x}^{2} - 12x + 36 = - 36[/tex]
[tex](x - 6) {}^{2} = - 36[/tex]
[tex](x - 6) {}^{} = 6i[/tex]
[tex]x = 6 + 6i[/tex]
[tex]x = 6 - 6i[/tex]
Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x, y)(x,y).
\def\arraystretch{2} \begin{alignedat}{1}3 x-2 y&=4\\5 x+10 y&=-60\end{alignedat}
3x−2y
5x+10y
=4
=−60
The value of ordered pair of (x,y) is (-2, -3)
How to solve the equation by substitution method ?x - 5y = 13
4x - 3y = 1
Solve the equation for x
x - 5y = 13
Move '5y' to R.H.S and change it's sign
x=13+5y
Substitute the given value of X into the equation
4x - 3y = 1
4(13+5y)-3y = 1
Solve the equation for y
distribute 4 through the parentheses
52+20y -3y =1
Collect like terms
52+17y = 1
Move constant to R.H.S and change it's sign
17y = 1 - 52
Calculate
17y = - 51
Divide both sides of the equation by 17
17y/17 = -51/17
Calculate
y = -3
Now, substitute the given value of y into the equation
x = 13 + 5y
x= =13+5x(-3)
Solve the equation for x
Multiply the numbers
= 13 - 15
Calculate the difference
= -2
The possible solution of the system is the ordered pair
( x , y )
( x , y ) = ( - 2 , - 3 )
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
-2-5×(-3)=15
4×(-2)-3×(-3)=1
Simplify the equalities
13 = 13
1=1
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( - 2 , - 3 )
Therefore the value of ordered pair of (x,y) is (-2, -3)
The complete question is : Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).
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What is the product of 7x -4 and 8x +8
Answer:
56x-32
Step-by-step explanation:
7x-4 Times 8x+8
7xtimes8x
56x-4times8
56x-32
Which inequality does not belong with the other three? Explain your reasoning
The inequality does not belong with the other three is - 1 ≤ x/1.25.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given,
1. 4x ≥ 12 ⇒ x ≥ 3.
2. - 1 ≤ x/5 ⇒ - 5 ≤ x.
3. 12 > x/1.25 ⇒ x < 15.
4. 2.5x > - 6.4 ⇒ x > - 2.56.
x ≥ 3 and x < 15 is, 3 ≤ x < 15.
- 5 ≤ x and x > - 2.56 here one common region is x > - 2.56 so - 5 ≤ x does not fit.
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Find the indicated angle using trigonometry
The measure of indicated angle in the given triangle is 71.035°.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.
Let the unknown angle be x.
We know that, tanθ =Perpendicular/Base
Now, tan x= 70/24
tan x= 2.91
x =71.035°
So, one of the angle in the triangle is 71.035°.
Therefore, the measure of unknown angle is 71.035° in the given triangle.
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if
[tex]a \sqrt{2 } + b \sqrt{5 } = 3(2 \sqrt{2} - 3 \sqrt{ {5} } ) \: find \: the \: value \: of \: a[/tex]
please tell the
answer
Answer:
see attached
Step-by-step explanation:
35x+10y help like rn pls
The value of the 35x + 10y is 330.
What is the linear equation?
A linear equation is an equation of a straight line, written in the form y = mx + b. In this equation, m is the slope of the line and b is the y-intercept. Linear equations are used to describe relationships between variables, and they can also be used to solve problems with multiple unknowns. For example, if you know the slope of a line and the y-intercept, you can use a linear equation to calculate the x-intercept. Linear equations can also be used to model real-world situations, such as calculating the cost of a product or the amount of money saved over a period of time.
We have given:
the value of 35x + 10y, When x=8 and y=5.
Using substitution, substitute the given values of x and y.
35x + 10y
35(8) + 10(5)
280 + 50 = 330
Hence, the value of the 35x + 10y is 330.
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Complete Question:
Find the value of 35x+10y, When x=8 and y=5
pls help due asap!!!!!!!!!!!!!!
Answer:
(0,2)
Step-by-step explanation:
im not too educated with this topic but i believe we multiple x and y by 1/2
0x1/2=0
4x1/2=2
(0,2) is the answer
:)
a triangle undergoes a dilation with a scale factor of 9/5. the resulting triangle is _[blank]_ the original triangle.
The resulting triangle is 9/5 the original triangle.
How triangle dilated with scale factor?
The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).
According to question:Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,
Then changed triangle is A'B'C'
So, relation between them is A'B'C' = 9/5(ABC)
Thus, the resulting triangle is 9/5 multiple of triangle ABC.
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Can you please help me find why these are perpendicular
Answer: It is perpendicular because it makes a 90-degree angles
Step-by-step explanation: A perpendicular is when it makes a 90-degree angle or has the same length!
About 68% of sixth-grade students will have heights between_____inches and____inches.
Answer: 55.7 inches and 60.3 inches
Step-by-step explanation:
I saw this question before in math class, so I know the answer! Hope you find this helpful!
Solve for the following
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:
C)117
Step-by-step explanation:
50%=1/2
If you want to figure out how much is left of a half all you do is have to divide the total number of whatever it is, in this case, its roses, by 2.
So now that we know that, let's get started.
234/2=117
Which we know is correct because it's one of your answer choices.
So 117 roses are not red. The other half was.
I hope this helps!!!
A cylinder has a height of 5 inches and a radius of 2 inches. What is the volume of the cylinder? use pi ≈ 3.14
Answer:
Volume= 62.8 cubic inch
Step-by-step explanation:
V=B×h
B=
[tex]\pi {r}^{2} [/tex]
= 3.14×2^2=12.56
V=12.56×5= 62.8 cubic inch
activity 2: Time is gold!
Answer:
time is gold ............
Answer:
q1: it arrived at 11:45
q2: 8 hours and 45 minutes
q3: a: 6:59 AM b: 498 minutes
Step-by-step explanation:
q1: 10:30 + 1:15 = 11:45
q2: 0:30 +7:30 +0:45 +8 hours and 45 minutes
q3: a(8:18 + 10:41 PM = 6:59 AM) b(8x60= 480 +18= 489)
Hello solve this with steps please
Answer: [tex]x^{2} -5x+3\\[/tex]
Step-by-step explanation:
On a math fact tet Paul got 1/8 of the quetion incorrect in percent and fraction form how many quetion did Paul get wrong
Fraction form 12.5% question did Paul get wrong .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided.
Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator.
Fraction of incorrect question = 1/8
Present of incorrect question
Computation:
Present of incorrect question = (Fraction of incorrect question)(100)
Present of incorrect question = (1/8)(100)
Present of incorrect question = 12.5%
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joe is a wrestler and during his workouts he loses 2 pounds. how much water would he have to drink to replenish this water weight loss?
Answer:
36 ounces or if over 150 lbs drink more water than 36 ounces
Step-by-step explanation:
For every pound of sweat you lose you need to drink 16 ounces of water!
HELP ASAP PLS!!!
Zachary purchased a computer for $1,400 on a payment plan. Two months after he purchased the computer his balance was $1,100. Four months after he purchased the computer, his balance was $800. What is an equation that models the balance y after x months?
The equation
models the balance y after x months:
Answer:
Zachary pays $150 per month for his computer
Step-by-step explanation:
after 2 months:
2x + 1100y = 1400..... equation 1
after 4 months:
4x + 800y = 1400...... equation 2
we can either multiply equation 1 by 2 or we can divide equation 2 by 2, the purpose is simply to get the x values equal so it can be eliminated from the equation.
dividing equation 2 by 2:
2x + 400y = 700 ...... equation 3
Now equation 1 minus equation 3:
0x + 700y = 700
700y = 700
y = 700/700
y = 1
substituting y=1 into equation 3
2x + 400(1) = 700
2x = 700 - 400
2x = 300
x = 300/2
x= 150
Therefore it is concluded that Zachary has a payment plan where he pays $150 each month for the computer