Answer:
g( [tex]\frac{3}{2}[/tex] ) = - [tex]\frac{35}{4}[/tex]
Step-by-step explanation:
substitute x = [tex]\frac{3}{2}[/tex] into g(x) , that is
g( [tex]\frac{3}{2}[/tex] )
= - 2( [tex]\frac{3}{2}[/tex] )³ - [tex]\frac{4}{3}[/tex] × [tex]\frac{3}{2}[/tex]
= - 2 × [tex]\frac{27}{8}[/tex] - 2
= = - [tex]\frac{27}{4}[/tex] - [tex]\frac{8}{4}[/tex]
= - [tex]\frac{35}{4}[/tex]
A company’s profit is shown in the graph. The shaded region represents values when the profits were less than projected.
What is the standard form of the quadratic inequality represented by the description?
The standard form of the quadratic inequality represented by the description is; y < -2x² + 160x - 2400
How to find the standard form of the quadratic inequality?An inequality with a quadratic expression is referred to as a quadratic inequality.
It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.
Let's assume that the equation is y = a(x - h)² + k
Where (h, k) is the coordinate of the vertex. Thus;
y = a(x - 40)² + 800
Put the point (60, 0) in the equation
0 = a(60 - 40)² + 800
0 = a(20)² + 800
-800 = 400a
a = -800/400
a = -2
Thus, the equation is;
y = -2(x - 40)² + 800
The inequality is a dashed line and shaded below the parabola and is;
y < -2(x - 40)² + 800
= y < -2(x² - 80x + 1600) + 800
y < -2x² + 160x - 3200 + 800
y < -2x² + 160x - 2400
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find the length of the curve y = x t3 − 1 dt 1 , 4 ≤ x ≤ 9.
The length of the curve y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9, is 211/4.
In calculus, arc length of curve is the distance between two points along a portion of the curve. Finding the length of an irregular arc segment by approximating the arc segments as connected (straight) line segments is also known as the integral variation of the curve-corrected distance formula. Arc length formula is
ₐ∫ᵇ√[ 1 + (dy/dx)²] dx --(*)
Where, x is the arc length,
a, b are the integral bounds of the closed interval [a, b],dy/dx is the first derivative.We have calculate the length of curve means the length of arc of curve.
Now, y = y (x) = ₁∫ˣ √(t³ − 1) dt
differentiate both sides with respect to x
=> dy/dx= d/dx( ₁∫ˣ√(t³ − 1 ) dt)
Using the fundamental theorem of calculus,
=> dy/dx = dy/dt × dt/dx
let t = x => dt/dx = 1
dy/dt = √x³ - 1 ( from leibnitz rule )
dy/dx = √x³ - 1
Required length of curve = ₄∫⁹√[ 1 + (√x³ - 1)²] dx
= ₄∫⁹√[ 1 + x³ - 1] dx
= ₄∫⁹√x³ dx
[tex] = ₄∫⁹{x}^{ \frac{3}{2} } dx[/tex]
[tex] = \frac{2}{5} ( {9}^{ \frac{5}{2} } - {4}^{ \frac{5}{2} } )[/tex]
[tex]= 211/4[/tex]
So, the required length is 211/4.
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Complete question:
Find out length of the curve
y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9.
R is the midpoint of segment PS, Q is the midpoint of segment RS. P is located at (10,-2) and S is located at (5,4). What are the coordinates of Q?
Answer:
(6.25,2.5)
Step-by-step explanation:
HELP PLEASE 100 Points!!!
Answer: cant read it
Step-by-step explanation:
Provide the missing statements and reasons for the following proof:
To prove that angle 1 is supplementary to angle 3, we must demonstrate that the two angles add up to 180 degrees.
What is angle?Angle is a term used to describe the shape formed when two straight lines cross or intersect. It is measured in degrees, and is typically represented by the symbol ∠. Angles are important in geometry, architecture, engineering and construction. They are also used in navigation and astronomy. Angles are a fundamental part of understanding the physical world around us.
Since line m is parallel to line n, then the two lines are essentially parallel lines, meaning that all of the angles made with the lines are the same. In this case, the angles made with line m and line n are both 90 degrees. Since the two angles are the same, then that means that angle 1 and angle 3 are also the same.
Since angle 1 and angle 3 are the same, then that means that the two angles add up to 180 degrees. Therefore, angle 1 is supplementary to angle 3.
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How to solve for the unknown
Answer:
x = 49
Step-by-step explanation:
the figure inside the circle is a cyclic quadrilateral.
the opposite vertices of a cyclic quadrilateral sum to 180° , then
x + 68 + 63 = 180
x + 131 = 180 ( subtract 131 from both sides )
x = 49
10. A quart of water is heated from 30°C to 68°C. The mass of the water is 15 kg. How much
thermal energy must be added to the water?
An amount of 150.478 kilojoules of thermal energy are needed to heat a quart of water from 30 °C to 68 °C.
How much energy is needed to heat the water?
In this problem we have the case of a quart of water being heated from 30 °C to 68 °C, the heating process does not involve any phase change, that is, the process is entirely sensible. The thermal energy required (Q), in kilojoules, is described by the following formula:
Q = m · c · (T' - T)
Where:
m - Mass, in kilograms.c - Specific heat of water, in kilojoules per kilogram-Celsius.T - Initial temperature, in Celsius.T' - Final temperature, in Celsius.Please notice that a quart of water has 0.946 kilograms of water. If we know that m = 0.946 kg, c = 4.186 kJ / (kg · °C), T = 30 °C and T' = 68 °C, then the thermal energy needed is:
Q = (0.946 kg) · [4.186 kJ / (kg · °C)] · (68 °C - 30 °C)
Q = 150.478 kJ
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Explain how the quotient of powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22.
We have been given the expression 2^5/8=2^2 was used to simplify this expression. 2 to the fifth power, over 8 = 22.
8 can be rewritten as 2^3
Hence, the given expression becomes
2^5/2^3=2^2
After subtracting the exponents on left hand side of the equation we get:
2^2=2^2
we can do it by simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents.
Linear expressions or equations are expressions in which the highest power of the variable is one.
Quadratic expressions or equations are expressions in which the highest power of the variable is two.
Cubic expressions or equations are expressions in which the highest power of the variable is three.
Quartic expressions or equations are expressions in which the highest power of the variable is four.
From the expression, 5x + 2 given,
the highest power of x is one. So it is a linear expression.
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The result is 4
A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2222 can be expressed as 24. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base." Generally speaking, xn denotes that x has been multiplied by itself n times.
The quotient of powers property states that if you have an expression in the form (a^m)/(a^n) where 'a' is the base and 'm' and 'n' are integers, it can be simplified to (a^(m-n)).
In the given expression, 2 to the fifth power (2^5) can be divided by 8 (which is equal to 2^3), using the quotient of powers property. The result is 2^(5-3) = 2^2 = 4
So 2^5 / 8 = 4
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Help please I’m struggling
Step-by-step explanation:
6x + 2y = 10
2y = -6x + 10
y=-6/2x +10/2
y= -3x + 5
x + 2y = 4
2y = -x + 4
y= -1/2x + 4/2
y=-1/2x +2
Jonas placed a dish of his favorite candies next to his seat while he sat down for a Netflix movie binge. He ate 1/2 of the candies during the first movie. During the second movie, he ate 1/3 of the remaining candies. Then, during the third movie, he ate only 1/4 of the candies he had left. At the end of the third movie, he had 24 candies left. How many candies did he have at the start of his movie watching binge?
Perform the following calculations and report your answer with three significant digits. 101,455,348 + 1,111,419 = 0.000000612 x 0.00031119 = 297,060 + 0.0004839 =
102,566,767, 1,9044828e-10, and 297,060 are the answers to the questions.
The questions above use addition and multiplication to solve the problem.
What exactly are multiplication and addition?Multiplication is the operation of multiplying one number by another. Usually, it is signified by the symbol +.Meanwhile, an addition is an operation to add one number to another. Usually, it is signified by the symbol x.Besides addition and multiplication, division and subtraction are also parts of four basic arithmetic in mathematics.
The questions are revealed, and the answers are:
101,455,348 + 1,111,419 = 102,566,767
0.000000612 x 0.00031119 = 1,9044828e-10
297,060 + 0.0004839 = 297,060
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You are given 3 different investment scenarios to choose. Answer questions 13 below. Option 1: Invest $20 and the balance is doubled each day. Option 2: Invest $0.20 and the balance is tripled each day. Option 3: Invest $0.01 and the balance is quadrupled each day.
The investment scenario that I will choose to would be = option 1 .
What is an investment?An investment is an official asset or item acquired with the goal of generating income or appreciation. Therefore,the investment scenario that is best chosen should be the one with a greater appreciation at Tue end of the end of the day.
Option 1 = $20 × 2 = $40 / day
Option 2 = $0.20 × 3 = $0.6/day
Option 3 = $0.01 × 4 = $0.04/day
Therefore, the best investment scenario would be = option 1 investment scenario.
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You buy a "gold" ring at a pawn shop. The ring has a mass of 0.014 g and a volume of 0.0022 cm^3. The standard density of gold is 19,300 kg/m^3. Is the ring solid gold?
Answer:
Below
Step-by-step explanation:
.014 g / .0022 cm^3 = 6.364 gm / cc = 6364 kg/m^3
density is too low to be pure gold
Is the following a quadratic equation x² 2x ² x² 3 4x³?
Answer:
no
Step-by-step explanation:
the greatest power is not 2 it is 3
Find the circumcenter of the triangle ABC.
A(-5,3), B(5, 8), C(-5.8).
The circumcenter is
(Type an ordered pair.)
The circumcenter of triangle ABC is (-5, 2)
What is the circumcenter?
The circumcenter of a triangle is the point that is equidistant from all three vertices of the triangle. It is the center of the circle that passes through all three vertices of the triangle.
To find the circumcenter of the triangle ABC with vertices A(-5,3), B(5, 8), C(-5.8) we can substitute the values of the coordinates into the formulas above:
x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2) - (3 - 8) * (-5^2 + 3^2 - (-5)^2 -3^2) / 2 * (3 - (-5)) * (8 - 3) - (3 - 8) * (-5.8 - (-5))
x = (-5)
y = (3 - (-5.8)) * (-5^2 + 3^2 - (-5)^2 -3^2) - (-5 - (-5)) * (3^2 + 3^2 - (-5.8)^2 - 8^2) / 2 * (3 - 8) * (-5 - (-5)) - (3 - 8) * (3 - (-5.8))
y = 2
Hence, the circumcenter of triangle ABC is (-5, 2)
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Answer:
(0, 5.5)
Step-by-step explanation:
Midpoint of BC: ([-5 + 5]/2, (8 + 8)/2) = (0, 8)
Perpendicular bisector of BC has equation: x = 0
Midpoint of AC: ([-5 + (-5)]/2, (3 + 8)/2) = (-5, 5.5)
Perpendicular bisector of AC has equation y = 5.5
Point of intersection of the two perpendicular bisectors:
(0, 5.5)
Answer: (0, 5.5)
Find the slope of the following ordered pairs:
(1, 5) and (4, 10)
Answer:
5/3
Step-by-step explanation:
The formula of finding slopes are:
Change in y over change in x, which is:
(10 - 5) / (4 - 1)
= 5/3
Use series to evaluate the limit.lim x → 0a. 1 − cos(2x)b. 1 + 2x − e^2x
The limit is evaluated by using the series expansion of 1 - cos(2x) and 1 + 2x - e^2x. The series expansion of 1 - cos(2x) is 2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ... and the series expansion of 1 + 2x - e^2x is 2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ... Therefore, the limit of both series is 0 as x approaches 0.
The limit of 1 - cos(2x) as x approaches 0 is calculated by taking the series expansion of 1 - cos(2x), which is
2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ...
When x is 0, all terms in the series are 0, so the limit is 0. Similarly, the limit of 1 + 2x - e^2x as x approaches 0 is calculated by taking the series expansion of 1 + 2x - e^2x, which is
2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ....
When x is 0, all terms in the series are 0, so the limit is also 0.
The limit of 1 - cos(2x) as x approaches 0 is also calculated numerically. When x is
0.0001, 1 - cos(2x) is 0.000399980.
When x is 0.00001, 1 - cos(2x) is 0.0000039998.
As x becomes closer to 0, the value of 1 - cos(2x) approaches 0. The same is true for
1 + 2x - e^2x.
When x is 0.0001, 1 + 2x - e^2x is 0.000399980.
When x is 0.00001, 1 + 2x - e^2x is 0.0000039998.
As x becomes closer to 0, the value of
1 + 2x - e^2x also approaches 0.
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Thelistshowsthelengthofadayontwodifferentplanets.
• Neptune: 16.11 hours
• Venus: 5,832.40 hours
Which statement is best supported by this information?
Answer:B
Step-by-step explanation: i got it right
Photographer is to camera is biologist is to
Answer: microscope
Step-by-step explanation:
a camera is equipment for a photographer
a microscope is equipment to a biologist
Barbara has $250 to rent a bike for 15 days. Does Barbara have enough money? Explain.
No, Barbara does not have enough money.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
Using the words here, we can create the expression 20d+7 where d is the number of days.
We can now substitute 15 in as d, to see how much this will cost.
20*15+7
=300+7 = 307
So the total cost will be $307.
Since $307 is more than $250, she does not have enough money.
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Question:
Susan plans to rent a bike in New Orleans to tour the city. The cost of the rental is $20 per day. The cost of a helmet is $7 for as long as Susan needs the bike. Barbara has $250 to rent a bike for 15 days. Does Barbara have enough money? Explain. First answer gets Brainiest and 48 points hurry please tho
7/10-w=1/2
Help please please please
Answer: 1/5
Step-by-step explanation:
7/10 - w = 1/2
7/10 - w = 5/10
7-5 = 2
2/10 = 1/5
Answer w=.2
Explanation: −w+7/10=1/2
−
a pattern using cubes is shown to the right. the number of cubes at a particular place in the pattern can be calculated using the expression. 2n-1 the variable n represents the place in the pattern. N-gen math algebra expressions six grade math pls I'm so stuck on this.
Based on the sequence formula, the number of cubes in the 5th pattern is 9
How to determine the number of cubes are in the 5th patternFrom the question, we have the following parameters that can be used in our computation:
Number of cubes in the nth pattern = 2n - 1
Also from the question, we have the pattern to be the 5th pattern
This means that n = 5
Substitute the known values in the above equation, so, we have the following representation
Number of cubes in the 5th pattern = 2 * 5 - 1
Evaluate the product
Number of cubes in the 5th pattern = 10 - 1
Evaluate the difference
Number of cubes in the 5th pattern = 9
Hence, the number of cubes is 9
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Complete question
a pattern using cubes is shown to the right. the number of cubes at a particular place in the pattern can be calculated using the expression. 2n-1 the variable n represents the place in the pattern
How many cubes are in the 5th pattern
Bob the Wizard makes magical brooms. He charges 125 gold pieces for each magical broom he makes for his customers. He also charges a one-time fee of 50 gold pieces for his initial consultation.
The total number (g) of gold pieces Bob charges is a function of x, the number of magical brooms he makes.
Write the function's formula.
The function that represent the total number of gold pieces as a function of the number of magical broom is g = 50 + 125x.
How to represent a situation with a function?Bob the Wizard makes magical brooms. He charges 125 gold pieces for each magical broom he makes for his customers.
He also charges a one-time fee of 50 gold pieces for his initial consultation.
The total number g of gold pieces Bob charges as a function of x, the number of magical broom he makes can be represented as a function as follows;
Therefore.
x = number of magical brooms
g = total number of gold pieces.
Hence, the function is as follows:
g = 50 + 125x
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Answer:
The answer is G=125x+50.
Step-by-step explanation:
Please help thank you
Answer:
m = -1/2
Step-by-step explanation:
Slope can be calculated using the following formula
slope(m) = (y2 - y1) / (x2 - x1)
Where the values of x and y derive from points (x1,y1) and (x2,y2) which can be found in the table.
Here the values of x and y may vary depending on the chosen points however I have chosen (-4,3) and (-2,2)
If we use these points then (x1,y1) = (-4,3) and (x2,y2) = (-2,2)
So, x1 = -4, y1 = 3, x2 = -2 and y2 = 2
We now plug these values into the formula
m = (y2 - y1) / (x2 - x1)
plug in x1 = -4, y1 = 3, x2 = -2 and y2 = 2
m = (2-3) / (-2-(-4)
==> simplify parenthesis
m = -1/2
No further simplification can be done so m = -1/2 is the final answer
Answer:
2 obv
Step-by-step explanation:
slope of -4 and 3 is 2
because -xcoefficient/ycoefficient
and the - × - becomes +
so it will be 4/2 and the answer is 2
Halley saves up twenty-pence coins. At the last count she had saved £64.80.
How many 20p coins does she have altogether?
How many more coins does Halley need in order to have saved £100?
(a)
(b)
She saved 324 number of 20p coins altogether.
And, Halley need 176 more 20p coins to saved £100.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Halley saves up twenty-pence coins.
And, At the last count she had saved £64.80.
Now,
We know that;
Number of 20p coins in £1 = 5
So, Number of 20p coins in £64.80 = 5 × 64.80
= 324
And, Number of 20p coins in £100 = 5 × 100
= 500
So, He need number of 20p coins = 500 - 324
= 176
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Suppose a coin is flipped five times and turns up heads each time. What is the probability that the next coin clip will yield a head
The probability that the next coin flip will yield a head is 50%, as each coin flip has an equal chance of landing either heads or tails.
The Importance of Understanding Probability in Everyday LifeProbability is an incredibly important concept to understand in our everyday lives. Understanding probability helps us make informed decisions about the chances of something happening. For example, when playing a game of chance, understanding probabilities can give us a better idea of the likelihood of winning or losing. Knowing the probability of an event happening can also help us make decisions in other areas of life, such as investing.
In the context of coin flipping, it is important to remember that the probability of a coin landing on heads or tails is always 50%. This means that no matter how many times the coin is flipped and no matter what the previous outcome, the probability of the next flip being heads or tails remains the same. This concept is the basis of probability theory, which can be applied to many other areas of life.
Understanding probabilities is also useful in understanding the chances of certain events occurring in the world. For example, understanding the probability of an earthquake happening in a certain area can help us make decisions about where to live or how to prepare for a potential disaster. Similarly, understanding the probability of a successful business venture can help us decide whether or not to invest in it.
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24/43 as a decimal rounded to the nearest thousandth
Answer:
0.56
Step-by-step explanation:
24/43 as decimal is approximately: 0.55814 (Rounded to fifth decimal place)
What is an equation of the line that passes through the point (1,7)(1,7) and is perpendicular to the line x+6y=42x+6y=42?.
An equation of the line that passes through the point (1,7) and perpendicular to the line x+6y=42 is y = 6x + 1
In this question we have been given an equation of line x + 6y = 42
We need to find an equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y = 42
Let m be tha slope of the required line.
We write equation of line x + 6y = 42 in slope-intercept form.
y = (42 - x)/7
y = 6 - x/6
y = -1/6 x + 6
Let m1 be the slope of line x + 6y = 42
m1 = -1/6
We know that the product of slopes of perpendicular lines is -1.
So, m * m1 = -1
m * (-1/6) = -1
m = (-1) * (-6)
m = 6
So, the slope of the required line is 6
We know that the point - slope form of equation of line is:
(y - y1) = m(x - x1)
Let (x1, y1) = (1, 7)
Substituting values in above equation,
(y - 7) = 6(x - 1)
y - 7 = 6x - 6
y = 6x - 6 + 7
y = 6x + 1
Therefore, equation of the required line is y = 6x + 1
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The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.
The equation of a line that passes through the given point (1,7) and is perpendicular to the line x+6y=42 can be determined by using the slope-intercept form of the equation of a line.
The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line, and b is the y-intercept.
First, we need to determine the slope of the line x+6y=42. To determine the slope, we can solve for y by subtracting x from both sides of the equation, yielding 6y = -x + 42. Then, we can divide both sides of the equation by 6 to obtain y = -x/6 + 7. Thus, the slope of the line x+6y=42 is -x/6.
Now, the slope of a line perpendicular to the line x+6y=42 is the negative reciprocal of the slope of x+6y=42, which is 6/-x.
The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 can then be determined using the point-slope form of the equation of a line, which is given by y - y1 = m(x - x1). Substituting the coordinates of the point (1,7) and the slope 6/-x, we obtain
y - 7 = 6/(-x)(x - 1)
Simplifying, we obtain
y = -6x - 5
Thus, the equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.
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Samuel pulled marbles from a bag that contained 15 red, 15 yellow, and 15 blue
marbles. He pulled one marble from the bag and replaced it 50 times. Samuel’s
results are shown in the table
Based on the results in the table, which statement about the theoretical and
experimental probabilities of Samuel’s experiment is true? I NEED IT RN IM IN A TEST
U rnt supposed to be cheating on a test but hope this helps. Its 2500.
Select the correct answer. two quadrilateral are plotted in the upper left and lower right quadrants, respectively. points correspond to a(-6,4), b(-6,6), c(-2,6) and d(-4,4). on the lower right, a'(2,-6), b'(2,-4), c(6,-4), and d(4,-6). quadrilateral abcd underwent a sequence of transformations to give quadrilateral a′b′c′d′. which transformations could have taken place? a. a reflection across the x-axis followed by a reflection across the y-axis b. a translation 10 units down followed by a translation 8 units to the right c. a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis d. a reflection across the line y = x followed by a reflection across the line y = -x
B) a translation 10 units down followed by a translation 8 units to the right.
As in rotation, reflection and translation the transformed image is congruent to the original figure(i.e all the points undergo same change), so analyzing any one point will give the series of transformation undertaken.
Taking point A(-6, 4) into consideration.
Translating a point (x, y) k units down, it becomes (x, y-k).
So translated 10 units down point A, it becomes (-6, -6).
Translating a point (x, y) k units right, it becomes (x+k, y)
So translated 8 units right point (-6, -6), it becomes (2, -6)
This is the coordinates for A'.
Therefore, quadrilateral ABCD underwent a translation 10 units down followed by a translation 8 units to the right.
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