Answer:
[tex]9x^2+14x+1[/tex]
Step-by-step explanation:
Hey there!
In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further
Our Equation:
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[tex](9x^2+5x+8)+(9x-7)[/tex]
1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive
[tex]9x^2+5x+8+9x-7[/tex]
2. Combine like terms in each parenthesis: This means combining the x values and the constants.
[tex]9x^2+14x+1[/tex]
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This means that when you add the two given values, the answer you get is: [tex]9x^2+14x+1[/tex]
What expression is equivlent to -4(3x-5)?
The answer to this question is -12x+20
two dimensions of a right triang;e are 5 units and 13 units. a student writes tje equation 5^2 13^2
The equation is incorrectly written by the student to find the third side of the triangle.
The right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or a right triangle.
(Hypotenuse)² = (Base)² + (Altitude)²
If the two sides are right angle triangle is 5 units and 13 units and the equation is 5²+13²=c² then the value of c is
c=√25+169
c=13.92 and 13.92 is not an integer number.
so, the equation written by the student to find the third side is incorrect.
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Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.a) ratiob) ordinal c) nominal d) interval
A ratio scale is used for measurements that have both a meaningful zero point and also an equal interval between each point. An ordinal scale is used for measurements that rank order items from highest to lowest. A nominal scale is used for measurements that have categories without any order. An interval scale is used for measurements that have an equal interval between each point but do not have a meaningful zero point.
A ratio scale is used for measurements that have both a meaningful zero point and also an equal interval between each point. It is often used for measurements that involve numbers, such as temperature or length. An ordinal scale is used for measurements that rank order items from highest to lowest. This type of measurement can be used to classify student performance on an exam, such as with letter grades (A, B, C, D, and E). A nominal scale is used for measurements that have categories without any order. This is typically used for measurements that involve assigning names or labels to categories, such as gender or ethnicity. An interval scale is used for measurements that have an equal interval between each point but do not have a meaningful zero point. This type of measurement is often used for measurements that involve numbers, such as temperature or time. In this example of classifying student performance on an exam, the ordinal scale is the most appropriate measurement to use.
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the population p of rabbits on a small island grows at a rate that is jointly proportional to the size of the rabbit population and the difference between the rabbit population and the carrying capacity of the population. if the carrying capacity of the population is 2400 rabbits, which of the following differential equations best models the growth rate of the rabbit population with respect to time t , where k is a constant? (A) = 2400 - kps
(B) = k (2400 – P)
(C) = k 1/p (2400 – P)
(D) = XP (2400 - P)
The differential equation that best models the growth rate of the rabbit population with respect to time t, where k is a constant is option D) [tex]\frac{dP}{dT}=KP(2400-P)[/tex].
A differential equation is an equation that relates a function and its derivatives to some independent variables. The solution to a differential equation is a function that satisfies the equation and is often used to model physical processes.
Differential equations come in many forms, including ordinary differential equations (ODEs) and partial differential equations (PDEs).
For the population in function of the time, is:
[tex]\frac{dP}{dT}[/tex]
The population P of rabbits on a small island grows at a rate that is jointly proportional to the size of the rabbit population and the difference between the rabbit population and the carrying capacity of the population
Carrying capacity is 2400.
This means that the differential equation is kP(size of the population multiplied by the constant) multiplied by 2400 - P(difference between the population and the carrying capacity).
=> [tex]\frac{dP}{dT}=KP(2400-P)[/tex]
Therefore, The differential equation that best models the growth rate of the rabbit population with respect to time t, where k is a constant is option D) [tex]\frac{dP}{dT}=KP(2400-P)[/tex].
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expand and simplify (3x-2) squared
Expanding and simplifying the expression gives:
(3x - 2)² = 9x² - 12x + 4
How to expand the given expression?
Here we want to expand and simplify the expression below:
(3x - 2)²
First let's expand that, we can rewrite this as:
(3x - 2)² = (3x - 2)*(3x - 2)
We can distribute that product to get:
(3x - 2)*(3x - 2) = (3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2)
Now we can keep simplifying this to get:
(3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2) = 9x² - 6x - 6x + 4
9x² - 6x - 6x + 4 = 9x² - 12x + 4
The simplified expression is:
9x² - 12x + 4
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how much should you invest at a 5% annual rate to have an annual interest of $150
Based on proportion, the amount of investment to have an annual interest of $150 at a 5% annual rate is $3,000.
What is the interest?The annual interest is the amount that is paid or received for accepting or giving credit.
The annual interest can be computed as the product of the annual percentage rate and the principal.
Where information for the interest rate and amount is available, the principal is the reciprocal of the interest and rate.
The annual interest rate = 5%
The annual interest (in dollars) = $150
Proportionately, $150 = 5%; therefore, 100% of $150 = $3,000 ($150/5%)
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find the indicated side of the right triangle 30 7 a=
The indicated side of the triangle of side a = 14 and side b =12.12.
How can the triangle of side be calculated?The concept that will be used here is trigonometry. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
From the triangle, of the side a which is the hypothenus:
sin(θ)=opposite/hypothenus
but the angle (θ)
sin30= 7/hypothenus
hypothenus *sin30=7
hypothenus=7/sin30
hypothenus = a=14
Then we can do that For b:
cos(θ)=b/hypothenus
but hypothenus =14
cos30= b/14
b=14*cos30
b= 12.12
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complete question:
Find the indicated side of the
triangle.
a
30°
b
b = [?][]
9 Show that efficiency E, the force ratio (MA) and the velocity ratio (VR) of a machine are related by the equation MA E= × 100%. VR The efficiency of a machine is 80%. Determine the work done by a person using this machine to raise a load of 200 kg through a vertical distance of 3.0 m (Take g = 10 ms ).show your workings
The Work done by a person is 24 x 103 J.
What is defined as force ratio and velocity ratio?Force ratio is the ratio of two forces. It is often used in the context of mechanics, where a force is the product of mass and acceleration, and is measured in newtons (N).
Velocity ratio, on the other hand, is the ratio of two velocities. It is also used in mechanics and is measured in meters per second (m/s).
Force ratio and velocity ratio are closely related, as they are both used to measure mechanical properties of an object.
Force ratio is used to measure the ratio of two forces acting on an object, while velocity ratio is used to measure the ratio of two velocities.
Both force ratio and velocity ratio can be used to analyze the movement of an object, as well as its response to external forces.
Force ratio and velocity ratio are important concepts in mechanics, as they can help to analyze the dynamics of an object and its behavior over time.
Let M.A. = F1 and V.R. = F2
E = M.A. x 100% V.R.
Substituting the given values,
E = 80 = F1 x 100% F2
Work done by a person = Force x Displacement
= F1 x F2 x 200 kg x 3.0 m
= (80 x 100%) x 200 kg x 3.0 m
= (8 x 103) N x 3.0 m
= 24 x 103 J
Work done by a person = 24 x 103 J
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Need help with this work
The required statistical parameters has been computed as follows:
Range = 17.
Standard deviation, SD = 6.87.
How to calculate the range?Mathematically, the range of a data set can be calculated by using this formula;
Range = Highest number - Lowest number
Range = 25 - 8
Range = 17.
How to calculate the mean?Mathematically, the mean for these set of data would be calculated by using this formula:
Mean = [F(x)]/n
F(x) = 11 + 8 + 5 + 11 + 25
F(x) = 60.
Mean = 60/5
Mean = 12
Next, we would calculate the standard deviation by using this formula:
SD = √(1/n × ∑(xi - u₁)²)
SD = √(1/5 × (11 - 12)² + (8 - 12)² + (5 - 12)² + (11 - 12)² + (25 - 12)²)
SD = √(1/5 × (1 + 16 + 49 + 1 + 169)
SD = √(1/5 × 236)
Standard deviation, SD = 6.87.
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grayson lives and works in indiana, which has a flat state income tax of 3.4% of his annual salary is 49,255$ and he gets paid once a month, how much is withheld from his gross income for state income tax each pay period
Answer:
Step-by-step explanation:
49255-1674.67=47580.33
The classic tradeoff between "guns and butter" states that when a society spends more on national defense, it has less to spend on consumer goods to raise the standard of living.
a. True
b. False
True, the classic tradeoff between "guns and butter" states that when a society spends more on national defense, it has less to spend on consumer goods to raise the standard of living.
The production possibility curve, which illustrates the concept of opportunity cost, has a famous economic example known as the "guns-and-butter" curve. One must decide how much of each good to create in a hypothetical economy with only two goods.
An economy must decrease its production of butter (food) as it increases its production of firearms (military spending), and vice versa. According to the guns-and-butter curve, you can only acquire something if you offer something else in exchange.
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an imperfectly elastic ball is projected with velocity √gh at an angle α with the horizontal, so that it strikes a vertical wall distant c from the point of projection, and returns to the point of projection. then
An imperfectly elastic ball is projected with the velocity [tex]\sqrt{gh}[/tex] at an angle α with the horizontal, so that it strikes a vertical wall distant c from the point of projection, and returns to the point of projection.
Then, The Time of flight (T) = [tex]\frac{2c}{ \sqrt{gh cosa } }[/tex]
When a ball is projected with the velocity [tex]\sqrt{gh}[/tex] at an angle α with the horizontal, it follows a parabolic path.
The ball will have a horizontal component of velocity (Vx) = [tex]\sqrt{gh cosa}[/tex] , and a vertical component of velocity (Vy) = [tex]\sqrt{ghsina}[/tex] .
The ball will travel a horizontal distance equal to c before reaching the wall. The total time of flight (T) for the ball is equal to the time it takes the ball to reach the wall plus the time it takes for the ball to return to the point of projection.
The time it takes for the ball to reach the wall is equal [tex]\frac{c}{vx}[/tex] , and the time it takes for the ball to return to the point of projection is also equal [tex]\frac{c}{vx}[/tex].
Since the horizontal component of velocity (Vx) is equal to [tex]\sqrt{gh cosa}[/tex] ,
the total time of flight (T) is equal to [tex]\frac{2c}{ \sqrt{gh cosa } }[/tex] .
The correct question is:
An imperfectly elastic ball is projected with velocity √gh at an angle α with the horizontal, so that it strikes a vertical wall distant c from the point of projection, and returns to the point of projection. Then the time of flight is equal to?
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Find the total surface area
The total surface area is 3994ft sq.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Surface area of rectangular prism = 2lb +2lh+2bh
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Given;
Length= 32ft
Breadth= 21ft
Height= 25ft
Now,
Surface area of rectangular prism = 2lb +2lh+2bh
=2*32*21+2*32*25+2*21*25
=1344+1600+1050
=3994
Therefore, the area will be 3994ft sq.
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(t-2)(t+5) = t-2 (t+5) describe and correct the error in finding the product of the binomials
In the given expression, t-2 (t+5) is incorrect. The correct expression is (t-2)(t+5) = t² + 3t - 10. The error in the original expression is that it is not using the distributive property. The correct way to find the product is by using either distributive property or FOIL method.
How to explain the expression?The expression (t-2)(t+5) is the product of two binomials. To find the product, we use the distributive property and the FOIL method. The distributive property states that for any two binomials (a+b)(c+d) = ac + ad + bc + bd.
The FOIL method stands for "first, outer, inner, last", and is a mnemonic for the distributive property. To use the FOIL method, we take the first term from the first binomial, the second term from the second binomial, the second term from the first binomial, and the last term from the second binomial.
In your original expression, the error is that there is no operator between the two binomials (t-2) and (t+5), which makes it unclear whether you are trying to multiply them or not. To correct this, you need to add the multiplication operator () between the two binomials, so it becomes (t-2)(t+5).
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Issues on which there are competing perspectives are generally most appropriate forpersuasive speeches.A)TrueB)False.
False. A persuasive speech is a type of public speaking that attempts to convince the audience to adopt a certain viewpoint or take a specific action.
While there are often competing perspectives on issues, a persuasive speech is not the most appropriate way to address them. Instead, a better approach to discussing issues with competing perspectives is to use an informative speech. An informative speech provides an unbiased overview of the issue, presenting both sides fairly and objectively. This allows the audience to develop their own opinion on the matter based on the facts presented. Although a persuasive speech may be used to present a particular point of view, informative speeches are the best tool for discussing issues with multiple perspectives.
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Calculate the percent relative average deviation for the following set of data. 20.96, 20.85, 20.89, 20.92
The percent relative average deviation for the data set is 0.30%.
((20.96 - 20.89) + (20.85 - 20.89) + (20.92 - 20.89)) / 3 / 20.89 * 100 = 0.30%
The percent relative average deviation for the given data set can be calculated by first finding the absolute differences between each value and the mean (20.89) then adding those differences together. Once the differences are added, divide that by the mean and multiply by 100. This will give you the percent relative average deviation, which in this case is 0.30%.
The percent relative average deviation for the data set is 0.30%.
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Mikhail wants to invest $3,800.00 in a savings account. Determine the simple interest rate required for Mikhail's investment to grow to $11,500.00 in 20 years.
The simple interest rate for Mikhail's investment to grow to $11,500.00 in 20 years is solved to be 10.13%
How to find the simple interest rateThe rate for the simple interest tis calculated using the formula for simple interest.
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = $3,800.00
rate = ?
time = 20 years
simple interest = $11,500.00 - $3,800.00 = $7700
plugging in the values
Simple interest = Principal * time * rate / 100
7700 = 3800 * 20 * r / 100
7700 * 100 = 3800 * 20 * r
770 000 / (3800 * 20 ) = r
r = 10.13%
The interest rate is 10.13%
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The figure shows a parallelogram inside a rectangle outline:
A parallelogram is shown within a rectangle. The length of the rectangle is 3 over 5 foot, and the width of the rectangle is 2 over 5 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 5 foot.
What is the area of the parallelogram? (1 point)
1 over 25 square foot
11 over 25 square foot
3 over 25 square foot
4 over 25 square foot
The area of the parallelogram is equal to: D. 4 over 25 square foot.
How to calculate the area of a parallelogram?Mathematically, the area of a parallelogram can be calculated by using this formula:
Area of a parallelogram = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.Based on the information provided above, the actual base of the parallelogram is given by:
Actual base of parallelogram = 3/5 - 1/5
Actual base of parallelogram = 2/5 foot.
Substituting the given parameters into the area of a parallelogram formula, we have the following;
Area of a parallelogram = 2/5 × 2/5
Area of a parallelogram = 4/25 square foot.
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Please help / por favor ayuda lo necesito para ahora
The value of the angles that are in the triangle will be 97°, 51° and 32°.
How to calculate the triangle?The first thing to note before solving the question is that the sum of the total angles that are in a triangle is 180°.
In this case, it should be noted that the angles that are given are represented by variables. Therefore, we'll add them together and equate them to 180°. This will be:
18x + 7 + 8x + 11 + 6x + 2 = 180
32x + 20 = 180
Collect the like terms
32x = 180 - 20
32x = 160
Divide
x = 160 / 32
x = 5
First angle = 18x + 7
= 18(5) + 7
= 97°
Second angle = 8x + 11
= 8(5) + 11
= 51°
Third angle = 6x + 2
= 6(5) + 2
= 32°
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y varies jointly with x and the square of z
The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.
How can the equation of variation be determined?The concept that will be used here is variation.
since Y varies jointly with respect to z^2 and x the we will introduce K which is the proportionality constant, then we have:
Y= Kxz^2.
The we can introduce Y, x and z to solve for the single unknown and have the answer for the equation of variation.
231=K (6) (7^2)
231=6*49*K
231=(K*294)
231/294=K.
K = 11/14
We can have Y= 11/14 xz^2 which is the equation of variation.
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complete question:
Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y
HELP PLEASE someone ?????
The answer are assuming the information provided, such as cost per visit, co-payments, admission charge etc . The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.
What is the total cost for Sharon and Franklin family for their deductible, co-payments, and hospital charges?"Sharon Wilson
a. The amount she paid for the deductible is $2,000.
b. In total co-payments, she paid $9 * $35 + $10 * $50 + $15 * $95 + $2 * $5 + $3 * $10 = $1,085 for physician and specialist visits, physical therapy and pharmacy co-payments.
c. In hospital charges, she paid $240 + $54,860 = $55,100.
d. In total costs, she paid $2,000 + $1,085 + $55,100 = $58,185.
The Franklin family
a. They paid $17 * $75 + $9 * $100 + $4 * $90 = $1,865 for physician and specialist visits and physical therapy.
b. They paid $2 * $1,500 + $350 = $3,650 for emergency room visits and ambulance fees.
c. They paid $350 + $21,675 = $22,025 in hospital charges.
d. The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.
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If 0= 27°, find the distance between two cities, A and B, to
the nearest mile. The radius of the Earth is approximately
4000 miles.
The distance between two cities, A and B is 1884 miles. The solution has been obtained using the concept of arc of circle.
What is arc of circle?
A circle's arc is referred to as a section or portion of its circumference. A chord of a circle is a straight line that can be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of the circle.
We are given that the angle is 27° and radius is 4000 miles
We know that circumference of circle = 2πr
So,
C=2*3.14*4000
C= 25120
Now, to find the length of arc AB,
⇒Arc length = (27° × 25120)/360°
⇒Arc length = 1884
Hence, the distance between two cities, A and B is 1884 miles.
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The complete question is attached below.
help me answer this pls
The value of x is 17. The solution has been obtained using mid-point theorem of triangle.
What is mid-point theorem of triangle?
The midpoint theorem states, "The line segment of a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of its length."
Let the triangle be ABC and the line dividing it be PQ
We are given AP = PB and AQ = QC
Now, as per mid-point theorem, PQ is parallel to BC and is also half of its length as the two sides are equal.
Therefore,
x= 34/2
x=17
Hence, the value of x is 17.
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NO LINKS!!!
13. Prove that the functions are inverses by showing that f(g(x))= x and g(f(x)) = x
f(x) = x^3 + 7 and g(x) = ∛(x-7)
Answer:
See below for proof.
Step-by-step explanation:
[tex]\large\boxed{\begin{minipage}{4 cm}\underline{Exponent Rules}\\\\$\sqrt[n]{a}=a^{\frac{1}{n}}$\\\\$(a^b)^c=a^{bc}$\\\end{minipage}}[/tex]
Given functions:
[tex]\begin{cases}f(x) = x^3 + 7\\g(x) = \sqrt[3]{x-7}\end{cases}[/tex]
The composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}f[g(x)]&=[g(x)]^3+7\\&=(\sqrt[3]{x-7})^3+7\\&=((x-7)^\frac{1}{3})^3+7\\&=(x-7)^\frac{3}{3}+7\\&=(x-7)^1+7\\&=x-7+7\\&=x\end{aligned}[/tex]
The composite function g[f(x)] means to substitute the function f(x) in place of the x in function g(x):
[tex]\begin{aligned}g[f(x)]&=\sqrt[3]{f(x)-7}\\&=\sqrt[3]{(x^3+7)-7}\\&=\sqrt[3]{x^3+7-7}\\&=\sqrt[3]{x^3}\\&=(x^3)^{\frac{1}{3}\\&=x^{\frac{3}{3}\\&=x^1\\&=x\end{aligned}[/tex]
Hence proving that the functions are inverses by showing that f(g(x))= x and g(f(x)) = x.
Dante wants to spend some of his allowance money, but he is having a hard time deciding what to buy. He loves baseball cards, packs of gum, and bouncy balls. Fill in the ratio tables and answer the questions to help Dante keep track of what he can buy C 1 Dante's favorite packs of baseball cards cost $1.70 each. Fill in the table below to show the cost of different numbers of packs of baseball cards. 10 Packs of Baseball Cards Cost Packs of Gum Cost Packs of Bouncy Balls Cost 1 $1.70 $0.60 1 2 Dante's favorite gum costs $0 60 a pack. Fill in the table below to show the cost of different numbers of packs of gum. J 2 5 $3.15 2 2 4 3 8 9 6 3 Bouncy balls come in packages that cost $3.15 each. Fill in the table below to show the cost of different numbers of packs of bouncy balls. 10 9 19 b Can he buy 30 packs of gum? Why or why not? 15 10 20 25 12 25 4 Dante decided to spend only $20.00 of his allowance and save the rest for later. a Can he buy 12 packs of baseball cards? Why or why not? 20 How much of the $20.00 will he still have after he buys 5 packs of bouncy balls?
Answer:
Step-by-step explanation:
a. No, he can't buy 12 packs of baseball cards because 12 packs * $1.70/pack = $20.40, which is more than $20.
b. Yes, he can buy 30 packs of gum because 30 packs * $0.60/pack = $18.00, which is less than or equal to $20.
c. He will still have $6.75 after he buys 5 packs of bouncy balls because $20.00 - (5 packs * $3.15/pack) = $20.00 - $15.75 = $6.75
In the table you provided, you can see the cost of different numbers of packs of baseball cards, gum and bouncy balls. This can help Dante to decide how much to spend on each item and how much he will save.
FILL IN THE BLANK for a positive angle, the rotation from the initial side to the terminal side takes place in a ______direction. For a negative angle, the rotation takes place in a _______direction. (?;?)
For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.
In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.
Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.
Here we need to find the missing term in the given statement.
According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.
If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.
Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.
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Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.
sin(t), cos(t); Quadrant II
sin(t)=_____________
If the terminal point determined by t is in the given quadrant.sin(t), cos(t); sin(t)= -cos(t) in Quadrant II.
In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.
Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:
1 - sin^2(t) = cos^2(t)
We can then take the square root of both sides to get:
cos(t) = sqrt(1 - sin^2(t))
And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:
sin(t) = -cos(t)
This equation is only valid in Quadrant II.
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MP Reason Hugo walk5/6 mile from his home to the library on
Monday. He walks 1/3 mile from his home to the park on Tuesday.
• How much farther does he walk on Monday than on Tuesday?
• Is your answer reasonable? Explain.
He travels 2.5 times as farther on Monday than on Tuesday.
How to obtain the ratio between the distances?The ratio between the distances is obtained applying the proportions in the context of this problem, as the Monday's distance is divided by the Tuesday's distance.
It gives how much farther he traveled on Monday than on Tuesday.
Then the ratio is given as follows:
(5/6)/(1/3) = 15/6 = 2.5.
(the ratio between two amounts is obtained dividing the two amounts).
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Which of the hypothesis of Rolle's Theorem is not satisfied for the function f(x) = x^3/3 over [ 0, 2 ]?
Answer:
C. [tex]f(0)=f(2)[/tex]
Step-by-step explanation:
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
The function is not differentiable over [0, 2]. Therefore, the option B is the correct answer.
What is the hypothesis of Rolle's theorem?Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
The given function is f(x)=x³/3 over [0, 2].
Here, f(0)= 2 and f(2)=2. Hence, according to the Rolle's theorem there should be at least one x for which f'(x)=0.
Now, f'(x)= 3x²/3
0=3x²/3
3x²=0
x²=0
x=0
Therefore, the option B is the correct answer.
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The average price of a certain model of piano in 1991 was $12,500. In 2013 the average price of the piano was $17,500. What is the percentage increase in the average price of the piano?
The percentage increase in the average price of the piano is 40%.
What is the percentage increase?
To calculate the percentage increase, we use the following formula:
Percentage increase = (New value - Old value) / Old value x 100
In this case, the old value is the average price of the piano in 1991 ($12,500), and the new value is the average price of the piano in 2013 ($17,500). So, we can substitute these values into the formula:
Percentage increase = (17,500 - 12,500) / 12,500 x 100 = 40%
Hence, the percentage increase in the average price of the piano is 40%.
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