After simplifying the given expression 9 p³ q¹ ( 3 p³ - 5 q ), we get 27 p⁶ q - 45 p³q².
We are given that:
9p³q¹(3p³ - 5q)
We need to simplify it:
So, we get that:
= ( 9 p³q¹ × 3 p³ ) - ( 9 p³q¹ × 5 q )
Simplify:
= 27 p³⁺³q - 45 p³q¹⁺¹
Simplifying it, we get that:
= 27 p⁶ q - 45 p³q²
Therefore, after simplifying the expression 9 p³q¹ ( 3 p³ - 5q ), we get 27 p⁶ q - 45 p³ q².
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a certain european automobile has a gas mileage of 19 km/l. what is the gas mileeage in miles per gallon
The gas mileage in miles per gallon = 44.690mi/gal.
What is a vehicle's mileage?A vehicle's mileage is the number of miles it can drive solely on a single gallon or liter of fuel. They are ready to pay up to $500 more for fuel-efficient vehicles. 3. a noncountable noun.
How can I figure out my mileage?Subtract the original tachometer reading from either the new one to get the miles traveled first from the trip odometer. Divide the distance traveled by the number of gallons used to fill the tank. As a result, your car's overall kilometers per gallon yield for that driving period will be calculated.
According to the given data:1 km = 0.621371 mi
1 L = 0.264172 gal
calculating that the amount of gas mileage in miles per gallon by multiplying with distance and gas used per miles.
19 km/L = (19*0.621371)/0.264172 mi/gal
= 44.690 mi/gal
the gas mileage in miles per gallon = 44.690mi/gal.
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does someone mind helping me with this? Thank you!
Sally can plant 14 plants in 2 hours. How many plants can Sally plant in 6 hours?
Answer:
42 plants
might be easier to find how many plants are planted in 1 hour then multiply that by 6. In this case, 7 plants will be planted within an hour. So, multiply 7 x 6 to get 42.
Rays DA and DC are perpendicular. Point B lies in the interior of {angle]ADC. If m[angle]ADB = (3a + 10) degrees and m[angle]BDC = 13a degrees, find a, m[angle]ADB, and m[angle]BDC
Applying the definition of the angle formed by perpendicular lines, the measures are:
a = 5
m<ADB = 25°
m<BDC = 65°
What is the Angle Formed by Perpendicular Lines?When two lines intersect perpendicularly at a point, they form a right angle, which is equal to 90 degrees.
Thus, angle ADC is a right angle. Therefore, angles ADB and BDC are complementary angles. This means that:
m<ADB + m<BDC = 90°
Substitute
3a + 10 + 13a = 90
16a + 10 = 90
16a = 90 - 10
16a = 80
16a/16 = 80/16
a = 5
m<ADB = (3a + 10) = 3(5) + 10 = 25°
m<BDC = 13a = 13(5) = 65°
Thus, applying the definition of the angle formed by perpendicular lines, the measures are:
a = 5
m<ADB = 25°
m<BDC = 65°
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Which domain would allow the inverse of y =cos(x)
The inverse of y = cos(x) could be a function in domain (A) [0, π].
What are domain and range?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value. To obtain the domain and range, simply solve the equation y = f(x) to determine the values of the independent variable x. To calculate the function's range, simply express x as x=g(y) and then find the domain of g(y).So, domain of y =cos(x):
The inverse cosine function has a domain of [1,1] and a range of [0, π].Therefore, domain (A) [0, π] would allow the inverse of y = cos(x) to be a function.
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The complete question is given below:
Which domain would allow the inverse of y = tan(x) to be a function?
A) [0, π]
B) [0, 2π]
C) (-∞, ∞)
D) [-π/2, π/2]
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-3y = -x - 7
Answer:
spam question
not able to answer
Step-by-step explanatio
mark me
I need some help with this
The properties used, in order, are:
Distributive.Addition or subtraction property of equality.Addition or subtraction property of equality.multiplicationn or division property of equality.What is used in each step of the demonstration?We start by writing the linear equation:
3*(x + 2) = 4x + 1
The first step is using the distributive property to distribute the left product.
3x + 6 = 4x + 1
Then we use the addition property of equality to subtract 4x in both sides, we will get:
-x + 6 = 1
And we use it again to subtract 6 in both sides:
-x = 1 - 6 = -5
Finally, we multiply both sides by -1 (multiplication property of the equality)
x = 5
That is the solution of the linear equation.
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for all composite integers $n$, what is the largest integer that always divides the difference between $n$ and the cube of $n$?
The product of three successive integers is represented by the symbol n3 n=(n1)(n)(n+1).
n3 n can be divided by 6.
What is consecutive integers ?Consecutive integers are the numbers that follow one another. They go either alphabetically or sequentially. For instance, a series of integers is a group of natural numbers. The term "consecutive" in mathematics refers to an unbroken flow or succession of numbers; hence, a sequence of consecutive integers is one where each following number is one more than the one before it. An array of consecutive integers (or numbers) has an identical mean and median. If x is a positive integer, then x + 1 and x + 2 are likewise positive integers. We shall learn in-depth details regarding formulas, characteristics, illustrations, and the significance.
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Find the value of x?
Step-by-step explanation:
so, we have a kite here.
a kite is a quadrilateral, that is totally symmetric along one of its diagonals.
the sum of all internal angles of a quadrilateral is always 360°.
remember, the sum of all angles around one point on one side of a line is always 180°.
a full circle airways represents 360°.
the inner angle at 140° is
180 - 140 = 40°
the inner angle at 250° is
360 - 250 = 110°
the inner angles at x and its opposing corner are equal (due to the symmetry) and are in sum with the other 2 inner angles 360°.
so, we have for the inner angles
360 = 110 + 40 + 2×xinner
210 = 2×xinner
the inner angle of x = 105°.
x (the outer angle of the inner angle of x) is
x = 360 - 105 = 255°
how many 23 digit numbers consisting of the digits, 1,2,3,7,8,9 are divisble by 3? (hint: consider the divisibility test for 3)
Answer:
Hello,
answer : 259269764699508231
Step-by-step explanation:
We must use permutations with repetitions
-3(-3v+4w-5) without parentheses
Answer:
Step-by-step explanation:
56/89
find the vertex and write the quadratic function in vertex form (which our openstax textbook also calls the standard form).
The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].
What is quadratic equation?Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").
As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation can be created from a quadratic equation.
Calculations:
[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]
Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]
h=3 and k=16
Hence, vertex is (3,16).
[tex]f(x)=(x-3)^{2}+16\\[/tex]
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f+B=m What does B equal?
[tex]f + b = m \\ f + b - f = m - f \\ b = m - f[/tex]
The quantity z varies directly with y and inversely with x When y = 12 and x = -12, z = -6. What is the value of k, the constant of variation?
Write your answer in the form A or A/B, where A and B are constants or variable expressions.
Answer:
Z = ky/x where y=12, x=-12 and z=-6
-6= k(12)/-12
-k = - 6
K = 6
Valeria bought a 9 foot length of ribbon from which she wants to cuut 2/3 foot pieces how many pieces can she cut what will be the length of the leftover pirece of ribbon?
The number of pieces she can cut is 13 and the length of the leftover piece of ribbon is 1/3 feet, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given:
Total length of ribbon = 9 feetLength of each piece of ribbon = 2/3 feetTo find: Number of pieces of ribbon cut and length of leftover pieces.
Finding:
Let x be the number of pieces of ribbon that can be cut.
Then, according to question, by basic algebra:
2x/3 = 9
=> x = [tex]\frac{27}{2}=13\frac{1}{2}[/tex]
That is, the number of pieces of ribbon that can be cut are 13
The leftover length of ribbon is then given by:
9 - 13 (2/3) = 9 - (26/3) = 1/3
That is, the leftover length of ribbon is 1/3 feet.
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5 1/2 + 3 4/5 + 1 1/4 =
Answer:
[tex]10\frac{11}{20}[/tex]
Step-by-step explanation:
[tex]5\frac{1}{2} + 3\frac{4}{5} + 1\frac{1}{4}[/tex]
1.Find the LCM(Least Common Multiple).
That would be 20.
2.Multiply so all denominators are equal.
[tex]5\frac{10}{20} + 3\frac{16}{20} + 1\frac{5}{20}[/tex]
3. Add
[tex]9\frac{31}{20}[/tex]
4. Simplify
[tex]10\frac{11}{20}[/tex]
(Geometry)
I need help on #4 and #11, 12 and 13 please
Problem 4
Let's define these point locations
A = (-2, 2)B = (0,0)C = (0,4)D = (4,0)Angle DBC is 90 degrees since it covers the upper right quadrant
Angle CBA is 45 degrees
Therefore, angle ABD is 90+45 = 135 degrees.
Check out the diagram below.
Answer: 135 degrees=========================================================
Problem 11
x = the unknown angle
angle x and 140 combine to a straight angle (180 degrees)
x+140 = 180
x = 180-140
x = 40
Answer: 40 degrees=========================================================
Problem 12
This time the angles add to 90
x+36 = 90
x = 90-36
x = 54
Answer: 54 degrees=========================================================
Problem 13
The two angles x and 90 combine to a 120 degree angle
x+90 = 120
x = 120-90
x = 30
Answer: 30 degreesWhich of the following describes the end behavior of the function f(x) = root(x, 3) - 4 as approaches infinity ?
Answer:1) An operator is missing in your statement. Most likely the right expression is:
Step-by-step explanation:
2x
f(x) = -------------
3x^2 - 3
So, I will work with it and find the result of each one of the statements given to determine their validiy.
2) Statement 1: The graph approaches 0 as x approaches infinity.
Find the limit of the function as x approaches infinity:
2x
Limit when x →∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
3 - 3/∞ 3 - 0 3
Therefore the statement is TRUE.
3) Statement 2: The graph approaches 0 as x approaches negative infinity.
Find the limit of the function as x approaches negative infinity:
2x
Limit when x → - ∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
3 - 3/(-∞) 3 - 0 3
Therefore, the statement is TRUE.
4) Statement 3: The graph approaches 2/3 as x approaches infinity.
FALSE, as we already found that the graph approaches 0 when x approaches infinity.
5) Statement 4: The graph approaches –1 as x approaches negative infinity.
FALSE, as we already found the graph approaches 0 when x approaches negative infinity.
max observes the zoo and the library from a helicopter flying at a height of 300 times square root of 3 feet above the ground, as shown below
The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.
What is the concept of applications of trigonometry?To roof a home, to make the roof slant (in the case of single-family bungalows), to determine the height of the roof in buildings, etc., utilize trigonometry. The navy and aviation industries use it. It's applied to cartography (creation of maps). Trigonometry is also used in satellite navigation systems.Given: height of helicopter = 300√3 feet from the ground.
To find: Distance between zoo and library.
Finding:
(Refer to the image attached.)
Let the distance from the plane to the zoo and library be d1 and d2 respectively.
Then, with the help of concepts of applications of trigonometry,
For the zoo:[tex]tan(60) = \frac{300\sqrt{3}}{d1}[/tex]
=> [tex]\sqrt{3}=\frac{300\sqrt{3}}{d1}[/tex]
=> d1 = 300 feet
For the library:[tex]tan(30) = \frac{300\sqrt{3}}{d2}[/tex]
=> [tex]\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}[/tex]
=> d2 = 300 (3) = 900 feet
The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.
Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.
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what is the total area under the normal curve? a. it depends on the mean b. 0.5 c. 1 d. it depends on the standard deviation
The total area under the normal curve is 1.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The more the data is distributed, the greater will be the standard deviation of that data. The standard deviation is used in finance by business owners to understand risk management and make better business decisions. It helps in calculating the margins of error that occur in the survey reports.the total area under the normal curve is 1.
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1/3y^2+2/3y+1 is it a polynomial function
Answer:
yes it is
Step-by-step explanation:
because it has the leading power of x as 2
How to estimate 6x219
Answer:
To estimate I would either do 6x220 then subtract 6 from that sum
Or you could do 6x200
6x10
6x9
And add that to get your answer but 6x219 is 1314
Step-by-step explanation:
A certain basketball player scores 60% of the free-throw shots she attempts. during a particular game, she gets six free throws. what is the probability that she scores on exactly four of the six shots? choose one.
The probability of scoring exactly four out of the given six shots is 0.311, calculated using the concept of binomial distribution in probability theory.
What is a Binomial Distribution?
Binomial Distribution in probability theory is defined as getting x number of successes on repetition of trial n times, the formula for binomial distribution is C(n,r) × (p)x × (q)n - r, where p denotes the probability of success and q denotes the probability of failure.
Calculation of the probability of scoring exactly four shots out of six
Let p denote the probability of success and q denote the probability of failure, which is equal to 1 - p.
Using Binomial Distribution, we get,
P(x = r) = C(n,x) × (p)x × (q)n - x
Taking r = 4,
P(x = 4) = C(6,4) × (0.6)4 × (0.4)2
= 6! / (4! 2!) × (0.6)4 × 0.16
= 0.31104
~ 0.311
Hence, the required probability using binomial distribution is 0.311.
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A machine starts working in 45 minutes at the temperature of 60degree celsius.how much machine required to work at temperature of75degree celsius?
The time required to work at temperature of75degree celsius is 56.25 minutes
Unit rateIf a machine starts working in 45 minutes at the temperature of 60degree celsius, the amount of time worked at a temperature of 1 degree is expressed as:
Unit rate = 45/60
Unit rate = 0.75degrees celsius/minute
Determine the time it required to work at temperature of 75degree celsius
Time required = 0.75 * 75
Time required = 56.25 minutes
Hence the time required to work at temperature of75degree celsius is 56.25 minutes
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what was the approximate average speed, in meters per second, of the ocean current that carried the ducks to shore? (rubber ducks from the same spill began to appear on the coast of maine in july 2003.) use an average month length of 30 days.
There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.
What is average velocity?A vector quantity is average velocity. The change in position and otherwise displacement (x) divided by that of the time intervals (t) during which the displacement happens is the definition of average velocity. The average velocity may be either positive or negative depending on the displacement's direction.
According to the given information is:The distance covered by the rubber ducks = 1600 miles.
The duration needed to cover this distance = 10 months.
The average ocean speed, according to definition, is
v = (1600 miles)/(10 months)
Now,
1 mile = 1609 m
10 months = (10 months)*(30 days/month) *(24 hours/day)
= 7200 hours (approx.)
= 7200*3600
= 2.592 x 10⁷ s
So that,
ν = [tex]\frac{(1600 \mathrm{~m}) *\left(1609 \frac{\mathrm{m}}{\mathrm{mi}}\right)}{(10 \mathrm{months}) *\left(2.592 \times 10^7 \frac{\mathrm{g}}{10 \mathrm{mon} t h}\right)}[/tex]
= 0.0993 m/s
Also,
ν = 1600/7200
= 0.222 mi/h
There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.
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I understand that the question you are looking for is:
A severe storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly 1600 miles away.
What was the approximate average speed of the ocean current that carried the ducks to shore in m/s and in mi/h? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)
Two angles are supplementary.
The measure of the larger angle is 12
less than 3 times the measure of the smaller angle. Find the measure of
the larger angle.
O A) 25.5°
O B) 64.5°
OC) 132°
O D) 144°
Answer:
c
Step-by-step explanation:
192=4x-12
A small insect viewed through a convex lens is 1.8 cmcm from the lens and appears 2.5 times larger than its actual size. part a what is the focal length of the lens?
Answer:
4.50
Step-by-step explanation:
There's 2 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
1 8
× 2 5
___________________
+ 9 0
+ 3 6
___________________
= 4 5 0Rewrite the product with 2 total decimal places.
Answer = 4.50
Therefore:
1.8 × 2.5 = 4.50
"Compare -√7 and -3.12345.... justify your reasoning." Please help ASAP!!! Thank you!
The comparison of the numbers is that -√7 is greater than -3.12345....
How to compare the numbers?The numbers are given as:
-√7 and -3.12345....
Using a calculator, we have:
-√7 = -2.6457.....
-2.6457.... is greater than -3.12345....
This means that
-√7 is greater than -3.12345....
Hence, the comparison of the numbers is that -√7 is greater than -3.12345....
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Solve inequality.
9 a<45
To solve the inequality, divide both sides by 9. The solution is a < 5 or (∞, 5)
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
9a < 45
Notice that the variable, a, is already isolated on the left side. Divide both sides by 9: (Note that the inequality sign is not flipped since 9 is a positive number)
9a : 9 < 45 : 9
a < 5
Using the interval notation, the solution is (∞, 5)
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please help
i need the answer please
Answer:
option C: 69
Step-by-step explanation:
We are to find approximately how many pink flowers are predicted to bloom on a shrub with 40 red flowers. The equation given is: y = 1.73x + 0.0924 and we see that red flowers are on the x-axis and pink flowers are on the y-axis.
Since we know there are 40 red flowers and red flowers are on the x-axis, x = 40. Plug into the equation:
y = 1.73x + 0.0924 where x = 40
y = 1.73(40) + 0.0924
y = 69.2 + 0.0924
y = 69.2924
best answer is C. 69.