the nth term of a sequence is n(n-8)÷√n+3
find the 1st and 6th terms
Answers
Answer:
-4 and -2✓6+3
Step-by-step explanation:
use pemdas
1(1-8)÷✓1 + 3
-7÷1+3
-4
6(6-8)÷✓6+3
-12÷✓6+3
multiply fraction by ✓6 on bottom and top to get rid of square root on bottom
-12✓6÷6+3
divide -12 by 6 and put radical next to it
-2✓6+3
Related Questions
what is the base of 3^x=8
Answers
Answer:
3
Step-by-step explanation:
I have a picture of a graph and I need to write the equation for a degree four polynomial
Answers
To find the polynomial equation of the graph.
Now, identify the x-intercept of the graph,
x=-3 , x=-1 , x=3, x=4.
these are the factors of the polynomial,
\((x+3),(x+1),(x-3),(x-4)\)The polynomial is,
\(p(x)=a(x+3)(x+1)(x-3)(x-4)\)to determine the sketch factor use the y-intercept point.
(0,1).
\(\begin{gathered} p(0)=a(0+3)(0+1)(0-3)(0-4) \\ 1=a(3)(1)(-3)(-4)_{} \\ 1=a\cdot36 \\ a=\frac{1}{36} \end{gathered}\)\(p(x)=\frac{1}{36}(x+3)(x+1)(x-3)(x-4)\)Type the correct answer in the box.
Winston is creating a rectangular piece of 8-bit art using squares that are x pixels wide. The length of the rectangular piece, in pixels, is represented by the function l(x) = x + 24, and the width of the rectangular piece is represented by w(x) = x + 16.
Write the standard form of the function which describes the total area of the rectangular piece, a(x), in terms of x, the side length of each square pixel.
Answers
Area=l×w
Function:-
\(\\ \sf\longmapsto (l*w)(x)\)
\(\\ \sf\longmapsto l(x)*w(x)\)
\(\\ \sf\longmapsto (x+24)(x+16)\)
\(\\ \sf\longmapsto x^2+40x+384\)
Find the hypotenuse of a right triangle with a side of 6 and a side of 8.
(ONLY put the number of your answer.) *
Answers
Answer:
10 (can't just write a number bcs i couldn't send yoy if i won't write something else)
When h=4 , j=5 , and k=−1 , the expression jkh+hj−jk equals?
Answers
When h = 4, j = 5, and k = -1, the expression jkh + hj - jk equals 5.
To solve the expression we have to substitute the value of each variable in the expression. Then simplify the expression according to mathematic rule. After solving we get the solution of the expression.
An expression is a combination of numbers, variables, and/or operations that can be evaluated or simplified to obtain a numerical or algebraic result.
The given expression is:
jkh + hj - jk
Substituting the given values of h, j, and k, we get:
jkh + hj - jk = (5 x (-1) x 4) + (5 x 4) - (5 x (-1))
Now simplify the expression
jkh + hj - jk = (-20) + 20 + 5
jkh + hj - jk = 5
Therefore, the value of jkh + hj - jk equals 5.
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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument? Plays an instrument Does not play an instrument Plays a sport 3 2 Does not play a sport 7 15
Answers
Answer:
play an instrument and a sport: 2
play an instrument but does not play a sport: 8
does not play an instrument but plays a sport: 10
does not play an instrument or a sport: 4
a store owner needs a rug with an area of at least 420 square feet select all that the store owner could use A 40 feet x 20 feet B 60 feet x 7 feet C 70 feet x 6 feet D 4 feet x 20 E 20 feet x 4 feet f 40 feet x 7 feet
Answers
Answer:
que
Step-by-step explanation:
no sé
Select the correct answer Rita is making a beaded bracelet she has a collection of 160 blue beads 80 gray beads and 240 pink beads what is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection use a table of randomly generated outcomes to answer the question each letter represents the first letter of the bead color 0.05 0.10 0.45 0.55
Answers
Answer:
the answer is .45 I am assuming
Using log evaluate 3^x=10
Answers
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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a. it calculates the return values for the class b. it invokes all the class methods in order c. it is a method used when instantiating an object d. it is defined in the client code for the class e. it provides access to methods and instance variables
Answers
The right answer is C. It is a technique applied when creating an object.
When an object is generated from a class in object-oriented programming, a constructor, a particular method, is called. It is in charge of initializing the object and establishing its starting state. Typically, constructors are specified in the class specification and called when an object is created with the new keyword. They are used to create and initialize objects of that class and share the same name as the class.
In the event that a constructor's arguments include default values, it is possible to call it without any arguments. Additionally, a class may have many constructors with various amounts or kinds of parameters due to overloading, which allows for this.
Option A is erroneous since a constructor does not figure out the class's return values. Because a constructor does not call each of the class methods sequentially, option B is incorrect. Option D is erroneous since the class definition, not the client code, contains the definition of a constructor. Because a constructor gives access to methods and instance variables, Option E is valid, but it's not the only one.
The complete question is:-
Which statement is true about a constructor?
A. It calculates the return values for the class
B. It invokes all the class methods in order
C. It is a method used when instantiating an object
D. It is defined in the client code for the class
E. It provides access to methods and instance variables
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Explain how you know that (3, 5) is not a solution to the given inequality by looking at the graph.
Answers
The reason that the point (3, 5) is not a solution to the given inequality is given below.
We are given that;
y > 2x + 1
Now,
The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.
If we have (3,5) as a point, we can see that it lies on the boundary line
y = 2x + 1.
Since the inequality is strict (y >), points on this line are not solutions to the inequality
Therefore, by the inequality the answer will be given above.
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what are exchange rates?
Answers
Answer:
Step-by-step explanation:
Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.
ASAP PLEASE
Mike and Jhon has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Mike uses the formula V = π(3)2(7) to find the volume whereas Jhon says his formula V= V = 1/3π(3)2(7) is correct to find the volume.
Who is incorrect ? and why?
Answers
Answer:
I can't really see the whole question, but for a cone the volume formula is πr2h
3
Step-by-step explanation:
Determine which box each reason should go in to justify each step taken to solve
the equation. Make the unused reason #4
54+2x=5x-3(2+6x)
Distributive Property
Multiplication Property
Division Property
>
Addition Property
<
Answers
Answer:
Am how should we answer this
) Quantifier negation.
Form the negation of the following statements. Then apply De Morgan’s law and/or conditional law, when
applicable. Negation should appear only within predicates, i.e., no negation should be outside a quantifier
or an expression involving logical connectives. Show all steps.
a) ∀x (P(x) ∧ R(x))
b) ∀y∃z(¬P(y) → Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
Answers
The negations of the given statements with the application of De Morgan's law and/or conditional law.
a) ∃x (¬P(x) ∨ ¬R(x))
De Morgan's law:
∃y ∀z(¬P(y) ∧ ¬Q(z))
b) ∃y ∀z(¬P(y) ∧ ¬Q(z))
The double negation:
∃y ¬∃z(P(y) ∨ Q(z))
c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
The conditional law:
¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))
Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:
a) ∀x (P(x) ∧ R(x))
The negation of this statement is:
∃x ¬(P(x) ∧ R(x))
Now let's apply De Morgan's law:
∃x (¬P(x) ∨ ¬R(x))
b) ∀y∃z(¬P(y) → Q(z))
The negation of this statement is:
∃y ¬∃z(¬P(y) → Q(z))
Using the conditional law, we can rewrite the negation as:
∃y ¬∃z(¬¬P(y) ∨ Q(z))
c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
The negation of this statement is:
¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))
Using the conditional law, we can rewrite the negation as:
¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))
Applying De Morgan's law:
¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))
Simplifying the double negation:
¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))
Using De Morgan's law again:
¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))
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What is the equation of a circle with center at (4,-6) and radius of 5?
Answers
Answer:
Since the centre of the circle is (−4,−5) and its radius =6
Then, the equation of the circle is
⇒(x−(−4))
2
+(y−(−5))
2
=6
2
⇒(x+4)
2
+(y+5)
2
=36
⇒x
2
+8x+16+y
2
+10y+25−36=0
⇒x
2
+y
2
+8x+10y+5=0
Step-by-step explanation:
Paki brainlilest na lng po salamaf
Convergent or divergent?
Answers
Answer:
Convergent
Step-by-step explanation:
This is an alternating series where bn = 2n / eⁿ. Apply the alternating series test:
lim(n→∞) bn
= lim(n→∞) (2n / eⁿ)
Use L'hopital's rule:
= lim(n→∞) (2 / eⁿ)
= 0
For n ≥ 1, the series is decreasing. 2(n+1) / eⁿ⁺¹ < 2n / eⁿ.
Therefore, the series converges.
there is a sales tax of $22 on an item that costs$272 before tax. the sales tax on the second item is $19.25 how much does the second item cost before tax
Answers
Answer:$240.62
Step-by-step explanation:
You divide 22/272 to get .08 then you divide 19.25 by .08 to get 240.62.
What is the mode of the data represented in this line plot?
Enter your answer in the box.
5 - xx
6 - xxxx
7 - xxx
8 - xxxxxx
9 - xx
10 - xxxx
11 - xx
Answers
The mode of the data represented in this line plot will be 8.
Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.
The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.
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help me with this asap please
Answers
Answer:
It is linear. The constant rate of change is 3 cents per hour.
Step-by-step explanation:
15/5 = 3
24/8 = 3
36/12 = 3
72/24 = 3
Solve the question below:
Answers
Answer:
x = 15
Step-by-step explanation:
3x+1+4x-3 = 103
7x = 105
x = 15
the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
Answers
Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
The x-intercept for the line 2x + 3y = 18 is (x, 0). What is the value of x?
Answers
Answer:
The answer is nine :)
Step-by-step explanation:
write a number to represent the situation: A withdrawal of $36
Answers
The number which represents the situation of a withdrawal of $36 is -$36.
In this question, we have to find out the number or integer which represents the situation of a withdrawal of $36. This question is from integers topic and for that we should have the definition of integers in our mind. So, an integer is defined as number which can be represented without the fractional form. It contains whole numbers and negative of natural numbers. The integers are generally denoted by the symbol 'Ζ'. And, the integers can be negative or positive.
In this question we have asked withdrawal of $36 from any source. So, withdrawal basically means money will decrease, so it will become negative.
To represent a withdrawal of $36, we will use the negative sign.
Hence, -$36 is the correct representation of the situation of a withdrawal of $36.
Therefore, -$36 is the required answer.
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13 of 14
If x= 6 and y = -2, evaluate the following expression:
-
7x - 3y/
3y + 2x
Answers
Answer:
6
Step-by-step explanation:
\(\frac{7x - 3y}{2x + 3y}\) Insert your x and y values to get 7(6) - 3 (-2) on the top and 2(6) + 3(-2) on the bottom. Simplify to get 42 - (-6) and 12 + (-6). Simplify further to get 36/6. Solving this gets you 6.
Ten major college football bowl games were played in January 2010, with the University of Alabama beating the University of Texas 37 to 21 to become the national champion of college football. The results of the ten bowl games are shown below (USA Today, January 8, 2010). The predicted winning point margin was based on Las Vegas betting odds approximately one week before the bowl games were played. For example, Auburn was predicted to beat Northwestern in the Outback Bowl by five points. The actual winning point margin for Auburn was three points. A negative predicted winning point margin means that the team that won the bowl game was an underdog and expected to lose. For example, in the Rose Bowl, Ohio State was a two-point underdog to Oregon and ended up winning by nine points.
Answers
The perimeter of a rectangular parking lot is 320 m.
If the length of the parking lot is 97 m, what is its width?
Answers
Answer:
63 metres
Step-by-step explanation:
A rectangle has 4 sides
2 of these sides are the lengths
The other 2 sides are the width
If the length of one side is 97 metres, the other side length must also be 97 metres
The two lengths then add together (97 + 97) to become 194 metres
Now we can use this information to calculate the width
320 (the total perimeter) subtract 194 (The total length) = 126 metres
This means that 126 metres is the total width
Because there are two sides which add up to the total width we divide 126 by 2
This allows us to get the measurement of the width
126 divided by 2 = 63 metres
What is the radius of the circle write your sneer in simplified, rationalized form
Answers
Solution:
The equation of a circle is expressed as
\(\begin{gathered} (x-a)^2+(y-b)^2=r^2\text{ -----equation 1} \\ where \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}\)Expanding equation 1 gives:
\(\begin{gathered} x^2+y^2-2ax-2by+(a^2+b^2)=r^2 \\ \Rightarrow x^2+y^2-2ax-2by+(a^2+b^2)-r^2=0\text{ ------- equation 2} \end{gathered}\)Given the equation of the circle to be expressed as
\(x^2+y^2-y-12=0\text{ ----- equation 3}\)Comparing equations 2 and 3, we have
\(\begin{gathered} \Rightarrow-2ax=0\text{ ---- equation 4} \\ \Rightarrow-2by=-y\text{ ----- equation 5} \\ \Rightarrow(a^2+b^2)-r^2=12\text{ ----- equation 6} \end{gathered}\)From equation 4,
\(\begin{gathered} -2ax=0 \\ divide\text{ both sides by -2x} \\ \Rightarrow a=0 \end{gathered}\)From equation 5,
\(\begin{gathered} -2by=-y \\ divide\text{ both sides by -2y} \\ -\frac{2by}{-2y}=-\frac{y}{-2y} \\ \Rightarrow b=\frac{1}{2} \end{gathered}\)From equation 6,
\(\begin{gathered} (a^2+b^2)-r^2=-12 \\ where\text{ } \\ a=0,\text{ b=}\frac{1}{2} \\ \Rightarrow(0^2+(\frac{1}{2})^2)-r^2=-12 \\ \frac{1}{4}-r^2=-12 \\ subtract\text{ }\frac{1}{4}\text{ from both sides of the equation,} \\ \frac{1}{4}-r^2-\frac{1}{4}=-12-\frac{1}{4} \\ \Rightarrow-r^2=-\frac{49}{4} \\ divide\text{ both sides by -1} \\ \Rightarrow r^2=\frac{49}{4} \\ take\text{ the square root of both sides,} \\ \sqrt{r^2}=\sqrt{\frac{49}{4}} \\ \sqrt{r\times r}\text{ =}\sqrt{\frac{7}{2}\times\frac{7}{2}} \\ \Rightarrow r=\frac{7}{2} \end{gathered}\)Hence, the radius of the circle is
\(\frac{7}{2}\)A pail holds 3 1/2 gallons of water. How much is this in cups?
Answers
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
3.5 * 4 * 2 * 2 = 56 cups
The price of a stock in a company drops $27 every hour. What integer represents
the change in the Stock price after 5 hours?
Answers
Answer:
2.25 and 11.25
Step-by-step explanation:
27/12=2.25 twelve is the number of hours and 27 is the total drop in price
2.25*5=11.25 because 2.25 is the drop per hour you want to multiple that by five hours.