The given expression fro the sum of n terms:
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ \text{ Where: }a_1\text{ is the firm term \& }a_n\text{ is the last term} \end{gathered}[/tex]From the given question we have:
[tex]a_1=8,a_n=79,\text{ n =6}[/tex]Substitute these value in the expression of sum of n terms
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ S_6=\frac{6}{2}(8+79) \\ S_6=3(87) \\ S_6=3\times87 \\ S_6=261 \end{gathered}[/tex]So, sum of 6 terms is 261
find the perimeter of ABC with vertices A(-4,4), B(4,-1) and C(-4,-1)
Answer: A=-16 B=-5 C=-3
Step-by-step explanation:
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-2, 3); y=-3/4x+4
Answer:
y=4/3x+17/3
Step-by-step explanation:
Perpendicular lines have reciprocal negative slopes, find the slope of the new line:
-3/4 --> m = 4/3
Write line in point slope form:
y-3 = 4/3(x+2)
Distribute:
y-3=4/3x+8/3
Simplify:
y=4/3x+17/3
Hi I have tried calling but I can’t do anything
For the given functions, we will find the first derivative of each function
Note:
a, and b are constants
y, f, and g are functions
2) y = (a+bf)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]=============================================================
3) y = (x+f)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]==========================================================
4) y = (x+f)³
We will use the exponent rule to find the derivative as follows:
[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]===========================================================
5) y = ax² + bg² + f
so, y' will be as follows:
[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]==========================================================
A car was valued at $41,000 in the year 1994. The value depreciated to $13,000 by the year 2004
Firstly, we have to write the general depreciation fomula as follows;
[tex]V(t)=I(1-r)^t[/tex]where V(t) represents the value of the commodity after a certain t years
I is the initial value of the item
r is the annual percentage change (rate of depreciation)
t is the number of years
a) Here, we want to calculate the annual rate of change
According to the data given in the question;
V(t) = $13,000
I = $41,000
r = ?
t = 2004-1994 = 10 years
Now, we proceed to substitute these values, to find the find of r as follows;
[tex]\begin{gathered} 13,000=41,000(1-r)^{10} \\ (1-r)^{10\text{ }}\text{ = }\frac{13,000}{41,000} \\ (1-r)^{10\text{ }}=\text{ }\frac{13}{41} \\ \\ (1-r)\text{ = }\sqrt[10]{\frac{13}{41}} \\ \\ 1-r\text{ = 0.8915} \\ r\text{ = 1-0.8915} \\ r\text{ = 0.1085} \end{gathered}[/tex]b) To write r in percentage form, we have to multiply the answer in 'a' above by 100
We have this as ;
[tex]0.1085\times100\text{ = 10.85 \%}[/tex]c) Here, we want to get the car value by year 2009
In that instance;
V(t) = ?
I = $41,000
r = 0.1085
t = 2009-1994 = 15
Substituting these values, we have;
[tex]\begin{gathered} V(15)=41,000(1-0.1085)^{15} \\ V(15)\text{ = \$7,321.56} \end{gathered}[/tex]To the nearest 50 dollars, this is $7,300
Raffle tickets are being sold for a fundraiser. The function a(n) relates theamount of money raised to the number of tickets sold, n.It takes as input the number of tickets sold and returns as output the amountof money raisedan) = 4n - 20Which equation represents the inverse function n(a), which takes the moneyraised as input and returns the number of tickets sold as output?O A. n(e) -47,20O B. n(e) – +20OC. n() - 0-20OD. n(a) -3 -20
A
Since The equation is
[tex]a(n)\text{ = 4n-20}[/tex]To find its inverse we have to proceed to some steps
a= 4n-20
1) Swap a for n, in this case,
n=4a-20
2) Isolate n on the left side by subtracting 4a on both sides:
n -4a =4a-4a -20
n-4a=-20
3) Subtract n on both sides
a-a-4n =-20-a
-4n=-20 -a
4) Multiply it by -1
4n = 20 + a
5) Divide by 4, there you have it. The inverse function:
[tex]n(a)=\frac{20+a}{4}[/tex]To find its in
Given the replacement set: {−9, −10, −11, −12}.
Which value of x correctly solves this equation?
3.2x−5=−40.2
Enter your answer in the box.
Answer:
x = -11
Step-by-step explanation:
You want to know the value of x that correctly solves the equation 3.2x -5 = -40.2.
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
3.2x -5 +5 = -40.2 +5 . . . . . . . . . add 5 to both sides
3.2x = -35.2 . . . . . . . . . . . . . simplify
Step 2: isolate the variable
3.2x/3.2 = -35.2/3.2 . . . . . . . . . . divide both sides by the coefficient of x
x = -11 . . . . . . . . . . . . . . . . . . simplify
An aeroplane flies between two cities that are 8100 km apart.
The aeroplane takes 9 hours to complete the journey.
Calculate the average speed of the aeroplane, in km/h.
Answer:
7,290,000.answer
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 minute
8100 km = 810000 m
9 hour=540 minute
60/540.00 cancel
6/54 will be than cut 6×9=54
SO,multiply 810000×9 = 7,290,000
Answer:
The answer is 7,290,00
Step-by-step explanation:
1 km= 100000 m
1 hour = 60 min
8100 km = 810000 m
9 hour=540 min
60/540.00 cancel
6/54 will be than cut 6×9=54
so ,multiply 810000×9 = 7,290,000
Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 16 cookies and 24 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
The greatest number of plates he can make to share is 6.
What is the greatest number of plates he can make to share?From the information, Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors and he has 16 cookies and 24 brownies to share.
It should be noted that this illustrates that we have to find the highest common factor for 16 and 24.
This will be:
18 = 2, 3, 6, 9 and 18.
24 = 2, 3, 4, 6, 8, 12 and 24
The highest common factor is 6.
Therefore, the number will be 6 plates.
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Two standard 6-
sided dice are
rolled. How would
you describe the
following events
of having their
sum be EVEN OR
GREATER THAN 9?
The probability of having an even or a number greater than 9 is 2/3.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.
The sample space of two 6-sided dice would be 36
Of this 36, there would be 18 which would have an even sum.
There would be 6 with a sum greater than 9.
The probability of having an even or a number greater than 9 = (18/36) + (6/36) = 24 / 36 = 2/3
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Answer:
5/9
Step-by-step explanation:
You want the probability that a roll of 2 dice will produce a sum that is even or greater than 9.
EvenHalf the numbers on each die are even. Their sum will be even when the dice show ...
even + even . . . . p = (1/2)(1/2) = 1/4
odd + odd . . . . . . p = (1/2)(1/2) = 1/4
So, the 36 possible outcomes will produce an even sum (1/4) +(1/4) = 1/2 of the time. That is, there are 1/2(36) = 18 outcomes with an even sum.
Greater than 9The sums that are greater than 9 are 10, 11, 12. Of these, 10 and 12 are outcomes that are even, so are already counted.
The sum 11 can be made two ways: 6 +5 or 5 +6.
So, "or greater than 9" adds 2 outcomes to the 18 we have already counted.
Final tallyThe final tally of outcomes of interest is ...
18 + 2 = 20 . . . . of 36 possible outcomes
That is ...
P(even or >9) = 20/36 = 5/9
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You volunteer at a nursing home for 3 hours a day. You volunteered 6 hours last week and 12 hours this week. How many days did you volunteer?
help help help help help help help
A local hamburger shop sold a combined total of 598 hamburgers and cheeseburgers on Wednesday. There were 52 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
In the local hamburger shop the total number of hamburgers sold on Wednesday , based on the given data is :
325 hamburgers.
Explanation:A General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.here form a equation based on given data ;
let , Hamburgers be = x
let, Cheeseburgers be = y
here , No. of burgers (hamburgers and cheeseburgers )sold = 598
here,
x + y = 598 =>(1)
y = x - 52 => (2)
solving 2 equations ,
x + ( x - 52 ) = 598
x + x - 52 = 598
2x = 598 + 52
x = 650 /2
x = 325
on Wednesday 325 hamburgers were sold.
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help l need help with this
Answer:
Step-by-step explanation:
Answer: Y = 3x + 3
Simply plug in points on graph calculator.
Answer:
Step-by-step explanation:
I think it might be y=3/1+6 ??? i might be wrong
a bucket contains 15 blue pens 35 black pins and 40 Red Pins. You pick one pin at random find the theoretical probabilities below . Express your answer as a percent to the nearest whole number p(black)=???p(blue or black)=???
The number of blue pen is 15
The number of black pens is 35
The number of red pens is 40
The total number of pens in the bucket = Blue pens + black pens + red pens
The total number of pens = 15 + 35 + 40
= 90
Therefore, the total number of pens in the bucket = 90 pens
The probability that black pen is picked is
Probablity = possible outcomes/ total outcomes
P(black) = 35 / 90 x 100%
P(black) = 0.3888 x 100%
P(black) = 38.88%
P(black) = 39%
P(blue or black)
If its pick at random without replacement then
If the first pick is blue, then the total number of pen in the bucket remains 89
For the first pick will be 15/90
Since the remaining pens is 89, then the second pick is
35/89
Then we have
15/90 + 35/89
LCM is 8010
8010 x 15 / 90 + 35 x 8010 /89 / 8010
89 x 15 + 35 x 90 / 8010
P(blue / black) = 1335 + 3150 / 8010
P(blue or black) = 4485 / 8010
P(blue or black) = 0.559 x 100%
P(blue or black) = 55.9%
P(blue or black) = 56%
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-18)°
40°
110°
The value of the variable x associated to the triangle is equal to 6.
What is the variable associated to internal angles of a triangle?
Triangles are figures with three sides and three internal angles. According to Euclidean geometry, the sum of the measures of the internal angles is equal to 180° and we must solve the following equation for x:
(8 · x - 18) + 40 + 110 = 180
(8 · x - 18) + 150 = 180
(8 · x - 18) = 30
8 · x = 48
x = 6
The triangle has internal angles of 30°, 40° and 110° and the value of variable x is 6.
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Would you please check this answer for me? Use elimnation to solve the system of equations:2x+2y=162x+3y=14My answer: (10, - 2)
Equation
[tex]\begin{gathered} 2x+2y=16 \\ 2x+3y=14 \\ \end{gathered}[/tex]Let's multiply -1 by Eq 1
[tex]\begin{gathered} -2x-2y=-16 \\ 2x+3y=14 \\ 2x-2x+3y-2y=-16+14 \\ y=-2 \end{gathered}[/tex]Now for x
[tex]\begin{gathered} 2x+2y=16 \\ x=\frac{16-2y}{2} \\ x=\frac{16-2\cdot(-2)}{2} \\ x=\frac{16+4}{2} \\ x=\frac{20}{2} \\ x=10 \end{gathered}[/tex]The answer would be (10, -2)
A store generates Monday through Thursday sales of $150, $125, $75, and $180. What sales on Friday would give a weekday average of $150?
Answer:
mi cola es grande
Step-by-step explanation:
uhh
718-119x+719 for x =0
please simplify and find the value
rectangle perimeter ; 36 unitswidth; xlength ; 4x - 2solve for x
Perimeter = 36 units
width = x
length = 4x - 2
Equation of perimeter = 2width + 2length
Substitution
36 = 2(x) + 2(4x - 2)
Expanding
36 = 2x + 8x - 4
36 = 10x - 4
36 + 4 = 10x
40 = 10x
x = 40/10
x = 4
Is -7. a rational number
A rational number can be represented by dividing two integers.
So, it can be represented as a ratio of 2 integers.
-7 = -7/1
-7 is a rational number
rewrite 13% into equivalent fraction
The number 13% as an equivalent fraction is 13/100
How to rewrite the percentage into equivalent fraction?From the question, the given parameter is
13%
This above number is a percentage or percentile
So, we have
Percentage = 13%
Next, we multiply the percentage by 1
So, we have
Percentage = 13% x 1
Express 1 as 100/100
So, we have
Percentage = 13% x 100/100
Evaluate the product of 13% and 100
So, we have
Percentage = 13/100
Rewrite as
Fraction = 13/100
The fraction cannot be further simplified
Hence, the equivalent fraction of 13% is 13/100
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Molly has 250 trading cards. She gives n trading cards to her friend Carol. Marcus has 430 trading cards. He gives away three times as many cards as Molly does. How many trading cards did Molly give away if Molly and Marcus have the same number of trading cards left?
Molly gave away 90 trading cards out of 250 trading cards to her friend Carol.
Initially molly had 250 cards.
She gave away n trading cards to her friend.
Now molly has (250 - n) trading cards.
Initially Marcus had 4430 trading cards.
The number of cards that Marcus gave away is is three times of molly.
Cards gave away by Marcus = 3n
Now, Marcus is left out with (430 - 3n) trading cards/
After giving away the cards,
Molly and Marcus had same number of trading cards.
So, we can write,
250-n = 430-3n
Now, we have a linear relation between the number of cards given away and the remaining cards,
Further solving,
2n = 180
n = 90.
So, Molly gave away 90 cards.
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Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)
ANSWER
ΔOMN ~ ΔOJK; SAS
EXPLANATION
As we can observe in the diagram, the triangles share angle O and we have information about the sides forming that angle, so the postulate to use, in case they are similar, is SAS.
If two triangles are similar, then the ratio between corresponding sides is constant.
Let's assume that the similar triangles are triangle OMN and triangle OJK. Then, the previous statement is,
[tex]\frac{OM}{OJ}=\frac{MN}{JK}=\frac{ON}{OK}[/tex]Replace the side lengths for the first and last ratios - since we don't know the lengths of sides MN and JK,
[tex]\begin{gathered} \frac{30+10}{30}=\frac{3+1}{3} \\ \\ \frac{40}{30}=\frac{4}{3} \\ \\ \frac{4}{3}=\frac{4}{3} \end{gathered}[/tex]The ratio between corresponding sides is constant, 4/3. Hence, triangles OMN and OJK are similar, by SAS.
Mental Math Using the slope formula, find the slope of the line through the points (0,0) and (3,6).Use pencil and paper. Explain how you can use mental math to find the slope of the line.
Given the points (0,0) and (3,6)
slope = y2 - y1 / x2 -x1
x1= 0, y1 = 0 , x2= 3, and y2 = 6
slope = 6 - 0 / 3 - 0
slope = 6 / 3
slope = 2
the answer is 2
7 is added to 11 divided by a number r write the algebraic expression
Answer: 7+(11/r)
Step-by-step explanation:
ANSWERS ASAPP
i got a 57 in this class
Answer:
Y=-1/4x+-6
Step-by-step explanation:
convert the line to slope intercept form
x is the slope and the last thing is the y intercept
2. Multiply the matrices.
Result of matrix multiplication [tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] = \left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right] [/tex].
What is a matrix?A matrix is a series of numbers forming a square or rectangle arranged in rows and columns enclosed in square brackets [ ] or regular brackets ( ).
Solution:
[tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] [/tex]
[tex] \left[ \begin{array}{cc} - 1 \times 2 + 2 \times 7 + 0 \times 1 & - 1 \times ( - 3) + 2 \times ( - 1) + 0 \times 2 \\3 \times 2 + ( - 2) \times 7 + 4 \times 1&3 \times ( - 3) + ( - 2) \times ( - 1) + 4 \times 2\\ - 5 \times 2 + ( - 1) \times 7 + 6 \times 1&( - 5) \times ( - 3) + ( - 1) \times ( - 1) + 6 \times 2 \end{array}\right ][/tex]
[tex]\left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right ][/tex]
Find the values of the variables so that the figure is aparallelogram.
Answer:
The image is given below as
From the image above, we can deduce that
[tex]\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}[/tex]From the image also, we will have that
[tex]\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}[/tex]Hence,
The value of x= 64°
The value of y = 116°
Suppose that the functions s and t are defined for all real numbers x as follows.
s(x)=x-3
t(x) = 3x+4
Write the expressions for (s•t) (x) and (s-t) (x) and evaluate (s+t) (-2).
7 is the value of function s and t .
What is function explain?
A relation between a set of inputs and a set of allowable outputs is called a function, and it has the property that every input is associated to exactly one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.Four main categories can be used to classify the many sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.s(x)= x-3
t(x) = 3x+4
(s•t) = ( x -3 ) ( 3x + 4 )
= ( 3x² + 4x - 3x² - 12 )
= 4x - 12
(s-t) (x) = ( x-3 ) - ( 3x+4 )
= x-3 - 3x + 4
= -2x + 1
(s + t) (-2) = x-3 + 3x+4
= 4x + 1
(s + t) (-2) = 4 * - 2 + 1
= 8 - 1 = 7
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Ken exercise at a park first he run 3 miles in 30 minutes.Then he rests for 15 minutes.Then he runs 2 miles in 15 minutes.Finally he walks 1 mile in 15 minutes.Assume each running and walking segment was done at a constant rate.skecth a graph to represent ken's exercing at the park.the fisrt segment should begin at (0,0).
The horizontal axis represents the time in hours, and the vertical axis represents the number of miles ran.
So for the first part we have 3 miles in 30 minutes (0.5 hour), so we can draw a line from point (0, 0) to point (0.5, 3)
For the second part, he rests for 15 minutes (0.25 hour), so the y-value doesn't change, therefore we have a horizontal line from (0.5, 3) to (0.75, 3).
Then, we have 2 miles in 15 minutes, so we have a line from (0.75, 3) to (1, 5).
And finally, 1 mile in 15 minutes, so a line from (1, 5) to (1.25, 6).
Sketching the graph, we have: