Therefore , the solution of the given problem of equation comes out to be x = -14/15 and y = -37/15 .
What is an equation?It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic integers numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from y + 6.
Here,
We can use the substitution or elimination technique to solve this system. Here, we'll employ the removal strategy.
given solution system:
=> y = 3x + 1 (1)
=>-x + 2y = -3 (2) (2)
By combining equations (1) and (2) multiplied by 1 and 3, respectively, we can remove the variable x:
=>3*(-x + 2y = -3)
=> -3x + 6y = -9
=> 1*(y = 3x + 1)
=> y = 3x + 1
Combining the two equations:
=>y = 3x + 1
=> -3x + 6y = -9
=> 6y - 3x = -8
By multiplying both parts of this equation by 3, we can make it simpler:
=> 2y - x = -8/3
However, we can still use equation (1) to replace y even though we have a new equation in terms of x and y:
=> y = 3x + 1
=> 2y - x = -8/3
y = 3x Plus 1 is substituted in the second equation:
=>2(3x + 1) - x = -8/3
=> 6x + 2 - x = -8/3
=>5x = -14/3
=>x = -14/15
Finding y by substituting this x number in equation (1):
=> y = 3x + 1 = 3(-14/15) + 1 = -37/15
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Simplify
to a single trig function with no fractions.
The simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
Recall that the secant function is defined as the reciprocal of the cosine function. In other words, sec(t) = 1/cos(t). Therefore, we can rewrite cos(t)/sec(t) as cos(t)/(1/cos(t)).
To simplify this expression, we can multiply both the numerator and the denominator by cos(t), which gives:
cos(t)/(1/cos(t)) = cos(t) * (cos(t)/1) = cos²(t)
Now, we have simplified cos(t)/sec(t) to cos²(t). Alternatively, we could have used the identity cos²(t) = 1 - sin²(t) to simplify the expression. This identity follows directly from the Pythagorean identity cos²(t) + sin²(t) = 1.
Starting with cos(t)/sec(t), we can substitute sec(t) = 1/cos(t) to get:
cos(t)/sec(t) = cos(t)/(1/cos(t)) = cos²(t)/1
Then, we can use the identity cos²(t) = 1 - sin²(t) to substitute cos²(t) in terms of sin(t):
cos(t)/sec(t) = cos²(t)/1 = (1 - sin²(t))/1 = 1 - sin²(t)
So, we have simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
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2. The back of Nico's truck is 7 feet long, 4 feet wide, and 8 feet tall. He has several boxes of important papers that he needs to move. Each box of papers is shaped like a cube, measuring 1 foot on each side. K How many boxes of papers can Nico pack into the back of his truck? Show your work. (Try drawing a picture of the back of the truck and how many boxes can stack in there to help you see the answer better. Possible extra credit for your drawing.) Answer:
Based on division operation, the number of boxes of papers that the back of Nico's truck can stack in is 224.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend divided by the divisor to produce a result known as the quotient.
In this situation, the volume of Nico's truck is determined as the dividend. The volume of each box of paper is determined as the divisor.
The result of the division operation is the quotient showing the number of boxes the truck can contain.
The length of Nico's truck = 7 feet
The width of Nico's truck = 4 feet
The height of Nico's truck = 8 feet
The volume that Nico's tuck can contain = 224 cubic feet (7 × 4 × 8)
= 224 feet³
The length of each box = 1 foot
The width of each box = 1 foot
The height of each box = 1 foot
The volume of each box of papers = 1 feet³ (1 × 1 × 1)
The number of boxes the truck can contain = 224 boxes (224/1)
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Kira is installing a railing that is 35 inches above the ramp Let each be the height of the railing from the ground and all be the height of the ramp from the ground which equation represents the situation
Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let h be the height of the railing from the ground and let r be the height of the ramp from the ground.
We are given that the railing is 35 inches above the ramp, which means that the total height of the railing from the ground is h = r + 35.
So the equation that represents the situation is:
h = r + 35
Therefore, Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35
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The following are reasons to put your money in a saving account. (Check all that apply)
Money collects interest.
Get a rebate back in the mail.
Money is safe and insured.
The cοrrect respοnse is that mοney cοllects interest and mοney is safe and insured.
Why nοt explain interest?The fee yοu spend tο bοrrοw the mοney οr the fee yοu pay tο lend the mοney is called interest. Interest is frequently calculated as a yearly percentage οf the amοunt bοrrοwed. This percentage represents the lοan's interest rate.
The interest fοrmula is what?Interest equals P, R, and T is the fundamental interest fοrmula. P is the initial value (the beginning balance). Rate οf Interest, R (usually per year, expressed as a decimal). T is the sum οf all time frames (generally οne-year time periοds).
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please help me find these angles, i dont want a wrong answer.
Answer:
<EAC=75
<BAD=36
<ACD=75
<FAB=75
<CAD=69
<BDA=69
Step-by-step explanation:
EAC= 180-105=75
BAD= CDA
ACD= 75 opposite <s congruent
FAB= 75 vertical <s congruent
CAD=105-36=69
BDA=69 Opposite <s congruent.
Hope this helps! Should be right we just finished this unit.
Use the word bank to help identify each part of the quadrilateral.
word bank: base, leg, parallel, midsegment, angle, diagonal, side.
Helena wants to change the figure shown into two or more figures so she can
more easily find the area. Draw a line or lines to show what she could do. Then
write an expression for the area of each smaller figure. Write an expression for
the total area of the figure. Explain.
The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
What is the tοtal area?A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.
Here, we have
Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.
The figure is cοmpοsed οf a square and a rectangle. See the attached image.
Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.
Area οf the rectangle = bh.
The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,
b = length οf the base= 4x-5
h = height = 4x+3x = 7x
A rectangle = bh = (4x-5)*7x = 28x²-35x
Area οf the square = l². The figure shοws that the sides fοr this square are equal tο 3x
l = length οf the side= 3x
Thus, A square = l² = (3x)² =9x²
We have tο find an expressiοn fοr the tοtal area οf the figure.
A tοtal= A rectangle+ A square
A tοtal= 28x²-35x+9x²
A tοtal= 37x²-35x
Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
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Two cross sections the same or different
Shape
Answer:same
Step-by-step explanation:because I said so
Refer to trapezoi EFGH WITH MEDIAN IJ if IJ=X,Hg=8 abd EF=12 what is the value of x
Answer:
x = 10
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of parallel sides.
The median of a trapezoid connects the midpoint of the non-parallel sides.
IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.
Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.
(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)
The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.
In the figure,
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
Substituting the values we have, HG = 8, EF = 12 gives us:
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
[tex]IJ=\dfrac{(8+12)}{2}[/tex]
[tex]IJ=\dfrac{20}{2}[/tex]
[tex]IJ=10[/tex]
IJ is 10 units.
A toy company is building dollhouse furniture. A rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 3.5?
Answer: To find the perimeter of the door on a scale drawing, we need to first determine the dimensions of the door on the scale drawing.
If the actual height of the door is 7 centimeters, then the height on the scale drawing will be:
7 cm ÷ 3.5 = 2 cm
Similarly, if the actual width of the door is 3 centimeters, then the width on the scale drawing will be:
3 cm ÷ 3.5 = 0.857 cm
Now we can use these dimensions to find the perimeter on the scale drawing:
Perimeter = 2 × (height + width) = 2 × (2 cm + 0.857 cm) = 2 × 2.857 cm = 5.714 cm
Therefore, the perimeter of the door on the scale drawing is 5.714 centimeters.
If you have anymore questions, feel free to comment and I will help you.
3: Managing Money
10. Which of the following is kept on record at the bank in order to identify you as the owner of your checking account?
OA. Account verification card
OB. Deposit slip
OC. Signature card
OD. Withdrawal slip
A document that is kept on record at the bank in order to identify you as the owner of your checking account include the following: C. signature card.
What is a checking account?In Economics, a checking account is sometimes referred to as a current account or transaction account and it can be defined as a type of bank account at a financial institution, that allows an accountholder to easily deposit and withdraw his or her money for daily activities.
This ultimately implies that, the use of a debit card is one of the ways through which money in a checking account can be accessed because it allows for deposits and withdrawals of cash at any given time.
In conclusion, a signature card is used by banks to determine the identity and ownership of a checking account (accountholder).
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The document that is kept on record at the bank for identification of the owner of a checking account is a signature card. The correct option is option C.
C. Signature cardWhat is a checking account?A checking account is an operational account which allows;
The deposit and withdrawal of funds when required
Payment of billsPurchase of itemsPayment receiptsA checking account holder is offered a debit card and or a set of cheques, which are then used to withdraw cash or make purchases.
Some of the details that are required to open a checking account are entered into a signature card by new customers.
A signature card includes the personal information of the owner of an account, including;
The signature of the person
The account holders name
The address of the account holder
The account holder identification number
The signature card is a document that is signed when opening a checking account, which the bank use to make references with regards to the account holders transactions.
With the signature card in the record of the bank, the bank can be able to identify a checking account holder's transactions such as issuing of cheque to third party, and also when the account holder makes requests for other banking services.
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The demand for a product is given by p+5q= 380 or, q = (380-p)/5 and the supply for this product is given by p-3q = 172 or, q = (p-172)/3 The price at which the quantity demande
Answer:
The equilibrium price is $250.
The equilibrium quantity is 26 units.
Step-by-step explanation:
To find the equilibrium price, we need to find the price at which the quantity demanded equals the quantity supplied. This occurs when q (quantity demanded) equals q (quantity supplied).
So, we can set the two equations for q equal to each other:
(380-p)/5 = (p-172)/3
To solve for p, we can cross-multiply and simplify:
3(380-p) = 5(p-172)
1140 - 3p = 5p - 860
1140 + 860 = 8p
2000 = 8p
p = 250
Therefore, the equilibrium price is $250. We can plug this value back into either equation for q to find the equilibrium quantity.
Using q = (380-p)/5, we get:
q = (380-250)/5 = 26
So the equilibrium quantity is 26 units.
PZ HURRY 15 POINTS
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
It can be estimated that approximately 3,042 people in attendance would prefer ketchup on a hot dog.
Thus, the correct answer is 3,042.
To determine how many people in attendance would prefer ketchup on a hot dog based on the data from the sample, we need to calculate the proportion of people who prefer ketchup and apply it to the total attendance.
The sample indicates that out of 150 people surveyed:
54 people prefer ketchup
36 people prefer relish
60 people prefer chili
To find the proportion of people who prefer ketchup, we divide the number of people who prefer ketchup by the total number of people surveyed:
Proportion of people who prefer ketchup = 54 / 150 = 0.36
Now, to estimate the number of people in attendance who would prefer ketchup on a hot dog, we multiply the proportion calculated above by the total attendance:
Estimated number of people who prefer ketchup = 0.36 [tex]\times[/tex] 8,450 = 3,042
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Please help its an emergency! Will give Brainliest! What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
Answer: 6.28 cm
Step-by-step explanation:
X - 0 , 2 , 4 , 6 , 8 , 10 , 12
Y - 18 , 15 , 13 , 10 , 7 , 5 , 1
1. Use GeoGebra Calculator Suite linked on the
task page to create a scatterplot of the data.
Post your screenshot of the scatterplot in the space provided below.
2. Use the same calculator linked on the task page to:
find the equation of the best-fit line,
draw the line, and
show the equation.
Post the screenshot of the graph in the space provided below.
The equation of the best-fit line is:
A natural history museum surveyed the people visiting the museum for one month and created a circle graph to show the age of the visitors for that month.
If 5000 people visited the museum during the month the survey was taken, how many visitors were there for each age group?
Age 18 and under:
Age 19 – 44:
Age 45 – 64:
Age 65 and over:
Will give brainliest
Write the equation of the line that passes through the points (3, -4) and (7, 6). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answer:
Step-by-step explanation:
To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:
Step 1: Find the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
slope = (6 - (-4)) / (7 - 3)
slope = 10 / 4
slope = 5 / 2
Step 2: Use point-slope form to write the equation of the line
Point-slope form of a line with slope m passing through a point (x1, y1) is given by:
y - y1 = m(x - x1)
We can use either of the given points to write the equation. Let's use (3, -4):
y - (-4) = (5/2)(x - 3)
Simplifying this equation, we get:
y + 4 = (5/2)x - (15/2)
Subtracting 4 from both sides, we get:
y = (5/2)x - (23/2)
This is the equation of the line in point-slope form.
Step 3: Simplify the equation if it is not in point-slope form
The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.
Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.
PLEASE HELP !! WILL GIVE BRAINLISET
[tex]-5x+4 = 29 \iff -5x =29-4 \iff -5x = 25\\[/tex]
[tex]x = 25:(-5) \implies \bf x = -5[/tex]
Answer: X = 5
Step-by-step explanation: f(x) is 29, plus it in to f(x)=-5x+4
29=-5x+4
Subtract the 4 with itself and 29
-5x=25
Divide both numbers by -5, you dont want x to be a negative
X = 5
answered
Find the points on the line x=1
where the circle with equation
2x²+2y²-5x+7y-36-0 intersect
Answer: To find the points where the circle intersects the line x=1, we substitute x=1 in the equation of the circle:
2(1)² + 2y² - 5(1) + 7y - 36 = 0
Simplifying, we get:
2y² + 7y - 31 = 0
We can solve this quadratic equation by using the quadratic formula:
y = (-7 ± √(7² - 4(2)(-31))) / (2(2))
y = (-7 ± √225) / 4
y = (-7 ± 15) / 4
So the two possible values of y are:
y = 2 or y = -8/2 = -4
Therefore, the points where the circle intersects the line x=1 are (1, 2) and (1, -4).
Step-by-step explanation:
If the total cost function for a lamp is C(x) =250+ 33x + 0.1x ^ 2 dollars, producing how many units, x, will result in a minimum average cost per unit? Find the minimum average cost.
In the circle below, suppose ark KLI = 247 deg and m angle LKJ = 124 deg . Find the following.
The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
What is circle?In geοmetry, a circle is a twο-dimensiοnal shape cοnsisting οf all pοints that are a fixed distance (called the radius) frοm a given pοint (called the center). A circle is a set οf pοints that are equidistant frοm the center. The distance between any pοint οn the circle and the center is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.
The measure of angle JLI can be found using the fact that angles on a straight line add up to 180 degrees. Therefore,
m angle JLI = 180 - m angle LKJ = 180 - 124 = 56 degrees.
The measure of arc JKI can be found using the fact that the measure of an inscribed angle is half the measure of the arc it intercepts. Therefore,
m arc JKI = 2 * m angle JLI = 2 * 56 = 112 degrees.
Therefore, The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
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What is the solution of x-1/x^2 +5x+4 less than or equal to 0
Answer:
[tex]x-1/x^2 +5x+4[/tex] = no real value
Step-by-step explanation:
Step 1 : Multiply through by x^2
[tex]x^{2} -1 +5x^{3}+ 4x^{2}[/tex]
Step 2 : Collect like terms
[tex]5x^{3}+5x^{2} -1\geq 0[/tex]
Step 3 : Ignore the sign and solve for x
[tex]5x^{3} +5x^{2} -1 = 0\\x =0.380609458\\x= 0.4(2dp)[/tex]
Step 4 : Input back into the equation
Step 5: This shows that x-1/x^2 +5x+4 has no real values.
Find the Product.
5(cos pi/4 + i sin pi/4) x 3(cos 5pi/3 + i sin 5pi/3)
Answer:
D. 15(cos(23π/12) +i·sin(23π/12))
Step-by-step explanation:
You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).
Complex productThe product is ...
A·cis(a) × B·cis(b) = AB·cis(a+b)
where "cis(x)" means (cos(x) +i·sin(x))
Application5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)
The product is 15·(cos(23π/12) +i·sin(23π/12)).
Help!!
Question
Triangle ABC is similar to triangle DEF. The length of BC¯¯¯¯¯ is 44 cm. The length of DE¯¯¯¯¯ is 14 cm. The length of EF¯¯¯¯¯ is 22 cm.
What is the length of AB¯¯¯¯¯?
Enter your answer in the box.
cm
The length of AB which is the missing length side of the similar triangles would be = 28 cm.
How to calculate the missing length of a triangle?To calculate the missing length of the triangle = AB , the scale factor should be determined.
The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.
The scale factor = dimensions of new object/ dimensions of original object.
A side of original = EF =22cm
A side of the new triangle = BC = 44
Scale factor = 44/22 = 2
Therefore the missing length of the new triangle = 14×2 = 28cm
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Determine the equation of the ellipse with foci (2, 4) and (2, -8), and co-vertices
(10,-2) and (-6, -2).
The equation of ellipse with foci (2, 4) and (2, -8) and co-vertices (10, -2) and (-6, -2) is ((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
What is the equation of ellipseTo find the equation of the ellipse, we first need to determine the center of the ellipse. Since the foci are on the same vertical line, the center of the ellipse is at the midpoint of the segment connecting the foci.
The midpoint of the segment connecting the foci is:
((2+2)/2, (4-8)/2) = (2, -2)
So the center of the ellipse is (2, -2).
Next, we need to determine the lengths of the semi-major and semi-minor axes. The semi-major axis is half the distance between the co-vertices, which is:
a = (10 - (-6))/2 = 8
The semi-minor axis is half the distance between the foci, which is:
c = (4 - (-8))/2 = 6
Now we can use the standard form of the equation of an ellipse centered at (h,k):
((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Plugging in the values we have:
((x - 2)^2 / 8^2) + ((y + 2)^2 / 6^2) = 1
Simplifying and rearranging:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
So the equation of the ellipse is:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
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1. Solve: (6 + 3)2 – 17 × 3 + 70
The solution of this expression is 37
Numerical expressionsTo solve this, first calculate the operations in parentheses.
Then perform the other operations, following the order of resolution
[tex]\begin{array}{l}\sf (6 + 3)2-17\times 3 + 70\\\sf 9\times 2-51+ 70\\\sf 18-51+ 70\\\sf 88-51\\\therefore \bf 37\end{array}[/tex]
For this expression, the result is 37
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What is 24 and 816,000 equals blank divided by 10 to the fifth power
Answer: We have the equation:
24,816,000 = x / 10^5
To solve for x, we can multiply both sides by 10^5:
24,816,000 * 10^5 = x
Using a calculator or long multiplication, we can simplify this to:
2,481,600,000,000 = x
Therefore, 24,816,000 is equal to 2,481,600,000,000 divided by 10 to the fifth power.
Step-by-step explanation:
Steven sold 10 cabbages at K2.00 each, 20 heaps of kaukau at K5 each, and 10 heaps of potato at K3.00 each. What is Steven's total earning?
Answer:
K150
Step-by-step explanation:
10 x K2.00 = K20.00
20 x K5.00 = K100.00
10 x K3.00= K30.00
20+100+30= K150
Find the sum of the first n terms
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
This would be a big help
The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^n)/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^n)/(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = [tex]3/2(1-(5/3)^n)[/tex]
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^4)[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
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The total of the first four terms is thus 8/3.
What does sum mean?The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.
The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.
We enter these numbers into the formula to determine the sum of the initial n terms:
S(n) = [tex]a(1-r^{n} )/(1-r)[/tex]
S(n) = [tex]1(1-(5/3)^{n} /(1-5/3)[/tex]
S(n) = [tex]3/2(1-(5/3)^{n} )[/tex]
So, we add n to this formula to get the sum of the initial n terms of a given sequence:
S(n) = 3/2(1 - [tex](5/3)^{n}[/tex] )
For instance, we replace n = 4 to get the sum of the initial four terms:
S(4) = [tex]3/2(1-(5/3)^{4} )[/tex]
S(4) = 3/2(1-625/81)
S(4) = 3/2(144/81)
S(4) = 72/27
S(4) = 8/3
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complete ques is:
Find the sum of the first n terms ( 1,2,3,4,5.......n)
using the formula:
a(1-r^n)/1-r
1, 5/3, 25/9, 125/27, 625/81
I need help with the graph about it increasing and decreasing!!
Answers:
Increasing: [tex](-1.5, 2)[/tex]
Decreasing: [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
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Explanation:
A function curve is considered increasing when moving uphill as you move to the right.
We're going uphill on the interval [tex]-1.5 < \text{x} < 2[/tex] which translates to the interval notation [tex](-1.5, 2)[/tex]. Be sure not to confuse this with ordered pair notation which unfortunately looks identical. The curved parenthesis are used to exclude each endpoint.
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When moving to the right, we go downhill on two separate regions:
When x < -1.5, aka [tex]-\infty < \text{x} < -1.5[/tex]When x > 2, aka [tex]2 < \text{x} < \infty[/tex]The first portion translates to the interval notation [tex](-\infty,-1.5)[/tex]
The second portion translates to [tex](2,\infty)[/tex]
We glue those regions together with a union symbol to get [tex](-\infty,-1.5) \cup (2,\infty)[/tex]
The union symbol basically means "or" when it comes to interval notation. So we are decreasing on the interval [tex](-\infty,-1.5)[/tex] or decreasing on the interval [tex](2,\infty)[/tex]